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Fitting Tanh curves with python

I need to fit an tanh curve like this one :

import numpy as np
import matplotlib.pyplot as plt
from lmfit import Model


def f(x, a1=0.00010, a2=0.00013, a3=0.00013, teta1=1, teta2=0.00555, teta3=0.00555, phi1=-50, phi2=600, phi3=-900,
      a=0.000000019, b=0):

    formule = a1 * np.tanh(teta1 * (x + phi1)) + a2 * np.tanh(teta2 * (x + phi2)) + a3 * np.tanh(
        teta3 * (x + phi3)) + a * x + b

    return formule

# generate points used to plot
x_plot = np.linspace(-10000, 10000, 1000)

gmodel = Model(f)

result = gmodel.fit(f(x_plot), x=x_plot, a1=1,a2=1,a3=1,teta1=1,teta2=1,teta3=1,phi1=0,phi2=0,phi3=0)

plt.plot(x_plot, f(x_plot), 'bo')
plt.plot(x_plot, result.best_fit, 'r-')
plt.show()

i try to do someting like that but i got this result:

enter image description here

There is an other way for fitting this curve ? I don't know what i'm doing wrong ?

Solution

  • Basically your fit is fine (although not very nice from the coding point of view). Like always, non-linear fits strongly rely on initial parameters. Yours are just chosen badly. You could either think how to determine them manually or use a pre-made package like differential_evolution from scipy.optimize. I am not using this package but you can find an example here on SE