import math
import numpy as np

# var 23



def main():
    m = 4
    x = np.array([1.0, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5.0])
    n = len(x)
    y = np.array([2.57, 2.96, 3.08, 2.56, 3.45, 3.16, 2.99, 4.0, 4.21])
    b = [0] * m
    for i in range(m):
        b[i] = sum(yk * xk ** (i) for xk, yk in zip(x, y))
    A = np.array(
        [
            [sum(x ** (i + j - 2)) for j in range(1, m + 1)]
            for i in range(1, m + 1)
        ]
    )
    print("A:", A)
    print("b:", b)
    l = np.linalg.inv(A) @ b
    print("lamda:", l)
    s = sum(
        (yk - l[0] - l[1] * xk - l[2] * xk ** 2 - l[3] * xk ** 3) ** 2
        for xk, yk in zip(x, y)
    )
    cko = 1 / math.sqrt(n) * math.sqrt(s)
    print("standard deviation:", cko)
    s = sum(yk ** 2 for yk in y)
    delta = cko / math.sqrt(s)
    print("delta:", delta)
    xx = [0] * (n - 1)
    for i in range(1, n):
        xx[i - 1] = (x[i] + x[i - 1]) / 2

    z = [0] * (n - 1)
    for i in range(n - 1):
        z[i] = l[0] + l[1] * xx[i] + l[2] * xx[i] ** 2 + l[3] * xx[i] ** 3
        print("xi", xx[i], "z", z[i])


main()