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annotate scripts/specfun/factor.m @ 19233:0976f9fccbbd

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isprime.m: Verify that input is a real number (bug #43041) * isprime.m: Use isreal() to validate input. Put input checking first in function. Add input validation tests.
author Rik <rik@octave.org>
date Thu, 21 Aug 2014 16:05:09 -0700
parents d63878346099
children e7bffcea619f 446c46af4b42
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rev   line source
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d63878346099 maint: Update copyright notices for release.
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1 ## Copyright (C) 2000-2013 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 the 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 ##
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31 ## Implementation Note: The input @var{q} must not be greater than
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32 ## @code{bitmax} (9.0072e+15) in order to factor correctly.
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33 ## @seealso{gcd, lcm, isprime}
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34 ## @end deftypefn
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35
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36 ## Author: Paul Kienzle
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37
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38 ## 2002-01-28 Paul Kienzle
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39 ## * remove recursion; only check existing primes for multiplicity > 1
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40 ## * return multiplicity as suggested by Dirk Laurie
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41 ## * add error handling
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42
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43 function [x, n] = factor (q)
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44
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45 if (nargin < 1)
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46 print_usage ();
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47 endif
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48
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49 if (! isscalar (q) || q != fix (q))
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50 error ("factor: Q must be a scalar integer");
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51 endif
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52
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53 ## Special case of no primes less than sqrt(q).
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54 if (q < 4)
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55 x = q;
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56 n = 1;
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57 return;
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58 endif
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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;
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62 x = [];
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63 ## There is at most one prime greater than sqrt(q), and if it exists,
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64 ## it has multiplicity 1, so no need to consider any factors greater
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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);
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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;
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74 endif
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75 x = [x, p];
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76 ## Reduce q.
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77 q /= prod (p);
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78 endwhile
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79 x = sort (x);
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80
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81 ## Verify algorithm was succesful
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82 q = prod (x);
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83 if (q != qorig)
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84 error ("factor: Input Q too large to factor");
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85 elseif (q > bitmax)
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86 warning ("factor: Input Q too large. Answer is unreliable");
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87 endif
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88
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89 ## Determine muliplicity.
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90 if (nargout > 1)
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91 idx = find ([0, x] != [x, 0]);
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92 x = x(idx(1:length (idx)-1));
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93 n = diff (idx);
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94 endif
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95
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96 endfunction
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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
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102 %! p = factor (i);
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103 %! assert (prod (p), i);
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104 %! assert (all (isprime (p)));
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105 %! [p,n] = factor (i);
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106 %! assert (prod (p.^n), i);
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107 %! assert (all ([0,p] != [p,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 ()
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112 %!error <Q must be a scalar integer> factor ([1,2])
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113 %!error <Q must be a scalar integer> factor (1.5)
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114