lsqcurvefit issues due to variables being several orders of magnitu... (2024)

What is "point" ? What is "Ip" ?

Please supply executable code.

Sorry, I thought I changed that. Ip(:,point) is just data(:,2)

Edit: I missed some stuff when I copied and pasted it over. I just fixed it. I clicked the MATLAB online tab and it ran.

I ran out of time at the moment, but no matter what I tried for initial guesses, the gradient was calculated to be essentially zero so it thinks it's converged no matter the input guess.

I changed parameters greatly to see the influence each has on the result and purely by trial and error found the above that aren't too terrible.

You may want to investigate the gradient calculations more thoroughly and see what might be going on there...

Thank you for the help. How do I look at the gradient calculations?

This is actually one of hundreds of points I need to look at so I need to figure out how to get it to work without me manually finding the best values.

So I tried scaling the variables and even the equation to see if it did have to do with my variables being to different in terms of order of magnitude. That didn't do anything.

I also tried using the trust-region-reflective algorithm. It didn't improve the fit most of the time. Interesting enough though, I have some data points that were near the edge of my plasma where my densities are pretty low and I didn't get the signature "S" shape I was looking for. Trust-region-reflective did tend to work better for those cases.

I ended messing around with the options and the bounds. The following options and bounds get me a pretty good fit for the majority of my data points. I realized my OptimalityTolerance and FunctionTolerance were causing it to step out. I cranked those down and then it started having issues with the StepTolerance the majority of the time and on occasion the ConstraintTolerance. It appears that the majority of the time, my stepsize is getting extremely small and causing it to step out. I need to look in to how the step size is calculated and figure out why this would be happening when the fit is still pretty far off. Also, my tolerances are probably overkill right now. I was just cranking them down to see what happens, but after a certain point it didn't really make a difference.

Edit: Adding the following option to the options appears to make it converge succesfully more often.

load('V1.mat')

load('Vp.mat')

load('data.mat')

V = [V1, Vp]; %voltages

a = 1.1792;

b = 0.5;

e = 1.60217662e-19;

Area = 4.7909e-7;

mi = 39.948./(6.022e23.*1000);

coeff0 = [1e-5 10]; %initial guess

Eqn7 = @(coeff, VV) coeff(1)*sqrt(coeff(2))*...

(a*(-VV(:,1)/coeff(2)).^b.*tanh(VV(:,2)/(2*coeff(2))) + ...

(a*(-VV(:,1)/coeff(2)).^b - a*(-(VV(:,1)+VV(:,2))/coeff(2)).^b)./(exp(VV(:,2)/coeff(2))+1));

%options = optimoptions('lsqcurvefit','Algorithm','levenberg-marquardt','OptimalityTolerance',1e-16,'FunctionTolerance',1e-16);

lb = [];

ub = [];

[vals, resnorm, out, flag] = lsqcurvefit(Eqn7, coeff0, V, data(:,2));

plot(data(:,1),data(:,2),'x',data(:,1),Eqn7(vals,V),'b-')

format long

vals(1)

vals(1)=vals(1)*sqrt(2*pi*mi)/(e^1.5*Area*100^3);

vals(1)

vals(2)