Mercurial > octave
annotate libinterp/corefcn/eig.cc @ 23219:3ac9f9ecfae5 stable
maint: Update copyright dates.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 22 Feb 2017 12:39:29 -0500 |
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2 | |
23219
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3 Copyright (C) 1996-2017 John W. Eaton |
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4 Copyright (C) 2016 Barbara Lócsi |
2928 | 5 |
6 This file is part of Octave. | |
7 | |
8 Octave is free software; you can redistribute it and/or modify it | |
9 under the terms of the GNU General Public License as published by the | |
7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
11 option) any later version. | |
2928 | 12 |
13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
16 for more details. | |
17 | |
18 You should have received a copy of the GNU General Public License | |
7016 | 19 along with Octave; see the file COPYING. If not, see |
20 <http://www.gnu.org/licenses/>. | |
2928 | 21 |
22 */ | |
23 | |
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24 #if defined (HAVE_CONFIG_H) |
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25 # include "config.h" |
2928 | 26 #endif |
27 | |
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28 #include "defun.h" |
2928 | 29 #include "error.h" |
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30 #include "errwarn.h" |
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31 #include "ovl.h" |
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32 |
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33 #include "EIG.h" |
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34 #include "fEIG.h" |
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35 #include "oct-string.h" |
2928 | 36 |
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37 DEFUN (eig, args, nargout, |
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38 doc: /* -*- texinfo -*- |
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39 @deftypefn {} {@var{lambda} =} eig (@var{A}) |
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40 @deftypefnx {} {@var{lambda} =} eig (@var{A}, @var{B}) |
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41 @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}) |
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42 @deftypefnx {} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B}) |
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43 @deftypefnx {} {[@var{V}, @var{lambda}, @var{W}] =} eig (@var{A}) |
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44 @deftypefnx {} {[@var{V}, @var{lambda}, @var{W}] =} eig (@var{A}, @var{B}) |
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45 @deftypefnx {} {[@dots{}] =} eig (@var{A}, @var{balanceOption}) |
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46 @deftypefnx {} {[@dots{}] =} eig (@var{A}, @var{B}, @var{algorithm}) |
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47 @deftypefnx {} {[@dots{}] =} eig (@dots{}, @var{eigvalOption}) |
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48 Compute the right eigenvalues(V) and optionally the eigenvectors(lambda) and |
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49 the left eigenvalues(W) of a matrix or a pair of matrices. |
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50 |
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51 The flag @var{balanceOption} can be one of: |
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52 |
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53 @table @asis |
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54 @item @qcode{"balance"} |
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55 Preliminary balancing is on. (default) |
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56 |
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57 @item @qcode{"nobalance"} |
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58 Disables preliminary balancing. |
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59 @end table |
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60 |
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61 The flag @var{eigvalOption} can be one of: |
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62 |
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63 @table @asis |
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64 @item @qcode{"matrix"} |
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65 Return the eigenvalues in a diagonal matrix. (default if 2 or 3 outputs |
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66 are specified) |
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67 |
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68 @item @qcode{"vector"} |
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69 Return the eigenvalues in a column vector. (default if 1 output is |
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70 specified, e.g. @var{lambda} = eig (@var{A})) |
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71 @end table |
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72 |
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73 The flag @var{algorithm} can be one of: |
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74 |
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75 @table @asis |
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76 @item @qcode{"chol"} |
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77 Uses the Cholesky factorization of B. (default if A is symmetric (Hermitian) |
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78 and B is symmetric (Hermitian) positive definite) |
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79 |
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80 @item @qcode{"qz"} |
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81 Uses the QZ algorithm. (When A or B are not symmetric always the |
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82 QZ algorithm will be used) |
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83 @end table |
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84 |
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85 @multitable @columnfractions .31 .23 .23 .23 |
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86 @headitem @tab no flag @tab chol @tab qz |
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87 @item both are symmetric |
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88 @tab @qcode{"chol"} |
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89 @tab @qcode{"chol"} |
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90 @tab @qcode{"qz"} |
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91 @item at least one is not symmetric |
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92 @tab @qcode{"qz"} |
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93 @tab @qcode{"qz"} |
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94 @tab @qcode{"qz"} |
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95 @end multitable |
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96 |
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97 The eigenvalues returned by @code{eig} are not ordered. |
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98 @seealso{eigs, svd} |
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99 @end deftypefn */) |
2928 | 100 { |
101 int nargin = args.length (); | |
102 | |
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103 if (nargin > 4 || nargin == 0) |
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104 print_usage (); |
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106 octave_value_list retval; |
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107 |
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108 octave_value arg_a, arg_b; |
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109 |
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110 arg_a = args(0); |
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112 if (arg_a.is_empty ()) |
2928 | 113 return octave_value_list (2, Matrix ()); |
114 | |
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115 if (! arg_a.is_float_type ()) |
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116 err_wrong_type_arg ("eig", arg_a); |
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117 |
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118 if (arg_a.rows () != arg_a.columns ()) |
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119 err_square_matrix_required ("eig", "A"); |
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120 |
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121 // determine if it's AEP or GEP |
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122 bool AEPcase = nargin == 1 || args(1).is_string (); |
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123 |
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124 if (! AEPcase) |
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125 { |
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126 arg_b = args(1); |
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127 |
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128 if (arg_b.is_empty ()) |
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129 return octave_value_list (2, Matrix ()); |
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130 |
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131 if (! arg_b.is_float_type ()) |
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132 err_wrong_type_arg ("eig", arg_b); |
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133 |
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134 if (arg_b.rows () != arg_b.columns ()) |
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135 err_square_matrix_required ("eig", "B"); |
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136 } |
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137 |
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138 bool qz_flag = false; |
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139 bool chol_flag = false; |
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140 bool balance_flag = false; |
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141 bool no_balance_flag = false; |
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142 bool matrix_flag = false; |
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143 bool vector_flag = false; |
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144 |
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145 for (int i = (AEPcase ? 1 : 2); i < args.length (); ++i) |
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146 { |
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147 if (! args(i).is_string ()) |
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148 err_wrong_type_arg ("eig", args(i)); |
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149 |
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150 std::string arg_i = args(i).string_value (); |
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151 if (octave::string::strcmpi (arg_i, "qz")) |
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152 qz_flag = true; |
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153 else if (octave::string::strcmpi (arg_i, "chol")) |
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154 chol_flag = true; |
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155 else if (octave::string::strcmpi (arg_i, "balance")) |
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156 balance_flag = true; |
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157 else if (octave::string::strcmpi (arg_i, "nobalance")) |
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158 no_balance_flag = true; |
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159 else if (octave::string::strcmpi (arg_i, "matrix")) |
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160 matrix_flag = true; |
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161 else if (octave::string::strcmpi (arg_i, "vector")) |
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162 vector_flag = true; |
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163 else |
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164 error ("eig: invalid option \"%s\"", arg_i.c_str ()); |
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165 } |
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166 |
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167 if (balance_flag && no_balance_flag) |
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168 error ("eig: \"balance\" and \"nobalance\" options are mutually exclusive"); |
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169 if (vector_flag && matrix_flag) |
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170 error ("eig: \"vector\" and \"matrix\" options are mutually exclusive"); |
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171 if (qz_flag && chol_flag) |
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172 error ("eig: \"qz\" and \"chol\" options are mutually exclusive"); |
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174 if (AEPcase) |
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175 { |
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176 if (qz_flag) |
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177 error ("eig: invalid \"qz\" option for algebraic eigenvalue problem"); |
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178 if (chol_flag) |
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179 error ("eig: invalid \"chol\" option for algebraic eigenvalue problem"); |
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180 } |
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181 else |
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182 { |
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183 if (balance_flag) |
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184 error ("eig: invalid \"balance\" option for generalized eigenvalue problem"); |
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185 if (no_balance_flag) |
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186 error ("eig: invalid \"nobalance\" option for generalized eigenvalue problem"); |
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187 } |
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188 |
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189 // Default is to balance |
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190 const bool balance = no_balance_flag ? false : true; |
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191 const bool force_qz = qz_flag; |
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192 |
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193 |
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194 Matrix tmp_a, tmp_b; |
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195 ComplexMatrix ctmp_a, ctmp_b; |
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196 FloatMatrix ftmp_a, ftmp_b; |
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197 FloatComplexMatrix fctmp_a, fctmp_b; |
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198 |
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199 if (arg_a.is_single_type ()) |
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200 { |
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201 FloatEIG result; |
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202 if (AEPcase) |
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203 { |
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204 if (arg_a.is_real_type ()) |
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205 { |
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206 ftmp_a = arg_a.float_matrix_value (); |
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207 |
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208 result = FloatEIG (ftmp_a, nargout > 1, nargout > 2, balance); |
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209 } |
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210 else |
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211 { |
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212 fctmp_a = arg_a.float_complex_matrix_value (); |
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213 |
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214 result = FloatEIG (fctmp_a, nargout > 1, nargout > 2, balance); |
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215 } |
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216 } |
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217 else |
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218 { |
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219 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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220 { |
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221 ftmp_a = arg_a.float_matrix_value (); |
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222 ftmp_b = arg_b.float_matrix_value (); |
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224 result = FloatEIG (ftmp_a, ftmp_b, nargout > 1, nargout > 2, |
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225 force_qz); |
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226 } |
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227 else |
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228 { |
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229 fctmp_a = arg_a.float_complex_matrix_value (); |
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230 fctmp_b = arg_b.float_complex_matrix_value (); |
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231 |
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232 result = FloatEIG (fctmp_a, fctmp_b, nargout > 1, nargout > 2, |
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233 force_qz); |
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234 } |
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235 } |
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237 if (nargout == 0 || nargout == 1) |
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238 { |
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239 if (matrix_flag) |
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240 retval = ovl (FloatComplexDiagMatrix (result.eigenvalues ())); |
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241 else |
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242 retval = ovl (result.eigenvalues ()); |
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243 } |
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244 else if (nargout == 2) |
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245 { |
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246 if (vector_flag) |
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247 retval = ovl (result.right_eigenvectors (), result.eigenvalues ()); |
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248 else |
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249 retval = ovl (result.right_eigenvectors (), |
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250 FloatComplexDiagMatrix (result.eigenvalues ())); |
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251 } |
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252 else |
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253 { |
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254 if (vector_flag) |
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255 retval = ovl (result.right_eigenvectors (), |
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256 result.eigenvalues (), |
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257 result.left_eigenvectors ()); |
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258 else |
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259 retval = ovl (result.right_eigenvectors (), |
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260 FloatComplexDiagMatrix (result.eigenvalues ()), |
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261 result.left_eigenvectors ()); |
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262 } |
2928 | 263 } |
264 else | |
265 { | |
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266 EIG result; |
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267 |
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268 if (AEPcase) |
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269 { |
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270 if (arg_a.is_real_type ()) |
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271 { |
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272 tmp_a = arg_a.matrix_value (); |
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273 |
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274 result = EIG (tmp_a, nargout > 1, nargout > 2, balance); |
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275 } |
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276 else |
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277 { |
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278 ctmp_a = arg_a.complex_matrix_value (); |
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279 |
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280 result = EIG (ctmp_a, nargout > 1, nargout > 2, balance); |
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281 } |
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282 } |
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283 else |
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284 { |
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285 if (arg_a.is_real_type () && arg_b.is_real_type ()) |
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286 { |
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287 tmp_a = arg_a.matrix_value (); |
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288 tmp_b = arg_b.matrix_value (); |
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289 |
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290 result = EIG (tmp_a, tmp_b, nargout > 1, nargout > 2, force_qz); |
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291 } |
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292 else |
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293 { |
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294 ctmp_a = arg_a.complex_matrix_value (); |
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295 ctmp_b = arg_b.complex_matrix_value (); |
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296 |
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297 result = EIG (ctmp_a, ctmp_b, nargout > 1, nargout > 2, force_qz); |
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298 } |
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299 } |
2928 | 300 |
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301 if (nargout == 0 || nargout == 1) |
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302 { |
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303 if (matrix_flag) |
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304 retval = ovl (ComplexDiagMatrix (result.eigenvalues ())); |
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305 else |
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306 retval = ovl (result.eigenvalues ()); |
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307 } |
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308 else if (nargout == 2) |
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309 { |
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310 if (vector_flag) |
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311 retval = ovl (result.right_eigenvectors (), result.eigenvalues ()); |
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312 else |
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313 retval = ovl (result.right_eigenvectors (), |
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314 ComplexDiagMatrix (result.eigenvalues ())); |
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315 } |
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316 else |
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317 { |
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318 if (vector_flag) |
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319 retval = ovl (result.right_eigenvectors (), |
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320 result.eigenvalues (), |
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321 result.left_eigenvectors ()); |
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322 else |
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323 retval = ovl (result.right_eigenvectors (), |
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324 ComplexDiagMatrix (result.eigenvalues ()), |
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325 result.left_eigenvectors ()); |
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326 } |
2928 | 327 } |
328 | |
329 return retval; | |
330 } | |
331 | |
332 /* | |
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333 %!assert (eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps)) |
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334 |
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335 %!test |
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336 %! [v, d] = eig ([1, 2; 2, 1]); |
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337 %! x = 1 / sqrt (2); |
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338 %! assert (d, [-1, 0; 0, 3], sqrt (eps)) |
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339 %! assert (v, [-x, x; x, x], sqrt (eps)) |
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340 |
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341 %!test |
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342 %! [v, d, w] = eig ([1, 2; 2, 1]); |
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343 %! x = 1 / sqrt (2); |
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344 %! assert (w, [-x, x; x, x], sqrt (eps)) |
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345 |
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346 %!test |
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347 %! [v, d] = eig ([1, 2; 2, 1], "balance"); |
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348 %! x = 1 / sqrt (2); |
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349 %! assert (d, [-1, 0; 0, 3], sqrt (eps)) |
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350 %! assert (v, [-x, x; x, x], sqrt (eps)) |
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351 |
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352 %!test |
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353 %! [v, d, w] = eig ([1, 2; 2, 1], "balance"); |
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354 %! x = 1 / sqrt (2); |
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355 %! assert (w, [-x, x; x, x], sqrt (eps)); |
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356 |
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357 %!assert (eig (single ([1, 2; 2, 1])), single ([-1; 3]), sqrt (eps ("single"))) |
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358 |
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359 %!assert (eig (single ([1, 2; 2, 1]), "balance"), |
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360 %! single ([-1; 3]), sqrt (eps ("single"))) |
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361 |
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362 %!test |
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363 %! [v, d] = eig (single ([1, 2; 2, 1])); |
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364 %! x = single (1 / sqrt (2)); |
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365 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))) |
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366 %! assert (v, [-x, x; x, x], sqrt (eps ("single"))) |
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367 |
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368 %!test |
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369 %! [v, d, w] = eig (single ([1, 2; 2, 1])); |
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370 %! x = single (1 / sqrt (2)); |
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371 %! assert (w, [-x, x; x, x], sqrt (eps ("single"))) |
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372 |
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373 %!test |
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374 %! [v, d] = eig (single ([1, 2; 2, 1]), "balance"); |
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375 %! x = single (1 / sqrt (2)); |
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376 %! assert (d, single ([-1, 0; 0, 3]), sqrt (eps ("single"))); |
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377 %! assert (v, [-x, x; x, x], sqrt (eps ("single"))) |
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378 |
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379 %!test |
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380 %! [v, d, w] = eig (single ([1, 2; 2, 1]), "balance"); |
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381 %! x = single (1 / sqrt (2)); |
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382 %! assert (w, [-x, x; x, x], sqrt (eps ("single"))) |
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383 |
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384 |
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385 ## If (at least one of) the matrices are non-symmetric, |
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386 ## regardless the algorithm flag the qz algorithm should be used. |
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387 ## So the results without algorithm flag, with "qz" and with "chol" |
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388 ## should be the same. |
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389 %!function nonsym_chol_2_output (A, B, res = sqrt (eps)) |
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390 %! [v, d] = eig (A, B); |
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391 %! [v2, d2] = eig (A, B, "qz"); |
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392 %! [v3, d3] = eig (A, B, "chol"); |
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393 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), res) |
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394 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), res) |
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395 %! assert (v, v2) |
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396 %! assert (v, v3) |
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397 %! assert (d, d2) |
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398 %! assert (d, d3) |
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399 %!endfunction |
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400 |
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401 %!test nonsym_chol_2_output ([1, 2; -1, 1], [3, 3; 1, 2]) |
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402 %!test nonsym_chol_2_output ([1+3i, 2+3i; 3-8i, 8+3i], [8+i, 3+i; 4-9i, 3+i]) |
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403 %!test nonsym_chol_2_output ([1, 2; 3, 8], [8, 3; 4, 3]) |
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404 |
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405 %!test nonsym_chol_2_output (single ([1, 2; -1, 1]), |
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406 %! single ([3, 3; 1, 2]), sqrt (eps ("single"))) |
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407 %!test nonsym_chol_2_output (single ([1+3i, 2+3i; 3-8i, 8+3i]), |
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408 %! single ([8+i, 3+i; 4-9i, 3+i]), |
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409 %! sqrt (eps ("single"))) |
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410 |
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411 %!function nonsym_chol_3_output (A, B, res = sqrt (eps)) |
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412 %! [v, d, w] = eig (A, B); |
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413 %! [v2, d2, w2] = eig (A, B, "qz"); |
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414 %! [v3, d3, w3] = eig (A, B, "chol"); |
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415 %! wt = w'; |
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416 %! assert (wt(1, :)* A, d(1, 1) * wt(1, :) * B, res) |
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417 %! assert (wt(2, :)* A, d(2, 2) * wt(2, :) * B, res) |
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418 %! assert (v, v2) |
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419 %! assert (v, v3) |
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420 %! assert (d, d2) |
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421 %! assert (d, d3) |
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422 %! assert (w, w2) |
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423 %! assert (w, w3) |
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424 %!endfunction |
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425 |
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426 %!test nonsym_chol_3_output ([1, 2; -1, 1], [3, 3; 1, 2]) |
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427 %!test nonsym_chol_3_output ([1+3i, 2+3i; 3-8i, 8+3i], [8+i, 3+i; 4-9i, 3+i]) |
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428 %!test nonsym_chol_3_output ([1, 2; 3, 8], [8, 3; 4, 3]) |
8339
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429 |
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430 %!test nonsym_chol_3_output (single ([1, 2; -1, 1]), |
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431 %! single ([3, 3; 1, 2]), sqrt (eps ("single"))) |
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432 %!test nonsym_chol_3_output (single ([1+3i, 2+3i; 3-8i, 8+3i]), |
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433 %! single ([8+i, 3+i; 4-9i, 3+i]), |
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434 %! sqrt (eps ("single"))) |
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435 |
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436 ## If the matrices are symmetric, |
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437 ## then the chol method is default. |
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438 ## So the results without algorithm flag and with "chol" should be the same. |
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439 %!function sym_chol_2_input (A, B, res = sqrt (eps)) |
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440 %! [v, d] = eig (A, B); |
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441 %! [v2, d2] = eig (A, B, "chol"); |
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442 %! assert (A * v(:, 1), d(1, 1) * B * v(:, 1), res) |
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443 %! assert (A * v(:, 2), d(2, 2) * B * v(:, 2), res) |
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444 %! assert (v, v2) |
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445 %! assert (d, d2) |
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446 %!endfunction |
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447 |
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448 %!test sym_chol_2_input ([1, 2; 2, 1], [3, -2; -2, 3]) |
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449 %!test sym_chol_2_input ([1+3i, 2+i; 2-i, 1+3i], [5+9i, 2+i; 2-i, 5+9i]) |
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450 %!test sym_chol_2_input ([1, 1+i; 1-i, 1], [2, 0; 0, 2]) |
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451 |
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452 %!test sym_chol_2_input (single ([1, 2; 2, 1]), single ([3, -2; -2, 3]), |
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453 %! sqrt (eps ("single"))) |
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454 %!test sym_chol_2_input (single ([1+3i, 2+i; 2-i, 1+3i]), |
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455 %! single ([5+9i, 2+i; 2-i, 5+9i]), sqrt (eps ("single"))) |
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456 %!test sym_chol_2_input (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2]), |
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457 %! sqrt (eps ("single"))) |
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|
458 |
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459 %!function sym_chol_3_input (A, B, res = sqrt (eps)) |
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460 %! [v, d, w] = eig (A, B); |
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461 %! [v2, d2, w2] = eig (A, B, "chol"); |
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462 %! wt = w'; |
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463 %! assert (wt(1, :)* A, d(1, 1) * wt(1, :) * B, res) |
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464 %! assert (wt(2, :)* A, d(2, 2) * wt(2, :) * B, res) |
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465 %! assert (v, v2) |
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466 %! assert (d, d2) |
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467 %! assert (w, w2) |
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468 %!endfunction |
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469 |
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470 %!test sym_chol_3_input ([1, 2; 2, 1], [3, -2; -2, 3]) |
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471 %!test sym_chol_3_input ([1+3i, 2+i; 2-i, 1+3i], [5+9i, 2+i; 2-i, 5+9i]) |
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472 %!test sym_chol_3_input ([1, 1+i; 1-i, 1], [2, 0; 0, 2]) |
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473 |
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474 %!test sym_chol_3_input (single ([1, 2; 2, 1]), single ([3, -2; -2, 3]), |
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475 %! sqrt (eps ("single"))) |
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476 %!test sym_chol_3_input (single ([1+3i, 2+i; 2-i, 1+3i]), |
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477 %! single ([5+9i, 2+i; 2-i, 5+9i]), sqrt (eps ("single"))) |
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478 %!test sym_chol_3_input (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2]), |
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479 %! sqrt (eps ("single"))) |
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480 |
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481 ## "balance" is always default |
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482 ## so the results with and without "balance" should be the same |
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483 ## while in this case "nobalance" should produce different result |
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484 %!test |
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485 %! A = [3 -2 -0.9 0; -2 4 1 -0; -0 0 -1 0; -0.5 -0.5 0.1 1]; |
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486 %! [V1, D1] = eig (A); |
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487 %! [V2, D2] = eig (A, "balance"); |
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488 %! [V3, D3] = eig (A, "nobalance"); |
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489 %! assert (V1, V2) |
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490 %! assert (D1, D2) |
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491 %! assert (isequal (V2, V3), false) |
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492 |
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493 ## Testing the flags in all combination. |
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494 ## If 2 flags are on, than the result should be the same regardless |
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495 ## of the flags order. |
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496 ## option1 represents the first order while option2 represents the other order. |
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497 ## d and d2 should be a diagonal matrix if "matrix" flag is on while |
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498 ## these should be column vectors if the "vector" flag is on. |
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499 %!function test_eig_args (args, options1, options2, testd = @() true) |
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500 %! [v, d, w] = eig (args{:}, options1{:}); |
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501 %! [v2, d2, w2] = eig (args{:}, options2{:}); |
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502 %! assert (testd (d)) |
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503 %! assert (testd (d2)) |
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504 %! assert (v, v2) |
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505 %! assert (d, d2) |
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506 %! assert (w, w2) |
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507 %!endfunction |
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508 |
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509 %!function qz_chol_with_shapes (A, B) |
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510 %! for shapes = struct ("name", {"vector", "matrix"}, |
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511 %! "test", {@isvector, @isdiag}) |
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512 %! test_eig_args ({A, B}, {"qz", shapes.name}, |
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513 %! {shapes.name, "qz"}, shapes.test); |
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514 %! test_eig_args ({A, B}, {"chol", shapes.name}, |
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515 %! {shapes.name, "chol"}, shapes.test); |
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516 %! endfor |
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517 %!endfunction |
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518 |
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519 %!function balance_nobalance_with_shapes (A) |
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520 %! for shapes = struct ("name", {"vector", "matrix"}, |
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521 %! "test", {@isvector, @isdiag}) |
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522 %! test_eig_args ({A}, {"balance", shapes.name}, |
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523 %! {shapes.name, "balance"}, shapes.test); |
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524 %! test_eig_args ({A}, {"nobalance", shapes.name}, |
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525 %! {shapes.name, "nobalance"}, shapes.test); |
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526 %! endfor |
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527 %!endfunction |
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528 |
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529 ## Default return format: |
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530 ## diagonal matrix if 2 or 3 outputs are specified |
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531 ## column vector if 1 output is specified |
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532 %!function test_shapes (args) |
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533 %! d = eig (args{:}); |
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534 %! assert (isvector(d)) |
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535 %! d2 = eig (args{:}, "vector"); |
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536 %! assert (isvector(d2)) |
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537 %! [v, d3] = eig (args{:}); |
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538 %! assert (isdiag(d3)) |
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539 %! d4 = eig (args{:}, "matrix"); |
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540 %! assert (isdiag(d4)) |
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541 %! [v, d5, w] = eig (args{:}); |
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542 %! assert (isdiag(d5)) |
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543 %! d6 = eig (args{:}, "matrix"); |
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544 %! assert (isdiag(d6)) |
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545 %! assert (d, d2) |
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546 %! assert (d3, d4) |
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547 %! assert (d5, d6) |
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548 %! assert (d, diag(d3)) |
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549 %! assert (d, diag(d5)) |
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550 %!endfunction |
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551 |
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552 %!function shapes_AEP (A) |
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553 %! test_shapes({A}); |
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554 %!endfunction |
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555 |
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556 %!function shapes_GEP (A, B) |
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557 %! test_shapes({A, B}); |
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558 %!endfunction |
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Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
559 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
560 %!test balance_nobalance_with_shapes ([1, 2; 2, 1]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
561 %!test balance_nobalance_with_shapes (single ([1, 2; 2, 1])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
562 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
563 %!test shapes_AEP ([1, 2; 2, 1]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
564 %!test shapes_AEP (single ([1, 2; 2, 1])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
565 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
566 %!test qz_chol_with_shapes ([1, 1+i; 1-i, 1], [2, 0; 0, 2]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
567 %!test qz_chol_with_shapes ([1, 2; 3, 8], [8, 3; 4, 3]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
568 %!test qz_chol_with_shapes ([1, 2; -1, 1], [3, 3; 1, 2]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
569 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
570 %!test qz_chol_with_shapes (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
571 %!test qz_chol_with_shapes (single ([1, 2; 3, 8]), single ([8, 3; 4, 3])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
572 %!test qz_chol_with_shapes (single ([1, 2; -1, 1]), single ([3, 3; 1, 2])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
573 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
574 %!test shapes_GEP ([1, 1+i; 1-i, 1], [2, 0; 0, 2]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
575 %!test shapes_GEP ([1, 2; 3, 8], [8, 3; 4, 3]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
576 %!test shapes_GEP ([1, 2; -1, 1], [3, 3; 1, 2]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
577 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
578 %!test shapes_GEP (single ([1, 1+i; 1-i, 1]), single ([2, 0; 0, 2])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
579 %!test shapes_GEP (single ([1, 2; 3, 8]), single ([8, 3; 4, 3])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
580 %!test shapes_GEP (single ([1, 2; -1, 1]), single ([3, 3; 1, 2])); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
581 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
582 %!function chol_qz_accuracy (A, B, is_qz_accurate, is_chol_accurate) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
583 %! [V1,D1] = eig (A,B, 'qz'); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
584 %! [V2,D2] = eig (A,B); #default is chol |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
585 %! assert (isequal (A*V1,A*V1*D1), is_qz_accurate) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
586 %! assert (isequal (A*V2, A*V2*D2), is_chol_accurate) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
587 %!endfunction |
8339
18c4ded8612a
Add generalized eigenvalue functions
Jarkko Kaleva <d3roga@gmail.com>
parents:
7814
diff
changeset
|
588 |
18c4ded8612a
Add generalized eigenvalue functions
Jarkko Kaleva <d3roga@gmail.com>
parents:
7814
diff
changeset
|
589 %!test |
22305
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
590 %! minij_100 = gallery('minij',100); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
591 %! chol_qz_accuracy (minij_100, minij_100, false, true); |
8339
18c4ded8612a
Add generalized eigenvalue functions
Jarkko Kaleva <d3roga@gmail.com>
parents:
7814
diff
changeset
|
592 |
20490
ff904ae0285b
eig: Return correct solution for a pair of hermitian matrices (bug #45511)
Mike Miller <mtmiller@octave.org>
parents:
20172
diff
changeset
|
593 %!test |
22305
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
594 %! moler_100 = gallery('moler',100); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
595 %! chol_qz_accuracy (moler_100, moler_100, false, true); |
20490
ff904ae0285b
eig: Return correct solution for a pair of hermitian matrices (bug #45511)
Mike Miller <mtmiller@octave.org>
parents:
20172
diff
changeset
|
596 |
ff904ae0285b
eig: Return correct solution for a pair of hermitian matrices (bug #45511)
Mike Miller <mtmiller@octave.org>
parents:
20172
diff
changeset
|
597 %!test |
22305
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
598 %! A = diag([10^-16, 10^-15]); |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
599 %! chol_qz_accuracy (A, A, true, false); |
20490
ff904ae0285b
eig: Return correct solution for a pair of hermitian matrices (bug #45511)
Mike Miller <mtmiller@octave.org>
parents:
20172
diff
changeset
|
600 |
14501
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
601 %!error eig () |
22305
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
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diff
changeset
|
602 %!error eig (false) |
14501
60e5cf354d80
Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents:
14138
diff
changeset
|
603 %!error eig ([1, 2; 3, 4], [4, 3; 2, 1], 1) |
22305
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
604 |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
605 %!error <EIG requires same size matrices> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
606 %! eig ([1, 2; 3, 4], 2) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
607 %!error <must be a square matrix> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
608 %! eig ([1, 2; 3, 4; 5, 6]) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
609 %!error <wrong type argument> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
610 %! eig ("abcd") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
611 %!error <invalid option "abcd"> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
612 %! eig ([1 2 ; 2 3], "abcd") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
613 %!error <invalid "chol" option for algebraic eigenvalue problem> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
614 %! eig ([1 2 ; 2 3], "chol") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
615 %!error <invalid "qz" option for algebraic eigenvalue problem> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
616 %! eig ([1 2 ; 2 3], "qz") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
617 %!error <wrong type argument> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
618 %! eig (false, [1 2 ; 2 3]) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
619 %!error <invalid option "abcd"> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
620 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "abcd") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
621 %!error <invalid "qz" option for algebraic eigenvalue problem> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
622 %! eig ([1 2 ; 2 3], "balance", "qz") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
623 %!error <invalid option "abcd"> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
624 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "vector", "abcd") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
625 %!error <invalid option "abcd"> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
626 %! eig ([1 2 ; 2 3], "balance", "matrix", "abcd") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
627 %!error <"balance" and "nobalance" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
628 %! eig ([1 2 ; 2 3], "balance", "nobalance") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
629 %!error <"balance" and "nobalance" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
630 %! eig ([1 2 ; 2 3], "nobalance", "balance") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
631 %!error <"vector" and "matrix" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
632 %! eig ([1 2 ; 2 3], "matrix", "vector") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
633 %!error <"vector" and "matrix" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
634 %! eig ([1 2 ; 2 3], "vector", "matrix") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
635 %!error <"vector" and "matrix" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
636 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "matrix", "vector") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
637 %!error <"vector" and "matrix" options are mutually exclusive> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
638 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], "vector", "matrix") |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
639 %!error <wrong type argument> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
640 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], false) |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
641 %!error <wrong type argument> |
510886d03ef2
eig: new options for choice of algorithm, balancing, and output (patch #8960)
Barbara Locsi <locsi.barbara@gmail.com>
parents:
21966
diff
changeset
|
642 %! eig ([1 2 ; 2 3], [1 2 ; 2 3], [1 2 ; 2 3]) |
2928 | 643 */ |