## Copyright (C) 2003, 2004, 2005, 2006, 2007, 2008 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{x}, @var{tol})
## Return 1 if @var{x} is symmetric positive definite within the
## tolerance specified by @var{tol} or 0 if @var{x} is symmetric
## positive semidefinite.  Otherwise, return -1.  If @var{tol}
## is omitted, use a tolerance equal to 100 times the machine precision.
## @seealso{issymmetric}
## @end deftypefn

## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
## Created: November 2003
## Adapted-By: jwe

function retval = isdefinite (x, tol)

  if (nargin == 1 || nargin == 2)
    if (nargin == 1)
      if (isa (x, "single"))
	tol = 100 * eps("single");
      else
	tol = 100*eps; 
      endif
    endif
    sym = issymmetric (x, tol);
    if (sym > 0)
      ## Matrix is symmetric, check eigenvalues.
      mineig = min (eig (x));
      if (mineig > tol)
	retval = 1;
      elseif (mineig > -tol)
	retval = 0;
      else
	retval = -1;
      endif
    else
      error ("isdefinite: matrix x must be symmetric");
    endif
  else
    print_usage ();
  endif

endfunction
