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09 Apr 2013 (Updated )

Subset of all possible combinations of a fixed number of elements of a vector (v1.1, june 2013)

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COMBNSUB - subset of all combinations of elements M = COMBNSUB(V,N,IX) returns a subset of all combinations of N elements of the elements in vector V. M has the size numel(IX)-by-N.
The output is the same as the sequence M=COMBN(V,N), M=M(IX,:) but this function avoids generating all possible combinations first. The total number of possible combinations increases exponentially (=numel(V)^N). COMBNSUB is particulary useful when you only need one or a small subset of these combinations at a given time.

      V = 1:5, N = 3, IX = [2 124 21 99]
      M = combnsub(V, N, IX) % returns the 4-by-3 matrix:
      % 1 1 2
      % 5 5 4
      % 1 5 1
      % 4 5 4
      % which are the IXth combinations
      % Check with COMBN
      M2 = combn(V,N) ; isequal(M2(IX,:),M)
      % M2 is a 125-by-3 matrix
[M,I] = COMBN(V,N,IX) also returns the index matrix I so that M = V(I).
V can be an array of numbers, cells or strings. All elements in V are regarded as unique. Values of IX that exceed the total number of possible combinations (numel(V)^N) are saturated to that value.
For empty vectors V, or for N = 0, an empty matrix will be returned.
See also perms, nchoosek


Combn (4.3) inspired this file.

MATLAB release MATLAB 7.14 (R2012a)
Other requirements Should work in most ML releases
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Comments and Ratings (1)
22 Jun 2013 Jan Simon

This is an excellent implementation of a very efficient method. Together with the exhaustive documentation this submission is useful, usable and valuable for the productive work and education. Thanks, Jos!

A tiny simplification: You do not need B(:)', because B is a row vector already.

24 Jun 2013

1.1 - implemented suggestion of Jan; output is now always a row vector

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