Mercurial > octave
view scripts/linear-algebra/isdefinite.m @ 27981:7f1cec12c240
maint: Remove simple "Adapted-By:" lines from code base.
* __ftp__.cc, urlwrite.cc, lin2mu.m, mu2lin.m, bincoeff.m, common_size.m,
nextpow2.m, shift.m, xor.m, griddata.m, colormap.m, gray.m, gray2ind.m,
image.m, imagesc.m, imshow.m, ind2gray.m, ind2rgb.m, ocean.m, rgb2ind.m,
findstr.m, commutation_matrix.m, cross.m, gls.m, isdefinite.m, ishermitian.m,
issymmetric.m, null.m, ols.m, orth.m, qzhess.m, vech.m, orderfields.m, untar.m,
unzip.m, orient.m, __pltopt__.m, __gnuplot_print__.m, subplot.m, compan.m,
conv.m, deconv.m, poly.m, polyder.m, polyfit.m, polyint.m, polyreduce.m,
polyval.m, polyvalm.m, residue.m, roots.m, detrend.m, fftconv.m, fftfilt.m,
fftshift.m, ifftshift.m, beta.m, lcm.m, pow2.m, corr.m, kurtosis.m, skewness.m,
base2dec.m, bin2dec.m, blanks.m, deblank.m, dec2base.m, dec2bin.m, dec2hex.m,
hex2dec.m, index.m, rindex.m, substr.m, calendar.m, datestr.m, datevec.m,
eomday.m, now.m, weekday.m:
Remove simple "Adapted-By:" lines from code base.
author | Rik <rik@octave.org> |
---|---|
date | Tue, 21 Jan 2020 13:15:15 -0800 |
parents | bdad8ca48700 |
children | 9f9ac219896d |
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######################################################################## ## ## Copyright (C) 2003-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## 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 ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {} isdefinite (@var{A}) ## @deftypefnx {} {} isdefinite (@var{A}, @var{tol}) ## Return true if @var{A} is symmetric positive definite matrix within the ## tolerance specified by @var{tol}. ## ## If @var{tol} is omitted, use a tolerance of ## @code{100 * eps * norm (@var{A}, "fro")}. ## ## Background: A positive definite matrix has eigenvalues which are all ## greater than zero. A positive semi-definite matrix has eigenvalues which ## are all greater than or equal to zero. The matrix @var{A} is very likely to ## be positive semi-definite if the following two conditions hold for a ## suitably small tolerance @var{tol}. ## ## @example ## @group ## isdefinite (@var{A}) @result{} 0 ## isdefinite (@var{A} + 5*@var{tol}, @var{tol}) @result{} 1 ## @end group ## @end example ## @seealso{issymmetric, ishermitian} ## @end deftypefn ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it> function retval = isdefinite (A, tol) if (nargin < 1 || nargin > 2) print_usage (); endif ## Validate inputs retval = false; if (! isnumeric (A)) return; endif if (! isfloat (A)) A = double (A); endif if (nargin == 1) tol = 100 * eps (class (A)) * norm (A, "fro"); elseif (! (isnumeric (tol) && isscalar (tol) && tol >= 0)) error ("isdefinite: TOL must be a scalar >= 0"); endif if (! ishermitian (A, tol)) return; endif e = tol * eye (rows (A)); [~, p] = chol (A - e); if (p == 0) retval = true; endif endfunction %!test %! A = [-1, 0; 0, -1]; %! assert (isdefinite (A), false); %!test %! A = [1, 0; 0, 1]; %! assert (isdefinite (A), true); %!test %! A = [2, -1, 0; -1, 2, -1; 0, -1, 2]; %! assert (isdefinite (A), true); ## Test for positive semi-definite matrix %!test %! A = [1, 0; 0, 0]; %! assert (isdefinite (A), false); %! tol = 100*eps; %! assert (isdefinite (A+5*tol, tol), true); %!assert (! isdefinite (magic (3))) %!error isdefinite () %!error isdefinite (1,2,3) %!error <TOL must be a scalar .= 0> isdefinite (1, {1}) %!error <TOL must be a scalar .= 0> isdefinite (1, [1 1]) %!error <TOL must be a scalar .= 0> isdefinite (1, -1)