Matrix of statuses or matching; discrete one-to-one mapping

Hello,

I need to create all possible matricies of zeros and ones, where the sums of rows and columns is 1, while the size of the matrix is NxK, where N and K are predefined variables. Is there a simple function for this problem?

Answer 1

[Dr. Seis]

You can't do this with any old NxK matrix, it must be a square NxN matrix. Otherwise your condition, that the sums of individual rows are 1 and sums of individual cols are also 1, will not be valid. There isn't a simple function (that I know of), but there is a simple solution (provided you are not trying to find for large N). See the example below for N = 4:

N = 4;

A = eye(N);
B = perms(1:N);
C = zeros(N,N,size(B,1));

for ii = 1 : size(B,1)
  C(:,:,ii) = A(:,B(ii,:));
end

disp(C)

[Alexander]

Fantastico! Perms!

Thank you very much.