Mercurial > hg > octave-nkf

annotate libinterp/corefcn/schur.cc @ 15467:049e8bbff782

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
maint: periodic merge of stable to default
author John W. Eaton <jwe@octave.org>
date Mon, 01 Oct 2012 18:30:44 -0400
parents src/DLD-FUNCTIONS/schur.cc@d174210ce1ec src/DLD-FUNCTIONS/schur.cc@2fc554ffbc28
children 53eaa83e4181
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
1 /*
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
2
14138
72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
parents: 13915
diff changeset
3 Copyright (C) 1996-2012 John W. Eaton
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
4
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
5 This file is part of Octave.
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
6
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
7 Octave is free software; you can redistribute it and/or modify it
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
8 under the terms of the GNU General Public License as published by the
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5823
diff changeset
9 Free Software Foundation; either version 3 of the License, or (at your
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5823
diff changeset
10 option) any later version.
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
11
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
12 Octave is distributed in the hope that it will be useful, but WITHOUT
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
15 for more details.
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
16
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
17 You should have received a copy of the GNU General Public License
7016
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5823
diff changeset
18 along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe]
jwe
parents: 5823
diff changeset
19 <http://www.gnu.org/licenses/>.
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
20
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
21 */
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
22
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
23 #ifdef HAVE_CONFIG_H
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
24 #include <config.h>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
25 #endif
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
26
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
27 #include <string>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
28
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
29 #include "CmplxSCHUR.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
30 #include "dbleSCHUR.h"
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
31 #include "fCmplxSCHUR.h"
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
32 #include "floatSCHUR.h"
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
33
15039
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
34 #include "defun.h"
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
35 #include "error.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
36 #include "gripes.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
37 #include "oct-obj.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
38 #include "utils.h"
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
39
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
40 template <class Matrix>
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
41 static octave_value
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
42 mark_upper_triangular (const Matrix& a)
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
43 {
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
44 octave_value retval = a;
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
45
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
46 octave_idx_type n = a.rows ();
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
47 assert (a.columns () == n);
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
48
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
49 const typename Matrix::element_type zero = typename Matrix::element_type ();
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
50
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
51 for (octave_idx_type i = 0; i < n; i++)
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
52 if (a(i,i) == zero)
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
53 return retval;
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
54
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
55 retval.matrix_type (MatrixType::Upper);
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
56
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
57 return retval;
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
58 }
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
59
15039
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
60 DEFUN (schur, args, nargout,
3548
ab7fa5a8f23f [project @ 2000-02-03 01:17:15 by jwe]
jwe
parents: 3523
diff changeset
61 "-*- texinfo -*-\n\
15039
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
62 @deftypefn {Built-in Function} {@var{S} =} schur (@var{A})\n\
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
63 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"real\")\n\
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
64 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, \"complex\")\n\
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
65 @deftypefnx {Built-in Function} {@var{S} =} schur (@var{A}, @var{opt})\n\
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
66 @deftypefnx {Built-in Function} {[@var{U}, @var{S}] =} schur (@var{A}, @dots{})\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
67 @cindex Schur decomposition\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
68 Compute the Schur@tie{}decomposition of @var{A}\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
69 @tex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
70 $$\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
71 S = U^T A U\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
72 $$\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
73 @end tex\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
74 @ifnottex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
75 \n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
76 @example\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
77 @code{@var{S} = @var{U}' * @var{A} * @var{U}}\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
78 @end example\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
79 \n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
80 @end ifnottex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
81 where @var{U} is a unitary matrix\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
82 @tex\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
83 ($U^T U$ is identity)\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
84 @end tex\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
85 @ifnottex\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
86 (@code{@var{U}'* @var{U}} is identity)\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
87 @end ifnottex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
88 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
89 are the diagonal elements of @var{S}. If the matrix @var{A}\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
90 is real, then the real Schur@tie{}decomposition is computed, in which the\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
91 matrix @var{U} is orthogonal and @var{S} is block upper triangular\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
92 with blocks of size at most\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
93 @tex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
94 $2 \\times 2$\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
95 @end tex\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
96 @ifnottex\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
97 @code{2 x 2}\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
98 @end ifnottex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
99 along the diagonal. The diagonal elements of @var{S}\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
100 (or the eigenvalues of the\n\
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
101 @tex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
102 $2 \\times 2$\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
103 @end tex\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
104 @ifnottex\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
105 @code{2 x 2}\n\
8517
81d6ab3ac93c Allow documentation tobe built for other formats than tex and info
sh@sh-laptop
parents: 7814
diff changeset
106 @end ifnottex\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
107 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.\n\
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
108 \n\
13224
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
109 The default for real matrices is a real Schur@tie{}decomposition.\n\
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
110 A complex decomposition may be forced by passing the flag \"complex\".\n\
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
111 \n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
112 The eigenvalues are optionally ordered along the diagonal according to\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
113 the value of @var{opt}. @code{@var{opt} = \"a\"} indicates that all\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
114 eigenvalues with negative real parts should be moved to the leading\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
115 block of @var{S}\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
116 (used in @code{are}), @code{@var{opt} = \"d\"} indicates that all eigenvalues\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
117 with magnitude less than one should be moved to the leading block of @var{S}\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
118 (used in @code{dare}), and @code{@var{opt} = \"u\"}, the default, indicates\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
119 that no ordering of eigenvalues should occur. The leading @var{k}\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
120 columns of @var{U} always span the @var{A}-invariant\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
121 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
122 \n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
123 The Schur@tie{}decomposition is used to compute eigenvalues of a\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
124 square matrix, and has applications in the solution of algebraic\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
125 Riccati equations in control (see @code{are} and @code{dare}).\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
126 @seealso{rsf2csf}\n\
3372
f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe]
jwe
parents: 3014
diff changeset
127 @end deftypefn")
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
128 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
129 octave_value_list retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
130
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
131 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
132
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
133 if (nargin < 1 || nargin > 2 || nargout > 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
134 {
5823
080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe]
jwe
parents: 5555
diff changeset
135 print_usage ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
136 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
137 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
138
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
139 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
140
3523
b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe]
jwe
parents: 3372
diff changeset
141 std::string ord;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
142
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
143 if (nargin == 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
144 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
145 ord = args(1).string_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
146
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
147 if (error_state)
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
148 {
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
149 error ("schur: second argument must be a string");
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
150 return retval;
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
151 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
152 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
153
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
154 bool force_complex = false;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
155
13224
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
156 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
157 {
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
158 ord = std::string ();
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
159 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012).
Rik <octave@nomad.inbox5.com>
parents: 12642
diff changeset
160 else if (ord == "complex")
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
161 {
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
162 force_complex = true;
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
163 ord = std::string ();
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
164 }
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
165 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
166 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
167 char ord_char = ord.empty () ? 'U' : ord[0];
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
168
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
169 if (ord_char != 'U' && ord_char != 'A' && ord_char != 'D'
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
170 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
171 {
15466
d174210ce1ec use ' instead of ` in error messages, warnings and most comments
John W. Eaton <jwe@octave.org>
parents: 14460
diff changeset
172 warning ("schur: incorrect ordered schur argument '%c'",
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
173 ord.c_str ());
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
174 return retval;
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
175 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
176 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
177
5275
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
178 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe]
jwe
parents: 5008
diff changeset
179 octave_idx_type nc = arg.columns ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
180
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
181 if (nr != nc)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
182 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
183 gripe_square_matrix_required ("schur");
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
184 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
185 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
186
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
187 if (! arg.is_numeric_type ())
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
188 gripe_wrong_type_arg ("schur", arg);
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
189 else if (arg.is_single_type ())
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
190 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
191 if (! force_complex && arg.is_real_type ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
192 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
193 FloatMatrix tmp = arg.float_matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
194
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
195 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
196 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
197 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
198 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
199 FloatSCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
200 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
201 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
202 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
203 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
204 FloatSCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
205 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
206 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
207 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
208 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
209 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
210 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
211 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
212 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
213
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
214 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
215 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
216
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
217 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
218 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
219 FloatComplexSCHUR result (ctmp, ord, false);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
220 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
221 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
222 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
223 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
224 FloatComplexSCHUR result (ctmp, ord, true);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
225 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
226 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
227 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
228 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
229 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
230 }
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
231 else
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
232 {
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
233 if (! force_complex && arg.is_real_type ())
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
234 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
235 Matrix tmp = arg.matrix_value ();
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
236
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
237 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
238 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
239 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
240 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
241 SCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
242 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
243 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
244 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
245 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
246 SCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
247 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
248 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
249 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
250 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
251 }
10607
f7501986e42d make schur more Matlab compatible
Jaroslav Hajek <highegg@gmail.com>
parents: 10155
diff changeset
252 else
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
253 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
254 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789
82be108cc558 First attempt at single precision tyeps
David Bateman <dbateman@free.fr>
parents: 7017
diff changeset
255
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
256 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
257 {
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
258
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
259 if (nargout == 0 || nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
260 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
261 ComplexSCHUR result (ctmp, ord, false);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
262 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
263 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
264 else
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
265 {
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
266 ComplexSCHUR result (ctmp, ord, true);
10617
9c9e07f5eb1c make schur mark triangular matrices on output
Jaroslav Hajek <highegg@gmail.com>
parents: 10607
diff changeset
267 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
268 retval(0) = result.unitary_matrix ();
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
269 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
270 }
40dfc0c99116 DLD-FUNCTIONS/*.cc: untabify
John W. Eaton <jwe@octave.org>
parents: 9758
diff changeset
271 }
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
272 }
11586
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
273
12df7854fa7c strip trailing whitespace from source files
John W. Eaton <jwe@octave.org>
parents: 11553
diff changeset
274 return retval;
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
275 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
276
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
277 /*
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
278 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
279 %! a = [1, 2, 3; 4, 5, 9; 7, 8, 6];
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
280 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
281 %! assert (u' * a * u, s, sqrt (eps));
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
282
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
283 %!test
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
284 %! a = single ([1, 2, 3; 4, 5, 9; 7, 8, 6]);
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
285 %! [u, s] = schur (a);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
286 %! assert (u' * a * u, s, sqrt (eps ("single")));
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
287
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
288 %!test
14854
5ae9f0f77635 maint: Use Octave coding conventions for coddling parenthis is DLD-FUNCTIONS directory
Rik <octave@nomad.inbox5.com>
parents: 14501
diff changeset
289 %! fail ("schur ([1, 2; 3, 4], 2)", "warning");
7814
87865ed7405f Second set of single precision test code and fix of resulting bugs
David Bateman <dbateman@free.fr>
parents: 7789
diff changeset
290
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
291 %!error schur ()
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
292 %!error <argument must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
2928
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe]
jwe
parents:
diff changeset
293 */
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
294
15039
e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory
Rik <rik@octave.org>
parents: 14854
diff changeset
295 DEFUN (rsf2csf, args, nargout,
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
296 "-*- texinfo -*-\n\
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
297 @deftypefn {Function File} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
298 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a complex,\n\
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
299 upper triangular Schur@tie{}form @var{T}.\n\
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
300 \n\
12642
f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation.
Rik <octave@nomad.inbox5.com>
parents: 12584
diff changeset
301 Note that the following relations hold:\n\
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
302 \n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
303 @tex\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
304 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
305 $U^{\\dagger} U$ is the identity matrix I.\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
306 @end tex\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
307 @ifnottex\n\
13780
990762e784fe Fix confusing interaction between @code macro and transpose operator (') in documentation (Bug #34661).
Rik <octave@nomad.inbox5.com>
parents: 13224
diff changeset
308 @xcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and\n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
309 @code{@var{U}' * @var{U}} is the identity matrix I.\n\
12584
7ef7e20057fa Improve documentation strings in Linear Algebra chapter.
Rik <octave@nomad.inbox5.com>
parents: 11586
diff changeset
310 @end ifnottex\n\
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
311 \n\
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
312 Note also that @var{U} and @var{T} are not unique.\n\
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
313 @seealso{schur}\n\
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
314 @end deftypefn")
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
315 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
316 octave_value_list retval;
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
317
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
318 if (args.length () == 2 && nargout <= 2)
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
319 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
320 if (! args(0).is_numeric_type ())
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
321 gripe_wrong_type_arg ("rsf2csf", args(0));
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
322 else if (! args(1).is_numeric_type ())
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
323 gripe_wrong_type_arg ("rsf2csf", args(1));
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
324 else if (args(0).is_complex_type () || args(1).is_complex_type ())
11553
01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory.
Rik <octave@nomad.inbox5.com>
parents: 11523
diff changeset
325 error ("rsf2csf: UR and TR must be real matrices");
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
326 else
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
327 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
328
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
329 if (args(0).is_single_type () || args(1).is_single_type ())
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
330 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
331 FloatMatrix u = args(0).float_matrix_value ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
332 FloatMatrix t = args(1).float_matrix_value ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
333 if (! error_state)
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
334 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
335 FloatComplexSCHUR cs (FloatSCHUR (t, u));
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
336
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
337 retval(1) = cs.schur_matrix ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
338 retval(0) = cs.unitary_matrix ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
339 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
340 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
341 else
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
342 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
343 Matrix u = args(0).matrix_value ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
344 Matrix t = args(1).matrix_value ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
345 if (! error_state)
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
346 {
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
347 ComplexSCHUR cs (SCHUR (t, u));
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
348
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
349 retval(1) = cs.schur_matrix ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
350 retval(0) = cs.unitary_matrix ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
351 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
352 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
353 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
354 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
355 else
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
356 print_usage ();
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
357
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
358 return retval;
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
359 }
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
360
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
361 /*
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
362 %!test
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
363 %! A = [1, 1, 1, 2; 1, 2, 1, 1; 1, 1, 3, 1; -2, 1, 1, 1];
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
364 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
365 %! [U, T] = rsf2csf (u, t);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
366 %! assert (norm (u * t * u' - U * T * U'), 0, 1e-12);
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
367 %! assert (norm (A - U * T * U'), 0, 1e-12);
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
368
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
369 %!test
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
370 %! A = rand (10);
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
371 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
372 %! [U, T] = rsf2csf (u, t);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
373 %! assert (norm (tril (T, -1)), 0);
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
374 %! assert (norm (U * U'), 1, 1e-14);
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
375
14460
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
diff changeset
376 %!test
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
diff changeset
377 %! A = [0, 1;-1, 0];
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
diff changeset
378 %! [u, t] = schur (A);
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893).
Marco Caliari <marco.caliari@univr.it>
parents: 14138
diff changeset
379 %! [U, T] = rsf2csf (u,t);
14501
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions.
Rik <octave@nomad.inbox5.com>
parents: 14460
diff changeset
380 %! assert (U * T * U', A, 1e-14);
10822
23d2378512a0 implement rsf2csf
Jaroslav Hajek <highegg@gmail.com>
parents: 10617
diff changeset
381 */