octave-nkf: libinterp/corefcn/schur.cc annotate

annotate libinterp/corefcn/schur.cc @ 17296:3a9efb68272d ss-3-7-6

snapshot 3.7.6 * configure.ac (OCTAVE_VERSION): Bump to 3.7.6.

author	John W. Eaton <jwe@octave.org>
date	Tue, 20 Aug 2013 15:17:54 -0400
parents	bc924baa2c4e
children	d63878346099

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\
17281 bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17268 diff changeset	110 A complex decomposition may be forced by passing the flag\n\
bc924baa2c4e doc: Add new @qcode macro for code samples which are quoted. Rik <rik@octave.org> parents: 17268 diff changeset	111 @qcode{\"complex\"}.\n\
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	112 \n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3014 diff changeset	113 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	114 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	115 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	116 block of @var{S}\n\
11553 01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	117 (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	118 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	119 (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	120 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	121 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	122 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	123 \n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	124 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	125 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	126 Riccati equations in control (see @code{are} and @code{dare}).\n\
16920 53eaa83e4181 doc: Add seealso links between various factorization forms. Rik <rik@octave.org> parents: 15467 diff changeset	127 @seealso{rsf2csf, lu, chol, hess, qr, qz, svd}\n\
3372 f16c2ce14886 [project @ 1999-11-23 19:07:09 by jwe] jwe parents: 3014 diff changeset	128 @end deftypefn")
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	129 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	130 octave_value_list retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	131
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	132 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	133
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	134 if (nargin < 1 \|\| nargin > 2 \|\| nargout > 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	135 {
5823 080c08b192d8 [project @ 2006-05-19 05:32:17 by jwe] jwe parents: 5555 diff changeset	136 print_usage ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	137 return retval;
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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	140 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	141
3523 b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe] jwe parents: 3372 diff changeset	142 std::string ord;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	143
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	144 if (nargin == 2)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	145 {
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	146 ord = args(1).string_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	147
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	148 if (error_state)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	149 {
11553 01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	150 error ("schur: second argument must be a string");
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	151 return retval;
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	152 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	153 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	154
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	155 bool force_complex = false;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	156
13224 0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	157 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	158 {
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	159 ord = std::string ();
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	160 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	161 else if (ord == "complex")
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	162 {
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	163 force_complex = true;
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	164 ord = std::string ();
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	165 }
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	166 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	167 {
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	168 char ord_char = ord.empty () ? 'U' : ord[0];
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	169
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	170 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	171 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	172 {
15466 d174210ce1ec use ' instead of ` in error messages, warnings and most comments John W. Eaton <jwe@octave.org> parents: 14460 diff changeset	173 warning ("schur: incorrect ordered schur argument '%c'",
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	174 ord.c_str ());
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	175 return retval;
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	176 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	177 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	178
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	179 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	180 octave_idx_type nc = arg.columns ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	181
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	182 if (nr != nc)
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	183 {
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	184 gripe_square_matrix_required ("schur");
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	185 return retval;
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	186 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	187
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	188 if (! arg.is_numeric_type ())
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	189 gripe_wrong_type_arg ("schur", arg);
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	190 else if (arg.is_single_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	191 {
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	192 if (! force_complex && arg.is_real_type ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	193 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	194 FloatMatrix tmp = arg.float_matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	195
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	196 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	197 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	198 if (nargout == 0 \|\| nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	199 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	200 FloatSCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	201 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	202 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	203 else
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	204 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	205 FloatSCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	206 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	207 retval(0) = result.unitary_matrix ();
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 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	210 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	211 else
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	212 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	213 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	214
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	215 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	216 {
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	217
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	218 if (nargout == 0 \|\| nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	219 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	220 FloatComplexSCHUR result (ctmp, ord, false);
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	221 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	222 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	223 else
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	224 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	225 FloatComplexSCHUR result (ctmp, ord, true);
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	226 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	227 retval(0) = result.unitary_matrix ();
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 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	230 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	231 }
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	232 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	233 {
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	234 if (! force_complex && arg.is_real_type ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	235 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	236 Matrix tmp = arg.matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	237
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	238 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	239 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	240 if (nargout == 0 \|\| nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	241 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	242 SCHUR result (tmp, ord, false);
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	243 retval(0) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	244 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	245 else
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	246 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	247 SCHUR result (tmp, ord, true);
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	248 retval(1) = result.schur_matrix ();
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	249 retval(0) = result.unitary_matrix ();
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 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	252 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	253 else
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	254 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	255 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	256
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	257 if (! error_state)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	258 {
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	259
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	260 if (nargout == 0 \|\| nargout == 1)
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	261 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	262 ComplexSCHUR result (ctmp, ord, false);
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	263 retval(0) = mark_upper_triangular (result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	264 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	265 else
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	266 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	267 ComplexSCHUR result (ctmp, ord, true);
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	268 retval(1) = mark_upper_triangular (result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	269 retval(0) = result.unitary_matrix ();
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 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	272 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	273 }
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	274
12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	275 return retval;
2928 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
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	278 /*
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	279 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	280 %! 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	281 %! [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	282 %! 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	283
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	284 %!test
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	285 %! 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	286 %! [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	287 %! 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	288
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	289 %!test
14854 5ae9f0f77635 maint: Use Octave coding conventions for coddling parenthis is DLD-FUNCTIONS directory Rik <octave@nomad.inbox5.com> parents: 14501 diff changeset	290 %! 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	291
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	292 %!error schur ()
60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	293 %!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	294 */
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	295
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	296 DEFUN (rsf2csf, args, nargout,
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	297 "-- texinfo --\n\
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	298 @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	299 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	300 upper triangular Schur@tie{}form @var{T}.\n\
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	301 \n\
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12584 diff changeset	302 Note that the following relations hold:\n\
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	303 \n\
12584 7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	304 @tex\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	305 $UR \\cdot TR \\cdot {UR}^T = U T U^{\\dagger}$ and\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	306 $U^{\\dagger} U$ is the identity matrix I.\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	307 @end tex\n\
7ef7e20057fa Improve documentation strings in Linear Algebra chapter. Rik <octave@nomad.inbox5.com> parents: 11586 diff changeset	308 @ifnottex\n\
17268 1c21f264d26f doc: Rename @xcode macro to @tcode (transpose code) for clarity. Rik <rik@octave.org> parents: 16920 diff changeset	309 @tcode{@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	310 @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	311 @end ifnottex\n\
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	312 \n\
11553 01f703952eff Improve docstrings for functions in DLD-FUNCTIONS directory. Rik <octave@nomad.inbox5.com> parents: 11523 diff changeset	313 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	314 @seealso{schur}\n\
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	315 @end deftypefn")
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	316 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	317 octave_value_list retval;
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	318
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	319 if (args.length () == 2 && nargout <= 2)
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	320 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	321 if (! args(0).is_numeric_type ())
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	322 gripe_wrong_type_arg ("rsf2csf", args(0));
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	323 else if (! args(1).is_numeric_type ())
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	324 gripe_wrong_type_arg ("rsf2csf", args(1));
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	325 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	326 error ("rsf2csf: UR and TR must be real matrices");
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	327 else
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
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	330 if (args(0).is_single_type () \|\| args(1).is_single_type ())
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	331 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	332 FloatMatrix u = args(0).float_matrix_value ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	333 FloatMatrix t = args(1).float_matrix_value ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	334 if (! error_state)
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	335 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	336 FloatComplexSCHUR cs (FloatSCHUR (t, u));
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	337
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	338 retval(1) = cs.schur_matrix ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	339 retval(0) = cs.unitary_matrix ();
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 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	342 else
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	343 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	344 Matrix u = args(0).matrix_value ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	345 Matrix t = args(1).matrix_value ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	346 if (! error_state)
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	347 {
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	348 ComplexSCHUR cs (SCHUR (t, u));
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	349
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	350 retval(1) = cs.schur_matrix ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	351 retval(0) = cs.unitary_matrix ();
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 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	356 else
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	357 print_usage ();
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	358
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	359 return retval;
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 /*
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	363 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	364 %! 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	365 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	366 %! [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	367 %! 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	368 %! assert (norm (A - U * T * U'), 0, 1e-12);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	369
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	370 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	371 %! A = rand (10);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	372 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	373 %! [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	374 %! 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	375 %! assert (norm (U * U'), 1, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	376
14460 6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	377 %!test
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	378 %! 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	379 %! [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	380 %! [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	381 %! assert (U * T * U', A, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	382 */

Mercurial > hg > octave-nkf

annotate libinterp/corefcn/schur.cc @ 17296:3a9efb68272d ss-3-7-6