How to speed for or while loop code?

Here is the following code I have written to find out the optimum truncation for my time series.

But this code is really very slow. Kindly help me on this.

P=0.2;  g=4; K=4;  % constants 
N=18000; % supposing a length of full time series 
n=1500; % length of the window

const=P^g+(1-P^g)*(K/(sqrt(2)*n));
syms m l nt
omeg=const*symsum(((-pi/2)*(((l/N)-m)^2)*K^2),m,1,round((n/2)-1));
nt=0;
esw=0;
while esw<0.8
    nt=nt+1;
    esw=symsum(omeg,l,0,nt)/symsum(omeg,l,0,round((n-1)/2));
    trunc(nt)=esw;
end

many thanks in advance.

[KALYAN ACHARJYA]

Yes, but it somwhow depends on the values of N & n also.

[Daniel M]

Do you require this code to be symbolic? Was trunc preallocated offscreen? What does the profile say is the bottleneck for performance?

[sanjay Negi]

Yes @Kalyan Acharjya, N and n are basically deciding the truncation point. The details I would like to explain down below. Kindly follow.

@ Daniel, It could be symbolic. No, trunc is not preallocated. This will provide me the truncated point (nk).

So, here what I am try to do.

If suppose x(t) is a time series.

then

xs (l)= x[l+(s-1)(n-m+1)] ,

where l=0,1,.....n-1.

n is the length of the window and m is the amount of overlap.

so, s are the number of segmented windows which can be represented as

s = 1,2,......(n-1)+(s-1)(n-m+1) ≤ N.

N is the length of the time series x(t)

Now, the the amount of overlap m will depend upon the rate of change of P^g, which is the polarization factor calculated with the first selected window ( in cour case n=1500).

K=nW is another parameter which we decide and defined as the time-bandwidth of the prolate taper.

So the truncation point is decided by the criterion,

,

where,

The following code is trying to adapt with each segment depending upon the window length(n), and full trace length N. The code should also change the estimated value of nt upon varying values of polarisation factor P, which I suppose is not doing so !!

In above code whatever the value range I insert for P = [0 to 1], g= [2 to 6] and K [4 to 6].

The main dependency goes with the length of segmented window.

Therefore, I keenly require your help to understand the basic ingredient.

More important is the performance of this code.

Thanks

[prasanth s]

in your code the variable 'esw' is not in double format after inside the loop. so it make a endless loop.

notes:

split the long formulas into smallel portions.

use temporary variables to store intermediate values. so the debugging becomes easy.