import math
import numpy as np


def fun(x):
    return math.exp(x)


def find_x(a, b, c, d):
    n = len(b)

    alphas = [0] * n
    betas = [0] * n

    for i in range(n-1):
        alphas[i+1] = -c[i]/(a[i]*alphas[i]+b[i])
        betas[i+1] = (d[i]-a[i]*betas[i])/(a[i]*alphas[i]+b[i])

    x = [0] * n
    x[-1] = (d[-1] - a[-1] * betas[-1])/(a[-1] * alphas[-1] + b[-1])
    for i in range(n-1, 0, -1):
        x[i - 1] = x[i]*alphas[i]+betas[i]
    return (x)


if __name__ == "__main__":
    p = 1
    q = -1
    n = 10
    a = fun(0)
    b = fun(1)
    h = 1/n
    x = [0] * (n + 1)
    for i in range(n+1):
        x[i] = round(i * h, 2)
    a_matrix = [1 - h/2 * p] * (n - 2)
    b_matrix = [h**2 * q - 2] * (n - 1)
    c_matrix = [1 + h/2 * p] * (n - 2)
    d_matrix = [0] * (n - 1)
    for i in range(n-1):
        d_matrix[i] = h**2 * fun(x[i+1])
    d_matrix[0] -= a_matrix[0] * a
    d_matrix[-1] -= c_matrix[0] * b
    y = find_x(a_matrix, b_matrix, c_matrix, d_matrix)
    y = np.concatenate(([a], y[:], [b]))
    e = [0] * (n + 1)
    for i in range(n + 1):
        e[i] = abs(fun(x[i]) - y[i])
        print('xi: ', x[i], '|', 'counted_y[i]: ', y[i], '|', 'yi: ', fun(x[i]), '|', 'error: ', e[i])
    print('max_error', max(e))