update packages

[CreaPhase.git] / octave_packages / m / specfun / factor.m

diff --git a/octave_packages/m/specfun/factor.m b/octave_packages/m/specfun/factor.m
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+## Copyright (C) 2000-2012 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 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- 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}} and every element of @var{p} is a prime
+## number.  If @code{@var{q} == 1}, return 1.
+##
+## With two output arguments, return the unique primes @var{p} and
+## their multiplicities.  That is, @code{prod (@var{p} .^ @var{n}) ==
+## @var{q}}.
+## @seealso{gcd, lcm}
+## @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, n] = factor (q)
+
+  if (nargin < 1)
+    print_usage ();
+  endif
+
+  if (! isscalar (q) || q != fix (q))
+    error ("factor: Q must be a scalar integer");
+  endif
+
+  ## Special case of no primes less than sqrt(q).
+  if (q < 4)
+    x = q;
+    n = 1;
+    return;
+  endif
+
+  x = [];
+  ## 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
+    x = [x, p];
+    ## Reduce q.
+    q = q / prod (p);
+  endwhile
+  x = sort (x);
+
+  ## Determine muliplicity.
+  if (nargout > 1)
+    idx = find ([0, x] != [x, 0]);
+    x = x(idx(1:length(idx)-1));
+    n = 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]));
+%!  endfor
+