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nchoosek: a better solution
From: |
Francesco Potortì |
Subject: |
nchoosek: a better solution |
Date: |
Tue, 25 Nov 2008 20:12:00 +0100 |
I think I have found a better solution for nchoosek. Here I use a
subfunction. I also added two tests.
I can make a new changeset, if people think this solution is better as I
do. How do I convince Mercurial to make a changeset against the
previous version?
===File /home/pot/gnu/octave/scripts/specfun/nchoosek.m=====
## Copyright (C) 2001, 2006, 2007 Rolf Fabian and 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} address@hidden =} nchoosek (@var{n}, @var{k})
##
## Compute the binomial coefficient or all combinations of @var{n}.
## If @var{n} is a scalar then, calculate the binomial coefficient
## of @var{n} and @var{k}, defined as
##
## @iftex
## @tex
## $$
## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
## = {n! \over k! (n-k)!}
## $$
## @end tex
## @end iftex
## @ifinfo
##
## @example
## @group
## / \
## | n | n (n-1) (n-2) ... (n-k+1) n!
## | | = ------------------------- = ---------
## | k | k! k! (n-k)!
## \ /
## @end group
## @end example
## @end ifinfo
##
## If @var{n} is a vector generate all combinations of the elements
## of @var{n}, taken @var{k} at a time, one row per combination. The
## resulting @var{c} has size @code{[nchoosek (length (@var{n}),
## @var{k}), @var{k}]}.
##
## @seealso{bincoeff}
## @end deftypefn
## Author: Rolf Fabian <address@hidden>
## Author: Paul Kienzle <address@hidden>
## FIXME -- This function is identical to bincoeff for scalar
## values, and so should probably be combined with bincoeff.
function A = nchoosek (v, k)
if (nargin != 2)
print_usage ();
endif
n = length (v);
if (n == 1)
A = round (exp (sum (log (k+1:v)) - sum (log (2:v-k))));
elseif (k == 0)
A = [];
elseif (k == 1)
A = v(:);
elseif (k == n)
A = v(:).';
else
oldmax = max_recursion_depth (2*n);
A = nck (v, k);
max_recursion_depth (oldmax);
endif
endfunction
function A = nck (v, k)
n = length (v);
if (n == 1 || k < 2 || k == n)
A = nchoosek (v, k);
else
m = nchoosek (n-1, k-1);
A = [v(1)*ones(m,1), nck(v(2:n),k-1);
nck(v(2:n), k)];
endif
endfunction
%!assert (nchoosek(100,45), bincoeff(100,45))
%!assert
(nchoosek(1:5,3),[1:3;1,2,4;1,2,5;1,3,4;1,3,5;1,4,5;2:4;2,3,5;2,4,5;3:5])
============================================================
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- nchoosek: a better solution,
Francesco Potortì <=