MATLAB: Speed up Matrix multiplication

Question

I want to do the following Matrix Multiplication. Problem – Example:

A = rand(3,3,1000000);
B = rand(3,1000000)

How to calculate C faster than with this For-loop? I tried parfor but its only slightly faster.

Furthermore i'd prefer not to install the Parallel Computing Toolbox or MTIMESX. Is it possible just with reshape/permute/bsxfun?

C = zeros(3,1,size(B,2));
for idx=1:size(B,2)
    C(:,:,idx) = A(:,:,idx) * B(:,idx);
end

Thanks!

Answer 1

C=sum( A.*reshape(B,1,3,[]),2);