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annotate libinterp/corefcn/hess.cc @ 20884:f1b2a2dbc0e1

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2015 Code Sprint: use ovl () in C++ files. * __dsearchn__.cc, balance.cc, colloc.cc, data.cc, debug.cc, dirfns.cc, eig.cc, file-io.cc, getgrent.cc, getpwent.cc, givens.cc, help.cc, hess.cc, mgorth.cc, quad.cc: Replace assignments to retval(?) with calls to ovl().
author José Luis García Pallero <jgpallero@gmail.com>
date Sun, 13 Dec 2015 07:59:40 -0800
parents 1142cf6abc0d
children 03e4ddd49396
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1 /*
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2
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4197fc428c7d maint: Update copyright notices for 2015.
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3 Copyright (C) 1996-2015 John W. Eaton
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4
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5 This file is part of Octave.
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6
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7 Octave is free software; you can redistribute it and/or modify it
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8 under the terms of the GNU General Public License as published by the
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9 Free Software Foundation; either version 3 of the License, or (at your
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10 option) any later version.
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11
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12 Octave is distributed in the hope that it will be useful, but WITHOUT
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 for more details.
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16
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17 You should have received a copy of the GNU General Public License
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18 along with Octave; see the file COPYING. If not, see
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19 <http://www.gnu.org/licenses/>.
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20
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21 */
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22
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23 #ifdef HAVE_CONFIG_H
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24 #include <config.h>
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25 #endif
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26
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27 #include "CmplxHESS.h"
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28 #include "dbleHESS.h"
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29 #include "fCmplxHESS.h"
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30 #include "floatHESS.h"
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31
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32 #include "defun.h"
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33 #include "error.h"
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34 #include "gripes.h"
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35 #include "oct-obj.h"
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36 #include "utils.h"
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37
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38 DEFUN (hess, args, nargout,
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39 "-*- texinfo -*-\n\
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40 @deftypefn {} {@var{H} =} hess (@var{A})\n\
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41 @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A})\n\
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42 @cindex Hessenberg decomposition\n\
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43 Compute the Hessenberg decomposition of the matrix @var{A}.\n\
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44 \n\
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45 The Hessenberg decomposition is\n\
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46 @tex\n\
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47 $$\n\
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48 A = PHP^T\n\
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49 $$\n\
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50 where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\
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51 is upper Hessenberg ($H_{i,j} = 0, \\forall i > j+1$).\n\
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52 @end tex\n\
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53 @ifnottex\n\
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54 @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\
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55 unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\
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56 transposition) and @var{H} is upper Hessenberg\n\
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57 (@code{@var{H}(i, j) = 0 forall i > j+1)}.\n\
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58 @end ifnottex\n\
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59 \n\
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60 The Hessenberg decomposition is usually used as the first step in an\n\
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61 eigenvalue computation, but has other applications as well\n\
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62 (see @nospell{Golub, Nash, and Van Loan},\n\
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63 IEEE Transactions on Automatic Control, 1979).\n\
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64 @seealso{eig, chol, lu, qr, qz, schur, svd}\n\
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65 @end deftypefn")
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66 {
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67 octave_value_list retval;
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68
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69 if (args.length () != 1 || nargout > 2)
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70 print_usage ();
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71
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72 octave_value arg = args(0);
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73
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74 octave_idx_type nr = arg.rows ();
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75 octave_idx_type nc = arg.columns ();
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76
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77 int arg_is_empty = empty_arg ("hess", nr, nc);
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78
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79 if (arg_is_empty < 0)
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80 return retval;
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81 else if (arg_is_empty > 0)
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82 return octave_value_list (2, Matrix ());
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83
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84 if (nr != nc)
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85 {
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86 gripe_square_matrix_required ("hess");
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87 return retval;
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88 }
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89
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90 if (arg.is_single_type ())
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91 {
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92 if (arg.is_real_type ())
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93 {
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94 FloatMatrix tmp = arg.float_matrix_value ();
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95
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96 FloatHESS result (tmp);
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97
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98 if (nargout <= 1)
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99 retval = ovl (result.hess_matrix ());
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100 else
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101 {
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102 retval = ovl (result.unitary_hess_matrix (),
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103 result.hess_matrix ());
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104 }
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105 }
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106 else if (arg.is_complex_type ())
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107 {
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108 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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109
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110 FloatComplexHESS result (ctmp);
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111
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112 if (nargout <= 1)
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113 retval = ovl (result.hess_matrix ());
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114 else
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115 {
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116 retval = ovl (result.unitary_hess_matrix (),
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117 result.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 HESS result (tmp);
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128
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129 if (nargout <= 1)
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130 retval = ovl (result.hess_matrix ());
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131 else
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132 {
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133 retval = ovl (result.unitary_hess_matrix (),
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134 result.hess_matrix ());
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135 }
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136 }
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137 else if (arg.is_complex_type ())
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138 {
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139 ComplexMatrix ctmp = arg.complex_matrix_value ();
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140
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141 ComplexHESS result (ctmp);
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142
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143 if (nargout <= 1)
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144 retval = ovl (result.hess_matrix ());
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145 else
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146 {
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147 retval = ovl (result.unitary_hess_matrix (),
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148 result.hess_matrix ());
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149 }
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150 }
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151 else
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152 {
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153 gripe_wrong_type_arg ("hess", arg);
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154 }
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155 }
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156
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157 return retval;
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158 }
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159
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160 /*
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161 %!test
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162 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
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163 %! [p, h] = hess (a);
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164 %! assert (p * h * p', a, sqrt (eps));
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165
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166 %!test
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167 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]);
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168 %! [p, h] = hess (a);
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169 %! assert (p * h * p', a, sqrt (eps ("single")));
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170
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171 %!error hess ()
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172 %!error hess ([1, 2; 3, 4], 2)
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173 %!error <argument must be a square matrix> hess ([1, 2; 3, 4; 5, 6])
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174 */