Multidimensional Array Optimization for Simulations
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Is it possible to further optimise the following script by adopting meshgrid, reshape, linear indexing, and/or any other good optimisation techniques?
clear all
% tic;
N1 = 5000;
Nt = 2500;
u = randn(Nt,2);
A = zeros(2,2,N1);
B = zeros(2,2,N1);
C = zeros(2,2,N1);
D = zeros(2,2,N1);
X = zeros(2,1,N1);
Y = zeros(2,Nt,N1);
U = zeros(2,Nt,N1);
tic;
parfor i=1:N1
A(:,:,i) = [unifrnd(0.25,0.75),unifrnd(0.15,0.45);unifrnd(0.4,1.2),unifrnd(0.25,0.75)];
B(:,:,i) = [unifrnd(1,3),unifrnd(2.5,7.5);unifrnd(-22.5,-7.5),unifrnd(-1.95,-0.65)];
C(:,:,i) = [unifrnd(-1,1),unifrnd(-19.5,-6.5);unifrnd(0.5,1.5),unifrnd(-22.5,-7.5)];
D(:,:,i) = [unifrnd(0.1,0.3),unifrnd(-1,1);unifrnd(1,3),unifrnd(-1,1)];
U(:,:,i) = u';
X(:,:,i) = zeros(2,1);
Y(:,:,i) = zeros(2,Nt);
end
toc;
A1 = gpuArray(A);
B1 = gpuArray(B);
C1 = gpuArray(C);
D1 = gpuArray(D);
X3 = gpuArray(X);
U3 = gpuArray(U);
AX = gpuArray(zeros(2,Nt,N1));
X3update = zeros(2,Nt,N1);
X3update = gpuArray(X3update);
tic;
DU = pagefun(@mtimes, D1, U3(:,1:Nt,:));
BU = pagefun(@mtimes, B1, U3(:,1:Nt,:));
for j = 1:Nt
X3update = pagefun(@mtimes,A1,X3) + BU(:,j,:);
AX(:,j,:) = X3;
X3 = X3update;
end
CX = pagefun(@mtimes, C1, AX(:,1:Nt,:));
Y3 = CX + DU;
toc;
Apologies in advance as this is quite a specific question. However, I am trying to increase the computational efficiency of state-space simulations, so quite widely applicable.
Thanks!
4 Comments
Jill Reese
on 16 Apr 2014
Note that tic/toc do not provide accurate timings for code containing gpuArrays as operations are executed asynchronously on the GPU. If at all possible, you should use:
gputimeit
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