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annotate src/DLD-FUNCTIONS/hess.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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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 "CmplxHESS.h"
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29 #include "dbleHESS.h"
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30 #include "fCmplxHESS.h"
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31 #include "floatHESS.h"
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32
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33 #include "defun-dld.h"
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34 #include "error.h"
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35 #include "gripes.h"
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36 #include "oct-obj.h"
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37 #include "utils.h"
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38
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39 DEFUN_DLD (hess, args, nargout,
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40 "-*- texinfo -*-\n\
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41 @deftypefn {Loadable Function} {@var{h} =} hess (@var{a})\n\
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42 @deftypefnx {Loadable Function} {[@var{p}, @var{h}] =} hess (@var{a})\n\
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43 @cindex Hessenberg decomposition\n\
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44 Compute the Hessenberg decomposition of the matrix @var{a}.\n\
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45 \n\
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46 The Hessenberg decomposition is usually used as the first step in an\n\
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47 eigenvalue computation, but has other applications as well (see Golub,\n\
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48 Nash, and Van Loan, IEEE Transactions on Automatic Control, 1979). The\n\
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49 Hessenberg decomposition is\n\
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50 @iftex\n\
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51 @tex\n\
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52 $$\n\
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53 A = PHP^T\n\
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54 $$\n\
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55 where $P$ is a square unitary matrix ($P^HP = I$), and $H$\n\
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56 is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\
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57 @end tex\n\
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58 @end iftex\n\
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59 @ifnottex\n\
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60 @code{p * h * p' = a} where @code{p} is a square unitary matrix\n\
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61 (@code{p' * p = I}, using complex-conjugate transposition) and @code{h}\n\
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62 is upper Hessenberg (@code{i >= j+1 => h (i, j) = 0}).\n\
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63 @end ifnottex\n\
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64 @end deftypefn")
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65 {
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66 octave_value_list retval;
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67
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68 int nargin = args.length ();
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69
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70 if (nargin != 1 || nargout > 2)
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71 {
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72 print_usage ();
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73 return retval;
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74 }
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75
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76 octave_value arg = args(0);
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77
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78 octave_idx_type nr = arg.rows ();
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79 octave_idx_type nc = arg.columns ();
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80
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81 int arg_is_empty = empty_arg ("hess", nr, nc);
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82
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83 if (arg_is_empty < 0)
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84 return retval;
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85 else if (arg_is_empty > 0)
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86 return octave_value_list (2, Matrix ());
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87
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88 if (nr != nc)
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89 {
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90 gripe_square_matrix_required ("hess");
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91 return retval;
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92 }
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93
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94 if (arg.is_single_type ())
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95 {
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96 if (arg.is_real_type ())
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97 {
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98 FloatMatrix tmp = arg.float_matrix_value ();
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99
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100 if (! error_state)
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101 {
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102 FloatHESS result (tmp);
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103
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104 retval(1) = result.hess_matrix ();
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105 retval(0) = result.unitary_hess_matrix ();
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106 }
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107 }
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108 else if (arg.is_complex_type ())
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109 {
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110 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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111
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112 if (! error_state)
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113 {
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114 FloatComplexHESS result (ctmp);
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115
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116 retval(1) = result.hess_matrix ();
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117 retval(0) = result.unitary_hess_matrix ();
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118 }
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119 }
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120 }
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121 else
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122 {
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123 if (arg.is_real_type ())
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124 {
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125 Matrix tmp = arg.matrix_value ();
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126
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127 if (! error_state)
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128 {
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129 HESS result (tmp);
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130
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131 retval(1) = result.hess_matrix ();
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132 retval(0) = result.unitary_hess_matrix ();
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133 }
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134 }
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135 else if (arg.is_complex_type ())
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136 {
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137 ComplexMatrix ctmp = arg.complex_matrix_value ();
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138
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139 if (! error_state)
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140 {
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141 ComplexHESS result (ctmp);
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142
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143 retval(1) = result.hess_matrix ();
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144 retval(0) = result.unitary_hess_matrix ();
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145 }
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146 }
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147 else
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148 {
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149 gripe_wrong_type_arg ("hess", arg);
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150 }
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151 }
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152
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153 return retval;
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154 }
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155
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156 /*
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158 %!test
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159 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
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160 %! [p, h] = hess (a);
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161 %! assert(p * h * p', a, sqrt(eps));
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162
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163 %!test
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164 %! a = single([1, 2, 3; 5, 4, 6; 8, 7, 9]);
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165 %! [p, h] = hess (a);
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166 %! assert(p * h * p', a, sqrt(eps ('single')));
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167
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168 %!error <Invalid call to hess.*> hess ();
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169 %!error <Invalid call to hess.*> hess ([1, 2; 3, 4], 2);
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170 %!error hess ([1, 2; 3, 4; 5, 6]);
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171
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172 */
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173
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174 /*
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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175 ;;; Local Variables: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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176 ;;; mode: C++ ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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177 ;;; End: ***
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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178 */