MATLAB: Numbers in random positions on a zero matrix

matrixnumbersonesrandomzeros

I want to generate a random matrix (let's say a 5×4 matrix) with the following properties:
  • There must be one 3, two 2s, nine 1s, eight 0s in the matrix.
  • In each row, there is at most one 3 or 2 and at most two 1s.
  • In each row, if there is a 3, then there is no 2.
  • In each row, if there is a 3, then there is one 1.
  • In each row, if there is a 2, then there are two 1s.
An example matrix:
0 0 1 1
3 1 0 0
2 1 1 0
0 1 1 2
0 1 1 0
How do I generate such a matrix? I don't even know where to begin. Any help is greatly appreciated.

Best Answer

m = 5;
n = 4;
T = [2 2 3 ones(1,9) zeros(1,8)];
out = reshape(T,m,[]);
[~,ii] = sort(rand([m,n]),2);
out = out(sub2ind([m,n],repmat((1:m)',1,n),ii));
out = out(randperm(m),:);
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