import numpy as np

N = 2
A = np.array([[4, 1, 1], [1, 6 + 0.2 * N, -1], [1, -1, 8 + 0.2 * N]])
b = np.array([1, -2, 3])

def func(x):
    return (1 / 2 * x.T @ A @ x + b.T @ x)
def grad(x):
    return (A @ x + b)

def mngs(eps):
    """
    this method should numerically find min(y),
    where y = 1/2*x.T*A*x + b.T*x
    :param A: matrix NxN
    :param b: matrix Nx1
    :param x_k: matrix Nx1
    :param eps: accuracy = 10^(-6))
    """
    x_k = b

    while np.linalg.norm(A @ x_k + b) >= eps :
        q = grad(x_k)
        mu = -(np.dot(q.T, q)/np.dot(q.T, A @ q))
        x_k = x_k + mu*q

    return x_k, func(x_k)


def mps(eps):
    """
    this method should numerically find min(y),
    where y = 1/2*x.T*A*x + b.T*x
    :param A: matrix NxN
    :param b: matrix Nx1
    :param x_k: matrix Nx1
    :param eps: accuracy = 10^(-6))
    """
    B = np.eye(3)
    x_k = b

    while np.linalg.norm(A @ x_k + b) > eps :
        for i in range(0, 3):
            q = B[i][:]
            mu = -(np.dot(q.T, q)/np.dot(q.T, A @ q))
            x_k = x_k + mu*q
    return x_k, func(x_k)

print("Решение  системы Ax=-b")
print(np.linalg.solve(A, -b))

print("Метод наискорейшего градиентного спуска")
#print(mngs(0.000001))
print("Метод покоординатного спуска")
print(mps(0.01))