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## Copyright (C) 1996 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, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.
## 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.
## Author: jwe
function retval = rank (A, tol)
if (nargin == 1)
sigma = svd (A);
tolerance = max (size (A)) * sigma (1) * eps;
elseif (nargin == 2)
sigma = svd (A);
tolerance = tol;
else
usage ("rank (A)");
endif
retval = sum (sigma > tolerance);
endfunction
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