Curve fitting

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams["figure.dpi"]=150
plt.rcParams["figure.facecolor"]="white"

# Generate our data
x = np.linspace(0, 5, num=100)
y = 2.5 * np.exp(0.5 * x) + np.random.rand(100)

# plot our data
plt.plot(x, y, '.')
plt.show()

Input:

from scipy import optimize

def fit_func(x, a, b):
    return a * np.exp(b * x)

params, params_covariance = optimize.curve_fit(fit_func, x, y, p0=[1, 1])

print(params)

Output:

[2.77004013 0.48224117]

The order of arguments for curve_fit: fitting function, independent variables, dependent variable, initialization values for the coefficients (p0).

# plot both data and fit function
plt.plot(x, y, 'o', markersize='4', label='Data')
plt.plot(x, fit_func(x, params[0], params[1]), c = 'r', label='Fit')
plt.legend(frameon=False, loc="upper center")
plt.show()