Speed up Matrix multiplication

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!

[Michael Soskind]

I see a marginal performance improvement by simply getting rid of the middle array index:

A = rand(3,3,1e6);
B = rand(3,1e6);

% original code
tic
C = zeros(3,1,size(B,2));
for idx=1:size(B,2)
    C(:,:,idx) = A(:,:,idx) * B(:,idx);
end
toc

% modified code with one fewer array dimension
tic
C = zeros(3,size(B,2));
for idx=1:size(B,2)
    C(:,idx) = A(:,:,idx) * B(:,idx);
end
toc

Not sure if that helps or hurts you, but I get about 0.3 sec faster execution time, on average (Goes from 2 sec to 1.7 sec).

Michael

Answer 1

[Matt J]

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

[Matt J]

Or, on pre-R2016b versions,

C=sum(  bsxfun( @times, A,  reshape(B,1,3,[]) )    ,2)

[Dustin Williams]

Thanks!