Multidimensional Array Optimization for Simulations

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!

[José-Luis]

If you want to optimize I would recommend you to profile you code first.

[Indu]

I have, and its the following line that takes the longest:

X3update = pagefun(@mtimes,A1,X3) + BU(:,j,:);

Next most intensive is the parfor loop.

Is it possible to get rid of the loops completely (or just the for-loop would be adequate) by adopting a different approach is my question?

[Jill Reese]

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

[Indu]

Thanks, I will replace the tic/toc where gpuArrays are used. However, I used the profiler to find the specific runtimes for script and learnt that the following line takes the longest to execute as it gets called repeatedly:

X3update = pagefun(@mtimes,A1,X3) + BU(:,j,:);

Just a thought, will it be faster if I use linear indexing when accessing BU(:,j,:)?