octave: libinterp/corefcn/schur.cc annotate

annotate libinterp/corefcn/schur.cc @ 30564:796f54d4ddbf stable

update Octave Project Developers copyright for the new year In files that have the "Octave Project Developers" copyright notice, update for 2021. In all .txi and .texi files except gpl.txi and gpl.texi in the doc/liboctave and doc/interpreter directories, change the copyright to "Octave Project Developers", the same as used for other source files. Update copyright notices for 2022 (not done since 2019). For gpl.txi and gpl.texi, change the copyright notice to be "Free Software Foundation, Inc." and leave the date at 2007 only because this file only contains the text of the GPL, not anything created by the Octave Project Developers. Add Paul Thomas to contributors.in.

author	John W. Eaton <jwe@octave.org>
date	Tue, 28 Dec 2021 18:22:40 -0500
parents	a61e1a0f6024
children	08b08b7f05b2 da3ac42a143d

rev	line source
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	1 ////////////////////////////////////////////////////////////////////////
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	2 //
30564 796f54d4ddbf update Octave Project Developers copyright for the new year John W. Eaton <jwe@octave.org> parents: 30390 diff changeset	3 // Copyright (C) 1996-2022 The Octave Project Developers
27923 bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	4 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	5 // See the file COPYRIGHT.md in the top-level directory of this
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	6 // distribution or <https://octave.org/copyright/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	7 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	8 // This file is part of Octave.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	9 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	10 // Octave is free software: you can redistribute it and/or modify it
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	11 // under the terms of the GNU General Public License as published by
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	12 // the Free Software Foundation, either version 3 of the License, or
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	13 // (at your option) any later version.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	14 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	15 // Octave is distributed in the hope that it will be useful, but
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	16 // WITHOUT ANY WARRANTY; without even the implied warranty of
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	17 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	18 // GNU General Public License for more details.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	19 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	20 // You should have received a copy of the GNU General Public License
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	21 // along with Octave; see the file COPYING. If not, see
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	22 // <https://www.gnu.org/licenses/>.
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	23 //
bd51beb6205e update formatting of copyright notices John W. Eaton <jwe@octave.org> parents: 27919 diff changeset	24 ////////////////////////////////////////////////////////////////////////
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	25
21724 aba2e6293dd8 use "#if ..." consistently instead of "#ifdef" and "#ifndef" John W. Eaton <jwe@octave.org> parents: 21547 diff changeset	26 #if defined (HAVE_CONFIG_H)
21301 40de9f8f23a6 Use '#include "config.h"' rather than <config.h>. Rik <rik@octave.org> parents: 21266 diff changeset	27 # include "config.h"
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	28 #endif
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	29
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	30 #include <string>
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	31
21266 e69eaee28737 make better use of templates for Schur decomposition John W. Eaton <jwe@octave.org> parents: 21200 diff changeset	32 #include "schur.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"
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	36 #include "errwarn.h"
20940 48b2ad5ee801 maint: Rename oct-obj.[cc\|h] to ovl.[cc\|h] for clarity. Rik <rik@octave.org> parents: 20939 diff changeset	37 #include "ovl.h"
2928 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
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	40 OCTAVE_NAMESPACE_BEGIN
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	41
21139 538b57866b90 consistently use "typename" intead of "class" in template declarations John W. Eaton <jwe@octave.org> parents: 21120 diff changeset	42 template <typename Matrix>
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	43 static octave_value
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	44 mark_upper_triangular (const Matrix& 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_value retval = a;
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	47
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	48 octave_idx_type n = a.rows ();
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	49 assert (a.columns () == n);
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 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	52
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	53 for (octave_idx_type i = 0; i < n; i++)
30390 a61e1a0f6024 maint: style check C++ files in libinterp/ ahead of 7.1 release. Rik <rik@octave.org> parents: 30073 diff changeset	54 if (a(i, i) == zero)
10617 9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	55 return retval;
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 retval.matrix_type (MatrixType::Upper);
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 return retval;
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	60 }
9c9e07f5eb1c make schur mark triangular matrices on output Jaroslav Hajek <highegg@gmail.com> parents: 10607 diff changeset	61
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	62 DEFUN (schur, args, nargout,
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	63 doc: /* -- texinfo --
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	64 @deftypefn {} {@var{S} =} schur (@var{A})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	65 @deftypefnx {} {@var{S} =} schur (@var{A}, "real")
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	66 @deftypefnx {} {@var{S} =} schur (@var{A}, "complex")
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	67 @deftypefnx {} {@var{S} =} schur (@var{A}, @var{opt})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	68 @deftypefnx {} {[@var{U}, @var{S}] =} schur (@dots{})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	69 @cindex Schur decomposition
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	70 Compute the Schur@tie{}decomposition of @var{A}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	71
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	72 The Schur@tie{}decomposition is defined as
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	73 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	74 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	75 S = U^T A U
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	76 $$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	77 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	78 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	79
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	80 @example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	81 @code{@var{S} = @var{U}' * @var{A} * @var{U}}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	82 @end example
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	83
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	84 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	85 where @var{U} is a unitary matrix
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	86 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	87 ($U^T U$ is identity)
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	88 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	89 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	90 (@code{@var{U}'* @var{U}} is identity)
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	91 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	92 and @var{S} is upper triangular. The eigenvalues of @var{A} (and @var{S})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	93 are the diagonal elements of @var{S}. If the matrix @var{A} is real, then
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	94 the real Schur@tie{}decomposition is computed, in which the matrix @var{U}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	95 is orthogonal and @var{S} is block upper triangular with blocks of size at
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	96 most
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	97 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	98 $2 \times 2$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	99 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	100 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	101 @code{2 x 2}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	102 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	103 along the diagonal. The diagonal elements of @var{S}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	104 (or the eigenvalues of the
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	105 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	106 $2 \times 2$
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	107 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	108 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	109 @code{2 x 2}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	110 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	111 blocks, when appropriate) are the eigenvalues of @var{A} and @var{S}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	112
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	113 The default for real matrices is a real Schur@tie{}decomposition.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	114 A complex decomposition may be forced by passing the flag
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	115 @qcode{"complex"}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	116
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	117 The eigenvalues are optionally ordered along the diagonal according to the
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	118 value of @var{opt}. @code{@var{opt} = "a"} indicates that all eigenvalues
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	119 with negative real parts should be moved to the leading block of @var{S}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	120 (used in @code{are}), @code{@var{opt} = "d"} indicates that all
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	121 eigenvalues with magnitude less than one should be moved to the leading
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	122 block of @var{S} (used in @code{dare}), and @code{@var{opt} = "u"}, the
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	123 default, indicates that no ordering of eigenvalues should occur. The
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	124 leading @var{k} columns of @var{U} always span the @var{A}-invariant
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	125 subspace corresponding to the @var{k} leading eigenvalues of @var{S}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	126
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	127 The Schur@tie{}decomposition is used to compute eigenvalues of a square
25003 2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24534 diff changeset	128 matrix, and has applications in the solution of algebraic @nospell{Riccati}
2365c2661b3c doc: Spellcheck documentation ahead of 4.4 release. Rik <rik@octave.org> parents: 24534 diff changeset	129 equations in control (see @code{are} and @code{dare}).
25734 c7095a755185 New function "ordeig" (patch #9670) Sébastien Villemot <sebastien@debian.org> parents: 25054 diff changeset	130 @seealso{rsf2csf, ordschur, ordeig, lu, chol, hess, qr, qz, svd}
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	131 @end deftypefn */)
2928 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 int nargin = args.length ();
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	134
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	135 if (nargin < 1 \|\| nargin > 2 \|\| nargout > 2)
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	136 print_usage ();
2928 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 octave_value arg = args(0);
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	139
3523 b80bbb43a1a9 [project @ 2000-02-02 10:25:52 by jwe] jwe parents: 3372 diff changeset	140 std::string ord;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	141 if (nargin == 2)
20700 68e3a747ca02 rename octave_value value extractors that accept error message args John W. Eaton <jwe@octave.org> parents: 20582 diff changeset	142 ord = args(1).xstring_value ("schur: second argument must be a string");
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	143
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	144 bool force_complex = false;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	145
13224 0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	146 if (ord == "real")
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	147 {
21017 93748bcaec17 maint: Replace emtpy 'std::string ()' calls with "". Rik <rik@octave.org> parents: 20941 diff changeset	148 ord = "";
13224 0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	149 }
0a67c717c652 Add support for additional argument "real" to schur() (Bug #34012). Rik <octave@nomad.inbox5.com> parents: 12642 diff changeset	150 else if (ord == "complex")
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	151 {
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	152 force_complex = true;
21017 93748bcaec17 maint: Replace emtpy 'std::string ()' calls with "". Rik <rik@octave.org> parents: 20941 diff changeset	153 ord = "";
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	154 }
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	155 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	156 {
23450 855122b993da maint: Wrap tertiary operator in parentheses "(COND ? x : y)". Rik <rik@octave.org> parents: 23220 diff changeset	157 char ord_char = (ord.empty () ? 'U' : ord[0]);
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	158
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	159 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	160 && ord_char != 'u' && ord_char != 'a' && ord_char != 'd')
f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	161 {
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	162 warning ("schur: incorrect ordered schur argument '%s'",
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	163 ord.c_str ());
20941 a4f5da7c5463 maint: Replace "octave_value_list ()" with "ovl ()". Rik <rik@octave.org> parents: 20940 diff changeset	164 return ovl ();
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	165 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	166 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	167
5275 23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	168 octave_idx_type nr = arg.rows ();
23b37da9fd5b [project @ 2005-04-08 16:07:35 by jwe] jwe parents: 5008 diff changeset	169 octave_idx_type nc = arg.columns ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	170
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	171 if (nr != nc)
21110 3d0d84305600 Use err_square_matrix_required more widely. Rik <rik@octave.org> parents: 21100 diff changeset	172 err_square_matrix_required ("schur", "A");
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	173
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	174 if (! arg.isnumeric ())
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	175 err_wrong_type_arg ("schur", arg);
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	176
20939 b17fda023ca6 maint: Use new C++ archetype in more files. Rik <rik@octave.org> parents: 20898 diff changeset	177 octave_value_list retval;
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	178
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	179 if (arg.is_single_type ())
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	180 {
23582 0cc2011d800e maint: Deprecate is_real_type and replace with isreal. Rik <rik@octave.org> parents: 23581 diff changeset	181 if (! force_complex && arg.isreal ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	182 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	183 FloatMatrix tmp = arg.float_matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	184
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	185 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	186 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	187 math::schur<FloatMatrix> result (tmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	188 retval = ovl (result.schur_matrix ());
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	189 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	190 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	191 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	192 math::schur<FloatMatrix> result (tmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	193 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	194 result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	195 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	196 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	197 else
10154 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 FloatComplexMatrix ctmp = arg.float_complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	200
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	201 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	202 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	203 math::schur<FloatComplexMatrix> result (ctmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	204 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	205 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	206 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	207 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	208 math::schur<FloatComplexMatrix> result (ctmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	209 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	210 mark_upper_triangular (result.schur_matrix ()));
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 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	213 }
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	214 else
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	215 {
23582 0cc2011d800e maint: Deprecate is_real_type and replace with isreal. Rik <rik@octave.org> parents: 23581 diff changeset	216 if (! force_complex && arg.isreal ())
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	217 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	218 Matrix tmp = arg.matrix_value ();
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	219
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	220 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	221 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	222 math::schur<Matrix> result (tmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	223 retval = ovl (result.schur_matrix ());
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	224 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	225 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	226 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	227 math::schur<Matrix> result (tmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	228 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	229 result.schur_matrix ());
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	230 }
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	231 }
10607 f7501986e42d make schur more Matlab compatible Jaroslav Hajek <highegg@gmail.com> parents: 10155 diff changeset	232 else
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	233 {
40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	234 ComplexMatrix ctmp = arg.complex_matrix_value ();
7789 82be108cc558 First attempt at single precision tyeps David Bateman <dbateman@free.fr> parents: 7017 diff changeset	235
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	236 if (nargout <= 1)
10154 40dfc0c99116 DLD-FUNCTIONS/.cc: untabify John W. Eaton <jwe@octave.org>* parents: 9758 diff changeset	237 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	238 math::schur<ComplexMatrix> result (ctmp, ord, false);
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	239 retval = ovl (mark_upper_triangular (result.schur_matrix ()));
20555 f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	240 }
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	241 else
f90c8372b7ba eliminate many more simple uses of error_state John W. Eaton <jwe@octave.org> parents: 20172 diff changeset	242 {
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	243 math::schur<ComplexMatrix> result (ctmp, ord, true);
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	244 retval = ovl (result.unitary_schur_matrix (),
20892 c07bee629973 2015 Code Sprint: use ovl (). Rik <rik@octave.org> parents: 20853 diff changeset	245 mark_upper_triangular (result.schur_matrix ()));
10154 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 }
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	248 }
11586 12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	249
12df7854fa7c strip trailing whitespace from source files John W. Eaton <jwe@octave.org> parents: 11553 diff changeset	250 return retval;
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	251 }
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	252
295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	253 /*
7814 87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	254 %!test
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	255 %! 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	256 %! [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	257 %! 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	258
87865ed7405f Second set of single precision test code and fix of resulting bugs David Bateman <dbateman@free.fr> parents: 7789 diff changeset	259 %!test
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	260 %! 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	261 %! [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	262 %! 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	263
14501 60e5cf354d80 Update %!tests in DLD-FUNCTIONS/ directory with Octave coding conventions. Rik <octave@nomad.inbox5.com> parents: 14460 diff changeset	264 %!error schur ()
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	265 %!error schur (1,2,3)
b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	266 %!error [a,b,c] = schur (1)
21110 3d0d84305600 Use err_square_matrix_required more widely. Rik <rik@octave.org> parents: 21100 diff changeset	267 %!error <must be a square matrix> schur ([1, 2, 3; 4, 5, 6])
19016 b155fad47055 Fix error messages and %!fail tests for schur(). Rik <rik@octave.org> parents: 17787 diff changeset	268 %!error <wrong type argument 'cell'> schur ({1})
19034 f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check' Rik <rik@octave.org> parents: 19016 diff changeset	269 %!warning <incorrect ordered schur argument> schur ([1, 2; 3, 4], "bad_opt");
f707835af867 Rewrite schur built-in test as a %!warning to stop failure during 'make check' Rik <rik@octave.org> parents: 19016 diff changeset	270
2928 295f037b4b3e [project @ 1997-05-05 05:32:33 by jwe] jwe parents: diff changeset	271 */
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	272
15039 e753177cde93 maint: Move non-dynamically linked functions from DLD-FUNCTIONS/ to corefcn/ directory Rik <rik@octave.org> parents: 14854 diff changeset	273 DEFUN (rsf2csf, args, nargout,
21966 112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	274 doc: /* -- texinfo --
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	275 @deftypefn {} {[@var{U}, @var{T}] =} rsf2csf (@var{UR}, @var{TR})
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	276 Convert a real, upper quasi-triangular Schur@tie{}form @var{TR} to a
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	277 complex, upper triangular Schur@tie{}form @var{T}.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	278
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	279 Note that the following relations hold:
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	280
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	281 @tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	282 $UR \cdot TR \cdot {UR}^T = U T U^{\dagger}$ and
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	283 $U^{\dagger} U$ is the identity matrix I.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	284 @end tex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	285 @ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	286 @tcode{@var{UR} * @var{TR} * @var{UR}' = @var{U} * @var{T} * @var{U}'} and
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	287 @code{@var{U}' * @var{U}} is the identity matrix I.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	288 @end ifnottex
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	289
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	290 Note also that @var{U} and @var{T} are not unique.
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	291 @seealso{schur}
112b20240c87 move docstrings in C++ files out of C strings and into comments John W. Eaton <jwe@octave.org> parents: 21724 diff changeset	292 @end deftypefn */)
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	293 {
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	294 if (args.length () != 2 \|\| nargout > 2)
8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	295 print_usage ();
8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	296
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	297 if (! args(0).isnumeric ())
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	298 err_wrong_type_arg ("rsf2csf", args(0));
23586 f6c5db0a02e7 maint: Deprecate is_numeric_type and replace with isnumeric. Rik <rik@octave.org> parents: 23582 diff changeset	299 if (! args(1).isnumeric ())
21100 e39e05d90788 Switch gripe_XXX to either err_XXX or warn_XXX naming scheme. Rik <rik@octave.org> parents: 21055 diff changeset	300 err_wrong_type_arg ("rsf2csf", args(1));
23581 c3075ae020e1 maint: Deprecate is_complex_type and replace with iscomplex. Rik <rik@octave.org> parents: 23450 diff changeset	301 if (args(0).iscomplex () \|\| args(1).iscomplex ())
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	302 error ("rsf2csf: UR and TR must be real matrices");
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	303
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	304 if (args(0).is_single_type () \|\| args(1).is_single_type ())
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	305 {
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	306 FloatMatrix u = args(0).float_matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	307 FloatMatrix t = args(1).float_matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	308
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	309 math::schur<FloatComplexMatrix> cs
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	310 = math::rsf2csf<FloatComplexMatrix, FloatMatrix> (t, u);
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	311
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	312 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	313 }
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	314 else
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	315 {
21120 499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	316 Matrix u = args(0).matrix_value ();
499b851fbfae Replace pattern if/err_XXX/else/code with if/err_XXX/ code. Rik <rik@octave.org> parents: 21110 diff changeset	317 Matrix t = args(1).matrix_value ();
20802 8bb38ba1bad6 eliminate return statements after calls to print_usage John W. Eaton <jwe@octave.org> parents: 20700 diff changeset	318
29961 7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	319 math::schur<ComplexMatrix> cs
7d6709900da7 eliminate octave:: namespace tags in DEFUN and DEFMETHOD and more John W. Eaton <jwe@octave.org> parents: 29958 diff changeset	320 = math::rsf2csf<ComplexMatrix, Matrix> (t, u);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	321
30073 1e277c6b6626 maint: rename schur member function from "unitary_matrix" to "unitary_schur_matrix" Rik <rik@octave.org> parents: 29961 diff changeset	322 return ovl (cs.unitary_schur_matrix (), cs.schur_matrix ());
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	323 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	324 }
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	325
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	326 /*
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	327 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	328 %! 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	329 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	330 %! [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	331 %! 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	332 %! assert (norm (A - U * T * U'), 0, 1e-12);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	333
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	334 %!test
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	335 %! A = rand (10);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	336 %! [u, t] = schur (A);
23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	337 %! [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	338 %! 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	339 %! assert (norm (U * U'), 1, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	340
14460 6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	341 %!test
6c3441f3146b Fix logm for complex matrix with real eigenvalues (bug #34893). Marco Caliari <marco.caliari@univr.it> parents: 14138 diff changeset	342 %! 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	343 %! [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	344 %! [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	345 %! assert (U * T * U', A, 1e-14);
10822 23d2378512a0 implement rsf2csf Jaroslav Hajek <highegg@gmail.com> parents: 10617 diff changeset	346 */
29958 32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	347
32c3a5805893 move DEFUN and DEFMETHOD functions inside octave namespace John W. Eaton <jwe@octave.org> parents: 29359 diff changeset	348 OCTAVE_NAMESPACE_END

Mercurial > octave

annotate libinterp/corefcn/schur.cc @ 30564:796f54d4ddbf stable