import sys
import numpy as np
import matplotlib.pyplot as plt

def Newton(f, x, dfdx, tol = 1.0E-7, max_n=100):
    n = 0
    while abs(f(x)) > tol and n <= max_n:
        x = x - f(x)/dfdx(x)
        n += 1
    return x, n, f(x)

def g(x):
    return np.exp(-0.1*x**2) * np.sin(np.pi / 2*x)

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


x = np.linspace(0,10,1001)
plt.plot(x,g(x))
plt.plot(x,np.zeros(len(x)), '--')
plt.show()

x0 = float(sys.argv[1])
x, n, val = Newton(g, x0, dg)
print('Computed root:', x)