How to use a user defined function inside the curve fitting function?

Hi all,

I have a funciton that takes into account various parameters:

function [concatz] = my_fit_functioncpe(freq,parameters)

Rsolc = parameters(1);

Cm = parameters(2);

Rq = parameters(3);

Rn = parameters(4);

Ln = parameters(5);

RKch = parameters(6);

Rm = parameters(7);

Lm = parameters(8);

Rl = parameters(9);

Rctc = parameters(10);

T = parameters(11);

qc = parameters(12);

w = 2 * pi * freq;

Z = Rctc + 1./((1./Rsolc+T*(1j*w).^qc)) + 1./((1j*w*Cm)+ 1/Rl + 1/Rq + 1/RKch + 1./(Rn + (1j*w*Ln)) + 1./(Rm + (1j*w*Lm)));%4c

%CPEIMPEDANCE = 1./(T*(1j*w).^qc);

%Z = 1./(1./(Rctc)+(1./(Rsolc+CPEIMPEDANCE))) + 1./((1j*w*Cm) +1./Rl+ 1./Rq + 1./RKch + 1./(Rn + (1j*w*Ln)) + 1./(Rm + (1j*w*Lm)));

reZ = real(Z);

imZ = imag(Z);

concatz = cat(2,reZ,imZ);

end

But I want it to take this initial values like a normal function and fit it to my data. I am not sure how to do that and I have searched everywhere. In python, curve_fit seems to do the trick but I need it for matlab.

Answer 1

[Torsten]

Use "lsqcurvefit".

There are lots of examples under

https://uk.mathworks.com/help/optim/ug/lsqcurvefit.html

that show how to use a function to define the response values from a model equation.

But your model is hopelessly overfitted. Reduce the number of parameters first.

As an example, for the expression 1./Rl+ 1./Rq + 1./RKch, the three parameters cannot be fitted independently. Substitute them by one parameter 1/R. Other cases where reductions are necessary are obvious.