# Copyright (C) 1993 John W. Eaton
# 
# 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 2, 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, write to the Free
# Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.

function retval = rank (A, tol)

# usage: rank (a, tol)
#
# Return the rank of the matrix a.  The rank is taken to be the number
# of singular values of a that are greater than tol.
#
# If the second argument is omitted, it is taken to be
#
#   tol =  max (size (a)) * sigma (1) * eps;
#
# where eps is machine precision and sigma is the largest singular
# value of a.

  if (nargin == 1)
    sigma = svd (A);
    tolerance = max (size (A)) * sigma (1) * eps;
  elseif (nargin == 2)
    sigma = svd (A);
    tolerance = tol;
  else
    error ("usage: rank (A)");
  endif
  retval = sum (sigma > tolerance);

endfunction