how do I vectorize a loop with multi-dimensional arrays/ outer product

Hi, would someone happen to know how I could vectorize the following loop?

      L=4;
      for t=1:N;
        A(:,:,t)=exp(a*(t-1)).*B(:,:,L);
      end

many thanks, Eli

[James Tursa]

Is "a" a scalar?

[Eli]

yes

Answer 1

[Andrei Bobrov]

B1 = B(:,:,4);
out = reshape(B1(:)*(0:N-1),[size(B1) N]);

[Eli]

thanks! this works, but didn't turn out to be more efficient than the loop, I think. here is my try, did I get this right?

clear all;
N=1000;
a=rand(1,1000);
B=rand(128,256,N);
C=NaN(128,256,N);

tic 
for t=1:N
  C(:,:,t)=B(:,:,4)*a(t);
end
toc

tic
B1 = B(:,:,4);
C1 = reshape(B1(:)*a,[size(B1) N]);
toc

difference=max(max(max(abs(C1-C))))

output:

Elapsed time is 0.097027 seconds. Elapsed time is 0.110844 seconds.

difference =

     0

[James Tursa]

Your timing is comparing apples to oranges. You preallocate the answer for your loop but do not include it in your timing, whereas you penalize the reshaped outer product by including its intrinsic allocation in the timing. Your loop timing should be this instead, which includes both the allocation and the operations:

tic 
C=NaN(128,256,N);
for t=1:N
  C(:,:,t)=B(:,:,4)*a(t);
end
toc

Also, the timings should be run several times to make sure background functions are loaded into memory (I assume you do not want the function loading times to bias your results). So don't clear all between timing runs, just clear the variables you allocate (e.g., C, B1, and C1).

[Eli]

Brilliant of you. the vectorized version seems significantly faster now. thanks! here it is:

%clear all;
N=1000;
a=rand(1,N);
B=rand(128,256,N);

tic 
C=NaN(128,256,N);
for t=1:N
  C(:,:,t)=B(:,:,4)*a(t);
end
toc

tic
C1 = reshape(reshape(B(:,:,4),[128*256*1,1])*a,[128 256 N]);
toc

difference=max(max(max(abs(C1-C))))

output:

Elapsed time is 0.230418 seconds.

Elapsed time is 0.123938 seconds.

difference = 0

Answer 2

[Iain]

 A = bsxfun(@times,exp(bsxfun(@times,a,0:(t-1)),B);

You need to make sure that a, 0:t-1 and B are all in the correct dimensions, and that "times", is the correct multiplication for your needs.

 A = bsxfun(@times,exp(bsxfun(@times,a,reshape(0:(t-1),1, 1,[]),B);

[Eli]

thanks! I am afraid I wasn't able to make this work. here is a more specific example in the hope this clarifies what the problem was:

clear all;
N=1000;
a=rand(1,1000);
B=rand(128,256,N);
C=NaN(128,256,N);

tic 
for t=1:N
  C(:,:,t)=B(:,:,4)*a(t);
end
toc