Generate a matrix containing all combinations of elements taken from n vectors

Question

This question pops up quite often in one form or another (see for example here or here). So I thought I\'d present it in a general form, and provide an answer which might se

Answer 1

A little bit simpler ... if you have the Neural Network toolbox you can simply use combvec:

vectors = {[1 2], [3 6 9], [10 20]};
combs = combvec(vectors{:}).' % Use cells as arguments

which returns a matrix in a slightly different order:

combs =

     1     3    10
     2     3    10
     1     6    10
     2     6    10
     1     9    10
     2     9    10
     1     3    20
     2     3    20
     1     6    20
     2     6    20
     1     9    20
     2     9    20

If you want the matrix that is in the question, you can use sortrows:

combs = sortrows(combvec(vectors{:}).')
% Or equivalently as per @LuisMendo in the comments: 
% combs = fliplr(combvec(vectors{end:-1:1}).') 

which gives

combs =

     1     3    10
     1     3    20
     1     6    10
     1     6    20
     1     9    10
     1     9    20
     2     3    10
     2     3    20
     2     6    10
     2     6    20
     2     9    10
     2     9    20

If you look at the internals of combvec (type edit combvec in the command window), you'll see that it uses different code than @LuisMendo's answer. I can't say which is more efficient overall.

If you happen to have a matrix whose rows are akin to the earlier cell array you can use:

vectors = [1 2;3 6;10 20];
vectors = num2cell(vectors,2);
combs = sortrows(combvec(vectors{:}).')