MATLAB: Making permutations in row elements in a matrix

permutation

Hi all,

I have an nxm matrix. I need to make permutations but the row sums must be fixed.

Example;

Original matrix = [15 20; 10 30; 40 30; 50 10; 15 35]

row sums: 35,40,70,60,50.

One of the permutations; [10 25; 20 20; 50 20; 25 35; 20 30]

row sums: 35,40,70,60,50 (row sums must be fixed).

How can I generate permutations like this? Will permutation test work?

If I generate my original matrix with random numbers taken from a specific distribution , how can I permutate the row elements -with holding the row sums fixed-?

Thanks..

Best Answer

A=[15 20; 10 30; 40 30; 50 10; 15 35]
id1=A(:,1)/5
id2=A(:,2)/5
id=id1+id2
idx1=arrayfun(@(x) randi(x,1,1),id)
idx2=id-idx1
B=[idx1*5 idx2*5]

Related Solutions

MATLAB: How to replace and interchange values

If I understand your question correctly, here is one way:

x= [15 30 45 60 -45 -30 0 90 15 30 45 60 -45 -30 0 90 15 45 60 -45 -30 0];
a = unique(x);
y = repmat(x,numel(a),1);
y(:,end) = a';
value = y;
rowToRemove = find(x(end)==a);
value(rowToRemove,:) = [];

MATLAB: Making permutations in a matrix

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.)

Best Answer

Related Solutions

MATLAB: How to replace and interchange values

MATLAB: Making permutations in a matrix

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