update packages

[CreaPhase.git] / octave_packages / m / linear-algebra / isdefinite.m

diff --git a/octave_packages/m/linear-algebra/isdefinite.m b/octave_packages/m/linear-algebra/isdefinite.m
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+## Copyright (C) 2003-2012 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})
+## @deftypefnx {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 of
+## @code{100 * eps * norm (@var{x}, "fro")}
+## @seealso{issymmetric, ishermitian}
+## @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)
+    print_usage ();
+  endif
+
+  if (! isfloat (x))
+    x = double (x);
+  endif
+
+  if (nargin == 1)
+    tol = 100 * eps (class (x)) * norm (x, "fro");
+  endif
+
+  if (! ishermitian (x, tol))
+    error ("isdefinite: X must be a Hermitian matrix");
+  endif
+
+  e = tol * eye (rows (x));
+  [r, p] = chol (x - e);
+  if (p == 0)
+    retval = 1;
+  else
+    [r, p] = chol (x + e);
+    if (p == 0)
+      retval = 0;
+    else
+      retval = -1;
+    endif
+  endif
+
+endfunction
+
+
+%!test
+%! A = [-1 0; 0 -1];
+%! assert (isdefinite (A), -1)
+
+%!test
+%! A = [1 0; 0 1];
+%! assert (isdefinite (A), 1)
+
+%!test
+%! A = [2 -1 0; -1 2 -1; 0 -1 2];
+%! assert (isdefinite (A), 1)
+
+%!test
+%! A = [1 0; 0 0];
+%! assert (isdefinite (A), 0)
+
+%!error isdefinite ()
+%!error isdefinite (1,2,3)
+%!error <X must be a Hermitian matrix> isdefinite ([1 2; 3 4])
+