Mercurial > octave-antonio
view scripts/polynomial/polygcd.m @ 20165:f1d0f506ee78 stable
doc: Update more docstrings to have one sentence summary as first line.
Reviewed optimization, polynomial, signal script directories.
* scripts/optimization/fminbnd.m, scripts/optimization/fminsearch.m,
scripts/optimization/fminunc.m, scripts/optimization/fsolve.m,
scripts/optimization/fzero.m, scripts/optimization/glpk.m,
scripts/optimization/lsqnonneg.m, scripts/optimization/pqpnonneg.m,
scripts/optimization/qp.m, scripts/optimization/sqp.m,
scripts/polynomial/compan.m, scripts/polynomial/mkpp.m,
scripts/polynomial/mpoles.m, scripts/polynomial/pchip.m,
scripts/polynomial/poly.m, scripts/polynomial/polyaffine.m,
scripts/polynomial/polyder.m, scripts/polynomial/polyeig.m,
scripts/polynomial/polyfit.m, scripts/polynomial/polygcd.m,
scripts/polynomial/polyint.m, scripts/polynomial/polyout.m,
scripts/polynomial/polyval.m, scripts/polynomial/ppder.m,
scripts/polynomial/ppint.m, scripts/polynomial/ppjumps.m,
scripts/polynomial/ppval.m, scripts/polynomial/residue.m,
scripts/polynomial/roots.m, scripts/polynomial/spline.m,
scripts/polynomial/splinefit.m, scripts/polynomial/unmkpp.m,
scripts/signal/arch_fit.m, scripts/signal/arch_rnd.m,
scripts/signal/arma_rnd.m, scripts/signal/autoreg_matrix.m,
scripts/signal/bartlett.m, scripts/signal/blackman.m, scripts/signal/detrend.m,
scripts/signal/diffpara.m, scripts/signal/durbinlevinson.m,
scripts/signal/fftconv.m, scripts/signal/fftfilt.m, scripts/signal/fftshift.m,
scripts/signal/filter2.m, scripts/signal/freqz.m, scripts/signal/hamming.m,
scripts/signal/hanning.m, scripts/signal/hurst.m, scripts/signal/ifftshift.m,
scripts/signal/periodogram.m, scripts/signal/sinc.m, scripts/signal/sinetone.m,
scripts/signal/sinewave.m, scripts/signal/spectral_adf.m,
scripts/signal/spectral_xdf.m, scripts/signal/spencer.m, scripts/signal/stft.m,
scripts/signal/synthesis.m, scripts/signal/unwrap.m,
scripts/signal/yulewalker.m:
Update more docstrings to have one sentence summary as first line.
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 May 2015 21:50:57 -0700 |
parents | 4197fc428c7d |
children |
line wrap: on
line source
## Copyright (C) 2000-2015 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)); %!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