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annotate src/DLD-FUNCTIONS/schur.cc @ 8920:eb63fbe60fab

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update copyright notices
author John W. Eaton <jwe@octave.org>
date Sat, 07 Mar 2009 10:41:27 -0500
parents 81d6ab3ac93c
children 09da0bd91412
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1 /*
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2
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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{u}, @var{s}] =} schur (@var{a}, @var{opt})\n\
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45 @cindex Schur decomposition\n\
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46 The Schur decomposition is used to compute eigenvalues of a\n\
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47 square matrix, and has applications in the solution of algebraic\n\
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48 Riccati equations in control (see @code{are} and @code{dare}).\n\
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49 @code{schur} always returns\n\
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50 @iftex\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 @end iftex\n\
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55 @ifnottex\n\
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56 @code{s = u' * a * u}\n\
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57 @end ifnottex\n\
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58 where\n\
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59 @iftex\n\
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60 @tex\n\
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61 $U$\n\
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62 @end tex\n\
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63 @end iftex\n\
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64 @ifnottex\n\
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65 @code{u}\n\
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66 @end ifnottex\n\
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67 is a unitary matrix\n\
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68 @iftex\n\
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69 @tex\n\
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70 ($U^T U$ is identity)\n\
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71 @end tex\n\
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72 @end iftex\n\
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73 @ifnottex\n\
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74 (@code{u'* u} is identity)\n\
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75 @end ifnottex\n\
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76 and\n\
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77 @iftex\n\
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78 @tex\n\
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79 $S$\n\
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80 @end tex\n\
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81 @end iftex\n\
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82 @ifnottex\n\
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83 @code{s}\n\
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84 @end ifnottex\n\
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85 is upper triangular. The eigenvalues of\n\
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86 @iftex\n\
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87 @tex\n\
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88 $A$ (and $S$)\n\
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89 @end tex\n\
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90 @end iftex\n\
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91 @ifnottex\n\
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92 @code{a} (and @code{s})\n\
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93 @end ifnottex\n\
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94 are the diagonal elements of\n\
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95 @iftex\n\
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96 @tex\n\
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97 $S$.\n\
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98 @end tex\n\
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99 @end iftex\n\
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100 @ifnottex\n\
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101 @code{s}.\n\
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102 @end ifnottex\n\
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103 If the matrix\n\
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104 @iftex\n\
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105 @tex\n\
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106 $A$\n\
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107 @end tex\n\
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108 @end iftex\n\
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109 @ifnottex\n\
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110 @code{a}\n\
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111 @end ifnottex\n\
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112 is real, then the real Schur decomposition is computed, in which the\n\
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113 matrix\n\
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114 @iftex\n\
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115 @tex\n\
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116 $U$\n\
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117 @end tex\n\
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118 @end iftex\n\
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119 @ifnottex\n\
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120 @code{u}\n\
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121 @end ifnottex\n\
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122 is orthogonal and\n\
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123 @iftex\n\
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124 @tex\n\
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125 $S$\n\
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126 @end tex\n\
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127 @end iftex\n\
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128 @ifnottex\n\
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129 @code{s}\n\
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130 @end ifnottex\n\
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131 is block upper triangular\n\
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132 with blocks of size at most\n\
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133 @iftex\n\
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134 @tex\n\
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135 $2\\times 2$\n\
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136 @end tex\n\
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137 @end iftex\n\
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138 @ifnottex\n\
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139 @code{2 x 2}\n\
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140 @end ifnottex\n\
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141 along the diagonal. The diagonal elements of\n\
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142 @iftex\n\
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143 @tex\n\
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144 $S$\n\
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145 @end tex\n\
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146 @end iftex\n\
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147 @ifnottex\n\
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148 @code{s}\n\
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149 @end ifnottex\n\
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150 (or the eigenvalues of the\n\
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151 @iftex\n\
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152 @tex\n\
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153 $2\\times 2$\n\
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154 @end tex\n\
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155 @end iftex\n\
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156 @ifnottex\n\
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157 @code{2 x 2}\n\
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158 @end ifnottex\n\
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159 blocks, when\n\
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160 appropriate) are the eigenvalues of\n\
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161 @iftex\n\
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162 @tex\n\
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163 $A$\n\
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164 @end tex\n\
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165 @end iftex\n\
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166 @ifnottex\n\
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167 @code{a}\n\
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168 @end ifnottex\n\
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169 and\n\
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170 @iftex\n\
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171 @tex\n\
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172 $S$.\n\
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173 @end tex\n\
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174 @end iftex\n\
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175 @ifnottex\n\
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176 @code{s}.\n\
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177 @end ifnottex\n\
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178 \n\
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179 The eigenvalues are optionally ordered along the diagonal according to\n\
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180 the value of @code{opt}. @code{opt = \"a\"} indicates that all\n\
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181 eigenvalues with negative real parts should be moved to the leading\n\
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182 block of\n\
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183 @iftex\n\
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184 @tex\n\
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185 $S$\n\
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186 @end tex\n\
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187 @end iftex\n\
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188 @ifnottex\n\
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189 @code{s}\n\
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190 @end ifnottex\n\
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191 (used in @code{are}), @code{opt = \"d\"} indicates that all eigenvalues\n\
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192 with magnitude less than one should be moved to the leading block of\n\
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193 @iftex\n\
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194 @tex\n\
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195 $S$\n\
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196 @end tex\n\
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197 @end iftex\n\
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198 @ifnottex\n\
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199 @code{s}\n\
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200 @end ifnottex\n\
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201 (used in @code{dare}), and @code{opt = \"u\"}, the default, indicates that\n\
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202 no ordering of eigenvalues should occur. The leading\n\
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203 @iftex\n\
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204 @tex\n\
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205 $k$\n\
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206 @end tex\n\
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207 @end iftex\n\
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208 @ifnottex\n\
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209 @code{k}\n\
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210 @end ifnottex\n\
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211 columns of\n\
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212 @iftex\n\
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213 @tex\n\
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214 $U$\n\
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215 @end tex\n\
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216 @end iftex\n\
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217 @ifnottex\n\
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218 @code{u}\n\
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219 @end ifnottex\n\
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220 always span the\n\
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221 @iftex\n\
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222 @tex\n\
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223 $A$-invariant\n\
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224 @end tex\n\
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225 @end iftex\n\
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226 @ifnottex\n\
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227 @code{a}-invariant\n\
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228 @end ifnottex\n\
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229 subspace corresponding to the\n\
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230 @iftex\n\
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231 @tex\n\
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232 $k$\n\
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233 @end tex\n\
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234 @end iftex\n\
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235 @ifnottex\n\
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236 @code{k}\n\
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237 @end ifnottex\n\
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238 leading eigenvalues of\n\
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239 @iftex\n\
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240 @tex\n\
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241 $S$.\n\
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242 @end tex\n\
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243 @end iftex\n\
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244 @ifnottex\n\
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245 @code{s}.\n\
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246 @end ifnottex\n\
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247 @end deftypefn")
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248 {
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249 octave_value_list retval;
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250
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251 int nargin = args.length ();
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252
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253 if (nargin < 1 || nargin > 2 || nargout > 2)
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254 {
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255 print_usage ();
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256 return retval;
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257 }
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258
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259 octave_value arg = args(0);
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260
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261 std::string ord;
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262
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263 if (nargin == 2)
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264 {
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265 ord = args(1).string_value ();
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266
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267 if (error_state)
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268 {
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269 error ("schur: expecting string as second argument");
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270 return retval;
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271 }
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272 }
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273
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274 char ord_char = ord.empty () ? 'U' : ord[0];
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275
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276 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
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277 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
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278 {
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279 warning ("schur: incorrect ordered schur argument `%c'",
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280 ord.c_str ());
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281 return retval;
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282 }
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283
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284 octave_idx_type nr = arg.rows ();
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285 octave_idx_type nc = arg.columns ();
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286
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287 int arg_is_empty = empty_arg ("schur", nr, nc);
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288
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289 if (arg_is_empty < 0)
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290 return retval;
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291 else if (arg_is_empty > 0)
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292 return octave_value_list (2, Matrix ());
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293
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294 if (nr != nc)
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295 {
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296 gripe_square_matrix_required ("schur");
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297 return retval;
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298 }
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299
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300 if (arg.is_single_type ())
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301 {
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302 if (arg.is_real_type ())
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303 {
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304 FloatMatrix tmp = arg.float_matrix_value ();
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305
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306 if (! error_state)
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307 {
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308 if (nargout == 0 || nargout == 1)
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309 {
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310 FloatSCHUR result (tmp, ord, false);
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311 retval(0) = result.schur_matrix ();
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312 }
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313 else
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314 {
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315 FloatSCHUR result (tmp, ord, true);
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316 retval(1) = result.schur_matrix ();
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317 retval(0) = result.unitary_matrix ();
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318 }
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319 }
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320 }
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321 else if (arg.is_complex_type ())
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322 {
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323 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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324
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325 if (! error_state)
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326 {
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327
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328 if (nargout == 0 || nargout == 1)
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329 {
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330 FloatComplexSCHUR result (ctmp, ord, false);
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331 retval(0) = result.schur_matrix ();
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332 }
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333 else
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334 {
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335 FloatComplexSCHUR result (ctmp, ord, true);
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336 retval(1) = result.schur_matrix ();
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337 retval(0) = result.unitary_matrix ();
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338 }
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339 }
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340 }
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341 }
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342 else
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343 {
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344 if (arg.is_real_type ())
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345 {
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346 Matrix tmp = arg.matrix_value ();
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347
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348 if (! error_state)
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349 {
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350 if (nargout == 0 || nargout == 1)
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351 {
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352 SCHUR result (tmp, ord, false);
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353 retval(0) = result.schur_matrix ();
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354 }
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355 else
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356 {
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357 SCHUR result (tmp, ord, true);
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358 retval(1) = result.schur_matrix ();
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359 retval(0) = result.unitary_matrix ();
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360 }
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361 }
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362 }
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363 else if (arg.is_complex_type ())
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364 {
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365 ComplexMatrix ctmp = arg.complex_matrix_value ();
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diff changeset
366
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367 if (! error_state)
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parents: 7017
diff changeset
368 {
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369
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370 if (nargout == 0 || nargout == 1)
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diff changeset
371 {
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diff changeset
372 ComplexSCHUR result (ctmp, ord, false);
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diff changeset
373 retval(0) = result.schur_matrix ();
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374 }
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375 else
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diff changeset
376 {
82be108cc558 First attempt at single precision tyeps
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diff changeset
377 ComplexSCHUR result (ctmp, ord, true);
82be108cc558 First attempt at single precision tyeps
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diff changeset
378 retval(1) = result.schur_matrix ();
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379 retval(0) = result.unitary_matrix ();
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diff changeset
380 }
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parents: 7017
diff changeset
381 }
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parents: 7017
diff changeset
382 }
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diff changeset
383 else
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parents: 7017
diff changeset
384 {
82be108cc558 First attempt at single precision tyeps
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diff changeset
385 gripe_wrong_type_arg ("schur", arg);
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diff changeset
386 }
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387 }
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diff changeset
388
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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diff changeset
389 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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390 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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diff changeset
391
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
diff changeset
392 /*
7814
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David Bateman <dbateman@free.fr>
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393
87865ed7405f Second set of single precision test code and fix of resulting bugs
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394 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
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395 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
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396 %! [u, s] = schur (a);
87865ed7405f Second set of single precision test code and fix of resulting bugs
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397 %! assert(u' * a * u, s, sqrt (eps));
87865ed7405f Second set of single precision test code and fix of resulting bugs
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398
87865ed7405f Second set of single precision test code and fix of resulting bugs
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diff changeset
399 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
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diff changeset
400 %! a = single([1, 2, 3; 4, 5, 9; 7, 8, 6]);
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parents: 7789
diff changeset
401 %! [u, s] = schur (a);
87865ed7405f Second set of single precision test code and fix of resulting bugs
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diff changeset
402 %! assert(u' * a * u, s, sqrt (eps('single')));
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
403
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
404 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
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diff changeset
405 %! fail("schur ([1, 2; 3, 4], 2)","warning");
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
406
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
407 %!error <Invalid call to schur.*> schur ();
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
408 %!error schur ([1, 2, 3; 4, 5, 6]);
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
409
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
410 */
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
411
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
412
87865ed7405f Second set of single precision test code and fix of resulting bugs
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parents: 7789
diff changeset
413 /*
2928
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parents:
diff changeset
414 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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parents:
diff changeset
415 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
416 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
417 */