MATLAB: Combinations of an arbitrary number of cell arrays

Question

Is there a command or one-line strategy in MATLAB that will return all the combinations of the components of n cell arrays, taken n at a time?

Answer 1

Although I address this in my answer to a related/near duplicate question, I'm posting a different version of my solution here since it appears you want a generalized solution, and my other answer is specific for the case of three input sets. Here's a function that should do what you want for any number of cell array inputs:

function combMat = allcombs(varargin)
  sizeVec = cellfun('prodofsize', varargin);
  indices = fliplr(arrayfun(@(n) {1:n}, sizeVec));
  [indices{:}] = ndgrid(indices{:});
  combMat = cellfun(@(c,i) {reshape(c(i(:)), [], 1)}, ...
                    varargin, fliplr(indices));
  combMat = [combMat{:}];
end

And here's how you would call it:

>> combMat = allcombs(A, B)

combMat = 

    'a1'    'b1'
    'a1'    'b2'
    'a1'    'b3'
    'a2'    'b1'
    'a2'    'b2'
    'a2'    'b3'