annotate libinterp/corefcn/hess.cc @ 21267:f5b8c3aca5f8

make better use of templates for Hessenberg decomposition * liboctave/numeric/hess.h, liboctave/numeric/hess.cc: New files generated from HESS.h, HESS.cc, CmplxHESS.h, CmplxHESS.cc, dbleHESS.h, dbleHESS.cc, fCmplxHESS.h, fCmplxHESS.cc, floatHESS.h, and floatHESS.cc and making them templates. * liboctave/numeric/module.mk: Update. * libinterp/corefcn/hess.cc, mx-defs.h, mx-ext.h: Use new template classes and header file.
author John W. Eaton <jwe@octave.org>
date Mon, 15 Feb 2016 22:33:45 -0500
parents fcac5dbbf9ed
children 40de9f8f23a6
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1 /*
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2
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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 "hess.h"
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29 #include "defun.h"
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30 #include "error.h"
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31 #include "errwarn.h"
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32 #include "ovl.h"
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33 #include "utils.h"
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34
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35 DEFUN (hess, args, nargout,
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36 "-*- texinfo -*-\n\
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37 @deftypefn {} {@var{H} =} hess (@var{A})\n\
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38 @deftypefnx {} {[@var{P}, @var{H}] =} hess (@var{A})\n\
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39 @cindex Hessenberg decomposition\n\
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40 Compute the Hessenberg decomposition of the matrix @var{A}.\n\
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41 \n\
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42 The Hessenberg decomposition is\n\
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43 @tex\n\
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44 $$\n\
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45 A = PHP^T\n\
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46 $$\n\
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47 where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\
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48 is upper Hessenberg ($H_{i,j} = 0, \\forall i > j+1$).\n\
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49 @end tex\n\
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50 @ifnottex\n\
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51 @code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\
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52 unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\
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53 transposition) and @var{H} is upper Hessenberg\n\
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54 (@code{@var{H}(i, j) = 0 forall i > j+1)}.\n\
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55 @end ifnottex\n\
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56 \n\
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57 The Hessenberg decomposition is usually used as the first step in an\n\
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58 eigenvalue computation, but has other applications as well\n\
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59 (see @nospell{Golub, Nash, and Van Loan},\n\
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60 IEEE Transactions on Automatic Control, 1979).\n\
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61 @seealso{eig, chol, lu, qr, qz, schur, svd}\n\
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62 @end deftypefn")
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63 {
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64 if (args.length () != 1)
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65 print_usage ();
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66
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67 octave_value arg = args(0);
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68
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69 octave_idx_type nr = arg.rows ();
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70 octave_idx_type nc = arg.columns ();
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71
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72 int arg_is_empty = empty_arg ("hess", nr, nc);
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73
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74 if (arg_is_empty < 0)
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75 return ovl ();
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76 else if (arg_is_empty > 0)
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77 return octave_value_list (2, Matrix ());
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78
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79 if (nr != nc)
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80 err_square_matrix_required ("hess", "A");
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81
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82 octave_value_list retval;
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83
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84 if (arg.is_single_type ())
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85 {
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86 if (arg.is_real_type ())
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87 {
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88 FloatMatrix tmp = arg.float_matrix_value ();
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89
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90 hess<FloatMatrix> result (tmp);
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91
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92 if (nargout <= 1)
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93 retval = ovl (result.hess_matrix ());
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94 else
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95 retval = ovl (result.unitary_hess_matrix (),
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96 result.hess_matrix ());
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97 }
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98 else if (arg.is_complex_type ())
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99 {
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100 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
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101
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102 hess<FloatComplexMatrix> result (ctmp);
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103
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104 if (nargout <= 1)
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105 retval = ovl (result.hess_matrix ());
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106 else
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107 retval = ovl (result.unitary_hess_matrix (),
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108 result.hess_matrix ());
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109 }
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110 }
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111 else
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112 {
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113 if (arg.is_real_type ())
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114 {
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115 Matrix tmp = arg.matrix_value ();
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116
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117 hess<Matrix> result (tmp);
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118
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119 if (nargout <= 1)
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120 retval = ovl (result.hess_matrix ());
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121 else
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122 retval = ovl (result.unitary_hess_matrix (),
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123 result.hess_matrix ());
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124 }
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125 else if (arg.is_complex_type ())
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126 {
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127 ComplexMatrix ctmp = arg.complex_matrix_value ();
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128
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129 hess<ComplexMatrix> result (ctmp);
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130
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131 if (nargout <= 1)
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132 retval = ovl (result.hess_matrix ());
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133 else
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134 retval = ovl (result.unitary_hess_matrix (),
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135 result.hess_matrix ());
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136 }
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137 else
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138 err_wrong_type_arg ("hess", arg);
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139 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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140
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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141 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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142 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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143
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
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144 /*
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145 %!test
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146 %! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
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147 %! [p, h] = hess (a);
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148 %! assert (p * h * p', a, sqrt (eps));
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149
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150 %!test
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151 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]);
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152 %! [p, h] = hess (a);
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153 %! assert (p * h * p', a, sqrt (eps ("single")));
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154
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155 %!error hess ()
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156 %!error hess ([1, 2; 3, 4], 2)
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157 %!error <must be a square matrix> hess ([1, 2; 3, 4; 5, 6])
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158 */