MATLAB: How to vectorize this for-loop

Question

Hi,

I have the following loop that is called lots of times within a function and is slowing down considerably

n=200;
F1=rand(n,4);
F2=rand(n,4);
dRad_dt=zeros(n,4)
for i=1:4
        for j=1:n
            for k=1:n
                if j+k<=n
                    dRad_dt(j+k,i)=dRad_dt(j+k,i)+F1(j,i)*F2(k,i);
                end
            end
        end
end

Any clues on how to vectorize this code or speed up considerably would be greatly appreciated

Answer 1

You've re-invented convolution,

    dRad_dt=zeros(n,4);
       tmp = fft(F1,2*n,1).*fft(F2,2*n,1); %fft-based convolution
       tmp= ifft(tmp, 'symmetric');
     dRad_dt(2:n,:) = tmp(1:n-1,:);