Using summation containing function for curve fitting

I was trying to fit my data in an equation given below:

where a=1,, also summation upto 250 terms is enough.

k & Cs are fitting parameters. I have data for t & S(t).

I tried the curve fitting tool. It doesnt support for summation functions.

Can you help me to code for this for this fit ?

I am attaching the data file.

Answer 1

[Stephan]

Hi,

you can use this script:

x0 = [12 3];
x = lsqcurvefit(@(x,t)equation_fit(x,t),x0,t,S)
S_calculated = equation_fit(x,t);
plot(t,S,t,S_calculated)

function S_calc = equation_fit(x,t)
n = 1:250; % Number of sumations
a = 1; % define a
w2n = n.^2.*pi^2./4000; % Definition of omega_n_squared
% Fitting values
Cs = x(1);
k =  x(2);
% Determine function
sum_parts = ((1-(-1).^n)./(n.^2)).*(exp(-w2n.*t)+...
    (k.*(1-(1+w2n.*t).*exp(-w2n.*t)))./(w2n+k.*(1-exp(-w2n.*t))));
S_calc = 1 + a.*Cs.*(1 - (4/pi^2 .* sum(sum_parts,2)));
end

But the resulting fit appears not to be a very good result to me:

Note that the last two lines of your data file contain invalid informations - i deleted them and attached the needed .mat-file to this answer, so that if you load the .mat-file to workspace you can execute the script and check the results by yourself. The result of sum_parts is a matrix with 89425x250 (number of samples of S(t) x n). In the second step the sum is build, so that you sum up from n=1...250 and the result is the S_calc with the needed dimenstion of 89425x1. This is the way you can solve this summation problem for curve fitting in Matlab.

Best regards

Stephan

[Aniket Masaye]

You did fantastic job. I am actually noob so, it is hard to get through your syntax.

I copied your script and ran it. There was something appeared in command windows

And how will i get the values of my fitting variables?

[Stephan]

Cs=x(1)
k=x(2)

if my answer was useful please accept it.

[Lisa97]

Hi Stephan: your code is really helpful. Thanks a lot!

Answer 2

[Andrew]

Dear Stephan,

I am trying to fit the attached data to the following model

using the curve fitting tool in Matlab without success. For the equation, t = time (min), l = 0.0023 m and n = 0 to infinity while D is the fitting parameter or unknown constant to be found once the data is fitted. Could you please help me with a code to fit the data? Thanks in anticipation to your positive response.

Kind regards,

Andrew