update packages

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

diff --git a/octave_packages/m/polynomial/polygcd.m b/octave_packages/m/polynomial/polygcd.m
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+## Copyright (C) 2000-2012 Paul Kienzle
+##
+## 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} {@var{q} =} polygcd (@var{b}, @var{a})
+## @deftypefnx {Function File} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol})
+##
+## Find the greatest common divisor of two polynomials.  This is equivalent
+## to the polynomial found by multiplying together all the common roots.
+## Together with deconv, you can reduce a ratio of two polynomials.
+## The tolerance @var{tol} defaults to @code{sqrt(eps)}.
+##
+## @strong{Caution:} This is a numerically unstable algorithm and should not
+## be used on large polynomials.
+##
+## Example code:
+##
+## @example
+## @group
+## polygcd (poly (1:8), poly (3:12)) - poly (3:8)
+## @result{} [ 0, 0, 0, 0, 0, 0, 0 ]
+## deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))) - poly(1:2)
+## @result{} [ 0, 0, 0 ]
+## @end group
+## @end example
+## @seealso{poly, roots, conv, deconv, residue}
+## @end deftypefn
+
+function x = polygcd (b, a, tol)
+
+  if (nargin == 2 || nargin == 3)
+    if (nargin == 2)
+      if (isa (a, "single") || isa (b, "single"))
+        tol = sqrt (eps ("single"));
+      else
+        tol = sqrt (eps);
+      endif
+    endif
+    if (length (a) == 1 || length (b) == 1)
+      if (a == 0)
+        x = b;
+      elseif (b == 0)
+        x = a;
+      else
+        x = 1;
+      endif
+    else
+      a /= a(1);
+      while (1)
+        [d, r] = deconv (b, a);
+        nz = find (abs (r) > tol);
+        if (isempty (nz))
+          x = a;
+          break;
+        else
+          r = r(nz(1):length(r));
+        endif
+        b = a;
+        a = r / r(1);
+      endwhile
+    endif
+  else
+    print_usage ();
+  endif
+
+endfunction
+
+
+%!test
+%! poly1 = [1 6 11 6]; % (x+1)(x+2)(x+3)
+%! poly2 = [1 3 2]; % (x+1)(x+2)
+%! poly3 = polygcd (poly1, poly2);
+%! assert (poly3, poly2, sqrt (eps))
+
+%!test
+%! assert (polygcd (poly(1:8), poly(3:12)), poly(3:8), sqrt (eps))
+
+%!test
+%! assert (deconv (poly(1:8), polygcd (poly(1:8), poly(3:12))), poly(1:2), sqrt (eps))
+
+%!test
+%! for ii=1:10
+%!   p  = (unique (randn (10, 1)) * 10).';
+%!   p1 = p(3:end);
+%!   p2 = p(1:end-2);
+%!   assert (polygcd (poly (-p1), poly (-p2)), poly (- intersect (p1, p2)), sqrt (eps))
+%! endfor