How i can create random array with fixed sum for each row and column?

a

Answer 1

[Roger Stafford]

I assume by "rounded off" you mean the elements are all to be integers. Do this:

 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;
   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

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,

[reshdev]

Thank You, Roger.....beautiful code