# lsqcurvefit does not follow convergence criteria in summation.

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Chris Pruefert on 27 May 2023
Commented: Torsten on 30 May 2023
I have a function that uses summation to fit an bi-exponential function. Because I have to retrieve other information from that fit, I cannot use the exp2-fit function unfortunately. As for the procedure over the 8 parts (n=8). The data is in t(xdata) and S(ydata). For each of the terms 1-8 the individual contribution (yfit_n) is calculated and then added up together to get the final results for the fit (yfit). The fucntion has 7 variables for the fitting in the vector x or x0 for the respective startin point (x(2) is not used at this stage).
FS_1=0.05;
FS_2=2.0264;
d=1E-4;
dy=1E-5;
n=1:8;
t=t_S_mathworks(:,1);
S=t_S_mathworks(:,2);
x0=rand(7,1);
fun=@(x,t) x(1)+x(3).*(FS_1+FS_2*sum(((-1.^n)./n.^2).*(1-cos(n*pi*dy/d))...
.*(x(4).*exp(-x(6)*(t).*n.^2.*pi^2./d^2)...
+x(5).*exp(-x(7)*(t).*n.^2.*pi^2./d^2)),2));
options.OptimalityTolerance = 1e-15;
[x,resnorm]=lsqcurvefit(fun,x0,t,S);
Because I got the flag that indicates that the convergence criterion is too low I wanted to change, but it was incorporated in the fit-options, I think.
After the fit has converged (but not giving a useful result) I checked for the convergence criterion and it wasn't replaced with the new one of 1E-15.
Optimization completed: The first-order optimality measure, 1.132517e-08,
is less than options.OptimalityTolerance = 1.000000e-06.
And when I check for the fit using
S_fitted =x(1)+x(3).*(FS_1+FS_2*sum(((-1.^n)./n.^2).*(1-cos(n*pi*dy/d))...
.*(x(4).*exp(-x(6)*(t).*n.^2.*pi^2./d^2)...
+x(5).*exp(-x(7)*(t).*n.^2.*pi^2./d^2)),2));
plot(t,S_fitted)
I see that only the first two data points gave a result other than the minium of data points. So it seems that the fitting itself did not happen. I inlcued the data to let you see of that error is reproducable. I hope that it is just a bening error I cannot seem locate right now.
All help is appreciated.
All the best,
Chris
Torsten on 30 May 2023
@Alex Sha has his own software - usually with extraordinary good results for fitting problems.

Matt J on 27 May 2023
After the fit has converged (but not giving a useful result) I checked for the convergence criterion and it wasn't replaced with the new one of 1E-15.
Because you have not passed the options variable to lsqcurvefit
options.OptimalityTolerance = 1e-15;
[x,resnorm]=lsqcurvefit(fun,x0,t,S,[],[],options);
Chris Pruefert on 30 May 2023
That is correct. Thank you.

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