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

Question

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

Answer 1

This late answers provides two additional solutions, where the second is the solution (in my opinion) and an improvement on Amro's answer solution with ndgrid by applying MATLAB's powerful comma-separated lists instead of cell arrays for high performance,

1. If you have the Neural Network Toolbox: use combvec
2. If you do not have the toolbox, as is usually the case: below is another way to generalize the Cartesian product for any number of sets.

Just as Amro did in his answer, the comma-separated lists syntax (v{:}) supplies both the inputs and outputs of ndgrid. The difference (fourth line) is that it avoids cellfun and cell2mat by applying comma-separated lists, again, now as the inputs to cat:

N = numel(a);
v = cell(N,1);
[v{:}] = ndgrid(a{:});
res = reshape(cat(N+1,v{:}),[],N);

The use of cat and reshape cuts execution time almost in half. This approach was demonstrated in my answer to an different question, and more formally by Luis Mendo.