# %%
import numpy as np
import sympy as sp
import matplotlib.pyplot as plt

# Parameter
N = 200
x = sp.Symbol("x")

# Funktion
f_sym = x**4 - 10 * x**2 + x
#f_sym = -sp.cos(2 * sp.pi * x)

# Ableitungen
f = sp.lambdify(x, f_sym, "numpy")
f_prime = sp.lambdify(x, sp.diff(f_sym, x), "numpy")
f_second = sp.lambdify(x, sp.diff(f_sym, x, 2), "numpy")

# Daten
# x_data = np.linspace(-4, 4, N)
x_data = np.linspace(-4, 4, N)
f_data = f(x_data)

# Plot
plt.figure(1)
plt.plot(x_data, f_data)
plt.xlabel("x")
plt.ylabel("y")
plt.grid("on")
plt.show()

# Newton Verfahren
# Startwert
#startwerte = [0.01, 0.02, 0.05, 0.1, 0.2, 0.23, 0.24, 0.245, 0.248, 0.249, 0.2499]
startwerte = [1.1]

# Iterationsformel
x_n = lambda x: x - f_prime(x) / np.abs(f_second(x))

print(60 * "-")
# Iteration
for x_0 in startwerte:
    n = 0
    x_i = x_0
    f_x = f(x_0)
    f_x_prime = f_prime(x_0)
    f_x_second = f_second(x_0)
    print(f"x_{n}: {x_0}\nf(x_{n}): {f_x}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")

    limit = 1000

    while np.abs(f_x_prime) > 1e-10 and limit > 0:
        n += 1
        x_i = x_n(x_i)
        f_x = f(x_i)
        f_x_prime = f_prime(x_i)
        f_x_second = f_second(x_i)
        print(f"x_{n}: {x_i}\nf(x_{n}): {f_x}\nf'(x_{n}): {f_x_prime}\nf''(x_{n}): {f_x_second}\n")
        limit -= 1
    print(60 * "-")
# %%