How can we calculate double summation quickly in MATLAB

[Riofunk7]

Hello, Guys

I am looking for a fast double summation method for the following calculation.

X=[0:N-1]; Y=[0:N-1];
Z=ExEy[exp(-(X-Y)^2)];

Thus, in MATLAB,

X=[0:N-1]; Y=[0:N-1];
for n=1:N
Zy = sum(exp(-(X-Y))^2)) / N;
end
Z = sum(Zy) / N;

As shown above, firstly I tried "for loop" and "sum()" function in matlab. But for large number of sequence this method is too slow if the sample size N is large.

Are there anyone who know faster calculation for this problem?


Thank you in advance.
Rio.

 

[zorro]

Hi Rio,

Please try this:

X=[0:N-1]; Y=[0:N-1];
Xr = repmat(X,N,1);
Yr = repmat(Y),1,N);
Dr = (Xr-Yr);
Z = sum(sum(exp(-Dr.*Dr)))/(N*N);

Regards

Z

 

[Riofunk7]

Thanks, Z.

I could reduce the simulation time to half.