Mercurial > octave-nkf
annotate libinterp/corefcn/hess.cc @ 20609:780431fc4137
linspace: add tests for the use of vectors as base and limit.
author | Carnë Draug <carandraug@octave.org> |
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date | Thu, 08 Oct 2015 20:06:45 +0100 |
parents | f90c8372b7ba |
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rev | line source |
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2928 | 1 /* |
2 | |
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3 Copyright (C) 1996-2015 John W. Eaton |
2928 | 4 |
5 This file is part of Octave. | |
6 | |
7 Octave is free software; you can redistribute it and/or modify it | |
8 under the terms of the GNU General Public License as published by the | |
7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
10 option) any later version. | |
2928 | 11 |
12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
15 for more details. | |
16 | |
17 You should have received a copy of the GNU General Public License | |
7016 | 18 along with Octave; see the file COPYING. If not, see |
19 <http://www.gnu.org/licenses/>. | |
2928 | 20 |
21 */ | |
22 | |
23 #ifdef HAVE_CONFIG_H | |
24 #include <config.h> | |
25 #endif | |
26 | |
27 #include "CmplxHESS.h" | |
28 #include "dbleHESS.h" | |
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29 #include "fCmplxHESS.h" |
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30 #include "floatHESS.h" |
2928 | 31 |
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32 #include "defun.h" |
2928 | 33 #include "error.h" |
34 #include "gripes.h" | |
35 #include "oct-obj.h" | |
36 #include "utils.h" | |
37 | |
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38 DEFUN (hess, args, nargout, |
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39 "-*- texinfo -*-\n\ |
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40 @deftypefn {Built-in Function} {@var{H} =} hess (@var{A})\n\ |
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41 @deftypefnx {Built-in Function} {[@var{P}, @var{H}] =} hess (@var{A})\n\ |
3372 | 42 @cindex Hessenberg decomposition\n\ |
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43 Compute the Hessenberg decomposition of the matrix @var{A}.\n\ |
3372 | 44 \n\ |
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45 The Hessenberg decomposition is\n\ |
3372 | 46 @tex\n\ |
47 $$\n\ | |
48 A = PHP^T\n\ | |
49 $$\n\ | |
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50 where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\ |
3372 | 51 is upper Hessenberg ($H_{i,j} = 0, \\forall i \\ge j+1$).\n\ |
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\ |
3372 | 65 @end deftypefn") |
2928 | 66 { |
67 octave_value_list retval; | |
68 | |
69 int nargin = args.length (); | |
70 | |
71 if (nargin != 1 || nargout > 2) | |
72 { | |
5823 | 73 print_usage (); |
2928 | 74 return retval; |
75 } | |
76 | |
77 octave_value arg = args(0); | |
78 | |
5275 | 79 octave_idx_type nr = arg.rows (); |
80 octave_idx_type nc = arg.columns (); | |
2928 | 81 |
82 int arg_is_empty = empty_arg ("hess", nr, nc); | |
83 | |
84 if (arg_is_empty < 0) | |
85 return retval; | |
86 else if (arg_is_empty > 0) | |
87 return octave_value_list (2, Matrix ()); | |
88 | |
89 if (nr != nc) | |
90 { | |
91 gripe_square_matrix_required ("hess"); | |
92 return retval; | |
93 } | |
94 | |
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95 if (arg.is_single_type ()) |
2928 | 96 { |
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97 if (arg.is_real_type ()) |
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98 { |
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99 FloatMatrix tmp = arg.float_matrix_value (); |
2928 | 100 |
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101 FloatHESS result (tmp); |
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102 |
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103 if (nargout <= 1) |
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104 retval(0) = result.hess_matrix (); |
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105 else |
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106 { |
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107 retval(1) = result.hess_matrix (); |
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108 retval(0) = result.unitary_hess_matrix (); |
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109 } |
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110 } |
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111 else if (arg.is_complex_type ()) |
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112 { |
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113 FloatComplexMatrix ctmp = arg.float_complex_matrix_value (); |
2928 | 114 |
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115 FloatComplexHESS result (ctmp); |
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116 |
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117 if (nargout <= 1) |
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118 retval(0) = result.hess_matrix (); |
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119 else |
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120 { |
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121 retval(1) = result.hess_matrix (); |
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122 retval(0) = result.unitary_hess_matrix (); |
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123 } |
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124 } |
2928 | 125 } |
126 else | |
127 { | |
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128 if (arg.is_real_type ()) |
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129 { |
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130 Matrix tmp = arg.matrix_value (); |
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131 |
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132 HESS result (tmp); |
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133 |
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134 if (nargout <= 1) |
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135 retval(0) = result.hess_matrix (); |
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136 else |
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137 { |
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138 retval(1) = result.hess_matrix (); |
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139 retval(0) = result.unitary_hess_matrix (); |
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140 } |
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141 } |
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142 else if (arg.is_complex_type ()) |
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143 { |
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144 ComplexMatrix ctmp = arg.complex_matrix_value (); |
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145 |
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146 ComplexHESS result (ctmp); |
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147 |
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148 if (nargout <= 1) |
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149 retval(0) = result.hess_matrix (); |
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150 else |
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151 { |
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152 retval(1) = result.hess_matrix (); |
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153 retval(0) = result.unitary_hess_matrix (); |
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154 } |
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155 } |
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156 else |
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157 { |
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158 gripe_wrong_type_arg ("hess", arg); |
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159 } |
2928 | 160 } |
161 | |
162 return retval; | |
163 } | |
164 | |
165 /* | |
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166 %!test |
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167 %! a = [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)); |
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170 |
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171 %!test |
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172 %! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]); |
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173 %! [p, h] = hess (a); |
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174 %! assert (p * h * p', a, sqrt (eps ("single"))); |
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175 |
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176 %!error hess () |
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177 %!error hess ([1, 2; 3, 4], 2) |
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178 %!error <argument must be a square matrix> hess ([1, 2; 3, 4; 5, 6]) |
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179 */ |