annotate libinterp/corefcn/eig.cc @ 20802:8bb38ba1bad6

eliminate return statements after calls to print_usage * __contourc__.cc, __dispatch__.cc, __dsearchn__.cc, __ichol__.cc, __lin_interpn__.cc, __qp__.cc, balance.cc, betainc.cc, bsxfun.cc, colloc.cc, daspk.cc, dasrt.cc, dassl.cc, defaults.cc, det.cc, dlmread.cc, dot.cc, eig.cc, ellipj.cc, fft.cc, fft2.cc, fftn.cc, filter.cc, find.cc, gcd.cc, givens.cc, hex2num.cc, inv.cc, lookup.cc, lu.cc, max.cc, mgorth.cc, ordschur.cc, pinv.cc, profiler.cc, quad.cc, qz.cc, rcond.cc, schur.cc, str2double.cc: Eliminate return statements after calls to print_usage.
author John W. Eaton <jwe@octave.org>
date Fri, 04 Dec 2015 12:03:44 -0500
parents f90c8372b7ba
children 1142cf6abc0d
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1 /*
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2
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3 Copyright (C) 1996-2015 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
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
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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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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27 #include "EIG.h"
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28 #include "fEIG.h"
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29
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30 #include "defun.h"
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31 #include "error.h"
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32 #include "gripes.h"
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33 #include "oct-obj.h"
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34 #include "utils.h"
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35
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36 DEFUN (eig, args, nargout,
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37 "-*- texinfo -*-\n\
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38 @deftypefn {Built-in Function} {@var{lambda} =} eig (@var{A})\n\
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39 @deftypefnx {Built-in Function} {@var{lambda} =} eig (@var{A}, @var{B})\n\
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40 @deftypefnx {Built-in Function} {[@var{V}, @var{lambda}] =} eig (@var{A})\n\
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41 @deftypefnx {Built-in Function} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B})\n\
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42 Compute the eigenvalues (and optionally the eigenvectors) of a matrix\n\
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43 or a pair of matrices\n\
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44 \n\
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45 The algorithm used depends on whether there are one or two input\n\
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46 matrices, if they are real or complex, and if they are symmetric\n\
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47 (Hermitian if complex) or non-symmetric.\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 @seealso{eigs, svd}\n\
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51 @end deftypefn")
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52 {
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53 octave_value_list retval;
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54
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55 int nargin = args.length ();
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56
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57 if (nargin > 2 || nargin == 0 || nargout > 2)
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58 print_usage ();
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59
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60 octave_value arg_a, arg_b;
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61
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62 octave_idx_type nr_a, nr_b, nc_a, nc_b;
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63 nr_a = nr_b = nc_a = nc_b = 0;
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64
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65 arg_a = args(0);
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66 nr_a = arg_a.rows ();
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67 nc_a = arg_a.columns ();
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68
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69 int arg_is_empty = empty_arg ("eig", nr_a, nc_a);
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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_list (2, Matrix ());
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74
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75 if (!(arg_a.is_single_type () || arg_a.is_double_type ()))
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76 {
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77 gripe_wrong_type_arg ("eig", arg_a);
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78 return retval;
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79 }
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80
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81 if (nargin == 2)
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82 {
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83 arg_b = args(1);
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84 nr_b = arg_b.rows ();
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85 nc_b = arg_b.columns ();
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86
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87 arg_is_empty = empty_arg ("eig", nr_b, nc_b);
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88 if (arg_is_empty < 0)
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89 return retval;
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90 else if (arg_is_empty > 0)
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91 return octave_value_list (2, Matrix ());
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92
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93 if (!(arg_b.is_single_type () || arg_b.is_double_type ()))
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94 {
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95 gripe_wrong_type_arg ("eig", arg_b);
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96 return retval;
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97 }
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98 }
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99
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100 if (nr_a != nc_a)
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101 {
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102 gripe_square_matrix_required ("eig");
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103 return retval;
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104 }
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105
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106 if (nargin == 2 && nr_b != nc_b)
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107 {
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108 gripe_square_matrix_required ("eig");
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109 return retval;
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110 }
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111
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112 Matrix tmp_a, tmp_b;
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113 ComplexMatrix ctmp_a, ctmp_b;
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114 FloatMatrix ftmp_a, ftmp_b;
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115 FloatComplexMatrix fctmp_a, fctmp_b;
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116
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117 if (arg_a.is_single_type ())
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118 {
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119 FloatEIG result;
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120
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121 if (nargin == 1)
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122 {
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123 if (arg_a.is_real_type ())
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124 {
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125 ftmp_a = arg_a.float_matrix_value ();
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126
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127 result = FloatEIG (ftmp_a, nargout > 1);
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128 }
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129 else
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130 {
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131 fctmp_a = arg_a.float_complex_matrix_value ();
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132
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133 result = FloatEIG (fctmp_a, nargout > 1);
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134 }
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135 }
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136 else if (nargin == 2)
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137 {
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138 if (arg_a.is_real_type () && arg_b.is_real_type ())
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139 {
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140 ftmp_a = arg_a.float_matrix_value ();
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141 ftmp_b = arg_b.float_matrix_value ();
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142
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143 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1);
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144 }
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145 else
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146 {
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147 fctmp_a = arg_a.float_complex_matrix_value ();
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148 fctmp_b = arg_b.float_complex_matrix_value ();
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149
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150 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1);
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151 }
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152 }
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153
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154 if (nargout == 0 || nargout == 1)
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155 {
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156 retval(0) = result.eigenvalues ();
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157 }
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158 else
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159 {
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160 // Blame it on Matlab.
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161
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162 FloatComplexDiagMatrix d (result.eigenvalues ());
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163
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164 retval(1) = d;
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165 retval(0) = result.eigenvectors ();
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166 }
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167 }
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168 else
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169 {
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170 EIG result;
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171
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172 if (nargin == 1)
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173 {
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174 if (arg_a.is_real_type ())
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175 {
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176 tmp_a = arg_a.matrix_value ();
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177
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178 result = EIG (tmp_a, nargout > 1);
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179 }
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180 else
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181 {
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182 ctmp_a = arg_a.complex_matrix_value ();
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183
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184 result = EIG (ctmp_a, nargout > 1);
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185 }
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186 }
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187 else if (nargin == 2)
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188 {
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189 if (arg_a.is_real_type () && arg_b.is_real_type ())
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190 {
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191 tmp_a = arg_a.matrix_value ();
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192 tmp_b = arg_b.matrix_value ();
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193
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194 result = EIG (tmp_a, tmp_b, nargout > 1);
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195 }
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196 else
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197 {
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198 ctmp_a = arg_a.complex_matrix_value ();
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199 ctmp_b = arg_b.complex_matrix_value ();
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200
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201 result = EIG (ctmp_a, ctmp_b, nargout > 1);
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202 }
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203 }
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204
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205 if (nargout == 0 || nargout == 1)
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206 {
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207 retval(0) = result.eigenvalues ();
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208 }
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209 else
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210 {
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211 // Blame it on Matlab.
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212
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213 ComplexDiagMatrix d (result.eigenvalues ());
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214
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215 retval(1) = d;
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216 retval(0) = result.eigenvectors ();
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217 }
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218 }
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219
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220 return retval;
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221 }
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222
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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223 /*
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224 %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps))
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225
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226 %!test
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227 %! [v, d] = eig ([1, 2; 2, 1]);
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228 %! x = 1 / sqrt (2);
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229 %! assert (d, [-1, 0; 0, 3], sqrt (eps));
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230 %! assert (v, [-x, x; x, x], sqrt (eps));
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231
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232 %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single")))
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233
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234 %!test
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235 %! [v, d] = eig (single ([1, 2; 2, 1]));
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236 %! x = single (1 / sqrt (2));
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237 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single")));
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238 %! assert (v, [-x, x; x, x], sqrt (eps ("single")));
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239
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240 %!test
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241 %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2];
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242 %! [v, d] = eig (A, B);
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243 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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244 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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245
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246 %!test
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247 %! A = single ([1, 2; -1, 1]); B = single ([3, 3; 1, 2]);
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248 %! [v, d] = eig (A, B);
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249 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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250 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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251
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252 %!test
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253 %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3];
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254 %! [v, d] = eig (A, B);
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255 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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256 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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257
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258 %!test
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259 %! A = single ([1, 2; 2, 1]); B = single ([3, -2; -2, 3]);
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260 %! [v, d] = eig (A, B);
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261 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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262 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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263
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264 %!test
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265 %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i];
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266 %! [v, d] = eig (A, B);
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267 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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268 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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269
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270 %!test
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271 %! A = single ([1+3i, 2+i; 2-i, 1+3i]); B = single ([5+9i, 2+i; 2-i, 5+9i]);
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272 %! [v, d] = eig (A, B);
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273 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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274 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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275
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276 %!test
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277 %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i];
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278 %! [v, d] = eig (A, B);
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279 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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280 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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281
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282 %!test
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283 %! A = single ([1+3i, 2+3i; 3-8i, 8+3i]); B = single ([8+i, 3+i; 4-9i, 3+i]);
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284 %! [v, d] = eig (A, B);
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285 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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286 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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287
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288 %!test
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289 %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3];
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290 %! [v, d] = eig (A, B);
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291 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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292 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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293
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294 %!test
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295 %! A = [1, 1+i; 1-i, 1]; B = [2, 0; 0, 2];
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296 %! [v, d] = eig (A, B);
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297 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
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298 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));
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299
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300 %!test
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301 %! A = single ([1, 1+i; 1-i, 1]); B = single ([2, 0; 0, 2]);
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302 %! [v, d] = eig (A, B);
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303 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single")));
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304 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single")));
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305
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306 %!error eig ()
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307 %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1)
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308 %!error <EIG requires same size matrices> eig ([1, 2; 3, 4], 2)
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309 %!error <argument must be a square matrix> eig ([1, 2; 3, 4; 5, 6])
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310 %!error <wrong type argument> eig ("abcd")
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311 %!error <wrong type argument> eig ([1 2 ; 2 3], "abcd")
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312 %!error <wrong type argument> eig (false, [1 2 ; 2 3])
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313 */