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DLD-FUNCTIONS/*.cc: delete Emacs local-variables settings
author John W. Eaton <jwe@octave.org>
date Wed, 20 Jan 2010 17:40:53 -0500
parents 40dfc0c99116
children f7501986e42d
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{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 @tex\n\
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51 $S = U^T A U$\n\
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52 @end tex\n\
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53 @ifnottex\n\
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54 @code{s = u' * a * u}\n\
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55 @end ifnottex\n\
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56 where\n\
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57 @tex\n\
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58 $U$\n\
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59 @end tex\n\
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60 @ifnottex\n\
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61 @code{u}\n\
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62 @end ifnottex\n\
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63 is a unitary matrix\n\
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64 @tex\n\
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65 ($U^T U$ is identity)\n\
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66 @end tex\n\
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67 @ifnottex\n\
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68 (@code{u'* u} is identity)\n\
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69 @end ifnottex\n\
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70 and\n\
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71 @tex\n\
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72 $S$\n\
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73 @end tex\n\
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74 @ifnottex\n\
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75 @code{s}\n\
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76 @end ifnottex\n\
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77 is upper triangular. The eigenvalues of\n\
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78 @tex\n\
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79 $A$ (and $S$)\n\
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80 @end tex\n\
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81 @ifnottex\n\
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82 @code{a} (and @code{s})\n\
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83 @end ifnottex\n\
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84 are the diagonal elements of\n\
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85 @tex\n\
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86 $S$.\n\
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87 @end tex\n\
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88 @ifnottex\n\
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89 @code{s}.\n\
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90 @end ifnottex\n\
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91 If the matrix\n\
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92 @tex\n\
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93 $A$\n\
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94 @end tex\n\
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95 @ifnottex\n\
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96 @code{a}\n\
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97 @end ifnottex\n\
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98 is real, then the real Schur decomposition is computed, in which the\n\
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99 matrix\n\
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100 @tex\n\
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101 $U$\n\
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102 @end tex\n\
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103 @ifnottex\n\
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104 @code{u}\n\
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105 @end ifnottex\n\
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106 is orthogonal and\n\
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107 @tex\n\
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108 $S$\n\
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109 @end tex\n\
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110 @ifnottex\n\
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111 @code{s}\n\
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112 @end ifnottex\n\
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113 is block upper triangular\n\
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114 with blocks of size at most\n\
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115 @tex\n\
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116 $2\\times 2$\n\
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117 @end tex\n\
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118 @ifnottex\n\
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119 @code{2 x 2}\n\
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120 @end ifnottex\n\
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121 along the diagonal. The diagonal elements of\n\
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122 @tex\n\
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123 $S$\n\
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124 @end tex\n\
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125 @ifnottex\n\
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126 @code{s}\n\
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127 @end ifnottex\n\
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128 (or the eigenvalues of the\n\
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129 @tex\n\
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130 $2\\times 2$\n\
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131 @end tex\n\
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132 @ifnottex\n\
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133 @code{2 x 2}\n\
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134 @end ifnottex\n\
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135 blocks, when\n\
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136 appropriate) are the eigenvalues of\n\
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137 @tex\n\
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138 $A$\n\
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139 @end tex\n\
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140 @ifnottex\n\
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141 @code{a}\n\
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142 @end ifnottex\n\
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143 and\n\
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144 @tex\n\
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145 $S$.\n\
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146 @end tex\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 \n\
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151 The eigenvalues are optionally ordered along the diagonal according to\n\
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152 the value of @code{opt}. @code{opt = \"a\"} indicates that all\n\
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153 eigenvalues with negative real parts should be moved to the leading\n\
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154 block of\n\
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155 @tex\n\
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156 $S$\n\
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157 @end tex\n\
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158 @ifnottex\n\
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159 @code{s}\n\
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160 @end ifnottex\n\
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161 (used in @code{are}), @code{opt = \"d\"} indicates that all eigenvalues\n\
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162 with magnitude less than one should be moved to the leading block of\n\
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163 @tex\n\
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164 $S$\n\
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165 @end tex\n\
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166 @ifnottex\n\
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167 @code{s}\n\
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168 @end ifnottex\n\
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169 (used in @code{dare}), and @code{opt = \"u\"}, the default, indicates that\n\
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170 no ordering of eigenvalues should occur. The leading\n\
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171 @tex\n\
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172 $k$\n\
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173 @end tex\n\
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174 @ifnottex\n\
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175 @code{k}\n\
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176 @end ifnottex\n\
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177 columns of\n\
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178 @tex\n\
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179 $U$\n\
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180 @end tex\n\
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181 @ifnottex\n\
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182 @code{u}\n\
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183 @end ifnottex\n\
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184 always span the\n\
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185 @tex\n\
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186 $A$-invariant\n\
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187 @end tex\n\
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188 @ifnottex\n\
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189 @code{a}-invariant\n\
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190 @end ifnottex\n\
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191 subspace corresponding to the\n\
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192 @tex\n\
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193 $k$\n\
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194 @end tex\n\
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195 @ifnottex\n\
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196 @code{k}\n\
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197 @end ifnottex\n\
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198 leading eigenvalues of\n\
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199 @tex\n\
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200 $S$.\n\
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201 @end tex\n\
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202 @ifnottex\n\
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203 @code{s}.\n\
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204 @end ifnottex\n\
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205 @end deftypefn")
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206 {
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207 octave_value_list retval;
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208
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209 int nargin = args.length ();
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210
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211 if (nargin < 1 || nargin > 2 || nargout > 2)
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212 {
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213 print_usage ();
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214 return retval;
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215 }
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216
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217 octave_value arg = args(0);
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218
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219 std::string ord;
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220
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221 if (nargin == 2)
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222 {
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223 ord = args(1).string_value ();
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224
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225 if (error_state)
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226 {
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227 error ("schur: expecting string as second argument");
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228 return retval;
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229 }
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230 }
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231
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232 char ord_char = ord.empty () ? 'U' : ord[0];
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233
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234 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
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235 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
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236 {
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237 warning ("schur: incorrect ordered schur argument `%c'",
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238 ord.c_str ());
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239 return retval;
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240 }
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241
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242 octave_idx_type nr = arg.rows ();
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243 octave_idx_type nc = arg.columns ();
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244
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245 int arg_is_empty = empty_arg ("schur", nr, nc);
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246
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247 if (arg_is_empty < 0)
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248 return retval;
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249 else if (arg_is_empty > 0)
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250 return octave_value_list (2, Matrix ());
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251
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252 if (nr != nc)
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253 {
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254 gripe_square_matrix_required ("schur");
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255 return retval;
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256 }
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257
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258 if (arg.is_single_type ())
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259 {
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260 if (arg.is_real_type ())
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261 {
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262 FloatMatrix tmp = arg.float_matrix_value ();
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263
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264 if (! error_state)
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265 {
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266 if (nargout == 0 || nargout == 1)
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267 {
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268 FloatSCHUR result (tmp, ord, false);
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269 retval(0) = result.schur_matrix ();
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270 }
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271 else
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272 {
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273 FloatSCHUR result (tmp, ord, true);
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274 retval(1) = result.schur_matrix ();
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275 retval(0) = result.unitary_matrix ();
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276 }
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277 }
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278 }
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279 else if (arg.is_complex_type ())
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280 {
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281 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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282
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283 if (! error_state)
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284 {
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285
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286 if (nargout == 0 || nargout == 1)
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287 {
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288 FloatComplexSCHUR result (ctmp, ord, false);
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289 retval(0) = result.schur_matrix ();
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290 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
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291 else
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292 {
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293 FloatComplexSCHUR result (ctmp, ord, true);
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294 retval(1) = result.schur_matrix ();
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295 retval(0) = result.unitary_matrix ();
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296 }
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297 }
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298 }
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299 }
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300 else
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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 Matrix tmp = arg.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 SCHUR 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 SCHUR 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 ComplexMatrix ctmp = arg.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 ComplexSCHUR 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 ComplexSCHUR 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 else
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342 {
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343 gripe_wrong_type_arg ("schur", arg);
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344 }
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345 }
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346
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347 return retval;
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348 }
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349
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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350 /*
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351
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352 %!test
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353 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
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354 %! [u, s] = schur (a);
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355 %! assert(u' * a * u, s, sqrt (eps));
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356
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357 %!test
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358 %! a = single([1, 2, 3; 4, 5, 9; 7, 8, 6]);
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359 %! [u, s] = schur (a);
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360 %! assert(u' * a * u, s, sqrt (eps('single')));
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361
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362 %!test
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363 %! fail("schur ([1, 2; 3, 4], 2)","warning");
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364
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365 %!error <Invalid call to schur.*> schur ();
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366 %!error schur ([1, 2, 3; 4, 5, 6]);
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367
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368 */