import matplotlib.pyplot as plt
import numpy as np

dich_steps = []
new_raph_steps = []

def f(x) -> float:
    return np.exp(x) - 2 * np.cos(x)


def dichotomie(x_0, a, b, epsilon, n=0) -> float:
    delta = f(a) * f(x_0)
    x_1 = (a + b) / 2

    dich_steps.append(x_1)

    if np.abs(b - a) <= epsilon:
        return x_1

    if delta < 0:
        return dichotomie(x_1, a, x_0, epsilon, n+1)
    elif delta == 0:
        return x_1
    else:
        return dichotomie(x_1, x_0, b, epsilon, n+1)


def f_prime(x) -> float:
    return 1 + np.sin(x)


def newton_raphson(x_0, epsilon) -> float:
    x_1 = x_0 - (f(x_0) / f_prime(x_0))
    new_raph_steps.append(x_1)

    if np.abs(x_1 - x_0) < epsilon:
        return x_1
    elif np.abs(f(x_0)) < epsilon:
        return x_1
    return newton_raphson(x_1, epsilon)


def ex1() -> None:
    x = np.arange(0, 1, 0.001)
    f = [np.exp(i) - 2 * np.cos(i) for i in x]
    f1 = [np.exp(i) for i in x]
    f2 = [2 * np.cos(i) for i in x]

    for i in range(len(x)):
        if f1[i] == f2[i]:
            print(f1[i])

    plt.plot(x, f)
    plt.plot(x, f1)
    plt.plot(x, f2)
    plt.grid()
    plt.show()

    dichotomie_res = dichotomie(0, 0, 1, 10e-6)
    print(dichotomie_res)

    plt.plot(dich_steps)
    plt.title('Convergence de la dichotomie')
    plt.show()

    newton_raphson_res = newton_raphson(0.1, 10e-6)
    print(newton_raphson_res)

    plt.plot(new_raph_steps)
    plt.title('Convergence de Newton-Raphson')
    plt.show()

    """
    La dichotomie à moins d'étape que NR, mais NR à l'air plus rapide,
    comme Flash McQueen
    """


if __name__ == '__main__':
    ex1()