MATLAB: Making permutations in a matrix

matrixpermutation

Hi,
I have an nxm matrix. I need to make permutations but the row and coloumn sums must be fixed (only the matrix elements will change).
How can I do that?
Thanks..

Best Answer

I can only guess at your meaning here of the word 'permutations'. Based on your other similar request at
 http://www.mathworks.com/matlabcentral/answers/75431,
I assume you mean that all matrix entries are to be non-negative integers and that, correspondingly, the permutations are to be considered as among objects for which these are the counts - that is, an arrangement of [5,7,11,4] like objects is considered a "permutation" or rearrangement of [4,7,3,13] objects. (This is not what I would call a true permutation, however.)
With N set to a very large number, the following can approach such a random adjustment in which the row and column sums are preserved with all elements remaining non-negative. Let A be your n x m matrix.
 N = 10000;
 for k = 1:N
   r = randperm(n,2); r1 = r(1); r2 = r(2);
   c = randperm(m,2); c1 = c(1); c2 = c(2);
   d = randi([-min(A(r1,c1),A(r2,c2)),min(A(r1,c2),A(r2,c1))]);
   A([r1,r2],[c1,c2]) = A([r1,r2],[c1,c2]) + [d,-d;-d,d];
 end
At each step this adjusts four elements lying in two columns and two rows so as to preserve row and column sums and such that those elements remain non-negative integers.
(This is a bit crude and cumbersome but it is all I could think of at the moment.)
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