Mercurial > octave
annotate scripts/specfun/factor.m @ 27978:a4268efb7334
maint: Eliminate single "Author:" lines from code base.
* color-picker.cc, color-picker.h, octave-qscintilla.cc, octave-qscintilla.h,
octave-txt-lexer.cc, octave-txt-lexer.h, balance.cc, kron.cc, lookup.cc,
ls-hdf5.cc, ls-mat5.cc, ls-oct-text.cc, sylvester.cc, tsearch.cc, jit-ir.cc,
jit-ir.h, jit-typeinfo.cc, jit-typeinfo.h, jit-util.cc, jit-util.h, pt-jit.cc,
pt-jit.h, Array-jit.cc, bsxfun.h, url-transfer.cc, url-transfer.h, acosd.m,
acotd.m, acscd.m, asecd.m, asind.m, atand.m, cosd.m, cotd.m, cscd.m, secd.m,
sind.m, tand.m, cart2pol.m, cart2sph.m, curl.m, del2.m, divergence.m, flip.m,
pol2cart.m, randi.m, sortrows.m, sph2cart.m, griddata3.m, griddatan.m,
rectint.m, voronoi.m, dialog.m, guidata.m, guihandles.m, __file_filter__.m,
__fltk_file_filter__.m, __get_funcname__.m, __is_function__.m,
__uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiobject_split_args__.m,
__uiputfile_fltk__.m, uibuttongroup.m, uicontextmenu.m, uicontrol.m,
uigetdir.m, uigetfile.m, uimenu.m, uipanel.m, uipushtool.m, uiputfile.m,
uiresume.m, uitoggletool.m, uitoolbar.m, uiwait.m, doc.m, autumn.m, bone.m,
cmpermute.m, cmunique.m, cool.m, copper.m, cubehelix.m, flag.m, frame2im.m,
hot.m, hsv.m, hsv2rgb.m, im2frame.m, imfinfo.m, imformats.m, iscolormap.m,
jet.m, pink.m, prism.m, __imfinfo__.m, rainbow.m, rgb2hsv.m, spinmap.m,
spring.m, viridis.m, white.m, winter.m, importdata.m, strmatch.m, bandwidth.m,
isbanded.m, isdiag.m, istril.m, istriu.m, krylov.m, linsolve.m, logm.m,
lscov.m, subspace.m, bunzip2.m, compare_versions.m, edit.m, fullfile.m,
getfield.m, gunzip.m, inputParser.m, license.m, nargchk.m, narginchk.m,
nthargout.m, python.m, setfield.m, tar.m, unpack.m, ver.m, zip.m, odeplot.m,
fminbnd.m, fminunc.m, fsolve.m, fzero.m, glpk.m, humps.m, pathdef.m,
savepath.m, diffuse.m, lighting.m, material.m, shading.m, specular.m,
contour.m, ellipsoid.m, isocaps.m, isocolors.m, isonormals.m, isosurface.m,
light.m, pcolor.m, __interp_cube__.m, __marching_cube__.m, __patch__.m,
__stem__.m, reducepatch.m, reducevolume.m, ribbon.m, shrinkfaces.m, slice.m,
stem.m, surf.m, surfl.m, tetramesh.m, waterfall.m, __actual_axis_position__.m,
__next_line_color__.m, allchild.m, figure.m, findall.m, findobj.m, gcf.m,
hggroup.m, isprop.m, ndgrid.m, __add_default_menu__.m, saveas.m,
__splinefit__.m, prefdir.m, preferences.m, profexplore.m, profexport.m,
profile.m, profshow.m, setdiff.m, freqz.m, freqz_plot.m, sinc.m, unwrap.m,
pcr.m, qmr.m, sprandn.m, betaincinv.m, cosint.m, ellipke.m, factor.m,
gammaincinv.m, legendre.m, nchoosek.m, primes.m, invhilb.m, toeplitz.m,
erase.m, mat2str.m, strtrim.m, validatestring.m, fail.m, compare_plot_demos.m,
dump_demos.m, html_compare_plot_demos.m, addtodate.m, datenum.m, jit.tst:
Eliminate single "Author:" lines from code base.
| author | Rik <rik@octave.org> |
|---|---|
| date | Tue, 21 Jan 2020 12:53:13 -0800 |
| parents | bd51beb6205e |
| children | de5f2f9a64ff 0a5b15007766 |
| rev | line source |
|---|---|
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1 ######################################################################## |
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2 ## |
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3 ## Copyright (C) 2000-2020 The Octave Project Developers |
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4 ## |
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5 ## See the file COPYRIGHT.md in the top-level directory of this |
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6 ## distribution or <https://octave.org/copyright/>. |
| 5827 | 7 ## |
| 8 ## This file is part of Octave. | |
| 9 ## | |
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10 ## Octave is free software: you can redistribute it and/or modify it |
| 5827 | 11 ## under the terms of the GNU General Public License as published by |
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12 ## the Free Software Foundation, either version 3 of the License, or |
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13 ## (at your option) any later version. |
| 5827 | 14 ## |
| 15 ## Octave is distributed in the hope that it will be useful, but | |
| 16 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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18 ## GNU General Public License for more details. |
| 5827 | 19 ## |
| 20 ## You should have received a copy of the GNU General Public License | |
| 7016 | 21 ## along with Octave; see the file COPYING. If not, see |
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22 ## <https://www.gnu.org/licenses/>. |
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23 ## |
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24 ######################################################################## |
| 5827 | 25 |
| 26 ## -*- texinfo -*- | |
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27 ## @deftypefn {} {@var{pf} =} factor (@var{q}) |
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28 ## @deftypefnx {} {[@var{pf}, @var{n}] =} factor (@var{q}) |
| 19097 | 29 ## Return the prime factorization of @var{q}. |
| 5827 | 30 ## |
| 19097 | 31 ## The prime factorization is defined as @code{prod (@var{pf}) == @var{q}} |
| 32 ## where every element of @var{pf} is a prime number. If @code{@var{q} == 1}, | |
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33 ## return 1. The output @var{pf} is of the same numeric class as the input. |
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34 ## |
| 19097 | 35 ## With two output arguments, return the unique prime factors @var{pf} and |
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36 ## their multiplicities. That is, |
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37 ## @code{prod (@var{pf} .^ @var{n}) == @var{q}}. |
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38 ## |
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39 ## Implementation Note: The input @var{q} must be less than @code{flintmax} |
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40 ## (9.0072e+15) in order to factor correctly. |
| 19097 | 41 ## @seealso{gcd, lcm, isprime, primes} |
| 5827 | 42 ## @end deftypefn |
| 43 | |
| 19097 | 44 function [pf, n] = factor (q) |
| 5827 | 45 |
| 19097 | 46 if (nargin != 1) |
| 5827 | 47 print_usage (); |
| 48 endif | |
| 49 | |
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50 if (! isscalar (q) || ! isreal (q) || q < 0 || q != fix (q)) |
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51 error ("factor: Q must be a real non-negative integer"); |
| 5827 | 52 endif |
| 53 | |
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54 ## Special case of no primes less than sqrt(q). |
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55 if (q < 4) |
| 19097 | 56 pf = q; |
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57 n = 1; |
| 5827 | 58 return; |
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59 endif |
| 5827 | 60 |
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61 cls = class (q); # store class |
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62 q = double (q); # internal algorithm relies on numbers being doubles. |
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63 qorig = q; |
| 19097 | 64 pf = []; |
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65 ## There is at most one prime greater than sqrt(q), and if it exists, |
| 5827 | 66 ## it has multiplicity 1, so no need to consider any factors greater |
| 19097 | 67 ## than sqrt(q) directly. [If there were two factors p1, p2 > sqrt(q), |
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68 ## then q >= p1*p2 > sqrt(q)*sqrt(q) == q. Contradiction.] |
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69 p = primes (sqrt (q)); |
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70 while (q > 1) |
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71 ## Find prime factors in remaining q. |
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72 p = p(rem (q, p) == 0); |
| 5827 | 73 if (isempty (p)) |
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74 ## Can't be reduced further, so q must itself be a prime. |
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75 p = q; |
| 5827 | 76 endif |
| 19097 | 77 pf = [pf, p]; |
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78 ## Reduce q. |
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79 q /= prod (p); |
| 5827 | 80 endwhile |
| 19097 | 81 pf = sort (pf); |
| 5827 | 82 |
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83 ## Verify algorithm was successful |
| 19097 | 84 q = prod (pf); |
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85 if (q != qorig) |
| 19097 | 86 error ("factor: Q too large to factor"); |
| 20486 | 87 elseif (q >= flintmax ()) |
| 19097 | 88 warning ("factor: Q too large. Answer is unreliable"); |
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89 endif |
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90 |
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91 ## Determine multiplicity. |
| 5827 | 92 if (nargout > 1) |
| 19097 | 93 idx = find ([0, pf] != [pf, 0]); |
| 94 pf = pf(idx(1:length (idx)-1)); | |
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95 n = diff (idx); |
| 5827 | 96 endif |
| 97 | |
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98 ## Restore class of input |
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99 pf = feval (cls, pf); |
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100 |
| 5827 | 101 endfunction |
| 102 | |
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103 |
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104 %!assert (factor (1), 1) |
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105 %!test |
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106 %! for i = 2:20 |
| 19097 | 107 %! pf = factor (i); |
| 108 %! assert (prod (pf), i); | |
| 109 %! assert (all (isprime (pf))); | |
| 110 %! [pf, n] = factor (i); | |
| 111 %! assert (prod (pf.^n), i); | |
| 112 %! assert (all ([0,pf] != [pf,0])); | |
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113 %! endfor |
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114 |
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115 %!assert (factor (uint8 (8)), uint8 ([2 2 2])) |
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116 %!assert (factor (single (8)), single ([2 2 2])) |
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117 %!test |
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118 %! [pf, n] = factor (int16 (8)); |
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119 %! assert (pf, int16 (2)); |
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120 %! assert (n, double (3)); |
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121 |
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122 ## Test input validation |
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123 %!error factor () |
| 19097 | 124 %!error factor (1,2) |
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125 %!error <Q must be a real non-negative integer> factor (6i) |
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126 %!error <Q must be a real non-negative integer> factor ([1,2]) |
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127 %!error <Q must be a real non-negative integer> factor (1.5) |
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128 %!error <Q must be a real non-negative integer> factor (-20) |