Mercurial > hg > octave-nkf
diff scripts/linear-algebra/ishermitian.m @ 9869:ecd750d1eabd
move issymmetric & isdefinite to linear-algebra, create ishermitian
author | Jaroslav Hajek <highegg@gmail.com> |
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date | Tue, 24 Nov 2009 15:02:04 +0100 |
parents | |
children | 73fc43e01f4c |
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new file mode 100644 --- /dev/null +++ b/scripts/linear-algebra/ishermitian.m @@ -0,0 +1,67 @@ +## Copyright (C) 1996, 1997, 2002, 2003, 2004, 2005, 2006, 2007, 2008 +## John W. Eaton +## Copyright (C) 2009 VZLU Prague +## +## 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} {} ishermitian (@var{x}, @var{tol}) +## Return true if @var{x} is symmetric within the tolerance specified by @var{tol}, +## otherwise return false. The default tolerance is zero (uses faster code). +## Matrix @var{x} is considered symmetric if +## @code{norm (@var{x} - @var{x}.', inf) / norm (@var{x}, inf) < @var{tol}}. +## @seealso{size, rows, columns, length, ismatrix, isscalar, +## issquare, isvector} +## @end deftypefn + +## Author: A. S. Hodel <scotte@eng.auburn.edu> +## Created: August 1993 +## Adapted-By: jwe + +function retval = ishermitian (x, tol = 0) + + if (nargin < 1 || nargin > 2) + print_usage (); + endif + + retval = issquare (x); + if (retval) + if (tol == 0) + retval = all ((x == x')(:)); + else + norm_x = norm (x, inf); + retval = norm_x == 0 || norm (x - x', inf) / norm_x <= tol; + endif + endif + +endfunction + +%!assert(ishermitian (1)); +%!assert(!(ishermitian ([1, 2]))); +%!assert(ishermitian ([])); +%!assert(ishermitian ([1, 2; 2, 1])); +%!assert(!(ishermitian ("test"))); +%!assert(ishermitian ([1, 2.1; 2, 1.1], 0.2)); +%!assert(ishermitian ([1, -2i; 2i, 1])); +%!assert(!(ishermitian ("t"))); +%!assert(!(ishermitian (["te"; "et"]))); +%!error ishermitian ([1, 2; 2, 1], 0, 0); +%!error ishermitian (); + +%!test +%! s.a = 1; +%! assert(!(ishermitian (s)));