MATLAB: Can anyone explain, how following program is working?(5th step)

random number generator

 A should be a randomly created 5 x 5 matrix whose elements are all integers ranging from 0 to 7 in such a way that
 1) row 1 and column 1 have equal sums,
 2) row 2 has a sum of 7 and column 2 has a sum of 0,
 3) row 3 and column 3 have equal sums,
 4) row 4 has a sum of 0 and column 4 has a sum of 7,
 5) row 5 and column 5 have equal sums,
 6) its diagonal elements are all zeros, and
 7) all column and row sums are 7 or less,
function test
    A = zeros(4);
 for k = 1:7
   p = randperm(4); %  <-- This is the source of randomness
   for ix = 1:4
     A(p(ix),ix) = A(p(ix),ix) + 1; **..,please explain this step**
   end
 end
 A = [A(:,1),zeros(4,1),A(:,2:4)]; % Insert a column of four zeros
 A = [A(1:3,:);zeros(1,5);A(4,:)]; % Insert a row of five zeros
A(1,1) = 0; A(3,3) = 0; A(5,5) = 0; % Set non-zero diagonal elements to 0
 disp(A);
end

Best Answer

The 'randperm' function is generating random permutations of the sequence, 1,2,3,4. For example suppose it generate p = 4,3,1,2. Then in the inner for-loop with ix = 1, we have p(ix) = 4. Hence
 A(p(ix),ix) = A(p(ix),ix) + 1
is doing this:
 A(4,1) = A(4,1) + 1;
It is adding 1 to the element of A in the fourth row of the first column. Then the next three steps are:
 A(3,2) = A(3,2) + 1
 A(1,3) = A(1,3) + 1
 A(2,4) = A(2,4) + 1
After those four steps you have
 A = [0 0 1 0;
      0 0 0 1;
      0 1 0 0;
      1 0 0 0]
Each row sum and each column sum is now 1. That is the property that any permutation, p, has. It would always leave you with equal row and column sums. When the outer loop is finished, all row and column sums are exactly 7.
Subsequent steps are of course meant to alter that situation.
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