Mercurial > jwe > octave
view scripts/linear-algebra/isdefinite.m @ 20160:03b9d17a2d95 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed io, java, linear-algebra, prefs, and set script directories.
* scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m,
scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m,
scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m,
scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m,
scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m,
scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m,
scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m,
scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m,
scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m,
scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m,
scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m,
scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m,
scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m,
scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m,
scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m,
scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m,
scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m,
scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m,
scripts/set/powerset.m, scripts/set/setdiff.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Sun, 03 May 2015 15:36:23 -0700 |
parents | 4197fc428c7d |
children | 516bb87ea72e |
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## Copyright (C) 2003-2015 Gabriele Pannocchia ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {} isdefinite (@var{A}) ## @deftypefnx {Function File} {} isdefinite (@var{A}, @var{tol}) ## Return 1 if @var{A} is symmetric positive definite within the ## tolerance specified by @var{tol} or 0 if @var{A} is symmetric ## positive semidefinite. Otherwise, return -1. ## ## If @var{tol} is omitted, use a tolerance of ## @code{100 * eps * norm (@var{A}, "fro")} ## @seealso{issymmetric, ishermitian} ## @end deftypefn ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it> ## Created: November 2003 ## Adapted-By: jwe function retval = isdefinite (A, tol) if (nargin < 1 || nargin > 2) print_usage (); endif if (! isfloat (A)) A = double (A); endif if (nargin == 1) tol = 100 * eps (class (A)) * norm (A, "fro"); endif if (! ishermitian (A, tol)) error ("isdefinite: A must be a Hermitian matrix"); endif e = tol * eye (rows (A)); [r, p] = chol (A - e); if (p == 0) retval = 1; else [r, p] = chol (A + e); if (p == 0) retval = 0; else retval = -1; endif endif endfunction %!test %! A = [-1 0; 0 -1]; %! assert (isdefinite (A), -1); %!test %! A = [1 0; 0 1]; %! assert (isdefinite (A), 1); %!test %! A = [2 -1 0; -1 2 -1; 0 -1 2]; %! assert (isdefinite (A), 1); %!test %! A = [1 0; 0 0]; %! assert (isdefinite (A), 0); %!error isdefinite () %!error isdefinite (1,2,3) %!error <A must be a Hermitian matrix> isdefinite ([1 2; 3 4])