## 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, 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
