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comparison scripts/specfun/factor.m @ 5827:1fe78adb91bc

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[project @ 2006-05-22 06:25:14 by jwe]
author jwe
date Mon, 22 May 2006 06:25:14 +0000
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1 ## Copyright (C) 2000 Paul Kienzle
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
7 ## the Free Software Foundation; either version 2, or (at your option)
8 ## any later version.
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
16 ## along with Octave; see the file COPYING. If not, write to the Free
17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
18 ## 02110-1301, USA.
19
20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {@var{p} =} factor (@var{q})
22 ## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q})
23 ##
24 ## Return prime factorization of @var{q}. That is @code{prod (@var{p})
25 ## == @var{q}}. If @code{@var{q} == 1}, returns 1.
26 ##
27 ## With two output arguments, returns the uniques primes @var{p} and
28 ## their mulyiplicities. That is @code{prod (@var{p} .^ @var{n}) ==
29 ## @var{q}).
30 ##
31 ## @end deftypefn
32
33 ## Author: Paul Kienzle
34
35 ## 2002-01-28 Paul Kienzle
36 ## * remove recursion; only check existing primes for multiplicity > 1
37 ## * return multiplicity as suggested by Dirk Laurie
38 ## * add error handling
39
40 function [x, m] = factor (n)
41
42 if (nargin < 1)
43 print_usage ();
44 endif
45
46 if (! isscalar (n) || n != fix (n))
47 error ("factor: n must be a scalar integer");
48 endif
49
50 ## special case of no primes less than sqrt(n)
51 if (n < 4)
52 x = n;
53 m = 1;
54 return;
55 endif
56
57 x = [];
58 ## There is at most one prime greater than sqrt(n), and if it exists,
59 ## it has multiplicity 1, so no need to consider any factors greater
60 ## than sqrt(n) directly. [If there were two factors p1, p2 > sqrt(n),
61 ## then n >= p1*p2 > sqrt(n)*sqrt(n) == n. Contradiction.]
62 p = primes (sqrt (n));
63 while (n > 1)
64 ## find prime factors in remaining n
65 q = n ./ p;
66 p = p (q == fix (q));
67 if (isempty (p))
68 p = n; # can't be reduced further, so n must itself be a prime.
69 endif
70 x = [x, p];
71 ## reduce n
72 n = n / prod (p);
73 endwhile
74 x = sort (x);
75
76 ## determine muliplicity
77 if (nargout > 1)
78 idx = find ([0, x] != [x, 0]);
79 x = x(idx(1:length(idx)-1));
80 m = diff (idx);
81 endif
82
83 endfunction
84
85 ## test:
86 ## assert(factor(1),1);
87 ## for i=2:20
88 ## p = factor(i);
89 ## assert(prod(p),i);
90 ## assert(all(isprime(p)));
91 ## [p,n] = factor(i);
92 ## assert(prod(p.^n),i);
93 ## assert(all([0,p]!=[p,0]));
94 ## end