# example from: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html#scipy.optimize.curve_fit

import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import curve_fit


def func(x, a, b, c):
    return a * np.exp(-b * x) + c

# Define the data to be fit with some noise:


xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5)
np.random.seed(1729)
y_noise = 0.2 * np.random.normal(size=xdata.size)
ydata = y + y_noise
plt.plot(xdata, ydata, 'b-', label='data')

# Fit for the parameters a, b, c of the function func:


popt, pcov = curve_fit(func, xdata, ydata)
popt

plt.plot(xdata, func(xdata, *popt), 'r-', label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

# Constrain the optimization to the region of 0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5:


popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5]))
popt

plt.plot(xdata, func(xdata, *popt), 'g--', label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))



plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

