# Why is pagemtimes slower on GPU than a CPU?

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David Ho on 1 Dec 2020
Answered: Joss Knight on 30 May 2021
I'm a physics researcher, and a lot of my numerical work involves batch multiplication of small, complex-valued matrices. This made me very excited to see that in R2020b the pagemtimes function has been implemented, as this is exactly what I need.
On a speed comparison test between GPU and CPU, however, GPU performs significantly worse. Here's a minimal example of such a test:
batchSize = [100 100 100];
matSize = [2 2];
a = complex(rand([matSize batchSize]), rand([matSize batchSize]));
gpuA = gpuArray(a);
f = @() pagemtimes(a,a);
gpuF = @() pagemtimes(gpuA, gpuA);
timeit(f) % I get around 0.05 seconds
gputimeit(gpuF) % I get around 0.3 seconds
Is the significant slowdown simply because the batch/matrix size is too small for GPU optimisation to beat the overheads? Or is there something else going on that I've missed?
I'm testing this on a NVIDIA Quadro P1000 GPU.
Joss Knight on 30 May 2021
Flattening and unflattening only changes array metadata so it is essentially a free operation.

Matt J on 1 Dec 2020
Edited: Matt J on 1 Dec 2020
I don't have a Matlab version that supports pagemtimes, but for the GPU version, it might be advisable to instead try pagefun(@mtimes,...). I do see an improvement relative to mtimesx.
batchSize = [100 100 100];
matSize = [2 2];
a = complex(rand([matSize batchSize]), rand([matSize batchSize]));
gpuA = gpuArray(a);
f = @() mtimesx(a,a);
gpuF = @() pagefun(@mtimes,gpuA, gpuA);
timeit(f) % I get around 0.8175 seconds
gputimeit(gpuF) % I get around 0.1033 seconds
David Ho on 2 Dec 2020
Hi Matt, thanks for answering. When I test pagefun I get exactly the same performance as pagemtimes. It's interesting that your CPU and GPU times are very different to mine, though.

Nathan Zechar on 29 May 2021
Hello David, I have a similiar problem and have found that pagemtimes is slower than just expanding an equation and coding it on both CPU and GPU. But for GPU it is exceptionally slow.
Here is an example. This can be coded up two different ways. Notice the performance of pagemtimes with just the CPU. clear all
Nx = 100;
Ny = 100;
Nz = 100;
[A1,A2,A3,B1,B2,B3,C1,C2,C3,...
E11,E12,E13,E21,E22,E23,E31,E32,E33,...
F11,F12,F13,F21,F22,F23,F31,F32,F33] = deal(rand(Nx,Ny,Nz));
tic
for i = 1:20
%% Electric Field Update
C1 = F11.*(A1.*E11+B1)+F12.*(A2.*E12+B2)+F13.*(A3.*E13+B3);
C2 = F21.*(A2.*E21+B2)+F22.*(A2.*E22+B2)+F23.*(A3.*E23+B3);
C3 = F31.*(A3.*E31+B3)+F32.*(A3.*E32+B3)+F33.*(A3.*E33+B3);
end
toc
[A,B,C] = deal(rand(3,1,Nx,Ny,Nz));
[E,F] = deal(rand(3,3,Nx,Ny,Nz));
tic
for i = 1:20
C = pagemtimes(F,(B+pagemtimes(E,A)));
end
toc
Without pagemtimes - "Elapsed time is 0.032141 seconds".
With pagemtimes - "Elapsed time is 0.325006 seconds"
Using gpuArray() on the variables in the deal() function the the difference in times are even slower!
Without pagemtimes - "Elapsed time is 0.012688 seconds."
With pagemtimes - "Elapsed time is 5.357220 seconds."

Joss Knight on 30 May 2021
This might be simply because you are running double-precision math on a device designed for single precision operations. gpuBench doesn't show much improvement for double precision operations over the CPU on these devices. Can you convert your data to single precision and see if there is an improvement on GPU?

R2020b

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