Mercurial > hg > octave-lojdl
changeset 14090:281ecc6fb431 stable
nchoosek.m: Update documentation, fix input validation, add more %!tests
* nchoosek.m: Update documentation, fix input validation, add more %!tests
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Wed, 21 Dec 2011 16:53:43 -0800 |
parents | 9c36b3b7c818 |
children | c3ea07298af4 |
files | scripts/specfun/nchoosek.m |
diffstat | 1 files changed, 60 insertions(+), 21 deletions(-) [+] |
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--- a/scripts/specfun/nchoosek.m +++ b/scripts/specfun/nchoosek.m @@ -18,11 +18,13 @@ ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- -## @deftypefn {Function File} {@var{c} =} nchoosek (@var{n}, @var{k}) +## @deftypefn {Function File} {@var{c} =} nchoosek (@var{n}, @var{k}) +## @deftypefnx {Function File} {@var{c} =} nchoosek (@var{set}, @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 +## Compute the binomial coefficient or all combinations of a set of items. +## +## If @var{n} is a scalar then calculate the binomial coefficient +## of @var{n} and @var{k} which is defined as ## @tex ## $$ ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} @@ -42,17 +44,43 @@ ## @end example ## ## @end ifnottex +## @noindent +## This is the number of combinations of @var{n} items taken in groups of +## size @var{k}. ## -## 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}]}. +## If the first argument is a vector, @var{set}, then generate all combinations +## of the elements of @var{set}, taken @var{k} at a time, with one row per +## combination. The result @var{c} has @var{k} columns and +## @w{@code{nchoosek (length (@var{set}), @var{k})}} rows. +## +## For example: +## +## How many ways can three items be grouped into pairs? ## -## @code{nchoosek} works only for non-negative integer arguments; use -## @code{bincoeff} for non-integer scalar arguments and for using vector -## arguments to compute many coefficients at once. +## @example +## @group +## nchoosek (3, 2) +## @result{} 3 +## @end group +## @end example +## +## What are the possible pairs? ## -## @seealso{bincoeff} +## @example +## @group +## nchoosek (1:3, 2) +## @result{} 1 2 +## 1 3 +## 2 3 +## @end group +## @end example +## +## @code{nchoosek} works only for non-negative, integer arguments. Use +## @code{bincoeff} for non-integer and negative scalar arguments, or for +## computing many binomial coefficients at once with vector inputs for @var{n} +## or @var{k}. +## +## @seealso{bincoeff, perms} ## @end deftypefn ## Author: Rolf Fabian <fabian@tu-cottbus.de> @@ -62,12 +90,12 @@ function A = nchoosek (v, k) if (nargin != 2 - || !isnumeric(k) || !isnumeric(v) - || !isscalar(k) || (!isscalar(v) && !isvector(v))) + || !isnumeric (k) || !isnumeric (v) + || !isscalar (k) || ! (isscalar (v) || isvector (v))) print_usage (); endif - if ((isscalar(v) && v < k) || k < 0 - || k != round(k) || any (v < 0 || v != round(v))) + if (k < 0 || k != fix (k) + || (isscalar (v) && (v < k || v < 0 || v != fix (v)))) error ("nchoosek: args are non-negative integers with V not less than K"); endif @@ -111,8 +139,19 @@ endif endfunction -%!warning (nchoosek(100,45)); -%!error (nchoosek(100,45.5)); -%!error (nchoosek(100,145)); -%!assert (nchoosek(80,10), bincoeff(80,10)) -%!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]) + +%!assert (nchoosek (80,10), bincoeff (80,10)) +%!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]) + +%% Test input validation +%!warning nchoosek (100,45); +%!error nchoosek ("100", 45) +%!error nchoosek (100, "45") +%!error nchoosek (100, ones (2,2)) +%!error nchoosek (repmat (100, [2 2]), 45) +%!error nchoosek (100, -45) +%!error nchoosek (100, 45.5) +%!error nchoosek (100, 145) +%!error nchoosek (-100, 45) +%!error nchoosek (100.5, 45) +