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########################################################################
##
## Copyright (C) 1994-2024 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{A} =} compan (@var{c})
## Compute the companion matrix corresponding to polynomial coefficient vector
## @var{c}.
##
## The companion matrix is
## @tex
## $$
## A = \left[\matrix{
## -c_2/c_1 & -c_3/c_1 & \cdots & -c_N/c_1 & -c_{N+1}/c_1\cr
## 1 & 0 & \cdots & 0 & 0 \cr
## 0 & 1 & \cdots & 0 & 0 \cr
## \vdots & \vdots & \ddots & \vdots & \vdots \cr
## 0 & 0 & \cdots & 1 & 0}\right].
## $$
## @end tex
## @ifnottex
## @c Set example in small font to prevent overfull line
##
## @smallexample
## @group
## _ _
## | -c(2)/c(1) -c(3)/c(1) @dots{} -c(N)/c(1) -c(N+1)/c(1) |
## | 1 0 @dots{} 0 0 |
## | 0 1 @dots{} 0 0 |
## A = | . . . . . |
## | . . . . . |
## | . . . . . |
## |_ 0 0 @dots{} 1 0 _|
## @end group
## @end smallexample
##
## @end ifnottex
## The eigenvalues of the companion matrix are equal to the roots of the
## polynomial.
## @seealso{roots, poly, eig}
## @end deftypefn
function A = compan (c)
if (nargin != 1)
print_usage ();
endif
if (! isvector (c))
error ("compan: C must be a vector");
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
%!assert (compan ([1, 2, 3]), [-2, -3; 1, 0])
%!assert (compan ([1; 2; 3]), [-2, -3; 1, 0])
%!assert (isempty (compan (4)))
%!assert (compan ([3, 2, 1]), [-2/3, -1/3; 1, 0])
%!error compan ([1,2;3,4])
%!error compan ([])
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