isdefinite.m

JAVA 数学程序库 提供常规的数值计算程序包

## Copyright (C) 2003 Gabriele Pannocchia
##
## This file is part of Octave.
##
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## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
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## General Public License for more details.
##
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## -*- 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 <[e-mail]>
## Created: November 2003
## Adapted-By: jwe

function retval = isdefinite (x, tol)

  if (nargin == 1 || nargin == 2)
    if (nargin == 1)
      tol = 100*eps;
    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;
      end
    else
      error ("isdefinite: matrix x must be symmetric");
    endif
  else
    print_usage ();
  endif

endfunction