import numpy as np
import math


if __name__ == '__main__':
    y = []
    x = []
    for i in range(1, 10, 1):
        x.append(i)
        y.append(math.sqrt(i) + math.log10(i))


    res = []
    for ix in x:
        result = 0
        for i in range(len(x)):
            result += c(x, y, i) * T(ix, i, len(x))
        res.append(result)
    print(res)

    delta = 0.025
    plt.figure(num=None, figsize=(8, 6), dpi=10, facecolor='w', edgecolor='k')
    fig, ax = plt.subplots()
    plt.grid()
    ax.plot(x, y, color="blue")
    ax.plot(x, res, color = "red")
    for i in range(len(x)):
        plt.plot(x[i], y[i],  'o')

    print(x)
    print(y)

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def T(x_number, j, n):
    T = []
    T.append(1)
    T.append(2 * x_number)
    for i in range(2, n + 1):
        T.append(2 * x_number * T[i - 1] - T[i - 2])
    return T[j]

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def c(x_list, y_list, i):
    num = 0
    den = 0

    for j in range(len(x)):
        num += y[j] * T(x[j], i, len(x))
        den += T(x[j], i, len(x)) ** 2

    return num / den
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def q(x):
    y = []
    for i in range(len(x)):
        y.append(0.06 * i ** 2 + 0.62 * i - 1.56)
    return y