Mercurial > octave
diff scripts/specfun/factor.m @ 5827:1fe78adb91bc
[project @ 2006-05-22 06:25:14 by jwe]
author | jwe |
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date | Mon, 22 May 2006 06:25:14 +0000 |
parents | |
children | 7fad1fad19e1 |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/scripts/specfun/factor.m Mon May 22 06:25:14 2006 +0000 @@ -0,0 +1,94 @@ +## Copyright (C) 2000 Paul Kienzle +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 2, or (at your option) +## any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, write to the Free +## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA +## 02110-1301, USA. + +## -*- texinfo -*- +## @deftypefn {Function File} {@var{p} =} factor (@var{q}) +## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q}) +## +## Return prime factorization of @var{q}. That is @code{prod (@var{p}) +## == @var{q}}. If @code{@var{q} == 1}, returns 1. +## +## With two output arguments, returns the uniques primes @var{p} and +## their mulyiplicities. That is @code{prod (@var{p} .^ @var{n}) == +## @var{q}). +## +## @end deftypefn + +## Author: Paul Kienzle + +## 2002-01-28 Paul Kienzle +## * remove recursion; only check existing primes for multiplicity > 1 +## * return multiplicity as suggested by Dirk Laurie +## * add error handling + +function [x, m] = factor (n) + + if (nargin < 1) + print_usage (); + endif + + if (! isscalar (n) || n != fix (n)) + error ("factor: n must be a scalar integer"); + endif + + ## special case of no primes less than sqrt(n) + if (n < 4) + x = n; + m = 1; + return; + endif + + x = []; + ## There is at most one prime greater than sqrt(n), and if it exists, + ## it has multiplicity 1, so no need to consider any factors greater + ## than sqrt(n) directly. [If there were two factors p1, p2 > sqrt(n), + ## then n >= p1*p2 > sqrt(n)*sqrt(n) == n. Contradiction.] + p = primes (sqrt (n)); + while (n > 1) + ## find prime factors in remaining n + q = n ./ p; + p = p (q == fix (q)); + if (isempty (p)) + p = n; # can't be reduced further, so n must itself be a prime. + endif + x = [x, p]; + ## reduce n + n = n / prod (p); + endwhile + x = sort (x); + + ## determine muliplicity + if (nargout > 1) + idx = find ([0, x] != [x, 0]); + x = x(idx(1:length(idx)-1)); + m = diff (idx); + endif + +endfunction + +## test: +## assert(factor(1),1); +## for i=2:20 +## p = factor(i); +## assert(prod(p),i); +## assert(all(isprime(p))); +## [p,n] = factor(i); +## assert(prod(p.^n),i); +## assert(all([0,p]!=[p,0])); +## end