Mercurial > octave
annotate libinterp/corefcn/ordqz.cc @ 33167:8f8bb94a1b83
for consistent coding style, use #if defined, not #ifdef or #ifndef
Affected files: documentation.cc, variable-editor-model.cc,
variable-editor.cc, gsvd.cc, latex-text-renderer.cc, ordqz.cc,
pt-anon-scopes.cc, Faddeeva.cc, and gsvd.cc.
author | John W. Eaton <jwe@octave.org> |
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date | Thu, 07 Mar 2024 13:55:46 -0500 |
parents | f53ac65ffba6 |
children | 3606817b9994 |
rev | line source |
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1 //////////////////////////////////////////////////////////////////////// |
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2 // |
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maint: update Octave Project Developers copyright for the new year
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3 // Copyright (C) 2020-2024 The Octave Project Developers |
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4 // |
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5 // See the file COPYRIGHT.md in the top-level directory of this |
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6 // distribution or <https://octave.org/copyright/>. |
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7 // |
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8 // This file is part of Octave. |
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9 // |
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10 // Octave is free software: you can redistribute it and/or modify it |
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11 // under the terms of the GNU General Public License as published by |
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12 // the Free Software Foundation, either version 3 of the License, or |
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13 // (at your option) any later version. |
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14 // |
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15 // Octave is distributed in the hope that it will be useful, but |
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16 // WITHOUT ANY WARRANTY; without even the implied warranty of |
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17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 // GNU General Public License for more details. |
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19 // |
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20 // You should have received a copy of the GNU General Public License |
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21 // along with Octave; see the file COPYING. If not, see |
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22 // <https://www.gnu.org/licenses/>. |
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23 // |
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24 //////////////////////////////////////////////////////////////////////// |
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25 |
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26 // Generalized eigenvalue reordering via LAPACK |
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27 |
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28 // Originally written by M. Koehler <koehlerm(AT)mpi-magdeburg.mpg.de> |
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29 |
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30 #undef DEBUG |
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31 |
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32 #if defined (HAVE_CONFIG_H) |
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33 # include "config.h" |
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34 #endif |
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35 |
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36 #include <cctype> |
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37 #include <cmath> |
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38 |
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39 #include "f77-fcn.h" |
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40 #include "lo-lapack-proto.h" |
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41 #include "qr.h" |
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42 #include "quit.h" |
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43 |
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44 #include "defun.h" |
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45 #include "error.h" |
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46 #include "errwarn.h" |
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47 #include "ovl.h" |
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48 |
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49 |
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50 #if defined (DEBUG) |
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51 # include "pager.h" |
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52 # include "pr-output.h" |
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53 #endif |
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54 |
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55 |
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56 OCTAVE_BEGIN_NAMESPACE(octave) |
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57 |
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58 DEFUN (ordqz, args, nargout, |
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59 doc: /* -*- texinfo -*- |
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60 @deftypefn {} {[@var{AR}, @var{BR}, @var{QR}, @var{ZR}] =} ordqz (@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{keyword}) |
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61 @deftypefnx {} {[@var{AR}, @var{BR}, @var{QR}, @var{ZR}] =} ordqz (@var{AA}, @var{BB}, @var{Q}, @var{Z}, @var{select}) |
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62 Reorder the QZ@tie{}decomposition of a generalized eigenvalue problem. |
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63 |
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64 The generalized eigenvalue problem is defined as |
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65 |
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66 @tex |
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67 $$A x = \lambda B x$$ |
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68 @end tex |
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69 @ifnottex |
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70 |
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71 @math{A x = @var{lambda} B x} |
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72 |
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73 @end ifnottex |
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74 |
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75 Its generalized Schur decomposition is computed using the @code{qz} algorithm: |
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76 |
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77 @code{[@var{AA}, @var{BB}, @var{Q}, @var{Z}] = qz (@var{A}, @var{B})} |
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78 |
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79 where @var{AA}, @var{BB}, @var{Q}, and @var{Z} fulfill |
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80 @tex |
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81 $$ AA = Q \cdot A \cdot Z, BB = Q \cdot B \cdot Z $$ |
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82 @end tex |
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83 @ifnottex |
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84 |
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85 @example |
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86 @group |
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87 |
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88 @var{AA} = @var{Q} * @var{A} * @var{Z}, @var{BB} = @var{Q} * @var{B} * @var{Z} |
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89 |
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90 @end group |
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91 @end example |
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92 |
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93 @end ifnottex |
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94 |
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95 The @code{ordqz} function computes a unitary transformation @var{QR} and |
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96 @var{ZR} such that the order of the eigenvalue on the diagonal of @var{AA} and |
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97 @var{BB} is changed. The resulting reordered matrices @var{AR} and @var{BR} |
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98 fulfill: |
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99 |
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100 @tex |
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101 $$ A_R = Q_R \cdot A \cdot Z_R, B_R = Q_R \cdot B \cdot Z_R $$ |
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102 @end tex |
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103 @ifnottex |
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104 |
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105 @example |
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106 @group |
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107 |
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108 @var{AR} = @var{QR} * @var{A} * @var{ZR}, @var{BR} = @var{QR} * @var{B} * @var{ZR} |
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109 |
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110 @end group |
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111 @end example |
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112 |
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113 @end ifnottex |
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114 |
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115 The function can either be called with the @var{keyword} argument which |
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116 selects the eigenvalues in the top left block of @var{AR} and @var{BR} in the |
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117 following way: |
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118 |
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119 @table @asis |
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120 @item @qcode{"S"}, @nospell{@qcode{"udi"}} |
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121 small: leading block has all |
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122 @tex |
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123 $|\lambda| < 1$ |
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124 @end tex |
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125 @ifnottex |
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126 |@var{lambda}| < 1 |
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127 @end ifnottex |
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128 |
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129 @item @qcode{"B"}, @nospell{@qcode{"udo"}} |
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130 big: leading block has all |
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131 @tex |
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132 $|\lambda| \geq 1$ |
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133 @end tex |
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134 @ifnottex |
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135 |@var{lambda}| @geq{} 1 |
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136 @end ifnottex |
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137 |
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138 @item @qcode{"-"}, @nospell{@qcode{"lhp"}} |
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139 negative real part: leading block has all eigenvalues in the open left |
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140 half-plane |
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141 |
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142 @item @qcode{"+"}, @nospell{@qcode{"rhp"}} |
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143 non-negative real part: leading block has all eigenvalues in the closed right |
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144 half-plane |
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145 @end table |
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146 |
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147 If a logical vector @var{select} is given instead of a keyword the @code{ordqz} |
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148 function reorders all eigenvalues @code{k} to the left block for which |
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149 @code{select(k)} is true. |
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150 |
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151 Note: The keywords are compatible with the ones from @code{qr}. |
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152 |
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153 @seealso{eig, ordeig, qz, schur, ordschur} |
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154 @end deftypefn */) |
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155 { |
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156 enum { LHP, RHP, UDI, UDO, VEC, NONE } select_mode = NONE; |
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157 |
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158 if (args.length () != 5) |
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159 print_usage (); |
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160 |
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161 // Check select argument |
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162 if (args(4).is_string()) |
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163 { |
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164 std::string opts = args(4).string_value (); |
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165 std::for_each (opts.begin (), opts.end (), |
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166 [] (char& c) { c = std::tolower (c); }); |
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167 if (opts == "lhp" || opts == "-") |
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168 select_mode = LHP; |
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169 else if (opts == "rhp" || opts == "+") |
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170 select_mode = RHP; |
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171 else if (opts == "udi" || opts == "s") |
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172 select_mode = UDI; |
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173 else if (opts == "udo" || opts == "b") |
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174 select_mode = UDO; |
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175 else |
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176 error_with_id ("Octave:ordqz:unknown-keyword", |
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177 "ordqz: unknown KEYWORD, possible values: " |
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178 "lhp, rhp, udi, udo"); |
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179 } |
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180 else if (args(4).isreal () || args(4).isinteger () || args(4).islogical ()) |
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181 { |
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182 if (args(4).rows () > 1 && args(4).columns () > 1) |
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183 error_with_id ("Octave:ordqz:select-not-vector", |
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184 "ordqz: SELECT argument must be a vector"); |
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185 select_mode = VEC; |
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186 } |
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187 else |
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188 error_with_id ("Octave:ordqz:unknown-arg", |
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189 "ordqz: OPT must be string or a logical vector"); |
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190 |
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191 if (nargout > 4) |
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192 error_with_id ("Octave:ordqz:nargout", |
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193 "ordqz: at most four output arguments possible"); |
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194 |
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195 // Matrix A: check dimensions. |
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196 F77_INT nn = to_f77_int (args(0).rows ()); |
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197 F77_INT nc = to_f77_int (args(0).columns ()); |
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198 |
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199 if (args(0).isempty ()) |
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200 { |
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201 warn_empty_arg ("qz: A"); |
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202 return octave_value_list (2, Matrix ()); |
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203 } |
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204 else if (nc != nn) |
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205 err_square_matrix_required ("qz", "A"); |
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206 |
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207 // Matrix A: get value. |
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208 Matrix aa; |
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209 ComplexMatrix caa; |
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210 |
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211 if (args(0).iscomplex ()) |
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212 caa = args(0).complex_matrix_value (); |
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213 else |
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214 aa = args(0).matrix_value (); |
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215 |
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216 // Extract argument 2 (bb, or cbb if complex). |
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217 F77_INT b_nr = to_f77_int (args(1).rows ()); |
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218 F77_INT b_nc = to_f77_int (args(1).columns ()); |
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219 |
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220 if (nn != b_nc || nn != b_nr) |
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221 ::err_nonconformant (); |
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222 |
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223 Matrix bb; |
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224 ComplexMatrix cbb; |
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225 |
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226 if (args(1).iscomplex ()) |
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227 cbb = args(1).complex_matrix_value (); |
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228 else |
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229 bb = args(1).matrix_value (); |
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230 |
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231 // Extract argument 3 (qq, or cqq if complex). |
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232 F77_INT q_nr = to_f77_int (args(2).rows ()); |
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233 F77_INT q_nc = to_f77_int (args(2).columns ()); |
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234 |
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235 if (nn != q_nc || nn != q_nr) |
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236 ::err_nonconformant (); |
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237 |
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238 Matrix qq; |
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239 ComplexMatrix cqq; |
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240 |
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241 if (args(2).iscomplex ()) |
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242 cqq = args(2).complex_matrix_value ().hermitian (); |
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243 else |
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244 qq = args(2).matrix_value ().transpose (); |
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245 |
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246 // Extract argument 4 (zz, or czz if complex). |
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247 F77_INT z_nr = to_f77_int (args(3).rows ()); |
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248 F77_INT z_nc = to_f77_int (args(3).columns ()); |
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249 |
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250 if (nn != z_nc || nn != z_nr) |
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251 ::err_nonconformant (); |
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252 |
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253 Matrix zz; |
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254 ComplexMatrix czz; |
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255 |
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256 if (args(3).iscomplex ()) |
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|
257 czz = args(3).complex_matrix_value (); |
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|
258 else |
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|
259 zz = args(3).matrix_value (); |
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260 |
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261 bool complex_case = (args(0).iscomplex () || args(1).iscomplex () |
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262 || args(2).iscomplex () || args(3).iscomplex ()); |
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263 |
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264 if (select_mode == VEC && args(4).rows () != nn && args(4).columns () != nn) |
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|
265 error_with_id ("Octave:ordqz:numel_select", |
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266 "ordqz: SELECT vector has the wrong number of elements"); |
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267 |
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|
268 Array<double> select_array (dim_vector (nn, 1)); |
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|
269 if (select_mode == VEC) |
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|
270 select_array = args(4).vector_value (); |
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|
271 |
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|
272 Array<F77_LOGICAL> select (dim_vector (nn, 1)); |
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|
273 |
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|
274 if (complex_case) |
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|
275 { |
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|
276 // Complex |
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|
277 if (args(0).isreal ()) |
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|
278 caa = ComplexMatrix (aa); |
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|
279 if (args(1).isreal ()) |
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|
280 cbb = ComplexMatrix (bb); |
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|
281 if (args(2).isreal ()) |
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|
282 cqq = ComplexMatrix (qq); |
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|
283 if (args(3).isreal ()) |
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|
284 czz = ComplexMatrix (zz); |
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|
285 |
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|
286 ComplexRowVector alpha (dim_vector (nn, 1)); |
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|
287 ComplexRowVector beta (dim_vector (nn, 1)); |
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changeset
|
288 octave_idx_type k; |
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|
289 |
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|
290 for (k = 0; k < nn-1; k++) |
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|
291 { |
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|
292 if (caa(k+1, k) != 0.0) |
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|
293 error_with_id ("Octave:ordqz:unsupported_AA", |
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|
294 "ordqz: quasi upper triangular matrices are not " |
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|
295 "allowed with complex data"); |
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|
296 } |
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|
297 |
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|
298 for (k = 0; k < nn; k++) |
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|
299 { |
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|
300 alpha(k) = caa(k, k); |
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|
301 beta(k) = cbb(k, k); |
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|
302 } |
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|
303 |
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|
304 for (k = 0; k < nn; k++) |
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|
305 { |
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|
306 switch (select_mode) |
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|
307 { |
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|
308 case LHP: |
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|
309 select(k) = real (alpha(k) * beta(k)) < 0; |
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310 break; |
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|
311 case RHP: |
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312 select(k) = real (alpha(k) * beta(k)) > 0; |
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|
313 break; |
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314 case UDI: |
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315 if (beta(k) != 0.0) |
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316 select(k) = abs (alpha(k)/beta(k)) < 1.0; |
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317 else |
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318 select(k) = false; |
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319 break; |
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320 case UDO: |
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321 if (beta(k) != 0.0) |
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322 select(k) = abs (alpha(k)/beta(k)) > 1.0; |
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323 else |
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324 select(k) = true; |
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325 break; |
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326 case VEC: |
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327 if (select_array(k) != 0.0) |
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328 select(k) = true; |
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|
329 else |
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330 select(k) = false; |
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331 break; |
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332 default: |
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333 // default: case just here to suppress compiler warning. |
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334 panic_impossible (); |
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335 } |
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336 } |
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337 |
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338 F77_LOGICAL wantq, wantz; |
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339 wantq = 1, wantz = 1; |
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340 F77_INT ijob, mm, lrwork3, liwork, info; |
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341 ijob = 0, lrwork3 = 1, liwork = 1; |
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342 F77_DBLE pl, pr; |
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343 ComplexRowVector work3 (lrwork3); |
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344 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
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345 |
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346 F77_XFCN (ztgsen, ZTGSEN, |
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347 (ijob, wantq, wantz, |
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348 select.rwdata (), nn, |
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349 F77_DBLE_CMPLX_ARG (caa.rwdata ()), nn, |
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350 F77_DBLE_CMPLX_ARG (cbb.rwdata ()), nn, |
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351 F77_DBLE_CMPLX_ARG (alpha.rwdata ()), |
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352 F77_DBLE_CMPLX_ARG (beta.rwdata ()), |
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353 F77_DBLE_CMPLX_ARG (cqq.rwdata ()), nn, |
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354 F77_DBLE_CMPLX_ARG (czz.rwdata ()), nn, |
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355 mm, |
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356 pl, pr, |
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357 nullptr, |
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358 F77_DBLE_CMPLX_ARG (work3.rwdata ()), lrwork3, |
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359 iwork.rwdata (), liwork, |
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360 info)); |
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361 if (info != 0) |
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362 error_with_id ("Octave:ordqz:ztgsen_failed", |
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363 "ordqz: failed to reorder eigenvalues"); |
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364 } |
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365 else |
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366 { |
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367 // Extract eigenvalues |
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368 RowVector alphar (dim_vector (nn, 1)); |
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369 RowVector alphai (dim_vector (nn, 1)); |
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370 RowVector beta (dim_vector (nn, 1)); |
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371 |
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372 octave_idx_type k; |
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373 |
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374 k = 0; |
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375 while (k < nn) |
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376 { |
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377 #if defined (DEBUG) |
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378 octave_stdout << "ordqz: k = " << k << " nn = " << nn << " \n"; |
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379 #endif |
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380 if ((k < nn-1 && aa(k+1, k) == 0.0) || k == nn-1) |
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381 { |
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382 alphar(k) = aa(k, k); |
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383 alphai(k) = 0.0; |
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384 beta(k) = bb(k, k); |
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385 k++; |
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386 } |
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387 else |
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388 { |
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389 double ar[2], ai[2], b[2], work[4]; |
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390 char qz_job = 'E'; |
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391 char comp_q = 'N'; |
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392 char comp_z = 'N'; |
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393 F77_INT nl = 2; |
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394 F77_INT ilo = 1; |
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395 F77_INT ihi = 2; |
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396 F77_INT lwork = 4; |
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397 F77_INT info = 0; |
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398 double *aa_vec = aa.rwdata (); |
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399 double *bb_vec = bb.rwdata (); |
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400 |
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|
401 F77_XFCN (dhgeqz, DHGEQZ, |
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|
402 (F77_CONST_CHAR_ARG2 (&qz_job, 1), |
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|
403 F77_CONST_CHAR_ARG2 (&comp_q, 1), |
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|
404 F77_CONST_CHAR_ARG2 (&comp_z, 1), |
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|
405 nl, ilo, ihi, |
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406 &aa_vec[k+k*nn], nn, |
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407 &bb_vec[k+k*nn], nn, |
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|
408 ar, ai, b, |
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409 nullptr, nn, |
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|
410 nullptr, nn, work, lwork, info |
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|
411 F77_CHAR_ARG_LEN (1) |
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|
412 F77_CHAR_ARG_LEN (1) |
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|
413 F77_CHAR_ARG_LEN (1))); |
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|
414 if (info != 0) |
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|
415 error("ordqz: failed to extract eigenvalues"); |
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|
416 |
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|
417 alphar(k) = ar[0]; |
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|
418 alphar(k+1) = ar[1]; |
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|
419 alphai(k) = ai[0]; |
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|
420 alphai(k+1) = ai[1]; |
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421 beta(k) = b[0]; |
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|
422 beta(k+1) = b[1]; |
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|
423 |
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|
424 k += 2; |
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|
425 } |
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|
426 |
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|
427 } |
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|
428 |
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|
429 for (k = 0; k < nn; k++) |
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|
430 { |
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|
431 switch (select_mode) |
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|
432 { |
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|
433 case LHP: |
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434 select(k) = alphar(k) * beta(k) < 0; |
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|
435 break; |
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|
436 case RHP: |
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|
437 select(k) = alphar(k) * beta(k) > 0; |
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|
438 break; |
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|
439 case UDI: |
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|
440 select(k) = alphar(k)*alphar(k) |
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441 + alphai(k)*alphai(k) < beta(k)*beta(k); |
0e86e50bebeb
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Rik <rik@octave.org>
parents:
28986
diff
changeset
|
442 break; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
443 case UDO: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
444 select(k) = alphar(k)*alphar(k) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
445 + alphai(k)*alphai(k) > beta(k)*beta(k); |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
446 break; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
447 case VEC: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
448 if (select_array(k) != 0.0) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
449 select(k) = true; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
450 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
451 select(k) = false; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
452 break; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
453 default: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
454 // default: case just here to suppress compiler warning. |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
455 panic_impossible(); |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
456 } |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
457 } |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
458 |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
459 F77_LOGICAL wantq, wantz; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
460 wantq = 1, wantz = 1; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
461 F77_INT ijob, mm, lrwork3, liwork, info; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
462 ijob = 0, lrwork3 = 4*nn+16, liwork = nn; |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
463 F77_DBLE pl, pr; |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
464 RowVector rwork3 (lrwork3); |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
465 Array<F77_INT> iwork (dim_vector (liwork, 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
466 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
467 F77_XFCN (dtgsen, DTGSEN, |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
468 (ijob, wantq, wantz, |
32660
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
469 select.rwdata (), nn, |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
470 aa.rwdata (), nn, |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
471 bb.rwdata (), nn, |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
472 alphar.rwdata (), |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
473 alphai.rwdata (), |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
474 beta.rwdata (), |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
475 qq.rwdata (), nn, |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
476 zz.rwdata (), nn, |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
477 mm, |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
478 pl, pr, |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
479 nullptr, |
32660
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
480 rwork3.rwdata (), lrwork3, |
f53ac65ffba6
maint: New method rwdata() as clearer alternative to fortran_vec().
Rik <rik@octave.org>
parents:
32632
diff
changeset
|
481 iwork.rwdata (), liwork, |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
482 info)); |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
483 if (info != 0) |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
484 error("ordqz: failed to reorder eigenvalues"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
485 } |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
486 |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
487 octave_value_list retval (nargout); |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
488 switch (nargout) |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
489 { |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
490 case 4: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
491 if (complex_case) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
492 retval(3) = czz; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
493 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
494 retval(3) = zz; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
495 OCTAVE_FALLTHROUGH; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
496 case 3: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
497 if (complex_case) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
498 retval(2) = cqq.hermitian(); |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
499 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
500 retval(2) = qq.transpose(); |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
501 OCTAVE_FALLTHROUGH; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
502 case 2: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
503 if (complex_case) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
504 retval(1) = cbb; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
505 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
506 retval(1) = bb; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
507 OCTAVE_FALLTHROUGH; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
508 case 1: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
509 if (complex_case) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
510 retval(0) = caa; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
511 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
512 retval(0) = aa; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
513 break; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
514 case 0: |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
515 if (complex_case) |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
516 retval(0) = caa; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
517 else |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
518 retval(0) = aa; |
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
519 break; |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
520 } |
28995
0e86e50bebeb
ordqz.cc: Review and update for Octave coding conventions.
Rik <rik@octave.org>
parents:
28986
diff
changeset
|
521 |
28986
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
522 return retval; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
523 } |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
524 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
525 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
526 /* |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
527 %!shared A, B, AA, BB, QQ, ZZ, AC, BC, AAC, BBC, QQC, ZZC, select, selectc |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
528 %! A = [ -1.03428 0.24929 0.43205 -0.12860; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
529 %! 1.16228 0.27870 2.12954 0.69250; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
530 %! -0.51524 -0.34939 -0.77820 2.13721; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
531 %! -1.32941 2.11870 0.72005 1.00835 ]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
532 %! B = [ 1.407302 -0.632956 -0.360628 0.068534; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
533 %! 0.149898 0.298248 0.991777 0.023652; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
534 %! 0.169281 -0.405205 -1.775834 1.511730; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
535 %! 0.717770 1.291390 -1.766607 -0.531352 ]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
536 %! AC = [ 0.4577 + 0.7199i 0.1476 + 0.6946i 0.6202 + 0.2092i 0.7559 + 0.2759i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
537 %! 0.5868 + 0.7275i 0.9174 + 0.8781i 0.6741 + 0.1985i 0.4320 + 0.7023i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
538 %! 0.2408 + 0.6359i 0.2959 + 0.8501i 0.3904 + 0.5613i 0.5000 + 0.1428i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
539 %! 0.8177 + 0.8581i 0.2583 + 0.8970i 0.7706 + 0.5451i 0.1068 + 0.1650i]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
540 %! BC = [ 0.089898 + 0.209257i 0.157769 + 0.311387i 0.018926 + 0.622517i 0.058825 + 0.374647i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
541 %! 0.009367 + 0.098211i 0.736087 + 0.095797i 0.973192 + 0.583765i 0.434018 + 0.461909i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
542 %! 0.880784 + 0.868215i 0.032839 + 0.569461i 0.873437 + 0.266081i 0.739426 + 0.362017i; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
543 %! 0.121649 + 0.115111i 0.426695 + 0.492222i 0.247670 + 0.034414i 0.771629 + 0.078153i]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
544 %! [AA, BB, QQ, ZZ] = qz (A, B); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
545 %! [AAC, BBC, QQC, ZZC] = qz (AC, BC); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
546 %! select = [0 0 1 1]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
547 %! selectc = [0 0 0 1]; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
548 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
549 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
550 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "rhp"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
551 %! assert (all (real (eig (AAX(1:3,1:3), BBX(1:3,1:3))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
552 %! assert (all (real (eig (AAX(4:4,4:4), BBX(4:4,4:4))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
553 %! assert (norm (QQX'*AAX*ZZX' - A, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
554 %! assert (norm (QQX'*BBX*ZZX' - B, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
555 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
556 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
557 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "+"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
558 %! assert (all (real (eig (AAX(1:3,1:3), BBX(1:3,1:3))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
559 %! assert (all (real (eig (AAX(4:4,4:4), BBX(4:4,4:4))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
560 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
561 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
562 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "lhp"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
563 %! assert (all (real (eig (AAX(2:4,2:4), BBX(2:4,2:4))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
564 %! assert (all (real (eig (AAX(1:1,1:1), BBX(1:1,1:1))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
565 %! assert (norm (QQX'*AAX*ZZX' - A, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
566 %! assert (norm (QQX'*BBX*ZZX' - B, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
567 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
568 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
569 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "-"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
570 %! assert (all (real (eig (AAX(2:4,2:4), BBX(2:4,2:4))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
571 %! assert (all (real (eig (AAX(1:1,1:1), BBX(1:1,1:1))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
572 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
573 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
574 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "udi"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
575 %! assert (all (abs (eig (AAX(1:1,1:1), BBX(1:1,1:1))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
576 %! assert (all (abs (eig (AAX(2:4,2:4), BBX(2:4,2:4))) > 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
577 %! assert (norm (QQX'*AAX*ZZX' - A, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
578 %! assert (norm (QQX'*BBX*ZZX' - B, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
579 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
580 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
581 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "S"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
582 %! assert (all (abs (eig (AAX(1:1,1:1), BBX(1:1,1:1))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
583 %! assert (all (abs (eig (AAX(2:4,2:4), BBX(2:4,2:4))) > 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
584 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
585 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
586 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "udo"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
587 %! assert (all (abs (eig (AAX(1:3,1:3), BBX(1:3,1:3))) >= 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
588 %! assert (all (abs (eig (AAX(4:4,4:4), BBX(4:4,4:4))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
589 %! assert (norm (QQX'*AAX*ZZX' - A, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
590 %! assert (norm (QQX'*BBX*ZZX' - B, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
591 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
592 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
593 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, "B"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
594 %! assert (all (abs (eig (AAX(1:3,1:3), BBX(1:3,1:3))) >= 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
595 %! assert (all (abs (eig (AAX(4:4,4:4), BBX(4:4,4:4))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
596 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
597 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
598 %! [AAX, BBX, QQX, ZZX] = ordqz (AA, BB, QQ, ZZ, select); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
599 %! assert (all (iscomplex (eig (AAX(1:2,1:2), BBX(1:2,1:2))))); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
600 %! assert (norm (QQX'*AAX*ZZX' - A, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
601 %! assert (norm (QQX'*BBX*ZZX' - B, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
602 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
603 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
604 %! [AACX, BBCX, QQCX, ZZCX] = ordqz (AAC, BBC, QQC, ZZC, "rhp"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
605 %! assert (all (real (eig (AACX(1:2,1:2), BBCX(1:2,1:2))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
606 %! assert (all (real (eig (AACX(3:4,3:4), BBCX(3:4,3:4))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
607 %! assert (norm (QQCX'*AACX*ZZCX' - AC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
608 %! assert (norm (QQCX'*BBCX*ZZCX' - BC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
609 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
610 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
611 %! [AACX, BBCX, QQCX, ZZCX] = ordqz (AAC, BBC, QQC, ZZC, "lhp"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
612 %! assert (all (real (eig (AACX(1:2,1:2), BBCX(1:2,1:2))) < 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
613 %! assert (all (real (eig (AACX(3:4,3:4), BBCX(3:4,3:4))) >= 0)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
614 %! assert (norm (QQCX'*AACX*ZZCX' - AC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
615 %! assert (norm (QQCX'*BBCX*ZZCX' - BC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
616 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
617 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
618 %! [AACX, BBCX, QQCX, ZZCX] = ordqz (AAC, BBC, QQC, ZZC, "udi"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
619 %! assert (all (abs (eig (AACX(1:2,1:2), BBCX(1:2,1:2))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
620 %! assert (all (abs (eig (AACX(3:4,3:4), BBCX(3:4,3:4))) >= 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
621 %! assert (norm (QQCX'*AACX*ZZCX' - AC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
622 %! assert (norm (QQCX'*BBCX*ZZCX' - BC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
623 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
624 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
625 %! [AACX, BBCX, QQCX, ZZCX] = ordqz (AAC, BBC, QQC, ZZC, "udo"); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
626 %! assert (all (abs (eig (AACX(1:2,1:2), BBCX(1:2,1:2))) >= 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
627 %! assert (all (abs (eig (AACX(3:4,3:4), BBCX(3:4,3:4))) < 1)); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
628 %! assert (norm (QQCX'*AACX*ZZCX' - AC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
629 %! assert (norm (QQCX'*BBCX*ZZCX' - BC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
630 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
631 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
632 %! [AACX, BBCX, QQCX, ZZCX] = ordqz (AAC, BBC, QQC, ZZC, selectc); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
633 %! ev = abs (eig (AACX(1:1,1:1), BBCX(1:1,1:1))); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
634 %! assert(ev > 0.6 && ev < 0.7); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
635 %! assert (norm (QQCX'*AACX*ZZCX' - AC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
636 %! assert (norm (QQCX'*BBCX*ZZCX' - BC, "fro"), 0, 1e-12); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
637 |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
638 %!test |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
639 %! A = toeplitz ([1,2,3,4]); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
640 %! [B, A] = qr (A); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
641 %! B = B'; |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
642 %! [AA, BB, Q, Z] = qz (A, B); |
69ec8d9e769b
Add function ordqz (patch #9897).
Martin Köhler <koehlerm@mpi-magdeburg.mpg.de>
parents:
diff
changeset
|
643 %! [AAS, BBS, QS, ZS] = ordqz (AA, BB, Q, Z, "lhp"); |
69ec8d9e769b
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644 %! E2 = ordeig (AAS, BBS); |
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645 %! ECOMP = [-3.414213562373092; -1.099019513592784; |
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646 %! -0.5857864376269046; 9.099019513592784]; |
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647 %! assert (norm (ECOMP - E2, "Inf"), 0, 1e-8); |
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648 |
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649 ## Test input validation |
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650 %!error <Invalid call> ordqz () |
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651 %!error <Invalid call> ordqz (eye (2)) |
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652 %!error <Invalid call> ordqz (eye (2), eye (2)) |
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653 %!error <Invalid call> ordqz (eye (2), eye (2), eye (2)) |
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654 %!error <Invalid call> ordqz (eye (2), eye (2), eye (2), eye (2)) |
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655 %!error id=Octave:ordqz:unknown-keyword |
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656 %! ordqz (eye (2), eye (2), eye (2), eye (2), "foobar"); |
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657 %!error id=Octave:ordqz:select-not-vector |
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658 %! ordqz (eye (2), eye (2), eye (2), eye (2), eye (2)); |
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659 %!error id=Octave:ordqz:unknown-arg |
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660 %! ordqz (eye (2), eye (2), eye (2), eye (2), {"foobar"}); |
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661 %!error id=Octave:ordqz:nargout |
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662 %! [a,b,c,d,e] = ordqz (eye (2), eye (2), eye (2), eye (2), "udi"); |
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663 %!warning <A: argument is empty matrix> ordqz ([], [], [], [], "udi"); |
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664 %!error <A must be a square matrix> ordqz (ones (1,2), [], [], [], "udi"); |
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665 %!error <nonconformant matrices> |
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666 %! ordqz (eye (3), eye (2), eye (2), eye (2), "udi"); |
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667 %!error <nonconformant matrices> |
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668 %! ordqz (eye (2), eye (3), eye (2), eye (2), "udi"); |
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669 %!error <nonconformant matrices> |
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670 %! ordqz (eye (2), eye (2), eye (3), eye (2), "udi"); |
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671 %!error <nonconformant matrices> |
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672 %! ordqz (eye (2), eye (2), eye (2), eye (3), "udi"); |
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673 %!error <SELECT vector .* wrong number of elements> |
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674 %! ordqz (eye (2), eye (2), eye (2), eye (2), ones (1,5)); |
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675 %!error <quasi upper triangular matrices are not allowed with complex data> |
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676 %! AA = zeros (2, 2); |
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677 %! AA(2,1) = i; |
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678 %! ordqz (AA, eye (2), eye (2), eye (2), "udi"); |
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679 |
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680 */ |
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681 |
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682 OCTAVE_END_NAMESPACE(octave) |