import numpy as np


def f(x, y):
    return np.log(1 + 3 * (x ** 2) + 5 * (y ** 2) + np.cos(x - y))


def dx(x, y):
    return (6 * x - np.sin(x - y)) / (
        1 + np.cos(x - y) + 3 * (x ** 2) + 5 * (y ** 2)
    )


def dy(x, y):
    return -(np.sin(y - x) - 10 * y) / (
        np.cos(y - x) + 5 * (y ** 2) + 3 * (x ** 2) + 1
    )


def dxdx(x, y):
    return (
        (6 - np.cos(x - y)) * (np.cos(x - y) + 3 * (x ** 2) + 5 * (y ** 2) + 1)
        - ((6 * x - np.sin(x - y))) ** 2
    ) / (((np.cos(x - y) + 3 * (x ** 2) + 5 * (y ** 2) + 1)) ** 2)


def dxdy(x, y):
    return (
        np.cos(y - x) * (np.cos(y - x) + 5 * (y ** 2) + 3 * (x ** 2) + 1)
        - (10 * y - np.sin(y - x)) * (np.sin(y - x) + 6 * x)
    ) / (((np.cos(y - x) + 5 * (y ** 2) + 3 * (x ** 2) + 1)) ** 2)


def dydy(x, y):
    return (
        (10 - np.cos(y - x))
        * (np.cos(y - x) + 5 * (y ** 2) + 3 * (x ** 2) + 1)
        - ((10 * y - np.sin(y - x))) ** 2
    ) / (((np.cos(y - x) + 5 * (y ** 2) + 3 * (x ** 2) + 1)) ** 2)


def phi_1(x, y):
    return -(dx(x, y) ** 2) - (dy(x, y) ** 2)


def phi_2(x, y):
    return (
        dxdx(x, y) * (dx(x, y) ** 2)
        + 2 * dxdy(x, y) * dx(x, y) * dy(x, y)
        + dydy(x, y) * (dy(x, y) ** 2)
    )


def grad(x, y):
    return max(dx(x, y), dy(x, y))


if __name__ == "__main__":
    xk = 0.1
    yk = 0.1
    eps = 0.001
    gradient = np.inf

    c = 0
    #print(phi_1(xk, yk))
    #print(phi_2(xk, yk))
    while eps < abs(gradient):
        t = -(phi_1(xk, yk)) / phi_2(xk, yk)
        xk, yk = xk - t * dx(xk, yk), yk - t * dy(xk, yk)
        gradient = grad(xk, yk)
        c += 1
        print(
            f"iteration {c} | x: {round(xk, 6)}, y: {round(yk, 6)}, f(x,y)={f(xk, yk)} ,gradient: {gradient}"
        )