Mercurial > octave
view scripts/specfun/factor.m @ 27919:1891570abac8
update Octave Project Developers copyright for the new year
In files that have the "Octave Project Developers" copyright notice,
update for 2020.
author | John W. Eaton <jwe@octave.org> |
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date | Mon, 06 Jan 2020 22:29:51 -0500 |
parents | b442ec6dda5c |
children | bd51beb6205e |
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## Copyright (C) 2000-2020 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this distribution ## or <https://octave.org/COPYRIGHT.html/>. ## ## ## 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 3 of the License, 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, see ## <https://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {} {@var{pf} =} factor (@var{q}) ## @deftypefnx {} {[@var{pf}, @var{n}] =} factor (@var{q}) ## Return the prime factorization of @var{q}. ## ## The prime factorization is defined as @code{prod (@var{pf}) == @var{q}} ## where every element of @var{pf} is a prime number. If @code{@var{q} == 1}, ## return 1. The output @var{pf} is of the same numeric class as the input. ## ## With two output arguments, return the unique prime factors @var{pf} and ## their multiplicities. That is, ## @code{prod (@var{pf} .^ @var{n}) == @var{q}}. ## ## Implementation Note: The input @var{q} must be less than @code{flintmax} ## (9.0072e+15) in order to factor correctly. ## @seealso{gcd, lcm, isprime, primes} ## @end deftypefn ## Author: Paul Kienzle function [pf, n] = factor (q) if (nargin != 1) print_usage (); endif if (! isscalar (q) || ! isreal (q) || q < 0 || q != fix (q)) error ("factor: Q must be a real non-negative integer"); endif ## Special case of no primes less than sqrt(q). if (q < 4) pf = q; n = 1; return; endif cls = class (q); # store class q = double (q); # internal algorithm relies on numbers being doubles. qorig = q; pf = []; ## There is at most one prime greater than sqrt(q), and if it exists, ## it has multiplicity 1, so no need to consider any factors greater ## than sqrt(q) directly. [If there were two factors p1, p2 > sqrt(q), ## then q >= p1*p2 > sqrt(q)*sqrt(q) == q. Contradiction.] p = primes (sqrt (q)); while (q > 1) ## Find prime factors in remaining q. p = p(rem (q, p) == 0); if (isempty (p)) ## Can't be reduced further, so q must itself be a prime. p = q; endif pf = [pf, p]; ## Reduce q. q /= prod (p); endwhile pf = sort (pf); ## Verify algorithm was successful q = prod (pf); if (q != qorig) error ("factor: Q too large to factor"); elseif (q >= flintmax ()) warning ("factor: Q too large. Answer is unreliable"); endif ## Determine multiplicity. if (nargout > 1) idx = find ([0, pf] != [pf, 0]); pf = pf(idx(1:length (idx)-1)); n = diff (idx); endif ## Restore class of input pf = feval (cls, pf); endfunction %!assert (factor (1), 1) %!test %! for i = 2:20 %! pf = factor (i); %! assert (prod (pf), i); %! assert (all (isprime (pf))); %! [pf, n] = factor (i); %! assert (prod (pf.^n), i); %! assert (all ([0,pf] != [pf,0])); %! endfor %!assert (factor (uint8 (8)), uint8 ([2 2 2])) %!assert (factor (single (8)), single ([2 2 2])) %!test %! [pf, n] = factor (int16 (8)); %! assert (pf, int16 (2)); %! assert (n, double (3)); ## Test input validation %!error factor () %!error factor (1,2) %!error <Q must be a real non-negative integer> factor (6i) %!error <Q must be a real non-negative integer> factor ([1,2]) %!error <Q must be a real non-negative integer> factor (1.5) %!error <Q must be a real non-negative integer> factor (-20)