MATLAB: Row / column summation constraints in random binary matrix.

matrixmatrix array

I want to generate a random binary matrix A(m, n) that meets two conditions:
  1. The summation of each column in A is 1.
  2. The summation of each row in A is less than a value in vector B={B1,…,Bm}, where B is a set of values.
Anyone knows, how can I implement it in MATLAB?
Thanks.

Best Answer

Here's one way, just using brute force try-and-see:
rows = 5;
columns = 11;
% Get some random B value, since we don't know what else to use.
B = randi(rows, rows, 1)
loopcounter = 1; % The failsafe.
maxAttempts = 100000; % A hundred thousand attempts.
while loopcounter < maxAttempts
  A = zeros(rows, columns);
  % Get rows to put 1's into
  rowsWith1s = randi(rows, 1, columns);
  % Load those 1s into A.
  for col = 1 : columns
    A(rowsWith1s(col), col) = 1;
  end
  %   A % Print to command window
  % Get row sums:
  rowSums = sum(A, 2);
  % Bail out if all sums are less than B
  if all(rowSums < B)
    fprintf('Succeeded after %d attempts\n', loopcounter);
    break;
  end
  loopcounter = loopcounter + 1;
end
if loopcounter == maxAttempts
  fprintf('Was not able to succeed after %d attempts.\n', loopcounter);
else
  fprintf('The final A:\n');
  rowSums % Print to command window

  A % Print to command window
end
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