annotate scripts/polynomial/polygcd.m @ 14868:5d3a684236b0

maint: Use Octave coding conventions for cuddling parentheses in scripts directory * lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m, colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m, int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m, __isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m, rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m, inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m, gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m, ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m, compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m, getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m, __xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m, fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m, copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m, installed_packages.m, is_architecture_dependent.m, load_package_dirs.m, print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m, allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m, comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m, fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, print.m, __add_datasource__.m, __add_default_menu__.m, __axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m, __errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m, __ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m, __go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m, __stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m, surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m, mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m, addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m, arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m, hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m, stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m, __sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m, magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m, quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m, bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m, kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m, z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m, strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m, test.m, now.m: Use Octave coding conventions for cuddling parentheses in scripts directory.
author Rik <octave@nomad.inbox5.com>
date Tue, 17 Jul 2012 07:08:39 -0700
parents f3d52523cde1
children d63878346099
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rev   line source
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1 ## Copyright (C) 2000-2012 Paul Kienzle
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{q} =} polygcd (@var{b}, @var{a})
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21 ## @deftypefnx {Function File} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol})
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22 ##
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23 ## Find the greatest common divisor of two polynomials. This is equivalent
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24 ## to the polynomial found by multiplying together all the common roots.
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25 ## Together with deconv, you can reduce a ratio of two polynomials.
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26 ## The tolerance @var{tol} defaults to @code{sqrt (eps)}.
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27 ##
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28 ## @strong{Caution:} This is a numerically unstable algorithm and should not
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29 ## be used on large polynomials.
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30 ##
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31 ## Example code:
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32 ##
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33 ## @example
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34 ## @group
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35 ## polygcd (poly (1:8), poly (3:12)) - poly (3:8)
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36 ## @result{} [ 0, 0, 0, 0, 0, 0, 0 ]
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37 ## deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))) - poly (1:2)
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38 ## @result{} [ 0, 0, 0 ]
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39 ## @end group
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40 ## @end example
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41 ## @seealso{poly, roots, conv, deconv, residue}
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42 ## @end deftypefn
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43
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44 function x = polygcd (b, a, tol)
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45
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46 if (nargin == 2 || nargin == 3)
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47 if (nargin == 2)
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48 if (isa (a, "single") || isa (b, "single"))
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49 tol = sqrt (eps ("single"));
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50 else
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51 tol = sqrt (eps);
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52 endif
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53 endif
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54 if (length (a) == 1 || length (b) == 1)
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55 if (a == 0)
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56 x = b;
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57 elseif (b == 0)
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58 x = a;
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59 else
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60 x = 1;
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61 endif
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62 else
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63 a /= a(1);
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64 while (1)
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65 [d, r] = deconv (b, a);
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66 nz = find (abs (r) > tol);
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67 if (isempty (nz))
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68 x = a;
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69 break;
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70 else
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71 r = r(nz(1):length(r));
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72 endif
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73 b = a;
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74 a = r / r(1);
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75 endwhile
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76 endif
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77 else
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78 print_usage ();
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79 endif
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80
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81 endfunction
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83
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84 %!test
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85 %! poly1 = [1 6 11 6]; # (x+1)(x+2)(x+3);
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86 %! poly2 = [1 3 2]; # (x+1)(x+2);
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87 %! poly3 = polygcd (poly1, poly2);
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88 %! assert (poly3, poly2, sqrt (eps));
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89
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90 %!assert (polygcd (poly (1:8), poly (3:12)), poly (3:8), sqrt (eps))
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91 %!assert (deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))), poly (1:2), sqrt (eps))
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92
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93 %!test
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94 %! for ii=1:10
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95 %! p = (unique (randn (10, 1)) * 10).';
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96 %! p1 = p(3:end);
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97 %! p2 = p(1:end-2);
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98 %! assert (polygcd (poly (-p1), poly (-p2)), poly (- intersect (p1, p2)), sqrt (eps));
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99 %! endfor
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100