# Matrix multiply slices of 3d Matricies

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Dan Ryan on 5 Feb 2013
Given two 3d matricies, A and B with
size(A) = (n, m, k)
and
size(B) = (m, p, k)
perform matrix multiplications on each slice obtained by fixing the last index, yielding a matrix C with
size(C) = (n, p, k).
To clarify, we would have
C(:, :, 1) = A(:, :, 1)*B(:, :, 1), ..., C(:, :, k) = A(:, :, k)*B(:, :, k).
I need to do this with gpuArrays in the most efficient manner possible.

Jill Reese on 9 Sep 2013
If you have MATLAB R2013b, you can use the new gpuArray pagefun function like so:
C = pagefun(@mtimes, A, B);
Dan Ryan on 9 Sep 2013
Brilliant! Thanks!

James Tursa on 14 Feb 2013
Edited: James Tursa on 14 Feb 2013
If you are not restricted to gpuArrays you can do this:
C = mtimesx(A,B);
The MTIMESX function passes pointers to the slice data to BLAS library functions in the background, so it is pretty fast. You can find MTIMESX here:
MTIMESX is not yet multi-threaded across the third dimension (but an update is in the works). A nD matrix multiply multi-threaded on the third dimension called MMX can also be used:
C = MMX('mult', A, B);
MMX can be found here:
Dan Ryan on 14 Feb 2013
great suggestion, I will keep an eye on this project

Azzi Abdelmalek on 5 Feb 2013
Edited: Azzi Abdelmalek on 5 Feb 2013
n=3;
m=4;
k=5;
p=2;
A=rand(n,m,k)
B=rand(m,p,k)
C=zeros(n,p,k)
for ii=1:k
C(:,:,ii)=A(:,:,ii)*B(:,:,ii)
end
Jill Reese on 14 Feb 2013
Dan,
Can you elaborate on the sizes of m, n , k, and p that you are interested in? It would be useful to know a ballpark number for the size of problem you want to solve. Do you have many small page sizes, a few large pages, or something else?
Thanks,
Jill