How can i speed up my nested for loops ?

Hello everyone,

Could you please help to speed up my code? It is a nested for loops code and running very slow. Is there any way to speed up the computation? I am a Matlab beginner, i have tried to vectorize the code but failed. The code is here:

p0=0.02;
n=100;
c=5000;
for n1 = 38 : 52 ; 
 for w = 0.5: 0.01: 3.4 ;
  for k1 = w+0.01: 0.25 : 7.5;
   for k2 = 0.5: 0.25: 5.5;
                        
 for R = RLi : 600
     
 for x = x1 : x2
     
   % n2
   d1 = floor((n1*x/c) + w*sqrt(n1*x/c*(1-x/c))) ;         
   d2 = ceil((n1*x/c) + k1*sqrt(n1*x/c*(1-x/c)))-1  ;     
   
    pps  = binocdf(d2, n1, p0) - binocdf(d1, n1, p0);
    
    n2=floor((n-n1)/pps); 
    
   
    % alfa 
    d3 = floor((n1*x/c) + w*sqrt(n1*x/c*(1-x/c)))+1 : ceil((n1*x/c)+k1*sqrt(n1*x/c*(1-x/c)))-1 ;
    d4 = floor(((n1+n2)*x/c) + k2*sqrt((n1+n2)*x/c*(1-x/c)))- d3 ;
    
    pa1= binopdf(0:floor(n1*x/c+w*sqrt(n1*x/c*(1-x/c))),n1,p0);      
    pa10=sum(pa1) 
    
    pa22 = binocdf(d4, n2, p0);
    pa21 = binopdf(d3, n1, p0);
    A = pra10 + sum(pra21.*pra22);
   
    cdf0 = (1-A^(R))*binopdf(x,c,p0);
    
 end
 end
   end
  end
 end
end

Thanks a lot.

Answer 1

[Jeff Miller]

You can speed this up to some degree by rearranging the order of your for loops. For example, consider:

   d1 = floor((n1*x/c) + w*sqrt(n1*x/c*(1-x/c))) ;         
   d2 = ceil((n1*x/c) + k1*sqrt(n1*x/c*(1-x/c)))-1  ;     
   pps  = binocdf(d2, n1, p0) - binocdf(d1, n1, p0);    

Of the looping variables, these lines only depend on n1, w, k1, and x, so you don't need to compute them again and again for all the different combinations of R and k2. That suggests an organization of loops something like:

for n1 = 38 : 52 ; 
 for w = 0.5: 0.01: 3.4 ;
  for k1 = w+0.01: 0.25 : 7.5;
  for x = x1 : x2     
   % n2
   d1 = floor((n1*x/c) + w*sqrt(n1*x/c*(1-x/c))) ;         
   d2 = ceil((n1*x/c) + k1*sqrt(n1*x/c*(1-x/c)))-1  ;     
   pps  = binocdf(d2, n1, p0) - binocdf(d1, n1, p0);
   for k2 = 0.5: 0.25: 5.5;
       for R = RLi : 600
     ...

I didn't look to see whether there are other analogous speed-ups involving d3, d4, etc, but hopefully this gives you one pattern of speed-up to look for.