Mercurial > hg > octave-lyh
annotate scripts/linear-algebra/isdefinite.m @ 9869:ecd750d1eabd
move issymmetric & isdefinite to linear-algebra, create ishermitian
| author | Jaroslav Hajek <highegg@gmail.com> |
|---|---|
| date | Tue, 24 Nov 2009 15:02:04 +0100 |
| parents | scripts/general/isdefinite.m@eb63fbe60fab |
| children | 5b733adba096 |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008 Gabriele Pannocchia |
| 4610 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 4610 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 4610 | 18 |
| 19 ## -*- texinfo -*- | |
| 4855 | 20 ## @deftypefn {Function File} {} isdefinite (@var{x}, @var{tol}) |
| 4610 | 21 ## Return 1 if @var{x} is symmetric positive definite within the |
| 22 ## tolerance specified by @var{tol} or 0 if @var{x} is symmetric | |
| 23 ## positive semidefinite. Otherwise, return -1. If @var{tol} | |
| 5642 | 24 ## is omitted, use a tolerance equal to 100 times the machine precision. |
| 25 ## @seealso{issymmetric} | |
| 4610 | 26 ## @end deftypefn |
| 27 | |
| 28 ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it> | |
| 29 ## Created: November 2003 | |
| 30 ## Adapted-By: jwe | |
| 31 | |
| 32 function retval = isdefinite (x, tol) | |
| 33 | |
| 34 if (nargin == 1 || nargin == 2) | |
| 35 if (nargin == 1) | |
|
7795
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7151
diff
changeset
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36 if (isa (x, "single")) |
|
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7151
diff
changeset
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37 tol = 100 * eps("single"); |
|
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7151
diff
changeset
|
38 else |
|
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7151
diff
changeset
|
39 tol = 100*eps; |
|
df9519e9990c
Handle single precision eps values
David Bateman <dbateman@free.fr>
parents:
7151
diff
changeset
|
40 endif |
| 4610 | 41 endif |
|
9869
ecd750d1eabd
move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
42 sym = ishermitian (x); |
|
ecd750d1eabd
move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
parents:
8920
diff
changeset
|
43 if (sym) |
| 4610 | 44 ## Matrix is symmetric, check eigenvalues. |
| 45 mineig = min (eig (x)); | |
| 46 if (mineig > tol) | |
| 47 retval = 1; | |
| 48 elseif (mineig > -tol) | |
| 49 retval = 0; | |
| 50 else | |
| 51 retval = -1; | |
| 7151 | 52 endif |
| 4610 | 53 else |
| 54 error ("isdefinite: matrix x must be symmetric"); | |
| 55 endif | |
| 56 else | |
| 6046 | 57 print_usage (); |
| 4610 | 58 endif |
| 59 | |
| 60 endfunction |