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annotate src/DLD-FUNCTIONS/schur.cc @ 10607:f7501986e42d

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make schur more Matlab compatible
author Jaroslav Hajek <highegg@gmail.com>
date Thu, 06 May 2010 09:49:36 +0200
parents d0ce5e973937
children 9c9e07f5eb1c
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /*
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2
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eb63fbe60fab update copyright notices
John W. Eaton <jwe@octave.org>
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3 Copyright (C) 1996, 1997, 1999, 2000, 2004, 2005, 2006, 2007, 2008, 2009
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4 John W. Eaton
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5
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6 This file is part of Octave.
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7
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8 Octave is free software; you can redistribute it and/or modify it
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9 under the terms of the GNU General Public License as published by the
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10 Free Software Foundation; either version 3 of the License, or (at your
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11 option) any later version.
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12
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13 Octave is distributed in the hope that it will be useful, but WITHOUT
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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16 for more details.
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17
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18 You should have received a copy of the GNU General Public License
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19 along with Octave; see the file COPYING. If not, see
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20 <http://www.gnu.org/licenses/>.
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21
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22 */
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23
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24 #ifdef HAVE_CONFIG_H
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25 #include <config.h>
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26 #endif
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27
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28 #include <string>
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29
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30 #include "CmplxSCHUR.h"
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31 #include "dbleSCHUR.h"
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32 #include "fCmplxSCHUR.h"
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33 #include "floatSCHUR.h"
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34
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35 #include "defun-dld.h"
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36 #include "error.h"
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37 #include "gripes.h"
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38 #include "oct-obj.h"
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39 #include "utils.h"
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40
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41 DEFUN_DLD (schur, args, nargout,
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42 "-*- texinfo -*-\n\
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43 @deftypefn {Loadable Function} {@var{s} =} schur (@var{a})\n\
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44 @deftypefnx {Loadable Function} {@var{s} =} schur (@var{a}, \"complex\")\n\
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45 @deftypefnx {Loadable Function} {[@var{u}, @var{s}] =} schur (@var{a}, @var{opt})\n\
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46 @cindex Schur decomposition\n\
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47 The Schur decomposition is used to compute eigenvalues of a\n\
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48 square matrix, and has applications in the solution of algebraic\n\
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49 Riccati equations in control (see @code{are} and @code{dare}).\n\
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50 @code{schur} always returns\n\
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51 @tex\n\
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52 $S = U^T A U$\n\
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53 @end tex\n\
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54 @ifnottex\n\
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55 @code{s = u' * a * u}\n\
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56 @end ifnottex\n\
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57 where\n\
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58 @tex\n\
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59 $U$\n\
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60 @end tex\n\
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61 @ifnottex\n\
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62 @code{u}\n\
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63 @end ifnottex\n\
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64 is a unitary matrix\n\
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65 @tex\n\
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66 ($U^T U$ is identity)\n\
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67 @end tex\n\
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68 @ifnottex\n\
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69 (@code{u'* u} is identity)\n\
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70 @end ifnottex\n\
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71 and\n\
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72 @tex\n\
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73 $S$\n\
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74 @end tex\n\
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75 @ifnottex\n\
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76 @code{s}\n\
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77 @end ifnottex\n\
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78 is upper triangular. The eigenvalues of\n\
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79 @tex\n\
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80 $A$ (and $S$)\n\
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81 @end tex\n\
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82 @ifnottex\n\
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83 @code{a} (and @code{s})\n\
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84 @end ifnottex\n\
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85 are the diagonal elements of\n\
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86 @tex\n\
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87 $S$.\n\
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88 @end tex\n\
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89 @ifnottex\n\
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90 @code{s}.\n\
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91 @end ifnottex\n\
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92 If the matrix\n\
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93 @tex\n\
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94 $A$\n\
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95 @end tex\n\
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96 @ifnottex\n\
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97 @code{a}\n\
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98 @end ifnottex\n\
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99 is real, then the real Schur decomposition is computed, in which the\n\
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100 matrix\n\
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101 @tex\n\
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102 $U$\n\
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103 @end tex\n\
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104 @ifnottex\n\
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105 @code{u}\n\
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106 @end ifnottex\n\
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107 is orthogonal and\n\
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108 @tex\n\
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109 $S$\n\
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110 @end tex\n\
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111 @ifnottex\n\
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112 @code{s}\n\
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113 @end ifnottex\n\
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114 is block upper triangular\n\
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115 with blocks of size at most\n\
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116 @tex\n\
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117 $2\\times 2$\n\
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118 @end tex\n\
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119 @ifnottex\n\
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120 @code{2 x 2}\n\
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121 @end ifnottex\n\
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122 along the diagonal. The diagonal elements of\n\
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123 @tex\n\
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124 $S$\n\
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125 @end tex\n\
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126 @ifnottex\n\
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127 @code{s}\n\
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128 @end ifnottex\n\
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129 (or the eigenvalues of the\n\
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130 @tex\n\
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131 $2\\times 2$\n\
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132 @end tex\n\
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133 @ifnottex\n\
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134 @code{2 x 2}\n\
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135 @end ifnottex\n\
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136 blocks, when\n\
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137 appropriate) are the eigenvalues of\n\
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138 @tex\n\
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139 $A$\n\
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140 @end tex\n\
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141 @ifnottex\n\
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142 @code{a}\n\
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143 @end ifnottex\n\
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144 and\n\
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145 @tex\n\
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146 $S$.\n\
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147 @end tex\n\
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148 @ifnottex\n\
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149 @code{s}.\n\
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150 @end ifnottex\n\
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151 \n\
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152 A complex decomposition may be forced by passing \"complex\" as @var{opt}.\n\
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153 \n\
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154 The eigenvalues are optionally ordered along the diagonal according to\n\
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155 the value of @code{opt}. @code{opt = \"a\"} indicates that all\n\
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156 eigenvalues with negative real parts should be moved to the leading\n\
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157 block of\n\
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158 @tex\n\
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159 $S$\n\
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160 @end tex\n\
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161 @ifnottex\n\
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162 @code{s}\n\
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163 @end ifnottex\n\
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164 (used in @code{are}), @code{opt = \"d\"} indicates that all eigenvalues\n\
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165 with magnitude less than one should be moved to the leading block of\n\
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166 @tex\n\
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167 $S$\n\
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168 @end tex\n\
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169 @ifnottex\n\
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170 @code{s}\n\
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171 @end ifnottex\n\
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172 (used in @code{dare}), and @code{opt = \"u\"}, the default, indicates that\n\
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173 no ordering of eigenvalues should occur. The leading\n\
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174 @tex\n\
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175 $k$\n\
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176 @end tex\n\
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177 @ifnottex\n\
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178 @code{k}\n\
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179 @end ifnottex\n\
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180 columns of\n\
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181 @tex\n\
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182 $U$\n\
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183 @end tex\n\
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184 @ifnottex\n\
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185 @code{u}\n\
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186 @end ifnottex\n\
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187 always span the\n\
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188 @tex\n\
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189 $A$-invariant\n\
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190 @end tex\n\
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191 @ifnottex\n\
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192 @code{a}-invariant\n\
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193 @end ifnottex\n\
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194 subspace corresponding to the\n\
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195 @tex\n\
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196 $k$\n\
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197 @end tex\n\
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198 @ifnottex\n\
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199 @code{k}\n\
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200 @end ifnottex\n\
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201 leading eigenvalues of\n\
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202 @tex\n\
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203 $S$.\n\
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204 @end tex\n\
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205 @ifnottex\n\
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206 @code{s}.\n\
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207 @end ifnottex\n\
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208 @end deftypefn")
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209 {
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210 octave_value_list retval;
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211
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212 int nargin = args.length ();
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213
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214 if (nargin < 1 || nargin > 2 || nargout > 2)
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215 {
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216 print_usage ();
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217 return retval;
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218 }
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219
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220 octave_value arg = args(0);
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221
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222 std::string ord;
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223
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224 if (nargin == 2)
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225 {
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226 ord = args(1).string_value ();
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227
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228 if (error_state)
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229 {
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230 error ("schur: expecting string as second argument");
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231 return retval;
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232 }
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233 }
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234
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235 bool force_complex = false;
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236
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237 if (ord == "complex")
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238 {
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239 force_complex = true;
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240 ord = std::string ();
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241 }
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242 else
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243 {
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244 char ord_char = ord.empty () ? 'U' : ord[0];
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245
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246 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
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247 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
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248 {
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249 warning ("schur: incorrect ordered schur argument `%c'",
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250 ord.c_str ());
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251 return retval;
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252 }
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253 }
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254
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255 octave_idx_type nr = arg.rows ();
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256 octave_idx_type nc = arg.columns ();
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257
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258 if (nr != nc)
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259 {
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260 gripe_square_matrix_required ("schur");
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261 return retval;
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262 }
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263
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264 if (! arg.is_numeric_type ())
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265 gripe_wrong_type_arg ("schur", arg);
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266 else if (arg.is_single_type ())
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267 {
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268 if (! force_complex && arg.is_real_type ())
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269 {
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270 FloatMatrix tmp = arg.float_matrix_value ();
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271
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272 if (! error_state)
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273 {
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274 if (nargout == 0 || nargout == 1)
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275 {
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276 FloatSCHUR result (tmp, ord, false);
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277 retval(0) = result.schur_matrix ();
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278 }
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279 else
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280 {
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281 FloatSCHUR result (tmp, ord, true);
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282 retval(1) = result.schur_matrix ();
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283 retval(0) = result.unitary_matrix ();
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284 }
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285 }
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286 }
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287 else
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288 {
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289 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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290
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291 if (! error_state)
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292 {
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293
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294 if (nargout == 0 || nargout == 1)
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295 {
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296 FloatComplexSCHUR result (ctmp, ord, false);
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297 retval(0) = result.schur_matrix ();
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298 }
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299 else
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300 {
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301 FloatComplexSCHUR result (ctmp, ord, true);
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302 retval(1) = result.schur_matrix ();
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303 retval(0) = result.unitary_matrix ();
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304 }
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305 }
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306 }
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307 }
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308 else
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309 {
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310 if (! force_complex && arg.is_real_type ())
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311 {
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312 Matrix tmp = arg.matrix_value ();
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313
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314 if (! error_state)
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315 {
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316 if (nargout == 0 || nargout == 1)
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317 {
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318 SCHUR result (tmp, ord, false);
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319 retval(0) = result.schur_matrix ();
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320 }
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321 else
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322 {
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323 SCHUR result (tmp, ord, true);
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324 retval(1) = result.schur_matrix ();
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325 retval(0) = result.unitary_matrix ();
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326 }
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327 }
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328 }
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329 else
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330 {
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331 ComplexMatrix ctmp = arg.complex_matrix_value ();
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332
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333 if (! error_state)
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334 {
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335
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336 if (nargout == 0 || nargout == 1)
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337 {
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338 ComplexSCHUR result (ctmp, ord, false);
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339 retval(0) = result.schur_matrix ();
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340 }
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341 else
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342 {
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343 ComplexSCHUR result (ctmp, ord, true);
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344 retval(1) = result.schur_matrix ();
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345 retval(0) = result.unitary_matrix ();
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346 }
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347 }
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348 }
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349 }
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350
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351 return retval;
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352 }
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353
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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diff changeset
354 /*
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355
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356 %!test
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357 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
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358 %! [u, s] = schur (a);
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359 %! assert(u' * a * u, s, sqrt (eps));
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360
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361 %!test
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362 %! a = single([1, 2, 3; 4, 5, 9; 7, 8, 6]);
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363 %! [u, s] = schur (a);
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364 %! assert(u' * a * u, s, sqrt (eps('single')));
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365
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366 %!test
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367 %! fail("schur ([1, 2; 3, 4], 2)","warning");
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368
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369 %!error <Invalid call to schur.*> schur ();
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370 %!error schur ([1, 2, 3; 4, 5, 6]);
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diff changeset
371
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diff changeset
372 */