MATLAB: How to vectorize three for loop or fast

differential equationsfor loopparforvectorization

% this is to do the grid-based central finite difference for the two vectors dimension as u(lon, lat, time) and v(lon,lat,time). the for loops works fine but it is too slow. I need a helpful loop that is faster than me from Matlab community.
    Ur = zeros(291,243,1459);
    [NR, NC]=size(lat);
    for k = 1: length(t)
    for i = 2:NR-1
    for j = 2:NC-1
         Ur(k,i,j)=sqrt((u(i+1,j,k)-2*u(i,j,k)+u(i-1,j,k))./(lon(i)-lon(i-1)^2) ...
                 +(v(i,j+1,k)-2*v(i,j,k)+v(i,j-1,k))./(lat(j)-lat(j-1)^2));
    end
    end
    end

Best Answer

  • Avoid repeated calculations.
  • Process the data in column order.
Ur = zeros(291,243,1459);
[NR, NC]=size(lat);
for j = 2:NC-1
   latj = lat(j) - lat(j-1)^2;
   for i = 2:NR-1
      loni = lon(i) - lon(i-1)^2;
      for k = 1: length(t)
         Ur(k,i,j) = sqrt((u(i+1,j,k) - 2 * u(i,j,k) + u(i-1,j,k)) ./ loni ...
                        + (v(i,j+1,k) - 2 * v(i,j,k) + v(i,j-1,k)) ./ latj);
      end
   end
end
If you provide all input arguments, e.g. created by some rand() command, we could check the speed. I assume the inner loop is easy to vectorize:
Ur = zeros(291,243,1459);
[NR, NC]=size(lat);
for j = 2:NC-1
   latj = lat(j) - lat(j-1)^2;
   for i = 2:NR-1
      loni = lon(i) - lon(i-1)^2;
      Ur(:,i,j) = sqrt((u(i+1,j,:) - 2 * u(i,j,:) + u(i-1,j,:)) ./ loni + ...
                       (v(i,j+1,:) - 2 * v(i,j,:) + v(i,j-1,:)) ./ latj);
   end
end
A further vectorization is possible, but I hesitate to implement it: It looks strange, that you treat lat as 2D in [NR, NC]=size(lat), but access the first column only by using 1 index later. Does the code really do, what you want?
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