MATLAB: Create new matrix with compine values

MATLAB

Hi everybody I want your help. what I want to do is to have a program to produce a main matrix by using submatrices but by combine some values. For example, I have
a = [0 0 1; 1 0 0; 1 0 1] b = [1 0 1; 1 1 1;1 1 1] c= [0 0 0 ; 1 0 0 ; 0 1 1] d = [ 1 0 1;1 1 1; 1 0 0]
the matrix a has 9 elements which 4 of them are 1 the, b 9 elements with 8 of them are 1, c matrix has 3 elements of 1 and d 6 aces. My question is can I have a new matrix let say S that it has three elements of the above matrixes ( for instance S1 = [a d a] or S2 = [ d d d] or S3 = [ b c b] ) but S it will be accept only if contains from 3 up to 6 aces in average and that means the S1 and S2 matrix is acceptable but S3 in not. S1 – S2 – S3 are examples and might be a different one

Best Answer

First, don't store your matrices in individual variables, it complicates everything. Since they're all the same size store them as pages of a 3D matrix:
M = cat(3, [0 0 1; 1 0 0; 1 0 1], [1 0 1; 1 1 1;1 1 1], [0 0 0 ; 1 0 0 ; 0 1 1],  [ 1 0 1;1 1 1; 1 0 0])
With that it's trivial to choose a combination of any 3 of the matrices:
selectedindices = randi(size(M, 4), 1, 3);  %select 3 indices at random

So, to get the result you want:
mean_ones = NaN;  %initial condition will always result in false, so we go at least once through the loop
while mean_ones < 3 | mean_ones < 6   %while we don't have a set that matches the criteria
    selectedindices = randi(size(M, 4), 1, 3);  %select 3 indices at random
    selectematrices = M(:, :, selectedindices);
    mean_ones = nnz(selectedmatrices) / 3;
end
edit: and if you want to generate all possible combinations or 3 matrices that follow your criteria, like fred did in his answer:
%M: 3D matrix as above
allcombs = dec2bin(0:size(M, 3)^3-1, size(M, 3)) - '0' + 1; %works for up to 10 matrices
allmatcombs = reshape(M(:, :, allcombs'), size(M, 1), size(M, 2), size(M, 3), []);
meanmat = sum(allmatcombs, 1:3) / 3; %requires 2018b or later. Earlier versions: sum(sum(sum(allmatcombs, 1), 2, 3) / 3
selectedmatcombs = allmatcombs(:, :, :, meanmat >= 3 & meanmat <= 6);
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