update packages

[CreaPhase.git] / octave_packages / m / polynomial / compan.m

diff --git a/octave_packages/m/polynomial/compan.m b/octave_packages/m/polynomial/compan.m
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+## Copyright (C) 1994-2012 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 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} 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
+
+## Author: Tony Richardson <arichard@stark.cc.oh.us>
+## Created: June 1994
+## Adapted-By: jwe
+
+function A = compan (c)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  if (! isvector (c))
+    error ("compan: expecting a vector argument");
+  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(all (all (compan ([1, 2, 3]) == [-2, -3; 1, 0])));
+
+%!assert(all (all (compan ([1; 2; 3]) == [-2, -3; 1, 0])));
+
+%!assert(isempty (compan (4)));
+
+%!assert(all (all (compan ([3, 2, 1]) == [-2/3, -1/3; 1, 0])));
+
+%!error compan ([1,2;3,4]);
+
+%!error compan ([]);
+