MATLAB: Extremely slow nested for loop

for loopperformancevectorization

Hi,
I have number of functions that I use to find roots to Neumann problem. One of the functions contains nested for loops which runs forever.
Please see below:
The function consists of three nested for loops as:
function [Lsn] = coefFourier_ll_log(k,ll)
N=length(ll);
ll_n=coefFourier1(k*ll);
lambda=zeros(1,N-1); lambda(N/2+1:N-1)=-0.5./(1:N/2-1);
lambda(1:N/2-1)=fliplr(lambda(N/2+1:N-1)); 
M=N/2-1; Lsn=zeros(N-1,N-1);
for s=-M:M
   for n=-M:M
       rmin=max(-M,max(-M-n,s-M)); 
       rmax=min(s+M,min(M-n,M));
       for r=rmin:rmax
          Lsn(s+M+1,n+M+1)=Lsn(s+M+1,n+M+1)+ll_n(s-r+M+1)*ll_n(n+r+M+1)*lambda(r+M+1);
       end
   end
end
Lsn=0.5*Lsn;
This function receives k(double), ll(1D array) and returns Lsn(Matrix). For the given time profile, the system size is 512, which means M is 255.
How I can vectorize it to increase its speed? I need to run this group of functions for couple of hundreds times and eventually with even bigger system size.
Thank you for your time.

Best Answer

Start with a slightly cleaned version:
function Lsn = coefFourier_ll_log(k,ll)
N      = length(ll);
ll_n   = coefFourier1(k*ll);
lambda = zeros(1, N-1);
lambda(N/2+1:N-1)  = -0.5 ./ (1:N/2-1);
lambda(N/2-1:-1:1) = lambda(N/2+1:N-1);  % Instead of FLIPLR
M   = N/2-1;
M1  = M + 1;
Lsn = zeros(N-1, N-1);
for s = -M:M
   for n = -M:M
       rmin = max(-M, max(-M-n, s-M)); 
       rmax = min(s+M, min(M-n, M));
       Lsn(s+M1, n+M1) = Lsn(s+M1, n+M1) + ...
                         sum(ll_n(s+M1-rmin:s+M1-rmax) .* ...
                             ll_n(n+M1+rmin:n+M1+rmax) .* ...
                             lambda(M1+rmin:M1+rmax));
   end
end
Lsn = 0.5 * Lsn;
Here the inner loop from rmin:rmax way vectorized. Please post the timing before and after the changes measure by tic/toc. The profiler disables the JIT acceleration, such that it is less useful. Providing some test input of a relevant size (e.g. created by rand) would allow us to run the tests by our own.
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