A Novel Method for Curvefitting the Stretched Exponential Function to Experimental Data
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lsqnonlin and stretched exponential function
I am currrently trying to fit my data with lsqnonlin instead lsqcurvefit for a comparative reason and I am facing some troubles.
Starting with the easiest example in https://se.mathworks.com/help/optim/ug/lsqnonlin.html, I modify the function as:
fun = @(r) r(1).*exp(-d.*r(2)).^r(3)-y
This function yields x = [1.0376 3.1962 0.4104].
From here, I calculate my errors in the way:
N = length(y(:,1));
[Q,R] = qr(J,0);
mse = sum(abs(residual).^2)/(size(J,1)-size(J,2));
Rinv = inv(R);
Sigma_var = Rinv*Rinv'*mse;
x_er = full(sqrt(diag(Sigma_var)));
Here, the values I get are not making any sense to me x_er = [0.02701 6458034.8422 829226.8633]; especially for x(2) and x(3).
Fit and errors are totally fine if I fit similar data in the form: (i) r(1).*exp(-d.*r(2)) or (ii) r(1).*exp(-d.*r(2))+r(3).*exp(-d.*r(4));
Could you please help me? Am I missing something?
Thanks a lot.
How do I fit an exponential curve to my data?
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Stretched exponential fit matlab
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