Mercurial > octave
view scripts/linear-algebra/ishermitian.m @ 30564:796f54d4ddbf stable
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2021.
In all .txi and .texi files except gpl.txi and gpl.texi in the
doc/liboctave and doc/interpreter directories, change the copyright
to "Octave Project Developers", the same as used for other source
files. Update copyright notices for 2022 (not done since 2019). For
gpl.txi and gpl.texi, change the copyright notice to be "Free Software
Foundation, Inc." and leave the date at 2007 only because this file
only contains the text of the GPL, not anything created by the Octave
Project Developers.
Add Paul Thomas to contributors.in.
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Tue, 28 Dec 2021 18:22:40 -0500 |
parents | 7854d5752dd2 |
children | 83f9f8bda883 |
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######################################################################## ## ## Copyright (C) 1996-2022 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 {} {} ishermitian (@var{A}) ## @deftypefnx {} {} ishermitian (@var{A}, @var{tol}) ## @deftypefnx {} {} ishermitian (@var{A}, @qcode{"skew"}) ## @deftypefnx {} {} ishermitian (@var{A}, @qcode{"skew"}, @var{tol}) ## Return true if @var{A} is a Hermitian or skew-Hermitian matrix within the ## tolerance specified by @var{tol}. ## ## The default tolerance is zero (uses faster code). ## ## The type of symmetry to check may be specified with the additional input ## @qcode{"nonskew"} (default) for regular Hermitian or @qcode{"skew"} for ## skew-Hermitian. ## ## Background: A matrix is Hermitian if the complex conjugate transpose of the ## matrix is equal to the original matrix: @w{@tcode{@var{A} == @var{A}'}}. If ## a tolerance is given then the calculation is ## @code{norm (@var{A} - @var{A}', Inf) / norm (@var{A}, Inf) < @var{tol}}. ## ## A matrix is skew-Hermitian if the complex conjugate transpose of the matrix ## is equal to the negative of the original matrix: ## @w{@tcode{@var{A} == -@var{A}'}}. If a ## tolerance is given then the calculation is ## @code{norm (@var{A} + @var{A}', Inf) / norm (@var{A}, Inf) < @var{tol}}. ## @seealso{issymmetric, isdefinite} ## @end deftypefn function retval = ishermitian (A, skewopt = "nonskew", tol = 0) if (nargin < 1) print_usage (); endif if (nargin == 2) ## Decode whether second argument is skewopt or tol if (isnumeric (skewopt)) tol = skewopt; skewopt = "nonskew"; elseif (! ischar (skewopt)) error ("ishermitian: second argument must be a non-negative scalar TOL, or one of the strings: 'skew' / 'nonskew'"); endif endif ## Validate inputs retval = (isnumeric (A) || islogical (A)) && issquare (A); if (! retval) return; endif if (! (strcmp (skewopt, "skew") || strcmp (skewopt, "nonskew"))) error ("ishermitian: SKEWOPT must be 'skew' or 'nonskew'"); endif if (! (isnumeric (tol) && isscalar (tol) && tol >= 0)) error ("ishermitian: TOL must be a scalar >= 0"); endif ## Calculate Hermitian-ness if (strcmp (skewopt, "nonskew")) if (tol == 0) ## check for exact symmetry retval = full (! any ((A != A')(:))); else if (islogical (A)) ## Hack to allow norm to work. Choose single to minimize memory. A = single (A); endif norm_x = norm (A, Inf); retval = norm_x == 0 || norm (A - A', Inf) / norm_x <= tol; endif else ## skew-Hermitian if (tol == 0) retval = full (! any ((A != -A')(:))); else if (islogical (A)) ## Hack to allow norm to work. Choose single to minimize memory. A = single (A); endif norm_x = norm (A, Inf); retval = norm_x == 0 || norm (A + A', Inf) / norm_x <= tol; endif endif endfunction %!assert (ishermitian (1)) %!assert (! ishermitian ([1, 2])) %!assert (ishermitian ([])) %!assert (ishermitian ([1, 2; 2, 1])) %!assert (ishermitian ([1, 2.1; 2, 1.1], 0.2)) %!assert (ishermitian ([1, -2i; 2i, 1])) %!assert (ishermitian (speye (100)), true) # Return full logical value. %!assert (ishermitian (logical (eye (2)))) %!assert (! ishermitian (logical ([1 1; 0 1]))) %!assert (ishermitian (logical ([1 1; 0 1]), 0.5)) %!assert (ishermitian ([0, 2i; 2i, 0], "skew")) %!assert (! ishermitian ([0, 2; -2, eps], "skew")) %!assert (ishermitian ([0, 2; -2, eps], "skew", eps)) %!assert (! (ishermitian ("test"))) %!assert (! (ishermitian ("t"))) %!assert (! (ishermitian (["te"; "et"]))) %!assert (! ishermitian ({1})) %!test %! s.a = 1; %! assert (! ishermitian (s)); ## Test input validation %!error <Invalid call> ishermitian () %!error <second argument must be> ishermitian (1, {"skew"}) %!error <SKEWOPT must be 'skew' or 'nonskew'> ishermitian (1, "foobar") %!error <SKEWOPT must be 'skew' or 'nonskew'> ishermitian (1, "foobar") %!error <TOL must be a scalar .= 0> ishermitian (1, "skew", {1}) %!error <TOL must be a scalar .= 0> ishermitian (1, "skew", [1 1]) %!error <TOL must be a scalar .= 0> ishermitian (1, -1)