Mercurial > octave-nkf
annotate libinterp/corefcn/eig.cc @ 20654:b65888ec820e draft default tip gccjit
dmalcom gcc jit import
author | Stefan Mahr <dac922@gmx.de> |
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date | Fri, 27 Feb 2015 16:59:36 +0100 |
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rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2015 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "EIG.h" | |
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28 #include "fEIG.h" |
2928 | 29 |
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30 #include "defun.h" |
2928 | 31 #include "error.h" |
32 #include "gripes.h" | |
33 #include "oct-obj.h" | |
34 #include "utils.h" | |
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\ |
14885 | 42 Compute the eigenvalues (and optionally the eigenvectors) of a matrix\n\ |
43 or a pair of matrices\n\ | |
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44 \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\ |
5829 | 48 \n\ |
49 The eigenvalues returned by @code{eig} are not ordered.\n\ | |
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50 @seealso{eigs, svd}\n\ |
3372 | 51 @end deftypefn") |
2928 | 52 { |
53 octave_value_list retval; | |
54 | |
55 int nargin = args.length (); | |
56 | |
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57 if (nargin > 2 || nargin == 0 || nargout > 2) |
2928 | 58 { |
5823 | 59 print_usage (); |
2928 | 60 return retval; |
61 } | |
62 | |
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63 octave_value arg_a, arg_b; |
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64 |
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65 octave_idx_type nr_a, nr_b, nc_a, nc_b; |
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66 nr_a = nr_b = nc_a = nc_b = 0; |
2928 | 67 |
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68 arg_a = args(0); |
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69 nr_a = arg_a.rows (); |
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70 nc_a = arg_a.columns (); |
2928 | 71 |
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72 int arg_is_empty = empty_arg ("eig", nr_a, nc_a); |
2928 | 73 if (arg_is_empty < 0) |
74 return retval; | |
75 else if (arg_is_empty > 0) | |
76 return octave_value_list (2, Matrix ()); | |
77 | |
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78 if (!(arg_a.is_single_type () || arg_a.is_double_type ())) |
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79 { |
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80 gripe_wrong_type_arg ("eig", arg_a); |
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81 return retval; |
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82 } |
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83 |
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84 if (nargin == 2) |
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85 { |
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86 arg_b = args(1); |
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87 nr_b = arg_b.rows (); |
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88 nc_b = arg_b.columns (); |
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89 |
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90 arg_is_empty = empty_arg ("eig", nr_b, nc_b); |
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91 if (arg_is_empty < 0) |
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92 return retval; |
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93 else if (arg_is_empty > 0) |
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94 return octave_value_list (2, Matrix ()); |
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95 |
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96 if (!(arg_b.is_single_type () || arg_b.is_double_type ())) |
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97 { |
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98 gripe_wrong_type_arg ("eig", arg_b); |
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99 return retval; |
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100 } |
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101 } |
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102 |
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103 if (nr_a != nc_a) |
2928 | 104 { |
105 gripe_square_matrix_required ("eig"); | |
106 return retval; | |
107 } | |
108 | |
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109 if (nargin == 2 && nr_b != nc_b) |
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110 { |
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111 gripe_square_matrix_required ("eig"); |
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112 return retval; |
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113 } |
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114 |
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115 Matrix tmp_a, tmp_b; |
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116 ComplexMatrix ctmp_a, ctmp_b; |
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117 FloatMatrix ftmp_a, ftmp_b; |
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118 FloatComplexMatrix fctmp_a, fctmp_b; |
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119 |
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120 if (arg_a.is_single_type ()) |
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121 { |
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122 FloatEIG result; |
2928 | 123 |
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124 if (nargin == 1) |
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125 { |
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126 if (arg_a.is_real_type ()) |
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127 { |
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128 ftmp_a = arg_a.float_matrix_value (); |
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129 |
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130 result = FloatEIG (ftmp_a, nargout > 1); |
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131 } |
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132 else |
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133 { |
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134 fctmp_a = arg_a.float_complex_matrix_value (); |
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135 |
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136 result = FloatEIG (fctmp_a, nargout > 1); |
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137 } |
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138 } |
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139 else if (nargin == 2) |
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140 { |
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141 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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142 { |
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143 ftmp_a = arg_a.float_matrix_value (); |
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144 ftmp_b = arg_b.float_matrix_value (); |
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146 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1); |
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147 } |
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148 else |
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149 { |
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150 fctmp_a = arg_a.float_complex_matrix_value (); |
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151 fctmp_b = arg_b.float_complex_matrix_value (); |
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152 |
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153 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1); |
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154 } |
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155 } |
2928 | 156 |
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157 if (nargout == 0 || nargout == 1) |
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158 { |
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159 retval(0) = result.eigenvalues (); |
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160 } |
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161 else |
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162 { |
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163 // Blame it on Matlab. |
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164 |
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165 FloatComplexDiagMatrix d (result.eigenvalues ()); |
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166 |
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167 retval(1) = d; |
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168 retval(0) = result.eigenvectors (); |
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169 } |
2928 | 170 } |
171 else | |
172 { | |
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173 EIG result; |
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174 |
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175 if (nargin == 1) |
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176 { |
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177 if (arg_a.is_real_type ()) |
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178 { |
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179 tmp_a = arg_a.matrix_value (); |
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180 |
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181 result = EIG (tmp_a, nargout > 1); |
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182 } |
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183 else |
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184 { |
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185 ctmp_a = arg_a.complex_matrix_value (); |
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186 |
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187 result = EIG (ctmp_a, nargout > 1); |
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188 } |
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189 } |
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190 else if (nargin == 2) |
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191 { |
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192 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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193 { |
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194 tmp_a = arg_a.matrix_value (); |
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195 tmp_b = arg_b.matrix_value (); |
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196 |
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197 result = EIG (tmp_a, tmp_b, nargout > 1); |
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198 } |
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199 else |
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200 { |
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201 ctmp_a = arg_a.complex_matrix_value (); |
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202 ctmp_b = arg_b.complex_matrix_value (); |
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203 |
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204 result = EIG (ctmp_a, ctmp_b, nargout > 1); |
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205 } |
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206 } |
2928 | 207 |
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208 if (nargout == 0 || nargout == 1) |
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209 { |
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210 retval(0) = result.eigenvalues (); |
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211 } |
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212 else |
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213 { |
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214 // Blame it on Matlab. |
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216 ComplexDiagMatrix d (result.eigenvalues ()); |
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217 |
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218 retval(1) = d; |
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219 retval(0) = result.eigenvectors (); |
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220 } |
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222 | |
223 return retval; | |
224 } | |
225 | |
226 /* | |
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227 %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)) |
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228 |
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229 %!test |
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230 %! [v, d] = eig ([1, 2; 2, 1]); |
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231 %! x = 1 / sqrt (2); |
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232 %! assert (d, [-1, 0; 0, 3], sqrt (eps)); |
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233 %! assert (v, [-x, x; x, x], sqrt (eps)); |
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234 |
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235 %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single"))) |
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236 |
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237 %!test |
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238 %! [v, d] = eig (single ([1, 2; 2, 1])); |
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239 %! x = single (1 / sqrt (2)); |
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240 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))); |
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241 %! assert (v, [-x, x; x, x], sqrt (eps ("single"))); |
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242 |
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243 %!test |
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244 %! A = [1, 2; -1, 1]; B = [3, 3; 1, 2]; |
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245 %! [v, d] = eig (A, B); |
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246 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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247 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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248 |
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249 %!test |
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250 %! A = single ([1, 2; -1, 1]); B = single ([3, 3; 1, 2]); |
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251 %! [v, d] = eig (A, B); |
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252 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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253 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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254 |
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255 %!test |
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256 %! A = [1, 2; 2, 1]; B = [3, -2; -2, 3]; |
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257 %! [v, d] = eig (A, B); |
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258 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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259 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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260 |
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261 %!test |
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262 %! A = single ([1, 2; 2, 1]); B = single ([3, -2; -2, 3]); |
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263 %! [v, d] = eig (A, B); |
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264 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps ("single"))); |
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265 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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266 |
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267 %!test |
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268 %! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i]; |
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269 %! [v, d] = eig (A, B); |
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270 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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271 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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272 |
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273 %!test |
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274 %! A = single ([1+3i, 2+i; 2-i, 1+3i]); B = single ([5+9i, 2+i; 2-i, 5+9i]); |
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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 ("single"))); |
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277 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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278 |
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279 %!test |
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280 %! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i]; |
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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)); |
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283 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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284 |
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285 %!test |
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286 %! A = single ([1+3i, 2+3i; 3-8i, 8+3i]); B = single ([8+i, 3+i; 4-9i, 3+i]); |
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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 ("single"))); |
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289 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps ("single"))); |
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290 |
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291 %!test |
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292 %! A = [1, 2; 3, 8]; B = [8, 3; 4, 3]; |
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293 %! [v, d] = eig (A, B); |
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294 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps)); |
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295 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps)); |
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296 |
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297 %!test |
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298 %! A = [1, 1+i; 1-i, 1]; B = [2, 0; 0, 2]; |
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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, 1+i; 1-i, 1]); B = single ([2, 0; 0, 2]); |
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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 %!error eig () |
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310 %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1) |
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311 %!error <EIG requires same size matrices> eig ([1, 2; 3, 4], 2) |
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312 %!error <argument must be a square matrix> eig ([1, 2; 3, 4; 5, 6]) |
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313 %!error <wrong type argument> eig ("abcd") |
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314 %!error <wrong type argument> eig ([1 2 ; 2 3], "abcd") |
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315 %!error <wrong type argument> eig (false, [1 2 ; 2 3]) |
2928 | 316 */ |