## Copyright (C) 1996, 1997 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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.
## -*- texinfo -*-
## @deftypefn {Function File} {} rank (@var{a}, @var{tol})
## Compute the rank of @var{a}, using the singular value decomposition.
## The rank is taken to be the number of singular values of @var{a} that
## are greater than the specified tolerance @var{tol}. If the second
## argument is omitted, it is taken to be
##
## @example
## tol = max (size (@var{a})) * sigma(1) * eps;
## @end example
##
## @noindent
## where @code{eps} is machine precision and @code{sigma(1)} is the largest
## singular value of @var{a}.
## @end deftypefn
## Author: jwe
function retval = rank (A, tol)
if (nargin == 1)
sigma = svd (A);
if (isempty (sigma))
tolerance = 0;
else
tolerance = max (size (A)) * sigma (1) * eps;
endif
elseif (nargin == 2)
sigma = svd (A);
tolerance = tol;
else
print_usage ();
endif
retval = sum (sigma > tolerance);
endfunction
/*
@GROUP
LinearAlgebra
@SYNTAX
rank()
@DOC
.
@EXAMPLES
@NOTES
@SEE
*/