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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: null (A, tol)
## null (A)
##
## Returns an orthonormal basis of the null space of A.
##
## The dimension of the null space is taken as the number of singular
## values of A not greater than tol; the default for tol is
## max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the
## maximal singular value of A.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 24 December 1993.
## Adapted-By: jwe
function retval = null (A, tol)
[U, S, V] = svd (A);
[rows, cols] = size (A);
[S_nr, S_nc] = size (S);
if (S_nr == 1 || S_nc == 1)
s = S(1);
else
s = diag (S);
endif
if (nargin == 1)
tol = max (size (A)) * s (1) * eps;
elseif (nargin != 2)
usage ("null (A [, tol])");
endif
rank = sum (s > tol);
if (rank < cols)
retval = V (:, rank+1:cols);
else
retval = zeros (cols, 0);
endif
endfunction
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