Accelerate eig with GPUs

Hi all, I need to diagonalize a lot of matrices. The problem is similar to:

A = rand(5000, 5000, 500); %this snipped is just a demo. It is real logic in the program
EVs = zeros(5000, 500);
for idx = 1:500
   EVs(:, idx) = eig(A(:,:,idx));
end

This is fine on CPUs and easily scalable with parfor and MDCS. As eig is faster on GPUs I tried this

A = rand(5000, 5000, 500); %this snipped is just a demo. It is real logic in the program
EVs = zeros(5000, 500, 'gpuArray');
for idx = 1:500
   B = gpuArray(A(:, :, idx));
   EVs(:, idx) = eig(B);
end
EVs = gather(EVs);

This does not lead to a much better performance. Is there a way to get around the gpuArray statement in each loop? Some kind of pagefun with eig would be the solution I guess. (unfortunately, eig is not supported by pagefun)

Best wishes Niklas

[Matt J]

Birk Andreas's comment moved here:

Please Mathworks, implement eig for use with pagefun as soon as possible!!!

Answer 1

[Matt J]

You need to build A directly on the GPU, for example,

EVs = zeros(5000, 500, 'gpuArray');

A=gpuArray.rand(5000,5000,500);

for idx = 1:500
   B = A(:, :, idx);
   EVs(:, idx) = eig(B);
end
EVs = gather(EVs);

For the case of your real A, you have to examine what operations you are currently using to build A on the host, and which of those operations would not also be available on the GPU.

[Niklas]

Hi Matt,

thanks, I guess that does the trick by avoiding unnecessary communication with the GPU. Unfortunately, the speedup is not as big as I expected:

Elapsed time is 118.457193 seconds. <- CPU time without parfor

Elapsed time is 107.845443 seconds. <- GPU on GeForce 1080Ti with 12GB

Used code:

mSize = 1000;
runs = 200;
A = rand(mSize, mSize, runs);

tic
EVC = zeros(mSize, runs);
for idx = 1:runs
    EVC(:, idx) = eig(A(:,:,idx));
end
toc

tic
EVG = zeros(mSize, runs, 'gpuArray');
A = gpuArray(A);
for idx = 1:runs
    G = A(:,:,idx);
    EVG(:, idx) = eig(G);
end
EVG = gather(EVG);
toc

[Niklas]

Using bigger matrices the speedup is higher.

Elapsed time is 1006.431223 seconds. <- CPU

Elapsed time is 295.168202 seconds. <- GPU

Unfortunately, nvidia-smi shows a low usage of the GPU. Maybe I will write a CUDA snipped to deal with it.

[Matt J]

Yeah, I can't see that there would be a lot of parallelism in eigenvalue computation.