Vectorizing a loop that calculates cosd on every element?

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PetterS 2015-3-16

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评论： David Young 2015-3-17

Hi. I have radiation data for every minute of a day that is spectrally resolved so each minute contains several wavelengths. I want to project this radiation on a tilted plane with a nested for loop that looks like this:

for minute=1:1440 %minute during day
     for beta = 1:length(Tilt) %tilt of surface
         for lambda = 1:length(DirectNormal) %wavelength of incoming light
TiltedDirect(minute,beta,lambda)=DirectNormal(lambda,minute)*cosd(AOFINCEQ15(minute,beta));
           end
       end
  end

And what I want to do is go through all minutes of the day and all the tilts (minute and beta) on an element by element basis. BUT I want to perform the same cosine calculation on all wavelengths within that minute and tilt, so I don’t really need to go through all the lambda values per element as I am now. And since I have over 2000 lambdas the loop is incredibly slow. I know very little about vectorization but I assume this would be an ideal situation to vectorize by performing the cosine on all lambda values at the same time. But I can’t figure out how to write that in the code.

Could someone advise me?

Thanks!

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Answer 1

David Young 2015-3-16

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You don't need vectorization to avoid computing the cosine on every iteration through the lambda loop - just put the calculation outside:

TiltedDirect = zeros(1440, length(Tilt), size(DirectNormal,1));  
for minute = 1:1440 %minute during day
     for beta = 1:length(Tilt) %tilt of surface
         c = cosd(AOFINCEQ15(minute,beta));
         for lambda = 1:size(DirectNormal,1) %wavelength of incoming light
           TiltedDirect(minute,beta,lambda) = DirectNormal(lambda,minute) * c;
         end
     end
end

Note that I've also changed length to size - you can't guarantee that length will give the size of the right dimensions. I've also preallocated TiltedDirect , which will help efficiency.

By the way, are you sure you want AOFINCEQ15(minute,beta) and not AOFINCEQ15(minute,Tilt(beta))?

If you'd still like to vectorize the inner loop, you can do this

TiltedDirect = zeros(1440, length(Tilt), size(DirectNormal,1));  
for minute = 1:1440 %minute during day
     for beta = 1:length(Tilt) %tilt of surface
         c = cosd(AOFINCEQ15(minute,beta));
         TiltedDirect(minute,beta,:) = DirectNormal(:, minute) * c;
       end
  end

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PetterS 2015-3-16

AOFINCEQ15 is a 1440x181 matrix, and I agree with you – it is strange that I’m not actually using the values within Tilt. The Tilt variable is simply this: “Tilt=(0:1:180)';”, equally spaced values between 0 and 180. But AOFINCEQ15 has been calculated using Tilt so think AOFINCEQ15(:,1) corresponds to a tilt of 0°, so if I’m not too confused here I guess that would mean that beta=1 is the same as Tilt 0°.

David Young 2015-3-17