## Matrix multiply slices of 3d Matricies

on 5 Feb 2013

### Jill Reese (view profile)

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

### Jill Reese (view profile)

님의 답변 9 Sep 2013
채택된 답변

If you have MATLAB R2013b, you can use the new gpuArray pagefun function like so:
C = pagefun(@mtimes, A, B);

Dan Ryan

### Dan Ryan (view profile)

9 Sep 2013
Brilliant! Thanks!

James Tursa

### James Tursa (view profile)

님의 답변 14 Feb 2013
James Tursa

### James Tursa (view profile)

님이 편집함. 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

### Dan Ryan (view profile)

14 Feb 2013
great suggestion, I will keep an eye on this project

Azzi Abdelmalek

님의 답변 5 Feb 2013
Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

님이 편집함. 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

Dan Ryan

### Dan Ryan (view profile)

5 Feb 2013
Big slowdown... for example:
A = gpuArray.rand(1000, 100, 100, 'single');
B = gpuArray.rand(1000, 100, 'single');
C = gpuArray.zeros(1000, 100, 100, 'single');
Compare
for idx = 1:100
C(:, :, idx) = A(:, :, idx).*B;
end
with
C = bsxfun(@times, A, B);
There is about a factor of 50 slowdown with the for loop.
Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

5 Feb 2013
bsxfun don't work with
n=3;
m=4;
k=5;
p=2;
A=rand(n,m,k)
B=rand(m,p,k)
C = bsxfun(@times, A, B);
Jill Reese

### Jill Reese (view profile)

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