custom equation fit in curveFitter is not working

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I'm looking to do a "custom equation" fit using the curveFitter in matlab with this data:
pc2 =
0
0.0001
0.0011
0.0216
0.2847
0.8708
1.0000
lam_2 =
0
30
55
110
200
320
460
After opening curveFitter, I load lam_2 as my X and pc2 as my Y.
My custom equation is: 0.5*(1+erf(b*(x-a)))
One time I got a good fit by choosing a good initial value, MATLAB calculated a to be a = 240.4
Now I wanted to recreate this fit and I'm choosing 240.4 or even numbers around that value as my starting point for "a" and the fit doesnt work anymore.
  3 Commenti
Fernanda Vargas
Fernanda Vargas il 30 Gen 2023
I didnt give it an initial value
but i also didnt give it the first time and it found a good fit just by me choosing a good value for a
Torsten
Torsten il 30 Gen 2023
I didn't know you can give an initial value to only one of the parameters to be fitted. And in my opinion - if MATLAB chooses the second one arbitrarily - it also doesn't make much sense. Better you plot the curve for your guessed parameters first before using the fitting tool.

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Torsten
Torsten il 30 Gen 2023
Modificato: Torsten il 30 Gen 2023
pc2 = [ 0
0.0001
0.0011
0.0216
0.2847
0.8708
1.0000];
lam_2 = [ 0
30
55
110
200
320
460];
hold on
plot(lam_2,pc2,'o')
fun = @(x,a,b)0.5*(1+erf(b*(x-a)));
a = 1000;
b = 1/2000;
sol = lsqcurvefit(@(x,xdata)fun(xdata,x(1),x(2)),[a b],lam_2,pc2)
Local minimum possible. lsqcurvefit stopped because the final change in the sum of squares relative to its initial value is less than the value of the function tolerance.
sol = 1×2
240.3831 0.0101
x = linspace(min(lam_2),max(lam_2),100);
plot(x,fun(x,sol(1),sol(2)))
hold off
grid on

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