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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: roots (v)
##
## For a vector v with n components, return the roots of the
## polynomial v(1) * z^(n-1) + ... + v(n-1) * z + v(n).
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 24 December 1993
## Adapted-By: jwe
function r = roots (v)
if (min (size (v)) > 1 || nargin != 1)
usage ("roots (v), where v is a vector");
endif
n = length (v);
v = reshape (v, 1, n);
## If v = [ 0 ... 0 v(k+1) ... v(k+l) 0 ... 0 ], we can remove the
## leading k zeros and n - k - l roots of the polynomial are zero.
f = find (v);
m = max (size (f));
if (m > 0 && n > 1)
v = v(f(1):f(m));
l = max (size (v));
if (l > 1)
A = diag (ones (1, l-2), -1);
A(1,:) = -v(2:l) ./ v(1);
r = eig (A);
if (f(m) < n)
tmp = zeros (n - f(m), 1);
r = [r; tmp];
endif
else
r = zeros (n - f(m), 1);
endif
else
r = [];
endif
endfunction
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