Mercurial > hg > octave-nkf
annotate scripts/specfun/factor.m @ 19344:0f9c5a15c8fa
doc: Periodic grammarcheck of documentation.
* doc/interpreter/contrib.txi, doc/interpreter/expr.txi,
doc/interpreter/func.txi, doc/interpreter/linalg.txi, doc/interpreter/plot.txi,
libinterp/corefcn/data.cc, libinterp/corefcn/debug.cc,
libinterp/corefcn/graphics.cc, libinterp/corefcn/help.cc,
libinterp/corefcn/load-save.cc, libinterp/corefcn/profiler.cc,
libinterp/corefcn/syscalls.cc, libinterp/corefcn/utils.cc,
libinterp/corefcn/variables.cc, libinterp/dldfcn/__init_fltk__.cc,
scripts/general/deal.m, scripts/help/__gripe_missing_component__.m,
scripts/miscellaneous/desktop.m, scripts/pkg/private/default_prefix.m,
scripts/plot/appearance/__getlegenddata__.m, scripts/plot/util/pan.m,
scripts/plot/util/rotate.m, scripts/plot/util/rotate3d.m,
scripts/plot/util/zoom.m, scripts/signal/periodogram.m,
scripts/specfun/factor.m, scripts/specfun/primes.m,
scripts/statistics/base/lscov.m, scripts/testfun/private/compare_plot_demos.m,
scripts/testfun/private/dump_demos.m,
scripts/testfun/private/html_compare_plot_demos.m, scripts/testfun/test.m:
Periodic grammarcheck of documentation.
| author | Rik <rik@octave.org> |
|---|---|
| date | Mon, 22 Sep 2014 20:46:54 -0700 |
| parents | e7bffcea619f |
| children | 0e1f5a750d00 |
| rev | line source |
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1 ## Copyright (C) 2000-2013 Paul Kienzle |
| 5827 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 5827 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5827 | 18 |
| 19 ## -*- texinfo -*- | |
| 19289 | 20 ## @deftypefn {Function File} {@var{pf} =} factor (@var{q}) |
| 21 ## @deftypefnx {Function File} {[@var{pf}, @var{n}] =} factor (@var{q}) | |
| 22 ## Return the prime factorization of @var{q}. | |
| 5827 | 23 ## |
| 19289 | 24 ## The prime factorization is defined as @code{prod (@var{pf}) == @var{q}} |
| 25 ## where every element of @var{pf} is a prime number. If @code{@var{q} == 1}, | |
| 26 ## return 1. | |
| 27 ## | |
| 28 ## With two output arguments, return the unique prime factors @var{pf} and | |
| 29 ## their multiplicities. That is, @code{prod (@var{pf} .^ @var{n}) == @var{q}}. | |
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30 ## |
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31 ## Implementation Note: The input @var{q} must be less than |
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32 ## @code{bitmax} (9.0072e+15) in order to factor correctly. |
| 19289 | 33 ## @seealso{gcd, lcm, isprime, primes} |
| 5827 | 34 ## @end deftypefn |
| 35 | |
| 36 ## Author: Paul Kienzle | |
| 37 | |
| 38 ## 2002-01-28 Paul Kienzle | |
| 39 ## * remove recursion; only check existing primes for multiplicity > 1 | |
| 40 ## * return multiplicity as suggested by Dirk Laurie | |
| 41 ## * add error handling | |
| 42 | |
| 19289 | 43 function [pf, n] = factor (q) |
| 5827 | 44 |
| 19289 | 45 if (nargin != 1) |
| 5827 | 46 print_usage (); |
| 47 endif | |
| 48 | |
| 19289 | 49 if (! isreal (q) || ! isscalar (q) || q != fix (q)) |
| 50 error ("factor: Q must be a real integer"); | |
| 5827 | 51 endif |
| 52 | |
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53 ## Special case of no primes less than sqrt(q). |
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54 if (q < 4) |
| 19289 | 55 pf = q; |
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56 n = 1; |
| 5827 | 57 return; |
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58 endif |
| 5827 | 59 |
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60 q = double (q); # For the time being, calcs rely on double precision var. |
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61 qorig = q; |
| 19289 | 62 pf = []; |
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63 ## There is at most one prime greater than sqrt(q), and if it exists, |
| 5827 | 64 ## it has multiplicity 1, so no need to consider any factors greater |
| 19289 | 65 ## than sqrt(q) directly. [If there were two factors p1, p2 > sqrt(q), |
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66 ## then q >= p1*p2 > sqrt(q)*sqrt(q) == q. Contradiction.] |
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67 p = primes (sqrt (q)); |
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68 while (q > 1) |
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69 ## Find prime factors in remaining q. |
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70 p = p(rem (q, p) == 0); |
| 5827 | 71 if (isempty (p)) |
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72 ## Can't be reduced further, so q must itself be a prime. |
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73 p = q; |
| 5827 | 74 endif |
| 19289 | 75 pf = [pf, p]; |
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76 ## Reduce q. |
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77 q /= prod (p); |
| 5827 | 78 endwhile |
| 19289 | 79 pf = sort (pf); |
| 5827 | 80 |
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81 ## Verify algorithm was succesful |
| 19289 | 82 q = prod (pf); |
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83 if (q != qorig) |
| 19289 | 84 error ("factor: Q too large to factor"); |
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85 elseif (q > bitmax) |
| 19289 | 86 warning ("factor: Q too large. Answer is unreliable"); |
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87 endif |
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88 |
| 8506 | 89 ## Determine muliplicity. |
| 5827 | 90 if (nargout > 1) |
| 19289 | 91 idx = find ([0, pf] != [pf, 0]); |
| 92 pf = pf(idx(1:length (idx)-1)); | |
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93 n = diff (idx); |
| 5827 | 94 endif |
| 95 | |
| 96 endfunction | |
| 97 | |
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98 |
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99 %!assert (factor (1), 1) |
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100 %!test |
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101 %! for i = 2:20 |
| 19289 | 102 %! pf = factor (i); |
| 103 %! assert (prod (pf), i); | |
| 104 %! assert (all (isprime (pf))); | |
| 105 %! [pf, n] = factor (i); | |
| 106 %! assert (prod (pf.^n), i); | |
| 107 %! assert (all ([0,pf] != [pf,0])); | |
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108 %! endfor |
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109 |
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110 %% Test input validation |
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111 %!error factor () |
| 19289 | 112 %!error factor (1,2) |
| 113 %!error <Q must be a real integer> factor (6i) | |
| 114 %!error <Q must be a real integer> factor ([1,2]) | |
| 115 %!error <Q must be a real integer> factor (1.5) | |
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116 |