ICHOOSE

Choose K indices from the set 1:N.

Description

ICHOOSE(N,K) gives all combinations of choosing K indices
from the set 1:N without order and without repetitions.

EXAMPLE:
ind = ichoose(4,2);
v = 'ABCD';
v(ind) % ['AB';'AC';'AD';'BC';'BD';'CD']

ICHOOSE is certainly not unique. Here is a comparison with other codes
using TIMEIT by Steve Eddins. Note that VCHOOSEK is a MEX-code.

f1 = @() nchoosek(1:24,8);
f2 = @() combinator(24,8,'c');
f3 = @() ichoose(24,8);
f4 = @() VChooseK(int8(1:24),8);

timeit(f1) % 16.1 sec (NCHOOSEK by MathWorks)
timeit(f2) % 1.17 sec (COMBINATOR by Matt Fig)
timeit(f3) % 0.110 sec (ICHOOSE by Jonas Lundgren)
timeit(f4) % 0.066 sec (VCHOOSEK by Jan Simon)

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
COMBINATOR -combinations AND permutations, VChooseK

• MATLAB release: MATLAB 7.10 (2010a)

[Jan Simon]

A very nice implementation. The speed difference to Matlab's NCHOOSEK is dramatic.
H1 line, short but descriptive help text, author and date mentioned, check of inputs => 5 stars.

How did you compile VChooseK.c? If I use MSVC2008 the Mex I get these timings (Matlab 2009a, 1.5GHz Pentium-M, WinXP 32):
tic; q=ichoose(24, 8);toc
=> 0.255sec
tic; q=VChooseK(uint8(1:):uint8(24), 8); toc
=> 0.049sec

[Jonas Lundgren]

Jan, thank you for the feedback. The compiler is the one that comes with Matlab 2010a. Sorry if that is a slow one. I rarely use MEX-code. I am fully satisfied if ichoose is five times slower than VChooseK.