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lagrange.py
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81 lines (65 loc) · 1.71 KB
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# Polynômes d'interpolation de Lagrange
import matplotlib.pyplot as plt
import numpy as np
# Affiche le graphe de la fonction f sur [a,b] avec N points
def trace(f, a, b, N=100, color='blue'):
list_x, list_y = [], []
for x in np.linspace(a, b, N):
list_x.append(x)
list_y.append(f(x))
plt.plot(list_x, list_y, color=color)
return
# Polynôme élémentaire Lagrange
def L(x, i, A):
p = 1
for j in range(len(A)):
if j != i:
p *= (x-A[j])/(A[i]-A[j])
return p
# Polynôme d'interpolation de Lagrange
def P(x, A, B):
# A = liste des abscisses
# B = liste des ordonnées
p = 0
for i in range(len(A)):
p += B[i]*L(x, i, A)
return p
# Exemple
def exemple1():
A = [0, 1, 2, 4, 6]
B = [1, 2, -2, 3, 1]
f = lambda x: P(x, A, B)
trace(f, min(A)-0.5, max(A)+0.5, color='blue')
plt.plot(A, B, 'o', color='red')
# plt.legend()
plt.grid(True, which='both')
plt.tight_layout()
# plt.savefig('approx-lagrange-01.png',dpi=600)
plt.show()
exemple1()
# Exemple
def exemple2():
A = [0, 1, 3]
B = [2, 1, 4]
f = lambda x: P(x, A, B)
trace(f, min(A)-1, max(A)+1, color='blue')
plt.plot(A, B, 'o', color='red')
# plt.legend()
plt.grid(True, which='both')
plt.tight_layout()
# plt.savefig('approx-lagrange-02.png',dpi=600)
plt.show()
# exemple2()
# Exemple
def exemple3():
A = [0, 1, 3, 6]
B = [0, 0.9, 3.1, 5.9]
f = lambda x: P(x, A, B)
trace(f, min(A)-5, max(A)+5, color='blue')
plt.plot(A, B, 'o', color='red')
# plt.legend()
plt.grid(True, which='both')
plt.tight_layout()
# plt.savefig('approx-lagrange-03.png',dpi=600)
plt.show()
# exemple3()