MATLAB: How to increase the number of inputs and outputs of ndgrid

Question

Dear all,

I am trying to create a matrix of all possible combinations of a set number of vectors. For instance, if I have 3 vectors (got this tip from the forum):

A = [1,2,3];B = [4,5,6];C = [7,8,9]; % For instance

     [ca, cb, cc] = ndgrid(A, B, C);
     combs = [ca(:), cb(:), cc(:)]

Now, if I want all combinations of 4 vectors I would use

     [ca, cb, cc, dd] = ndgrid(A, B, C, D);
     combs = [ca(:), cb(:), cc(:), cd(::)]

I'm wondering if there is a way of automating this by having the number of variables in the inputs and outputs to increase automatically. Tried everything so far.. Please help

Thanks!!

Answer 1

The trick is to use cell arrays and comma-separated lists:

C = {1:3,4:6,7:9};
D = cell(size(C));
[D{:}] = ndgrid(C{:})

Simply define C to have size 1xN or Nx1, where N is the number of inputs (and hence also the outputs).

https://www.mathworks.com/matlabcentral/answers/320713-how-to-operate-on-comma-separated-lists

https://www.mathworks.com/company/newsletters/articles/matlab-tips-and-tricks-exploiting-the-comma-separated-list-vectorizing-cell-array-and-structure-references.html

See also:

https://www.mathworks.com/matlabcentral/answers/5827-ndgrid-with-unknown-number-of-output-arguments