import math


def my_iteration(n, x0, y0):
    func1 = lambda x, y: math.tan(x * y + 0.5) - x ** 2
    deriv1x = lambda x, y: y / (math.cos(x * y + 0.5) ** 2) - 2 * x
    deriv1y = lambda x, y: x / (math.cos(x * y + 0.5) ** 2)
    func2 = lambda x, y: x ** 2 + y ** 2 - 1
    deriv2x = lambda x, y: 2 * x
    deriv2y = lambda x, y: 2 * y
    matrix = [[0 for x in range(2)] for y in range(2)]
    for i in range(0, n):
        matrix[0][0] = deriv2y(x0, y0)
        matrix[1][0] = -deriv2x(x0, y0)
        matrix[0][1] = -deriv1y(x0, y0)
        matrix[1][1] = deriv1x(x0, y0)
        print(matrix)
        det = matrix[0][0] * matrix[1][1] - matrix[1][0] * matrix[0][1]
        for k in range(2):
            for j in range(2):
                matrix[k][j] /= det
        f = [0, 0]
        f[0] = func1(x0, y0)
        f[1] = func2(x0, y0)
        x0 -= matrix[0][0] * f[0] - matrix[0][1] * f[1]
        y0 -= matrix[1][0] * f[0] - matrix[1][1] * f[1]
        print(i, " : ", x0, " ", y0)


my_iteration(20, 0.5, 0.5)