Generating a matrix containing 3 numbers - matlab

Question

I am trying to create an 8x8 matrix containing 0s, 1s and 2s. Each row and each column should contain two 0s, three 1s and three 2s.
Previously I have used the below to generate an example containing only 1s and 0s.
output = zeros(8, 8);
for i=1:8
tmp = (1:8) + (i);
tmp = rem(tmp, 4);
output(i,:) = tmp;
output(i,:) = tmp > 0;
end
output =
1 1 0 1 1 1 0 1
1 0 1 1 1 0 1 1
0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0
1 1 0 1 1 1 0 1
1 0 1 1 1 0 1 1
0 1 1 1 0 1 1 1
1 1 1 0 1 1 1 0
However I would now like something similar to the following:
output =
1 1 0 1 2 2 0 2
1 0 1 2 2 0 2 1
0 1 2 2 0 2 1 1
1 2 2 0 2 1 1 0
2 2 0 2 1 1 0 1
2 0 2 1 1 0 1 2
0 2 1 1 0 1 2 2
2 1 1 0 1 2 2 0
Thanks for your help.

Answer 1

What you have in your example is a Hankel matrix so you could use the hankel function
c = [1 1 0 1 2 2 0 2];
k = [2 1 1 0 1 2 2 0];
A = hankel(c,k)
where c is the first column of the output matrix and k is the last row.
Making your output matrix a Hankel matrix is a good idea (based on your requirements) as it will enforce the row and column frequency counts for each value. You would not necessarily get this just by creating rows that are random permutations of a base row (using randperm for example) as duplicate rows would be possible which would break your column requirements.
As an example, if you want random c with fixed numbers of specific elements, you can randomly permute a base vector containing the required values and frequencies - as per your requirement this would be
c = [0 0 1 1 1 2 2 2];
index = randperm(numel(c));
c = c(index);
c =
0 2 0 2 2 1 1 1
To get the square Hankel structure then choose k to be the next cyclic permutation of c
k = circshift(c',1)'
k =
1 0 2 0 2 2 1 1
and just call hankel with these as mentioned above
A = hankel(c,k)
A =
0 2 0 2 2 1 1 1
2 0 2 2 1 1 1 0
0 2 2 1 1 1 0 2
2 2 1 1 1 0 2 0
2 1 1 1 0 2 0 2
1 1 1 0 2 0 2 2
1 1 0 2 0 2 2 1
1 0 2 0 2 2 1 1
The above output is based on what I got on my machine based on the output from randperm.
Any output matrix generated using the above will meet your requirements specified in the question.