Making a for-loop in Matlab faster by using arrayfun?

Question

currently I have the following portion of code:

for i = 2:N-1
  res(i) = k(i)/m(i)*x(i-1) -(c(i)+c(i+1))/m(i)*x(N+i) +e(i+1)/m(i)*x(i+1);
end

where as the variables k, m, c and e are vectors of size N and x is a vector of size 2*N. Is there any way to do this a lot faster using something like arrayfun!? I couldn't figure this out :( I especially want to make it faster by running on the GPU later and thus, arrayfun would be also helpfull since matlab doesn't support parallelizing for-loops and I don't want to buy the jacket package... Thanks a lot!

Answer 1

You don't have to use arrayfun. It works if use use some smart indexing:

    clear all

    N=20;
    k=rand(N,1);
    m=rand(N,1);
    c=rand(N,1);
    e=rand(N,1);
    x=rand(2*N,1);

    % for-based implementation
    %Watch out, you are not filling the first element of forres!
    forres=zeros(N-1,1); %Initialize array first to gain some speed.
    for i = 2:N-1
      forres(i) = k(i)/m(i)*x(i-1) -(c(i)+c(i+1))/m(i)*x(N+i) +e(i+1)/m(i)*x(i+1);
    end

    %vectorized implementation
    parres=k(2:N-1)./m(2:N-1).*x(1:N-2) -(c(2:N-1)+c(3:N))./m(2:N-1).*x(N+2:2*N-1) +e(3:N)./m(2:N-1).*x(3:N);

    %compare results; strip the first element from forres
    difference=forres(2:end)-parres %#ok<NOPTS>