Reduce the computional time to calculate the mutilplying two matrixes

I calculate this loop for thousands of time.

How can i optimize it to reduce the computational time?

for i=1:n     
  f(i,:)=w'*Q0(:,:,i)  
end 

with w =(2000,1) matrix and Q0=(2000,2000,100)

Thanks a lot.

[dpb]

1. Preallocate f -- f=zeros(n,numel(w));
2. Reorient w outside the loop

The first may help enough to be noticeable if haven't; the second is very minor aid to the optimizer and likely will make little, if any, difference.

[Thu Nguyen]

Thank you a lot. I also made preallocate and reorient as you made and only reduce little time. I need reduce more such as ~ 100 times.

Answer 1

[David Goodmanson]

Hi Thu,

try

% N = 1000;
% M = 200;
Q00 = reshape(Q0,N,N*M);
ff = reshape(w'*Q00,N,M)';

This is approximately four times faster on my PC, compared to the first way with f preallocated.

[Thu Nguyen]

Thank you so much. I found this solution very interesting. But on my PC, it reduce time a little. I want to reduce the computational time about 100 times. Any solution?