update packages

[CreaPhase.git] / octave_packages / m / polynomial / poly.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} {} poly (@var{A})
+## @deftypefnx {Function File} {} poly (@var{x})
+## If @var{A} is a square @math{N}-by-@math{N} matrix, @code{poly (@var{A})}
+## is the row vector of the coefficients of @code{det (z * eye (N) - A)},
+## the characteristic polynomial of @var{A}.  For example,
+## the following code finds the eigenvalues of @var{A} which are the roots of
+## @code{poly (@var{A})}.
+##
+## @example
+## @group
+## roots (poly (eye (3)))
+##     @result{} 1.00001 + 0.00001i
+##        1.00001 - 0.00001i
+##        0.99999 + 0.00000i
+## @end group
+## @end example
+##
+## In fact, all three eigenvalues are exactly 1 which emphasizes that for
+## numerical performance the @code{eig} function should be used to compute
+## eigenvalues.
+##
+## If @var{x} is a vector, @code{poly (@var{x})} is a vector of the
+## coefficients of the polynomial whose roots are the elements of @var{x}. 
+## That is, if @var{c} is a polynomial, then the elements of @code{@var{d} =
+## roots (poly (@var{c}))} are contained in @var{c}.  The vectors @var{c} and
+## @var{d} are not identical, however, due to sorting and numerical errors.
+## @seealso{roots, eig}
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Created: 24 December 1993
+## Adapted-By: jwe
+
+function y = poly (x)
+
+  if (nargin != 1)
+    print_usage ();
+  endif
+
+  m = min (size (x));
+  n = max (size (x));
+  if (m == 0)
+    y = 1;
+    return;
+  elseif (m == 1)
+    v = x;
+  elseif (m == n)
+    v = eig (x);
+  else
+    print_usage ();
+  endif
+
+  y = zeros (1, n+1);
+  y(1) = 1;
+  for j = 1:n;
+    y(2:(j+1)) = y(2:(j+1)) - v(j) .* y(1:j);
+  endfor
+
+  if (all (all (imag (x) == 0)))
+    y = real (y);
+  endif
+
+endfunction
+
+%!assert(all (all (poly ([1, 2, 3]) == [1, -6, 11, -6])));
+
+%!assert(all (all (abs (poly ([1, 2; 3, 4]) - [1, -5, -2]) < sqrt (eps))));
+
+%!error poly ([1, 2, 3; 4, 5, 6]);
+
+%!assert(poly ([]),1);
+