import numpy as np


def multiplying_matrix(a, b, c, x):
    res = [0 for _ in range(len(x))]

    for i in range(len(x)):
        if i != 0:
            res[i] += a[i - 1] * x[i - 1]
        res[i] += b[i] * x[i]
        if i != len(x) - 1:
            res[i] += c[i] * x[i + 1]
    return res


def find_x(a, b, c, d):
    alphas = [-c[0] / b[0]]
    betas = [d[0] / b[0]]
    for i in range(1, len(d) - 1):
        alpha = round(-c[i] / (b[i] + alphas[i - 1] * a[i - 1]), 5)
        alphas.append(alpha)
        beta = (d[i] - a[i - 1] * betas[i - 1]) / (
            b[i] + alphas[i - 1] * a[i - 1]
        )
        betas.append(beta)
    beta = (d[len(d) - 1] - a[len(d) - 2] * betas[len(d) - 2]) / (
        b[len(d) - 1] + alphas[len(d) - 2] * a[len(d) - 2]
    )
    betas.append(beta)
    local_x = [0 for _ in range(len(d))]
    local_x[len(d) - 1] = betas[len(d) - 1]
    for i in range(len(d) - 2, -1, -1):
        local_x[i] = local_x[i + 1] * alphas[i] + betas[i]
    return local_x


def find_error(a, b, c, d, d2, x):
    d = np.array(d)
    d2 = np.array(d2)
    r = d2 - d
    m = np.zeros([len(x), len(x)])
    for i in range(len(x)):
        m[i][i] = b[i]
        if i > 0:
            m[i][i - 1] = a[i - 1]
        if i < len(x) - 1:
            m[i][i + 1] = c[i]
    m_reversed = np.matrix(m).I
    err = np.matmul(m_reversed, r).tolist()[0]
    return [x[i] - err[i] for i in range(len(x))], err


def filling(matrix):
    a = [
        matrix[i][i + 1] for i in range(len(matrix) - 1)
    ]
    b = [
        matrix[i][i] for i in range(len(matrix))
    ]
    c = [
        matrix[i + 1][i] for i in range(len(matrix) - 1)
    ]
    return a, b, c


if __name__ == "__main__":
    M = [
        [4, 1, 0, 0],
        [1, 4, 1, 0],
        [0, 1, 4, 1],
        [0, 0, 1, 4],
    ]
    a, b, c = filling(M)
    d = [5, 6, 6, 5]

    x = find_x(a, b, c, d)
    print("Полученный вектор X:", x)

    d2 = multiplying_matrix(a, b, c, x)
    print("M * x:", d2)

    x_real, error = find_error(a, b, c, d, d2, x)
    print("Ошибка:", error)