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VChooseKRO

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VChooseKRO

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Choose K elements from a vector with repetitions and order [MEX]

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Description

VChooseKRO(V, K) creates a matrix, which rows are all permutations created by choosing K elements of the vector V with order and with repetitions.

INPUT:
   V: Array of class DOUBLE, SINGLE, (U)INT8/16/32/64, LOGICAL, CHAR.
      Prefer (U)INT8 or (U)INT16 for speed.
   K: Number of elements to choose.

OUTPUT:
  Y: Matrix of size [NUMEL(V)^K, K].
    Y has the same class as the input V.

EXAMPLES:
   Choose 2 elements from [1,2,3]:
     VChooseKRO(1:3, 2) ==> [1,1; 1,2; 1,3; 2,1; 2,2; 2,3; 3,1; 3,2; 3,3]
   For speed cast the input to integer types if possible:
     Y = double(VChooseKRO(int16(1:1000), 2));
   is faster than:
     Y = VChooseKRO(1:1000, 2);
   To get the permutations of cell arrays, permute the index:
     C = {'a', 'b', 'c', 'd'};
     C2 = C(VChooseKRO(1:4, 2))
     ==> C2 = {'a', 'b'; 'a', 'c'; 'a', 'd'; 'b', 'c'; 'b', 'd'; 'c', 'd'}

This MEX version is faster than NPERMUTEK and the more general COMBINATOR of Matt Fig: ~8 times for small arrays, ~2 times for (N=2000, K=2), ~10 times for (N=2, K=16, Class=INT8). COMBN of Jos is again slower than Matt's functions and it does not handle INT classes. See screen shot.

Tested: Matlab 6.5, 7.7, 7.8, WinXP, Compilers: BCC5.5, LCC2.4/3.8, Open Watcom 1.8
The unit-test TestVChooseKRO should be called after compiling. It compares the speed of VChooseKRO with COMBN, NPERMUTEK and COMBINATOR, if these files are found in the path.

See also: VChooseK (no repetitions, no order):
  http://www.mathworks.com/matlabcentral/fileexchange/26190

I'd appreciate suggestions for improvements and bug reports sent through email - thanks.

Acknowledgements

Combn (4.3), N Permute K, and Combinator Combinations And Permutations inspired this file.

This file inspired V Choose Ko.

MATLAB release MATLAB 7.8 (R2009a)
Other requirements Precompiled mex: http://www.n-simon.de/mex
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