### 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.

function y = polyvalm (c, x)

  ## usage: polyvalm (c, x)
  ##
  ## Evaluate a polynomial in the matrix sense.
  ##
  ## 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).
  ##
  ## polyvalm(c,X) will evaluate the polynomial in the matrix sense, i.e. matrix
  ## multiplication is used instead of element by element multiplication as is
  ## used in polyval.
  ##
  ## X must be a square matrix.
  ##
  ## SEE ALSO: polyval, poly, roots, conv, deconv, residue, filter,
  ##           polyderiv, polyinteg

  ## Written by Tony Richardson (amr@mpl.ucsd.edu) June 1994.

  if(nargin != 2)
    usage ("polyvalm (c, x)");
  endif

  if (is_matrix (c))
    error("poly: first argument must be a vector.");
  endif

  if(! is_square (x))
    error("poly: second argument must be a square matrix.");
  endif

  [v, d] = eig(x);

  y = v * diag (polyval (c, diag (d))) * v';

endfunction