import numpy as np
import matplotlib.pyplot as plt


def Newton(f, x, dfdx, epsilon=1.0E-7, max_n=100,
           store = False):
    f_value = f(x)
    n = 0
    if store: info = [(x, f_value)]
    while abs(f_value) > epsilon and n <= max_n:
        x = x - f_value / dfdx(x)
        n += 1
        f_value = f(x)
        if store: info.append((x, f_value))
    if store:
        return x, info
    else:
        return x, n, f_value

def f(x):
    return np.sin(x) * np.exp(-0.1 * x)

def dfdx(x):
    df1 = np.cos(x) * np.exp(-0.1 * x)
    df2 = np.sin(x) * (-0.1) * np.exp(-0.1 * x)
    return df1 + df2

x_val, iter, f_val = Newton(f, 4.0, dfdx)

print(f'Found approximate root x = {x_val:g} with f(x) = {f_val:g}, in {iter} iterations')

"""
Terminal> python newton.py 
Found approximate root x = 3.14159 with f(x) = 1.11874e-11, in 4 iterations
"""