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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: 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
## Author: Tony Richardson <arichard@stark.cc.oh.us>
## Created: June 1994
## Adapted-By: jwe
function y = polyvalm (c, x)
if (nargin != 2)
usage ("polyvalm (c, x)");
endif
if (! (is_vector (c) || isempty (c)))
error ("polyvalm: first argument must be a vector.");
endif
if (! is_square (x))
error ("polyvalm: second argument must be a square matrix.");
endif
if (isempty (c))
y = [];
return;
endif
[v, d] = eig (x);
if (is_symmetric (x))
y = v * diag (polyval (c, diag (d))) * v';
else
y = v * (diag (polyval (c, diag (d))) / v);
endif
endfunction
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