from matplotlib import pyplot as plt
import numpy as np
from scipy import optimize as opt

f = lambda x: np.sin(x**2)-6*x+1
phi = lambda x: (np.sin(x**2)+1)/6
x = np.arange(0, 1, 0.1)
plt.plot(x, f(x), x, np.zeros(len(x)))
plt.show()


def fixed_point_iter(f, x0, eps):
     x = x0
     while True:
         y = f(x)

         if abs(y - x) < eps:
             return y
         else:
             x = y


my_sol = fixed_point_iter(phi, 2, 1e-6)
print(my_sol)

sc_sol = opt.root_scalar(f, method='brentq', bracket=[1, 2]).root
print(sc_sol)

print(abs(sc_sol - my_sol))