Generate All Possible combinations of a Matrix in Matlab

Question

How can I generate ALL possible values for an N*M matrix, knowing that elements of this matrix can only be either be 0 or 1?

For example if I want a 2*2 matrix, we g

Answer 1

Use dec2base -

combs = dec2base(0:power(2,N*M)-1,2) - '0'

This generates all the possible combinations in rows. So, to select any combination, you need to index into combs. Thus, the first combination [0,0,0,0] would be available at combs(1,:) and the last one [1,1,1,1] would be at comb(end,:).

If your possible values are from a different set, like 0,1,2,3 instead, make this edit -

combs = dec2base(0:power(4,N*M)-1,4) - '0'

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If you would to get the combinations that would be sized identically to the input matrix, use this -

combs_matshaped = reshape(permute(combs,[3 2 1]),N,M,[])

This creates a 3D array of as many 2D slices as there are combinations and each combination for the matrix is "index-able" with the third dimension index. For example, if you intend to get the first combination, use combs_matshaped(:,:,1) and for the last one, use combs_matshaped(:,:,end).

Answer 2

Another possibility (although Divakar's answer is simpler and probably faster):

c = cell(1,N*M);
[c{end:-1:1}] = ndgrid([0 1 2 3 ]); %// or change set of values: [0 1 2 3] etc
combs = cell2mat(cellfun(@(x) x(:), c, 'uni', 0)); %// results as row vectors
combs = reshape(combs.',N,M,[]); %// NxM matrices: combs(:,:,1), combs(:,:,2),...