Mercurial > hg > octave-lyh
annotate scripts/specfun/factor.m @ 9051:1bf0ce0930be
Grammar check TexInfo in all .m files
Cleanup documentation sources to follow a few consistent rules.
Spellcheck was NOT done. (but will be in another changeset)
| author | Rik <rdrider0-list@yahoo.com> |
|---|---|
| date | Fri, 27 Mar 2009 22:31:03 -0700 |
| parents | eb63fbe60fab |
| children | c1fff751b5a8 |
| rev | line source |
|---|---|
| 8920 | 1 ## Copyright (C) 2000, 2006, 2007, 2009 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 -*- | |
| 20 ## @deftypefn {Function File} {@var{p} =} factor (@var{q}) | |
| 21 ## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q}) | |
| 22 ## | |
|
9051
1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
23 ## Return prime factorization of @var{q}. That is @code{prod (@var{p}) |
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1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
24 ## == @var{q}}. If @code{@var{q} == 1}, returns 1. |
| 5827 | 25 ## |
| 7001 | 26 ## With two output arguments, returns the unique primes @var{p} and |
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9051
1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
27 ## their multiplicities. That is @code{prod (@var{p} .^ @var{n}) == |
| 6248 | 28 ## @var{q}}. |
| 5827 | 29 ## |
| 30 ## @end deftypefn | |
| 31 | |
| 32 ## Author: Paul Kienzle | |
| 33 | |
| 34 ## 2002-01-28 Paul Kienzle | |
| 35 ## * remove recursion; only check existing primes for multiplicity > 1 | |
| 36 ## * return multiplicity as suggested by Dirk Laurie | |
| 37 ## * add error handling | |
| 38 | |
| 39 function [x, m] = factor (n) | |
| 40 | |
| 41 if (nargin < 1) | |
| 42 print_usage (); | |
| 43 endif | |
| 44 | |
| 45 if (! isscalar (n) || n != fix (n)) | |
| 46 error ("factor: n must be a scalar integer"); | |
| 47 endif | |
| 48 | |
| 8506 | 49 ## Special case of no primes less than sqrt(n). |
| 5827 | 50 if (n < 4) |
| 51 x = n; | |
| 52 m = 1; | |
| 53 return; | |
| 54 endif | |
| 55 | |
| 56 x = []; | |
| 57 ## There is at most one prime greater than sqrt(n), and if it exists, | |
| 58 ## it has multiplicity 1, so no need to consider any factors greater | |
| 59 ## than sqrt(n) directly. [If there were two factors p1, p2 > sqrt(n), | |
| 60 ## then n >= p1*p2 > sqrt(n)*sqrt(n) == n. Contradiction.] | |
| 61 p = primes (sqrt (n)); | |
| 62 while (n > 1) | |
| 8506 | 63 ## Find prime factors in remaining n. |
| 5827 | 64 q = n ./ p; |
| 65 p = p (q == fix (q)); | |
| 66 if (isempty (p)) | |
| 8506 | 67 ## Can't be reduced further, so n must itself be a prime. |
| 68 p = n; | |
| 5827 | 69 endif |
| 70 x = [x, p]; | |
| 8506 | 71 ## Reduce n. |
| 5827 | 72 n = n / prod (p); |
| 73 endwhile | |
| 74 x = sort (x); | |
| 75 | |
| 8506 | 76 ## Determine muliplicity. |
| 5827 | 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 |