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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: compan (c)
##
## Compute the companion matrix corresponding to polynomial vector c.
##
## In octave a polynomial is represented by it's coefficients (arranged
## in descending order). For example a vector c of length n+1 corresponds
## to the following nth order polynomial
##
## p(x) = c(1) x^n + ... + c(n) x + c(n+1).
##
## The corresponding companion matrix is
## _ _
## | -c(2)/c(1) -c(3)/c(1) ... -c(n)/c(1) -c(n+1)/c(1) |
## | 1 0 ... 0 0 |
## | 0 1 ... 0 0 |
## A = | . . . . . |
## | . . . . . |
## | . . . . . |
## |_ 0 0 ... 1 0 _|
##
## The eigenvalues of the companion matrix are equal to the roots of the
## polynomial.
##
## SEE ALSO: poly, roots, residue, conv, deconv, polyval, polyderiv, polyinteg
## Author: Tony Richardson <arichard@stark.cc.oh.us>
## Created: June 1994
## Adapted-By: jwe
function A = compan (c)
if (nargin != 1)
usage ("compan (vector)");
endif
if (! is_vector (c))
error("compan: expecting a vector argument.");
endif
## Ensure that c is a row vector.
if (rows (c) > 1)
c = c.';
endif
n = length (c);
if (n == 1)
A = [];
else
A = diag (ones (n-2, 1), -1);
A(1,:) = -c(2:n) / c(1);
endif
endfunction
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