Is there any way that I can optimise this code. It takes lot of time to run and for larger iteration like 'nc=10e6' its stops stating runtime error.

clear all 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Simulation of transmission signal decay from a high Finesse Fabry-Perot cavity
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%Author-Jayash
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

nc=1000000;  % no. of cycles inside the cavity
t=1;
Finesse=140000; 
%x=-5e4:1:5e4;
ni=1;
f=1/t;

while ni < nc
     syms x n r fsr 

       ESm = symsum((r)^(2*n - 2).*exp(-1i*(x./(2*fsr))*(n - 1)),n,0,ni); % summation of signal(s) to be deducted in each cycle.

       R = 0.9999775603;    % Reflectivity of cavity mirrors
       T = 1 - R;
       x = sqrt(R);
       r=x;

       fsr=10e9;

       Itn=1./(1+(Finesse.*((sin(f./(2*fsr)))^2)));   % Transmission Intensity from Cavity

       ESe = T.*ESm;
       ISe = ESe.*conj(ESe);

       Itn1=Itn-ISe;         % Decay in each cycle 

       %plot(Itn1,t);
       plot(t,double(subs(Itn1)),'*');
       hold on

       ns=ni+10000;
       ni=ns;
       t=t+ni.*(10e-9);

end

[Geoff Hayes]

When you say that it takes a lot of time to run, what exactly does that mean? More than a few minutes, hours, more?

When nc=1000000, you say that its stops stating runtime error? Please include the full error message that you observe.

Note that there are a couple of errors in the above code

    fsr=

    if true
      % code
    end10e9;

What should fsr be initialized to? Why is there a 10e9?

The code

 ns=ni+10000;
 ni=ns;

can be replaced by

 ni = ni + 10000;

[jayash]

lot of time implied hours,I mean more than 5-6 hours for nc=10e6. For nc=1000 it takes 2 mins.

There was some typo mistakes while pasting the code.

yeah my bad it is ni=ni+10000...

Answer 1

[Roger Stafford]

The use of 'symsum' repeatedly in your while-loop could be slowing you down. After all, what you have there is a geometric series and there is an easy formula for its sum. See:

   http://en.wikipedia.org/wiki/Geometric_series

Just use that formula for 'ESm' instead of calling on 'symsum' and see if it doesn't go a lot faster.

In fact I would remove all references to symbolic variables in your code. They can slow down computations considerably.

[jayash]

yeah I could use that. Thanks :)