lab4

import matplotlib.pyplot as plt
import numpy as np

xs = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]
ys = [5, 6, 8, 10, 12, 13, 12, 10, 8, 10, 8, 11, 7, 9, 11, 10, 9, 12, 11, 6]

gx = []
gy = []
t = []
deg = 6

for k in range(deg):
    t.append(0)
    for i in range(len(xs)):
        t[k] += ys[i] * xs[i] ** k

t = np.array(t)


def get_matrix():
    res = np.zeros((deg, deg))
    for k in range(deg):
        for i in range(len(xs)):
            for d in range(deg):
                res[k][d] += xs[i] ** (d + k)
    return res


a = np.linalg.solve(get_matrix(), t)


def f(x):
    res = 0
    for i in range(len(a)):
        res += a[i] * x ** i
    return res


for i in range(len(xs)):
    print(ys[i], f(xs[i]))

gx = []
gy = []

x = xs[0]
deltaX = 0.01

while x <= xs[-1]:
    gx.append(x)
    gy.append(f(x))
    x += deltaX

fig, ax = plt.subplots()
ax.plot(gx, gy, color='green')
ax.scatter(np.array(xs), np.array(ys), color='red')

plt.show()