# -*- coding: utf-8 -*-
"""
Created on Fri Dec 12 17:51:56 2014

@author: grivet

Listing 4.2 : Construction du polynôme de Newton
"""

import numpy as np
import matplotlib.pyplot as plt

npiv = 4
npt = 200

xpiv = np.array([-0.5,0.5,1.5,2.0])
fpiv = np.exp(xpiv)
x = np.linspace(-2,3,200)
t = np.zeros(4); a = np.zeros(4)
neff = int(input("ordre d'interpolation (<= 3): "))

#calcul des différences divisées
for i in range(0,neff+1):
    t[i] = fpiv[i]
    for j in range(i-1,-1,-1):
        t[j] = (t[j+1]-t[j])/(xpiv[i]-xpiv[j])
    a[i] = t[0]

#calcul du polynôme
pol = a[neff]
for i in range(neff-1,-1,-1):
    pol = pol*(x-xpiv[i])+a[i]
plt.plot (xpiv,fpiv,'ok')
plt.plot(x,np.exp(x),'--k')
plt.plot(x,pol,'-r')
plt.title("interpolation de Newton pour la fonction $e^x$")
plt.xlabel("$x$")