# matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

# Data x dan y
xd = [5, 12, 15, 20]
yd = [125, 257, 497, 676]

n = len (xd)

# Nilai x
x = 17

# HItung nilai interpolasi p_n(17)
p = 0
for k in range (n) :
  t = yd[k]
  # HItung L-k(x)
  for j in range (n):
    if k != j:
      t *= (x-xd[j])/(xd[k]-xd[j])

  p += t

# Hasil akhir
print(p)

# Posisi interpolasi sebanyak 101 titik
xi = xd[0] + np.arange(101)*(xd[n-1] - xd[0])/100
# Array untuk menampung yi
yi = np.zeros(101)
for i in range(101):
  x = xi[i]
  p = 0
  for k in range(n):
    t = yd[k]
    # HItung L-k(x)
    for j in range (n):
      if k != j:
        t *= (x-xd[j])/(xd[k]-xd[j])
    p += t
  yi[i] = p

# Visualisasi
plt.plot(xi,yi,'-b')
plt.plot(xd,yd,'or')
plt.xlabel('x')
plt.ylabel('y')
plt.show()