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########################################################################
##
## Copyright (C) 1994-2025 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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 3 of the License, 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, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{y} =} polyvalm (@var{c}, @var{x})
## Evaluate a polynomial in the matrix sense.
##
## @code{polyvalm (@var{c}, @var{x})} will evaluate the polynomial in the
## matrix sense, i.e., matrix multiplication is used instead of element by
## element multiplication as used in @code{polyval}.
##
## The argument @var{x} must be a square matrix.
## @seealso{polyval, roots, poly}
## @end deftypefn
function y = polyvalm (c, x)
if (nargin != 2)
print_usage ();
endif
if (! (isvector (c) || isempty (c)))
error ("polyvalm: first argument must be a vector");
endif
if (! issquare (x))
error ("polyvalm: second argument must be a square matrix");
endif
n = length (c);
if (n == 0)
y = zeros (rows (x), class (x));
else
id = eye (rows (x), class (x));
y = c(1) * id;
for i = 2:n
y = y * x + c(i) * id;
endfor
endif
endfunction
%!assert (! any (polyvalm ([], [1, 2; 3, 4]))(:))
%!assert (polyvalm ([1, 2, 3, 4], [3, -4, 1; -2, 0, 2; -1, 4, -3]),
%! [117, -124, 11; -70, 36, 38; -43, 92, -45])
%!error <must be a square matrix> polyvalm ([1, 1, 1], [1, 2; 3, 4; 5, 6])
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