1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
|
/*
Copyright (C) 1996-2015 John W. Eaton
This file is part of Octave.
Octave is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
Octave is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING. If not, see
<http://www.gnu.org/licenses/>.
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include "CmplxHESS.h"
#include "dbleHESS.h"
#include "fCmplxHESS.h"
#include "floatHESS.h"
#include "defun.h"
#include "error.h"
#include "gripes.h"
#include "oct-obj.h"
#include "utils.h"
DEFUN (hess, args, nargout,
"-*- texinfo -*-\n\
@deftypefn {Built-in Function} {@var{H} =} hess (@var{A})\n\
@deftypefnx {Built-in Function} {[@var{P}, @var{H}] =} hess (@var{A})\n\
@cindex Hessenberg decomposition\n\
Compute the Hessenberg decomposition of the matrix @var{A}.\n\
\n\
The Hessenberg decomposition is\n\
@tex\n\
$$\n\
A = PHP^T\n\
$$\n\
where $P$ is a square unitary matrix ($P^TP = I$), and $H$\n\
is upper Hessenberg ($H_{i,j} = 0, \\forall i > j+1$).\n\
@end tex\n\
@ifnottex\n\
@code{@var{P} * @var{H} * @var{P}' = @var{A}} where @var{P} is a square\n\
unitary matrix (@code{@var{P}' * @var{P} = I}, using complex-conjugate\n\
transposition) and @var{H} is upper Hessenberg\n\
(@code{@var{H}(i, j) = 0 forall i > j+1)}.\n\
@end ifnottex\n\
\n\
The Hessenberg decomposition is usually used as the first step in an\n\
eigenvalue computation, but has other applications as well\n\
(see @nospell{Golub, Nash, and Van Loan},\n\
IEEE Transactions on Automatic Control, 1979).\n\
@seealso{eig, chol, lu, qr, qz, schur, svd}\n\
@end deftypefn")
{
octave_value_list retval;
int nargin = args.length ();
if (nargin != 1 || nargout > 2)
{
print_usage ();
return retval;
}
octave_value arg = args(0);
octave_idx_type nr = arg.rows ();
octave_idx_type nc = arg.columns ();
int arg_is_empty = empty_arg ("hess", nr, nc);
if (arg_is_empty < 0)
return retval;
else if (arg_is_empty > 0)
return octave_value_list (2, Matrix ());
if (nr != nc)
{
gripe_square_matrix_required ("hess");
return retval;
}
if (arg.is_single_type ())
{
if (arg.is_real_type ())
{
FloatMatrix tmp = arg.float_matrix_value ();
if (! error_state)
{
FloatHESS result (tmp);
if (nargout <= 1)
retval(0) = result.hess_matrix ();
else
{
retval(1) = result.hess_matrix ();
retval(0) = result.unitary_hess_matrix ();
}
}
}
else if (arg.is_complex_type ())
{
FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
if (! error_state)
{
FloatComplexHESS result (ctmp);
if (nargout <= 1)
retval(0) = result.hess_matrix ();
else
{
retval(1) = result.hess_matrix ();
retval(0) = result.unitary_hess_matrix ();
}
}
}
}
else
{
if (arg.is_real_type ())
{
Matrix tmp = arg.matrix_value ();
if (! error_state)
{
HESS result (tmp);
if (nargout <= 1)
retval(0) = result.hess_matrix ();
else
{
retval(1) = result.hess_matrix ();
retval(0) = result.unitary_hess_matrix ();
}
}
}
else if (arg.is_complex_type ())
{
ComplexMatrix ctmp = arg.complex_matrix_value ();
if (! error_state)
{
ComplexHESS result (ctmp);
if (nargout <= 1)
retval(0) = result.hess_matrix ();
else
{
retval(1) = result.hess_matrix ();
retval(0) = result.unitary_hess_matrix ();
}
}
}
else
{
gripe_wrong_type_arg ("hess", arg);
}
}
return retval;
}
/*
%!test
%! a = [1, 2, 3; 5, 4, 6; 8, 7, 9];
%! [p, h] = hess (a);
%! assert (p * h * p', a, sqrt (eps));
%!test
%! a = single ([1, 2, 3; 5, 4, 6; 8, 7, 9]);
%! [p, h] = hess (a);
%! assert (p * h * p', a, sqrt (eps ("single")));
%!error hess ()
%!error hess ([1, 2; 3, 4], 2)
%!error <argument must be a square matrix> hess ([1, 2; 3, 4; 5, 6])
*/
|
