MATLAB: Eliminating outer for-loop

loop separationoptimization

Hi,
I have an outer for-loop that I can't manage to get rid of. Code as follows
   for t= 1: epochs
      ... code
      for i= 1: n
          for j = 1:n
          h= exp(-sum(([i j]'- [r c]').^2)/(2*(sigma(t)^2)));
          w(:, i, j)= w(:, i, j)+ eta(t)*h*((xiCurrent- w(:, i, j)));
          dist(i, j)= sqrt(sum((xiCurrent- w(:, i, j)).^2));
          end
      end
      ... code
  end
Observe that in the loop over i nothing gets calculated before entering the loop over j, and I would therefore like to eliminate the i-loop, but with no success.
Constraint's are that one xiCurrent are fed per iteration t, and all computations within the t-loop must be finished before t can take a step. An indexed-value of w must be updated before being applied to dist(i, j).
If necessary; n= 30; size(w)= 57000 x 30 x 30; size(xiCurrent)= 57000 x 1 size(dist)= 30 x 30 r and c are constants in the context.
I've used e.g. repmat on xiCurrent, but that gave slower execution than the above code.
I'm grateful for any help, best regards, Daniell

Best Answer

I don't see any recursion going on. So I don't see why you can't compute it without any loops. To compute h, try
      I = ones(n)*diag([1:n]);
      J = I';
      I = I(:);
      J = J(:);
      h = exp(-sum(([I-r J-c]).^2)./(2*(sigma(t).^2)));
Not sure about w. Is it initialized? You should be able to do the same kind of thing with w and dist.
          w(:, I, J)= w(:, I, J)+ eta(t).*h.*((xiCurrent- w(:, I, J)));
          dist(I, J)= sqrt(sum((xiCurrent- w(:, J, J)).^2));
Also, if xiCurrent is not recursive either, then you might be able to eliminate the t loop as well.
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