Can this be accelerated?

Hi,

The following computations are very expensive for large matrices A, B and the coefficient q.

C=reshape(A,a1*q,b1)*B;
C=reshape(C,a1,b2*q);

a1 and a2 are the dimensions of A, while b1 and b2 are the dimensions of B and with the restriction that a2=b1*q.

In my applications, matrices A and B can have dimensions in the orders of thousands or more.

There is one way of implementing these operations using loops

C=zeros(a1,b2*q);
acols=0:q:(b1-1)*q;
ccols=0:q:(b2-1)*q;
for ii=q:-1:1
    C(:,ccols+ii)=A(:,acols+ii)*B;
end

but that strategy is not as fast as the one above. Is there any way to accelerate these operations?

try them for instance with the following

b1=1300;
b2=500;
q=350;
a1=300;
a2=b1*q;
B=rand(b1,b2);
A=rand(a1,a2);

Thanks

Answer 1

[Azzi Abdelmalek]

http://www.mathworks.com/matlabcentral/fileexchange/25977-mtimesx-fast-matrix-multiply-with-multi-dimensional-support/content//mtimesx_build.m

[Patrick Mboma]

Dear Azzi,

Thanks for the link. I think the problem is more about the reshaping than with the actual matrix multiplication. I am more than happy to run multiplication at Matlab's speed.

[Azzi Abdelmalek]

You can test the reshaping speed

b1=1300;
b2=500;
q=350;
a1=300;
a2=b1*q;
B=rand(b1,b2);
A=rand(a1,a2);
tic
C1=reshape(A,a1*q,b1);
toc
tic
C=C1*B;
toc

The reshaping takes 0.075 seconds

Elapsed time is 0.075266 seconds.
Elapsed time is 3.929999 seconds.

[Patrick Mboma]

Looks like I may have overlooked something... Thanks for pointing that out.

[James Tursa]

Are any of the matrices sparse? For full matrices, reshape is extremely fast since it returns a shared data copy. But for sparse matrices, reshape is expensive since it requires a deep data copy.