octave-lyh: scripts/linear-algebra/isdefinite.m annotate

annotate scripts/linear-algebra/isdefinite.m @ 11587:c792872f8942

all script files: untabify and strip trailing whitespace

author	John W. Eaton <jwe@octave.org>
date	Thu, 20 Jan 2011 17:35:29 -0500
parents	fd0a3ac60b0e
children	6fdf4927fefc

rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 11472 diff changeset	1 ## Copyright (C) 2003-2011 Gabriele Pannocchia
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	2 ##
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	3 ## This file is part of Octave.
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	4 ##
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
7016 93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	8 ## your option) any later version.
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	9 ##
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	13 ## General Public License for more details.
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	14 ##
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	15 ## 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: 6046 diff changeset	16 ## along with Octave; see the file COPYING. If not, see
93c65f2a5668 [project @ 2007-10-12 06:40:56 by jwe] jwe parents: 6046 diff changeset	17 ## <http://www.gnu.org/licenses/>.
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	18
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	19 ## -- texinfo --
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9870 diff changeset	20 ## @deftypefn {Function File} {} isdefinite (@var{x})
a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9870 diff changeset	21 ## @deftypefnx {Function File} {} isdefinite (@var{x}, @var{tol})
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	22 ## Return 1 if @var{x} is symmetric positive definite within the
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	23 ## tolerance specified by @var{tol} or 0 if @var{x} is symmetric
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	24 ## positive semidefinite. Otherwise, return -1. If @var{tol}
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	25 ## is omitted, use a tolerance of
10687 a8ce6bdecce5 Improve documentation strings. Rik <octave@nomad.inbox5.com> parents: 9870 diff changeset	26 ## @code{100 * eps * norm (@var{x}, "fro")}
11431 0d9640d755b1 Improve docstrings for all isXXX functions. Rik <octave@nomad.inbox5.com> parents: 10687 diff changeset	27 ## @seealso{issymmetric, ishermitian}
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	28 ## @end deftypefn
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	29
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	30 ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	31 ## Created: November 2003
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	32 ## Adapted-By: jwe
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	33
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	34 function retval = isdefinite (x, tol)
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	35
9870 5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	36 if (nargin < 1 \|\| nargin > 2)
6046 34f96dd5441b [project @ 2006-10-10 16:10:25 by jwe] jwe parents: 5642 diff changeset	37 print_usage ();
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	38 endif
02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	39
9870 5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	40 if (! ishermitian (x))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11431 diff changeset	41 error ("isdefinite: X must be a hermitian matrix");
9870 5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	42 endif
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	43
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	44 if (! isfloat (x))
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	45 x = double (x);
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	46 endif
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	47
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	48 if (nargin == 1)
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	49 tol = 100 * eps(class (x)) * norm (x, "fro");
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	50 endif
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	51
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	52 e = tol * eye (rows (x));
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	53 [r, p] = chol (x - e);
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	54 if (p == 0)
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	55 retval = 1;
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	56 else
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	57 [r, p] = chol (x + e);
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	58 if (p == 0)
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	59 retval = 0;
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	60 else
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	61 retval = -1;
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	62 endif
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	63 endif
5b733adba096 base isdefinite on cholesky decomposition Jaroslav Hajek <highegg@gmail.com> parents: 9869 diff changeset	64
4610 02d2fcf835fc [project @ 2003-11-14 17:08:59 by jwe] jwe parents: diff changeset	65 endfunction

Mercurial > hg > octave-lyh

annotate scripts/linear-algebra/isdefinite.m @ 11587:c792872f8942