1######################################################################## 2## 3## Copyright (C) 1994-2021 The Octave Project Developers 4## 5## See the file COPYRIGHT.md in the top-level directory of this 6## distribution or <https://octave.org/copyright/>. 7## 8## This file is part of Octave. 9## 10## Octave is free software: you can redistribute it and/or modify it 11## under the terms of the GNU General Public License as published by 12## the Free Software Foundation, either version 3 of the License, or 13## (at your option) any later version. 14## 15## Octave is distributed in the hope that it will be useful, but 16## WITHOUT ANY WARRANTY; without even the implied warranty of 17## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 18## GNU General Public License for more details. 19## 20## You should have received a copy of the GNU General Public License 21## along with Octave; see the file COPYING. If not, see 22## <https://www.gnu.org/licenses/>. 23## 24######################################################################## 25 26## -*- texinfo -*- 27## @deftypefn {} {} polyvalm (@var{c}, @var{x}) 28## Evaluate a polynomial in the matrix sense. 29## 30## @code{polyvalm (@var{c}, @var{x})} will evaluate the polynomial in the 31## matrix sense, i.e., matrix multiplication is used instead of element by 32## element multiplication as used in @code{polyval}. 33## 34## The argument @var{x} must be a square matrix. 35## @seealso{polyval, roots, poly} 36## @end deftypefn 37 38function y = polyvalm (c, x) 39 40 if (nargin != 2) 41 print_usage (); 42 endif 43 44 if (! (isvector (c) || isempty (c))) 45 error ("polyvalm: first argument must be a vector"); 46 endif 47 48 if (! issquare (x)) 49 error ("polyvalm: second argument must be a square matrix"); 50 endif 51 52 n = length (c); 53 if (n == 0) 54 y = zeros (rows (x), class (x)); 55 else 56 id = eye (rows (x), class (x)); 57 y = c(1) * id; 58 for i = 2:n 59 y = y * x + c(i) * id; 60 endfor 61 endif 62 63endfunction 64 65 66%!assert (! any (polyvalm ([], [1, 2; 3, 4]))(:)) 67%!assert (polyvalm ([1, 2, 3, 4], [3, -4, 1; -2, 0, 2; -1, 4, -3]), [117, -124, 11; -70, 36, 38; -43, 92, -45]) 68 69%!error <must be a square matrix> polyvalm ([1, 1, 1], [1, 2; 3, 4; 5, 6]) 70