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matlabcombinatoricscartesian-product

Generate all possible combinations of the elements of some vectors (Cartesian product)

I would like to generate all the possible combinations of the elements of a given number of vectors.

For example, for [1 2], [1 2] and [4 5] I want to generate the elements:

[1 1 4; 1 1 5; 1 2 4; 1 2 5; 2 1 4; 2 1 5; 2 2 4; 2 2 5]

The problem is that I don't know the number of vectors for which I need to calculate the combinations. There might be 3 as in this case, or there may be 10, and I need a generalization. Can you please help me to this in MATLAB? Is there already a predefined function that can do this task?

Solution

  • Try ALLCOMB function at FileExchange.

    If you store you vectors in a cell array, you can run it like this:

    a = {[1 2], [1 2], [4 5]};
allcomb(a{:})
ans =

     1     1     4
     1     1     5
     1     2     4
     1     2     5
     2     1     4
     2     1     5
     2     2     4
     2     2     5