## Copyright (C) 1996-2018 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
## <https://www.gnu.org/licenses/>.

## -*- texinfo -*-
## @deftypefn  {} {} issymmetric (@var{A})
## @deftypefnx {} {} issymmetric (@var{A}, @var{tol})
## Return true if @var{A} is a symmetric matrix within the tolerance specified
## by @var{tol}.
##
## The default tolerance is zero (uses faster code).
##
## Matrix @var{A} is considered symmetric if
## @code{norm (@var{A} - @var{A}.', Inf) / norm (@var{A}, Inf) < @var{tol}}.
## @seealso{ishermitian, isdefinite}
## @end deftypefn

## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe

function retval = issymmetric (A, tol = 0)

  if (nargin < 1 || nargin > 2)
    print_usage ();
  endif

  retval = (isnumeric (A) || islogical (A)) && issquare (A);
  if (retval)
    if (tol == 0)
      ## Handle large sparse matrices as well as full ones
      retval = nnz (A != A.') == 0;
    else
      norm_x = norm (A, inf);
      retval = norm_x == 0 || norm (A - A.', inf) / norm_x <= tol;
    endif
  endif

endfunction


%!assert (issymmetric (1))
%!assert (! issymmetric ([1, 2]))
%!assert (issymmetric ([]))
%!assert (issymmetric ([1, 2; 2, 1]))
%!assert (! (issymmetric ("test")))
%!assert (issymmetric ([1, 2.1; 2, 1.1], 0.2))
%!assert (issymmetric ([1, 2i; 2i, 1]))
%!assert (! (issymmetric ("t")))
%!assert (! (issymmetric (["te"; "et"])))
%!assert (issymmetric (speye (100000)))
%!assert (issymmetric (logical (eye (2))))

%!test
%! s.a = 1;
%! assert (! issymmetric (s));

%!error issymmetric ([1, 2; 2, 1], 0, 0)
%!error issymmetric ()
