Mercurial > octave
view scripts/polynomial/polygcd.m @ 31237:e3016248ca5d
uifigure.m: Call set () only if varargin is not empty (bug #63088)
* uifigure.m: Call set () only if varargin is not empty.
author | John Donoghue <john.donoghue@ieee.org> |
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date | Wed, 21 Sep 2022 09:55:32 -0400 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2000-2022 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{q} =} polygcd (@var{b}, @var{a}) ## @deftypefnx {} {@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) print_usage (); endif if (nargin == 2) if (isa (a, "single") || isa (b, "single")) tol = sqrt (eps ("single")); else tol = sqrt (eps); endif endif ## FIXME: No input validation of tol if it was user-supplied 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 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)); %!assert (polygcd (poly (1:8), poly (3:12)), poly (3:8), sqrt (eps)) %!assert (deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))), %! poly (1:2), sqrt (eps)) %!test %! for ii=1:100 %! ## Exhibits numerical problems for multipliers of ~4 and greater. %! p = (unique (randn (10, 1)) * 3).'; %! p1 = p(3:end); %! p2 = p(1:end-2); %! assert (polygcd (poly (-p1), poly (-p2)), %! poly (- intersect (p1, p2)), sqrt (eps)); %! endfor