MATLAB: Optimize the for loop with vectors

arraryvector

Hi, I read that vectorizing your matlab program will speed it up so I am trying to vectorize the following for loop:
mysum = 0;
  for kx = -1:dk:1
      kyMax = sqrt(1^2-kx^2);
      for ky = 0:dk:kyMax
        myeps = kx^2 + ky^2;
        mysum = mysum + myeps;
       end
  end
I'm not sure how to do it since {kx,ky} is not a rectangular array but rather one who's ky dimension changes depending on the kx.

Best Answer

kx = -1:dk:1;
[xx,yy] = ndgrid(0:dk:1,kx);
t = xx <= sqrt(1-kx.^2);
m = [xx(:),yy(:)];
a = m(t(:),:).^2;
out = sum(a(:));
or
kx = -1:dk:1;
B = arrayfun(@(x)0:dk:x,sqrt(1-kx.^2),'un',0);
n = cellfun(@numel,B);
out = sum(repelem(kx,n).^2 + [B{:}].^2);
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