MATLAB: Generating all unique permutations of a matrix with a defined set of arrays

Question

I'm trying to generate all the unique permutations of an 8×3 matrix that is created when each row is one of the following:

[1,0,0] [0,1,0] or [0,0,1]

For example, one output would be:

ans = 
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0

Another output would be:

ans = 
    0   1   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0
    1   0   0

And so on…

The following would not be accepted, because the third row [1,1,0] does not match one of the three input arrays.

ans = 
    0   0   1
    0   1   0
    1   1   0
    0   1   0
    1   0   0
    0   0   1
    1   0   0
    0   0   1

Ideally, this can be run in a for loop, so I don't have to store all of the permutations at once. However, I'd also like to know if there's an effective way to store this many matrices (perhaps a 3D matrix), so they can be referenced later.

Thank you,

Peter

Answer 1

Try this. It create a 3D array, where each slice in third dimension is an 8x3 matrix.

A = {[1, 0, 0], [0, 1, 0], [0, 0, 1]};
 
x = repmat({[1 2 3]}, 1, 8);
combs = combvec(x{:}).';
M = A(combs);
M = cell2mat(M).';
M = reshape(M, 3, 8, []);
M = permute(M, [2 1 3]);