ERROR: Fitting a custom function to my data

I implemented a function into my script, that models the value of T:

function T_model_MILS = exactmils(lambda,cv,vD,t,rb,q)
 
cw = 4.15*10^6;
alpha = lambda/cv;
r = rb; % case r = rb
R = r/rb;
vT = vD*cw/cv;
Pe = rb*vT/alpha;
b = (R*Pe/4)^2;
Fo = alpha*t/rb^2;
tau = 4*Fo/R^2;
u = 1./tau;

n = length(u);
aa = besseli(0,2*sqrt(b));    
G = zeros(n,1);
    
for i = 1:n
    A = quadgk(@funa,u(i),inf,'AbsTol',1.0e-12);
    G(i) = 0.5*A*aa;
end
    
function  y = funa(x)
    y = exp(-x - b./x)./x;
end

T_model_MILS = q.*G./(2*pi*lambda);
T_model_MILS(isnan(T_model_MILS))=0; % NaN to zero for fitting alg.
end

The function works fine with preset parameters (green: model, red: my measured dataset). But surely, I want the parameters to be estimated by matlab ...

Now, when I want to fit my function parameters x1,x2 and x3 to my data:

% Initial model parameters
lambda2 = 2;
cv2 = 2*10^6;
vD2 = 1*10^(-7);
x = [lambda2 cv2 vD2];

tic; 

%trying out function with set parameters
T2 = exactmils(x(1),x(2),x(3),tsekunden,rb,q);

% fitting to dTLOG-data
F2 = @(x,tsekunden) exactmils(x(1),x(2),x(3),tsekunden,rb,q); 
[x,resnorm,~,exitflag,output] = lsqcurvefit(F2,x,tsekunden,dTLOG);
T_modelfit_MILSexact = exactmils(x(1),x(2),x(3),tsekunden,rb,q);

toc; 

I get an error ...

__________________________

Solver stopped prematurely.

lsqcurvefit stopped because it exceeded the function evaluation limit,

options.MaxFunctionEvaluations = 3.000000e+02.

Elapsed time is 364.096528 seconds.

___________________________

How can I improve my fitting algorithm? It works fine with easier functions, but the function exactmils() is computationally more intense (elapsed time with set parameters = 0.966603 seconds).

Thank you very much for your help! :)

Answer 1

[Torsten]

Since we don't have data to test your code, we are not able to comment on your question.

Most probably, the line

T_model_MILS(isnan(T_model_MILS))=0; % NaN to zero for fitting alg.

will cause severe problems for an optimizer if there really are NaN values in T_model_MILS.