Nested loops

Here's a tricky one! How can I get rid of the loops?

for pix = 1:NumPixels
    for ji = min(ShellNumbers(:,pix)):max(ShellNumbers(:,pix))
        for jj = min(AngleNumbers(:,pix)):max(AngleNumbers(:,pix))
            pos = ShellNumbers(:,pix) == ji & AngleNumbers(:,pix) == jj;
            W(ji,jj) = W(ji,jj) + sum(PathLengths(pos,pix));
            L(ji,jj,1,pix) = sum(PathLengths(pos,pix));
            clear pos
        end
    end
end

Answer 1

[Jan]

I cannot omit the loops, but it can be made faster:

% Pre-allocate!
s1 = max(ShellNumbers(:));
s2 = max(angleNumbers(:));
W  = zeros(s1, s2);
L  = zeros(s1, s2, 1, NumPixels);  % What is "i"?!

for pix = 1:NumPixels
  jjLow  = min(AngleNumbers(:,pix));
  jjHigh = max(AngleNumbers(:,pix));
  for ji = min(ShellNumbers(:,pix)):max(ShellNumbers(:,pix))
      a = ShellNumbers(:,pix) == ji;
      for jj = jjLow:jjHigh
          pos = a & AngleNumbers(:,pix) == jj;
          B   = sum(PathLengths(pos,pix));
          W(ji,jj) = W(ji,jj) + B;
          L(ji,jj,i,pix) = B;  % What is "i"?!
      end
  end
end