## Speed up big matrix multiplication (Parallel Processing/GPU)

Asked by Andreas Dorner

### Andreas Dorner (view profile)

on 10 Jan 2019
Latest activity Commented on by Andreas Dorner

### Andreas Dorner (view profile)

on 11 Jan 2019
Accepted Answer by Edric Ellis

### Edric Ellis (view profile)

Hello there,
below is the code i want to run. The rand()-calls are only for code simplicity. In my code the variables obviously have meaningful content.
for N = 1024 this takes about 2 hrs to run on my machine. I've tried so many things, e.g. precalculate the cosArgs.
N = 1024;
img = rand(N);
cosArg1 = rand(N^2,1);
cosArg2 = rand(N^2,1);
[q, p] = meshgrid(0:N-1, 0:N-1); %p and q are just another NxN size matrices respectively
recon = zeros(numel(img),1);
for k = 1:numel(img)
a = img.*cos(cosArg1(k)*p).*cos(cosArg2(k)*q);
recon(k) = sum(a(:));% sum of vec is faster then sumsum of matrix although we need to save it as variable
end
Is there any clever way to speed this code up?
_______
I also just bought Parallel Processing Toolbox to make it work with GPU-Arrays. This nown takes abouzt 17 min with a GTX 1060. The variables ending with GPU are just gpuArray-Casts of their original.
EDIT: by first casting to single, i cut it down to 10 min.
Is there something I can do better?
cosArg1GPU = gpuArray(single(cosArg1));
cosArg2GPU = gpuArray(single(cosArg2));
imgGPU = gpuArray(single(img));
reconGPU = gpuArray(single(recon));
pGPU = gpuArray(single(p));
qGPU = gpuArray(single(q));
for k = 1:numel(imgDCTGPU)
% sum of vec is faster then sumsum of matrix although we need to save it as variable
a = imgDCTGPU.*cos(cosArg1GPU(k)*pGPU).*cos(cosArg2GPU(k)*qGPU);
reconGPU(k) = sum(a(:));
end

### Edric Ellis (view profile)

Answer by Edric Ellis

### Edric Ellis (view profile)

on 11 Jan 2019
Edited by Edric Ellis

### Edric Ellis (view profile)

on 11 Jan 2019

You should take advantage of:
1. Implicit dimension expansion, and
2. The new multi-dimension arguments to sum
and then perform the calculation in chunks. The idea is that instead of looping over single pages, you calculate multiple pages simultaneously. I'm not sure how much better this is than your original case though.
N = 1024;
img = rand(N, 'gpuArray');
cosArg1 = rand(1,1,N^2, 'gpuArray');
cosArg2 = rand(1,1,N^2, 'gpuArray');
[q, p] = meshgrid(gpuArray(0:N-1), gpuArray(0:N-1));
recon = zeros(numel(img),1, 'gpuArray');
chunk = 128; % Might need to reduce this if it takes too much memory
tic
for k = 1:chunk:numel(img)
range = k:(k+chunk-1);
% The following line relies on implicit dimension expansion
% to calculate "chunk" pages of "a" simultaneously
a = img .* cos(p .* cosArg1(1,1,range)) .* cos(q .* cosArg2(1,1,range));
% Use the vector syntax of SUM to reduce to a 1x1xchunk "vector",
recon(range) = sum(a, [1 2]);
end
toc

Andreas Dorner

### Andreas Dorner (view profile)

on 11 Jan 2019
that cut it in half. Thank you very much. I added the use of arrayfun. scraped a few seconds off too:
reconPixel = @(imgDCTGPU, icosArg1GPU, icosArg2GPU, pGPU, qGPU) imgDCTGPU.*cos(pGPU.*icosArg1GPU).*cos(qGPU.*icosArg2GPU);
for k = 1:chunk:nEntries
lim = (k+chunk-1);
if lim > nEntries
lim = nEntries;
end
range = k:lim;
% Use the vector syntax of SUM to reduce to a 1x1xchunk "vector",