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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 5b49cafe0599
children 050bc580cb60
comparison
equal deleted inserted replaced
14089:9c36b3b7c818 14090:281ecc6fb431
16 ## You should have received a copy of the GNU General Public License 16 ## You should have received a copy of the GNU General Public License
17 ## along with Octave; see the file COPYING. If not, see 17 ## along with Octave; see the file COPYING. If not, see
18 ## <http://www.gnu.org/licenses/>. 18 ## <http://www.gnu.org/licenses/>.
19 19
20 ## -*- texinfo -*- 20 ## -*- texinfo -*-
21 ## @deftypefn {Function File} {@var{c} =} nchoosek (@var{n}, @var{k}) 21 ## @deftypefn {Function File} {@var{c} =} nchoosek (@var{n}, @var{k})
22 ## @deftypefnx {Function File} {@var{c} =} nchoosek (@var{set}, @var{k})
22 ## 23 ##
23 ## Compute the binomial coefficient or all combinations of @var{n}. 24 ## Compute the binomial coefficient or all combinations of a set of items.
24 ## If @var{n} is a scalar then, calculate the binomial coefficient 25 ##
25 ## of @var{n} and @var{k}, defined as 26 ## If @var{n} is a scalar then calculate the binomial coefficient
27 ## of @var{n} and @var{k} which is defined as
26 ## @tex 28 ## @tex
27 ## $$ 29 ## $$
28 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!} 30 ## {n \choose k} = {n (n-1) (n-2) \cdots (n-k+1) \over k!}
29 ## = {n! \over k! (n-k)!} 31 ## = {n! \over k! (n-k)!}
30 ## $$ 32 ## $$
40 ## \ / 42 ## \ /
41 ## @end group 43 ## @end group
42 ## @end example 44 ## @end example
43 ## 45 ##
44 ## @end ifnottex 46 ## @end ifnottex
47 ## @noindent
48 ## This is the number of combinations of @var{n} items taken in groups of
49 ## size @var{k}.
45 ## 50 ##
46 ## If @var{n} is a vector generate all combinations of the elements 51 ## If the first argument is a vector, @var{set}, then generate all combinations
47 ## of @var{n}, taken @var{k} at a time, one row per combination. The 52 ## of the elements of @var{set}, taken @var{k} at a time, with one row per
48 ## resulting @var{c} has size @code{[nchoosek (length (@var{n}), 53 ## combination. The result @var{c} has @var{k} columns and
49 ## @var{k}), @var{k}]}. 54 ## @w{@code{nchoosek (length (@var{set}), @var{k})}} rows.
50 ## 55 ##
51 ## @code{nchoosek} works only for non-negative integer arguments; use 56 ## For example:
52 ## @code{bincoeff} for non-integer scalar arguments and for using vector
53 ## arguments to compute many coefficients at once.
54 ## 57 ##
55 ## @seealso{bincoeff} 58 ## How many ways can three items be grouped into pairs?
59 ##
60 ## @example
61 ## @group
62 ## nchoosek (3, 2)
63 ## @result{} 3
64 ## @end group
65 ## @end example
66 ##
67 ## What are the possible pairs?
68 ##
69 ## @example
70 ## @group
71 ## nchoosek (1:3, 2)
72 ## @result{} 1 2
73 ## 1 3
74 ## 2 3
75 ## @end group
76 ## @end example
77 ##
78 ## @code{nchoosek} works only for non-negative, integer arguments. Use
79 ## @code{bincoeff} for non-integer and negative scalar arguments, or for
80 ## computing many binomial coefficients at once with vector inputs for @var{n}
81 ## or @var{k}.
82 ##
83 ## @seealso{bincoeff, perms}
56 ## @end deftypefn 84 ## @end deftypefn
57 85
58 ## Author: Rolf Fabian <fabian@tu-cottbus.de> 86 ## Author: Rolf Fabian <fabian@tu-cottbus.de>
59 ## Author: Paul Kienzle <pkienzle@users.sf.net> 87 ## Author: Paul Kienzle <pkienzle@users.sf.net>
60 ## Author: Jaroslav Hajek 88 ## Author: Jaroslav Hajek
61 89
62 function A = nchoosek (v, k) 90 function A = nchoosek (v, k)
63 91
64 if (nargin != 2 92 if (nargin != 2
65 || !isnumeric(k) || !isnumeric(v) 93 || !isnumeric (k) || !isnumeric (v)
66 || !isscalar(k) || (!isscalar(v) && !isvector(v))) 94 || !isscalar (k) || ! (isscalar (v) || isvector (v)))
67 print_usage (); 95 print_usage ();
68 endif 96 endif
69 if ((isscalar(v) && v < k) || k < 0 97 if (k < 0 || k != fix (k)
70 || k != round(k) || any (v < 0 || v != round(v))) 98 || (isscalar (v) && (v < k || v < 0 || v != fix (v))))
71 error ("nchoosek: args are non-negative integers with V not less than K"); 99 error ("nchoosek: args are non-negative integers with V not less than K");
72 endif 100 endif
73 101
74 n = length (v); 102 n = length (v);
75 103
109 clear cA b; 137 clear cA b;
110 A = A.'; 138 A = A.';
111 endif 139 endif
112 endfunction 140 endfunction
113 141
114 %!warning (nchoosek(100,45)); 142
115 %!error (nchoosek(100,45.5)); 143 %!assert (nchoosek (80,10), bincoeff (80,10))
116 %!error (nchoosek(100,145)); 144 %!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])
117 %!assert (nchoosek(80,10), bincoeff(80,10)) 145
118 %!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]) 146 %% Test input validation
147 %!warning nchoosek (100,45);
148 %!error nchoosek ("100", 45)
149 %!error nchoosek (100, "45")
150 %!error nchoosek (100, ones (2,2))
151 %!error nchoosek (repmat (100, [2 2]), 45)
152 %!error nchoosek (100, -45)
153 %!error nchoosek (100, 45.5)
154 %!error nchoosek (100, 145)
155 %!error nchoosek (-100, 45)
156 %!error nchoosek (100.5, 45)
157