MATLAB: Accelerating code in matlab – for loop

accelerating codefor loopoptimization

Hi Guys,
    int = zeros(1,length(x));
    if k <= 0
        int = x ;
        return
    end
    for n = 3:length(x)
          y1 = x(2:n) ;
          t1 = ((n-2):-1:0)*dt ;
         y2 = x(1:n-1) ;
          t2 = t1 +dt; 
          int(n) = sum (t1.^(k-1)/factorial(k-1).*y1 + t2.^(k-1)/factorial(k-1).*y2)*dt/2 ;
    end
is there any suggestion to write this part of code more optimal? It is used for computing Integration. The most time consuming line is int(n)= … Whether I can change and remove the for loop here, and implement the for functionality in another way, e.g. vectors? Any suggestions would be appreciated …

Best Answer

At first I've clean up your code a bit:
if k <= 0
   int = x ;
   return
end
int = zeros(1, length(x));
fk1 = factorial(k - 1);
dt2 = dt / 2;
for n = 3:length(x)
  y1 = x(2:n);
  t1 = ((n-2):-1:0) * dt;
  y2 = x(1:n-1);
  t2 = t1 + dt; 
  int(n) = sum(t1 .^ (k-1) / fk1 .* y1 + t2 .^ (k-1) / fk1 .* y2) * dt2;
end
Now some improvements:
lenx = length(x);
fk1 = factorial(k - 1);
t1Vec = (((lenx - 2):-1:0) * dt) .^ (k-1) * dt / fk1;
int = zeros(1, lenx);
dt2 = dt / 2;
for n = 3:lenx
  y1 = x(2:n);
  t1 = t1vec(lenx-a-n:lenx-b);  % **see comment**
  y2 = x(1:n-1);
  t2 = t1 + dt; 
  int(n) = sum(t1 .* y1 + t2 .^ (k-1) / fk1 .* y2) * dt2;
end
I do not have the time to find the right constantd for a and b. Without access to Matlab I cannot simply try it, but you can. The idea is to avoid the repeated expensive calculation of t1 .^(k-1), when all elements except for one have been processed already. The same works for t2. I leave it up to you to elaborate this.
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