La Grange Polynomial

p_inter.py

#!/usr/bin/env python3

import numpy as np
from matplotlib import pyplot as plt
from numpy.polynomial import polynomial as poly

x = np.array([1,2, 3])
y = np.array([-1, 12, 39])

L = []
for i, x_i in enumerate(x):
    L_i = poly.Polynomial(poly.polyfromroots(np.delete(x, i)))
    L_i /= L_i(x_i)
    L.append(L_i)

P = np.sum(y * l for y, l in zip(y, L))

print(P)
exit()


t = np.linspace(0, 1, 5000)
plt.plot(t, f(t), 'blue')
plt.plot(t, P(t), 'green')
plt.plot(t, (P(t) - f(t)), 'red')
plt.plot([t[0], t[-1]], [0, 0], 'purple')
plt.show()
print(np.linalg.norm(P(t) - f(t), np.inf))