custom equation fit in curveFitter is not working

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.

[Torsten]

And what is your initial value for b ?

[Fernanda Vargas]

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]

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.

Answer 1

[Torsten]

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

[Fernanda Vargas]

thank you so much!