import math
import numpy as np


def progonka(a, b, c, d, n):
    # print(n)
    n = len(b)
    al = [0]*n
    bet = [0]*n
    x = [0]*n
    # al[0] = -c[0] / b[0]
    # bet[0] = d[0] / b[0]
    for i in range(n-1):
        al[i+1] = -c[i]/(a[i]*al[i]+b[i])
        bet[i+1] = (d[i]-a[i]*bet[i])/(a[i]*al[i]+b[i])
    # print("alpha: ", al, "beta: ", bet)

    x[-1] = (d[-1]-a[-1]*bet[-1])/(a[-1]*al[-1]+b[-1])
    # print(x[n-1])
    for i in range(n-1, 0, -1):
        x[i-1] = al[i]*x[i]+bet[i]
    # print(x)
    return (x)


def f(x):
    return math.exp(x)
    #return math.sin(x)


def diff(x):
    return math.exp(x)
    #return math.sin(2*x) / 3 + math.cos(2*x) + math.sin(x) / 3


def main():
    p = 1  # 0
    q = -1  # 4

    n = 10 # -> 9й порядок
    a = diff(0)
    b = diff(1)
    # print("a ", a, "b ", b)
    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 * f(x[i+1])
    d_matrix[0] -= a_matrix[0] * a
    d_matrix[-1] -= c_matrix[0] * b
    # print("a_matrix: ", a_matrix)
    # print("b_matrix: ", b_matrix)
    # print("c_matrix: ", c_matrix)
    # print("d_matrix: ", d_matrix)

    y = progonka(a_matrix, b_matrix, c_matrix, d_matrix, n-1)
    y = np.concatenate(([a], y[:], [b]))
    # y[0] = a
    # y[-1] = b
    # print("y: ", y)
    e = [0]*(n+1)
    for i in range(n+1):
        e[i] = abs(diff(x[i]) - y[i])
        # print("xi", x[i], "yi_", y[i], "yi", diff(x[i]), "e", e[i])
    print("max error1", max(e))

    y0 = [1]*(n+1)
    yi = [0]*(n+1)
    # y0[1] = 1
    yi[1] = h
    for i in range(1, n):
        y0[i+1] = (f(x[i])*h**2 + (2-q*h**2)*y0[i] -
                   (1-p*h/2)*y0[i-1])/(1+p*h/2)
        yi[i+1] = ((2-q*h**2)*yi[i] - (1-p*h/2)*yi[i-1])/(1+p*h/2)

    c1 = (b - y0[-1])/yi[-1]
    yy = [0]*(n+1)
    for i in range(n+1):
        yy[i] = y0[i]+c1*yi[i]
    # print(yy)

    e2 = [0]*(n+1)
    for i in range(n+1):
        e2[i] = abs(diff(x[i]) - yy[i])
        print("xi", x[i], "yi_", yy[i], "yi", diff(x[i]), "e", e2[i])
    print("max error2", max(e2))


main()