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annotate scripts/specfun/factor.m @ 16163:34898b3fc32a

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build: Fix unused variable warning in compiling input.cc. * libinterp/interpfcn/input.cc(get_user_input): Remove unused len variable.
author Rik <rik@octave.org>
date Thu, 28 Feb 2013 12:07:23 -0800
parents 5d3a684236b0
children e48f5a52e838
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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{p} =} factor (@var{q})
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21 ## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q})
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22 ##
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23 ## Return prime factorization of @var{q}. That is,
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24 ## @code{prod (@var{p}) == @var{q}} and every element of @var{p} is a prime
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25 ## number. If @code{@var{q} == 1}, return 1.
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26 ##
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27 ## With two output arguments, return the unique primes @var{p} and
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28 ## their multiplicities. That is, @code{prod (@var{p} .^ @var{n}) ==
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29 ## @var{q}}.
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30 ## @seealso{gcd, lcm}
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31 ## @end deftypefn
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32
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33 ## Author: Paul Kienzle
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34
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35 ## 2002-01-28 Paul Kienzle
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36 ## * remove recursion; only check existing primes for multiplicity > 1
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37 ## * return multiplicity as suggested by Dirk Laurie
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38 ## * add error handling
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39
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40 function [x, n] = factor (q)
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41
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42 if (nargin < 1)
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43 print_usage ();
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44 endif
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45
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46 if (! isscalar (q) || q != fix (q))
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47 error ("factor: Q must be a scalar integer");
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48 endif
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49
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50 ## Special case of no primes less than sqrt(q).
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51 if (q < 4)
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52 x = q;
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53 n = 1;
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54 return;
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55 endif
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56
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57 x = [];
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58 ## There is at most one prime greater than sqrt(q), and if it exists,
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59 ## it has multiplicity 1, so no need to consider any factors greater
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60 ## than sqrt(q) directly. [If there were two factors p1, p2 > sqrt(q),
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61 ## then q >= p1*p2 > sqrt(q)*sqrt(q) == q. Contradiction.]
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62 p = primes (sqrt (q));
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63 while (q > 1)
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64 ## Find prime factors in remaining q.
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65 p = p (rem (q, p) == 0);
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66 if (isempty (p))
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67 ## Can't be reduced further, so q must itself be a prime.
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68 p = q;
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69 endif
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70 x = [x, p];
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71 ## Reduce q.
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72 q = q / prod (p);
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73 endwhile
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74 x = sort (x);
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75
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76 ## Determine muliplicity.
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77 if (nargout > 1)
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78 idx = find ([0, x] != [x, 0]);
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79 x = x(idx(1:length (idx)-1));
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80 n = diff (idx);
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81 endif
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82
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83 endfunction
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84
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85
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86 %!assert (factor (1), 1)
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87 %!test
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88 %! for i = 2:20
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89 %! p = factor (i);
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90 %! assert (prod (p), i);
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91 %! assert (all (isprime (p)));
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92 %! [p,n] = factor (i);
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93 %! assert (prod (p.^n), i);
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94 %! assert (all ([0,p] != [p,0]));
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95 %! endfor
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96