Mercurial > hg > octave-lyh

annotate scripts/linear-algebra/isdefinite.m @ 11188:4cb1522e4d0f

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
Use function handle as input to cellfun, rather than quoted function name or anonymous function wrapper.
author Rik <octave@nomad.inbox5.com>
date Wed, 03 Nov 2010 17:20:56 -0700
parents a8ce6bdecce5
children 0d9640d755b1
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
8920
eb63fbe60fab update copyright notices
John W. Eaton <jwe@octave.org>
parents: 7795
diff changeset
1 ## Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008 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}
10687
a8ce6bdecce5 Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents: 9870
diff changeset
25 ## is omitted, use a tolerance of
a8ce6bdecce5 Improve documentation strings.
Rik <octave@nomad.inbox5.com>
parents: 9870
diff changeset
26 ## @code{100 * eps * norm (@var{x}, "fro")}
5642
2618a0750ae6 [project @ 2006-03-06 21:26:48 by jwe]
jwe
parents: 5307
diff changeset
27 ## @seealso{issymmetric}
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))
5b733adba096 base isdefinite on cholesky decomposition
Jaroslav Hajek <highegg@gmail.com>
parents: 9869
diff changeset
41 error ("isdefinite: x must be a hermitian matrix");
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