Efficient implementation for loops

I have a for loop which is slowing down the performance, which I'm sure there is a way to speed it up but I don't know how.

Suppose you have two matrices

 A = randn(4,2,10); B = randn(2,10);

The result you want is C of dimension 4 * 10. In a for loop implementation, it is:

for i = 1 : 10
  C(:,i) = A(:,:,i) * B(:,i)
end

How can I get C without using for loops?

Thanks in advance

Answer 1

[Sean de Wolski]

Preallocating C will make this much faster:

Before the loop:

C = zeros(4,10);

[Tao Yang]

Thanks.

Is there a way to avoid the for loop?

[Sean de Wolski]

Yeah, it could be rewritten as a larger matrix multiplication with a few reshapes and permutes but why bother? It's already blazingly fast!

Let me make it a little bigger and time it:

A = randn(400,20,10000); 
B = randn(20,10000);
tic
C = zeros(400,10000);
for i = 1:10000
C(:,i) = A(:,:,i)*B(:,i);
end
toc

So now I'm doing a whole lot more math in (on my wimpy laptop) ... drum roll

Elapsed time is 0.213792 seconds.

Less than a quarter of a second!

Loops aren't slow in MATLAB. Inefficiencies within loops like not preallocating slow MATLAB down.

http://www.mathworks.com/matlabcentral/answers/40977-how-to-improve-computing-in-matlab#answer_50587

[Tao Yang]

Thanks Sean.

Actually I simplified the original question. The above operation is just a small part of my entire code and needs to be repeated a lot of times (I'm running a big Monte Carlo simulations).

So I would appreciate if you could help me with the loop-free solution.

Many thanks, Tao

[Sean de Wolski]

Have you profiled it to see if that is the bottleneck?