import numpy as np


def point_info(x, f):
    return f"x = {x}, f(x) = {f(x)}"


def hooke_jeeves(f, x0, delta0, epsilon, alpha, r=lambda x: True):
    x = np.array(x0)
    delta = np.array(delta0)

    iteration = 0

    while np.linalg.norm(delta) > epsilon:
        iteration += 1

        print()
        print("=" * 40)
        print("Итерация", iteration)

        print("Текущая базовая точка", point_info(x, f))

        sample_x = exploratory_search(f, x, delta, r=r)

        if f(sample_x) < f(x):
            print("Исследующий поиск УДАЧНЫЙ")

            x_p = sample_search(f, x, sample_x, r=r)

            if f(x_p) < f(x):
                print("Поиск по образцу УДАЧНЫЙ")
                x = x_p
            else:
                print("Поиск по образцу ПРОВАЛЕН")
                x = sample_x

            print()
            print("Новая базовая точка", point_info(x, f))

        else:
            print("Исследующий поиск ПРОВАЛЕН")

            print("Уменьшаем шаг", delta, "->", delta / alpha)
            delta = delta / alpha
            print("ε =", np.linalg.norm(delta))

    return x, f(x)


def exploratory_search(f, x, delta, r=lambda x: True):
    print()
    print("Выполняем исследующий поиск")

    x_new = np.array(x)
    f_x_new = f(x_new)

    for i in range(len(x)):
        x_up = x_new.copy()
        x_down = x_new.copy()

        x_up[i] += delta[i]
        x_down[i] -= delta[i]

        f_x_up = f(x_up)
        f_x_down = f(x_down)

        if f_x_up < f_x_new and f_x_up < f_x_down:
            x_new = x_up
            f_x_new = f_x_up
        elif f_x_down < f_x_new:
            x_new = x_down
            f_x_new = f_x_down

    if any([x_new[i] != x[i] for i in range(len(x))]):
        print("Найдена точка", x_new, f(x_new))
    return x_new


def sample_search(f, x1, x2, r=lambda x: True):
    print()
    print("Выполняем поиск по образцу")
    while f(x2) < f(x1):
        x2, x1 = x2 + (x2 - x1), x2
    print("Найдена точка", x2, f(x2))
    return x2


def f1():
    x0 = [0, 0]
    delta0 = [1e6, 1e6, 1e6]
    alpha = 2
    epsilon = 1e-4

    c = [[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]]

    r = [[-1000, 1000], [-100, 100]]

    def f(x):
        return sum(
            [
                sum([c[i][j] * x[i] ** j for j in range(len(c[i]))])
                for i in range(len(c))
            ]
        )

    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha, r=r)
    return x, val


def f2():
    x0 = [1, 1]
    delta0 = [1, 1]
    alpha = 2
    epsilon = 1e-6

    def f(x):
        return x[0] ** 4 + x[1] ** 2 - 4 * x[0] * x[1]

    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
    return x, val


def f3():
    x0 = [1, 0]
    delta0 = [1, 1]
    alpha = 2
    epsilon = 1e-5

    def f(x):
        return x[0] * np.exp(x[0]) - (1 + np.exp(x[0])) * np.sin(x[1])

    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
    return x, val


def example():
    x0 = [-4, -4]
    delta0 = [1, 1]
    alpha = 2
    epsilon = 1e-4

    def f(x):
        return 8 * (x[0] ** 2) + 4 * x[0] * x[1] + 5 * (x[1] ** 2)

    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
    return x, val


if __name__ == "__main__":

    x, val = f1()
    # x, val = f2()
    # x, val = f3()
    # x, val = example()

    print()
    print("=" * 40)
    print("Точка экстремумв:", x)
    print("Минимальное значение функции:", val)