"""
Implementation of Newton's method, from lecture 29/9.
"""

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


#solve the equation e**(-0.1* x**2) * sin(pi * x / 2) = 0:
def g(x):
    return np.exp(-0.1 * x**2) * np.sin(np.pi * 0.5 * x) 

def dg(x):
    dg1 = -2*0.1*x*np.exp(-0.1*x**2)*np.sin(np.pi/2*x)
    dg2 = np.pi/2*np.exp(-0.1*x**2)*np.cos(np.pi/2*x)
    return dg1 + dg2


x = np.linspace(0,20,201)
y = g(x)

#plt.plot(x, y)
#plt.show()


#print(g(1.5))
#print(dg(1.5))

x_val, iter, f_val = Newton(g, 1.5, dg)
print(f'Found approximate root x = {x_val:g} with f(x) = {f_val:g}, in {iter} iterations')