indexing problem in a matrix.

I have n particles scattered in space. I measured the distances of all the particles relative to all the other particles by giving the following code:

for i = 1:n
   for j = 1:n
   matrix(i:j) = distance_function(i,j)
   end
end

I now have an n by n symmetric matrix with the main diagonal zero. (because the distance of the i-th particle to itself is zero. and symmetric, because the distance from first to second particle is the same as second to first particle.)

Let's say for example I have the following distance matrix:

matrix = [0 1 1 2; 
          1 0 3 1;
          1 3 0 2;
          2 1 2 0]

Now, I want to see which of these particles are within a distance of, lets say for fun: 3, from anyone else.I will be moving them because of a force of repulsion.

This means that for particle 1: those that will contribute to the repulsion are: particles 2, 3, 4. repulsion of 2 is due to: 1, 4. repulsion of 3 is due to: 1 ,4. repulsion of 4 is due to 1, 2, 3.

How do I say this in Matlab? idx = find(matrix < 3 & matrix ~=0) gives you the indices linearly (in this case from 1 to 16.) It is difficult to pinpoint which particle contributes to which.

Please help.

Answer 1

[Walter Roberson]

[r,c] = ind2sub(size(matrix), idx);

now r(K), c(K) are row/column pair versions of idx