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

Eli (view profile)

on 21 Jun 2013
Accepted Answer by Andrei Bobrov

Andrei Bobrov (view profile)

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

on 21 Jun 2013
Is "a" a scalar?
Eli

on 21 Jun 2013
yes

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Answer by Andrei Bobrov

Andrei Bobrov (view profile)

on 21 Jun 2013

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

Eli

Eli (view profile)

on 21 Jun 2013
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

James Tursa (view profile)

on 22 Jun 2013
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

Eli (view profile)

on 22 Jun 2013
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

on 21 Jun 2013
Edited by Iain

Iain (view profile)

on 21 Jun 2013

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

Eli (view profile)

on 21 Jun 2013
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