diff --git a/ISC_421_Controle_4_Saroukhanian_Iliya.py b/ISC_421_Controle_4_Saroukhanian_Iliya.py
index 0f56bf868b39cb2e9abe41bb55c6474b43738448..459460916b9f0f2a8632db73d925d3c882861219 100644
--- a/ISC_421_Controle_4_Saroukhanian_Iliya.py
+++ b/ISC_421_Controle_4_Saroukhanian_Iliya.py
@@ -139,6 +139,8 @@ print()
print(f"valeur de la fonction en x = {SD.Taylor_points} : {
[SD.f(x) for x in SD.Taylor_points]}")
print(f"valeur de la fonction en a et b: {SD.f(SD.a), SD.f(SD.b)}")
+# print("===============================")
+# print(SD.Maximal_derivatives_values)
# Exemple de graphe de la fonction f.
# t = np.linspace(SD.a, SD.b, Nmbre_pts)
@@ -205,9 +207,11 @@ def ex2_taylor_poly():
def ex3_lagrange_interpolation_poly():
- nb_points = np.linspace(3, 19, 6, dtype=np.uint64)
+ nb_points = np.linspace(1, 13, 6, dtype=np.uint64)
fig, axes = plt.subplots(2, 3, figsize=(20, 12))
+ t = np.linspace(SD.a, SD.b, Nmbre_pts)
+
for i, ax in enumerate(axes.flat):
chebyshev_points = np.cos(
(2 * np.arange(nb_points[i]) + 1) / (2 * nb_points[i]) * np.pi)
@@ -221,13 +225,15 @@ def ex3_lagrange_interpolation_poly():
l_poly_chebyshev_pts = lagrange(
chebyshev_points_mapped, SD.f(chebyshev_points_mapped))
- t = np.linspace(SD.a, SD.b, Nmbre_pts)
-
ax.plot(t, SD.f(t), color='black', label='f')
ax.plot(t, l_poly_uniform(t), color='red',
label='$L_{f}$, intervalle équidistants')
+ ax.plot(t, np.abs(SD.f(t) - l_poly_uniform(t)), '--', color='red',
+ label='$L_{f}$, intervalle équidistants, erreur')
ax.plot(t, l_poly_chebyshev_pts(t), color='blue',
label='$L_{f}$, points de Chebyshev')
+ ax.plot(t, np.abs(SD.f(t) - l_poly_chebyshev_pts(t)), '--', color='blue',
+ label='$L_{f}$, points de Chebyshev, erreur')
ax.plot(interpolate_pts, SD.f(interpolate_pts), 'o', color='red',
label='Points équidistants')
ax.plot(chebyshev_points_mapped[::-1],
@@ -244,85 +250,71 @@ def ex3_lagrange_interpolation_poly():
plt.show()
-def ex3_newton_interpolation_poly():
- # merce l'ami
- def divided_differences(x, y):
- n = len(y)
- coef = np.zeros([n, n])
- coef[:, 0] = y
-
- for j in range(1, n):
- for i in range(n - j):
- coef[i, j] = (coef[i + 1, j - 1] - coef[i, j - 1]) / \
- (x[i + j] - x[i])
-
- return coef[0, :]
-
- def newton_polynomial(x, x_points, coef):
- n = len(coef)
- p = coef[n - 1]
- for k in range(1, n):
- p = coef[n - k - 1] + (x - x_points[n - k - 1]) * p
-
- return p
-
- nb_points = np.linspace(3, 19, 6, dtype=np.uint64)
- fig, axes = plt.subplots(2, 3, figsize=(20, 12))
-
- t = np.linspace(SD.a, SD.b, Nmbre_pts)
-
- for i, ax in enumerate(axes.flat):
- chebyshev_points = np.cos(
- (2 * np.arange(nb_points[i]) + 1) / (2 * nb_points[i]) * np.pi)
-
- chebyshev_points_mapped = 0.5 * \
- (SD.b - SD.a) * (chebyshev_points + 1) + SD.a
-
- interpolate_pts = np.linspace(SD.a, SD.b, nb_points[i])
-
- y_points_uni = SD.f(interpolate_pts)
-
- coef_uni = divided_differences(interpolate_pts, y_points_uni)
- y_plot_uni = newton_polynomial(t, interpolate_pts, coef_uni)
-
- y_points_cheb = SD.f(chebyshev_points_mapped)
-
- coef_cheb = divided_differences(chebyshev_points_mapped, y_points_cheb)
- y_plot_cheb = newton_polynomial(t, chebyshev_points_mapped, coef_cheb)
-
- ax.plot(t, SD.f(t), color='black', label='f')
- ax.plot(t, y_plot_uni, color='red',
- label='$N_{f}$, intervalle équidistants')
- ax.plot(t, y_plot_cheb, color='blue',
- label='$N_{f}$, points de Chebyshev')
- ax.plot(interpolate_pts, SD.f(interpolate_pts), 'o', color='red',
- label='Points équidistants')
- ax.plot(chebyshev_points_mapped[::-1],
- SD.f(chebyshev_points_mapped[::-1]), 'o', color='blue',
- label='Points de Chebyshev')
- ax.set_title(f'n = {nb_points[i]}')
- ax.set_ylim([-1.2, 1.2])
-
- ax.legend()
-
- fig.suptitle(f'Polynôme d\'interpolation de Newton de $f$ avec 2 subdivisions différentes d\'intervalle: Équidistantes (rouge) / Points de Chebyshev (bleu)')
-
- fig.tight_layout()
- plt.show()
-
-
-ex3_newton_interpolation_poly()
-
-
-# Graphique des polynômes de Taylor
-# fig, axes = plt.subplots(1, 3)
-# for i, pt in enumerate(SD.Taylor_points):
-# ax = axes[i]
+ex3_lagrange_interpolation_poly()
+
+
+# def ex3_newton_interpolation_poly():
+# # merce l'ami
+# def divided_differences(x, y):
+# n = len(y)
+# coef = np.zeros([n, n])
+# coef[:, 0] = y
+#
+# for j in range(1, n):
+# for i in range(n - j):
+# coef[i, j] = (coef[i + 1, j - 1] - coef[i, j - 1]) / \
+# (x[i + j] - x[i])
+#
+# return coef[0, :]
+#
+# def newton_polynomial(x, x_points, coef):
+# n = len(coef)
+# p = coef[n - 1]
+# for k in range(1, n):
+# p = coef[n - k - 1] + (x - x_points[n - k - 1]) * p
+#
+# return p
+#
+# nb_points = np.linspace(3, 19, 6, dtype=np.uint64)
+# fig, axes = plt.subplots(2, 3, figsize=(20, 12))
+#
# t = np.linspace(SD.a, SD.b, Nmbre_pts)
-# ax.plot(t, SD.f(t), label="Fonction f(x)")
-# taylor_poly = np.poly1d(
-# SD.Taylor_derivatives_values[SD.Taylor_points[i]][::-1])
-# ax.plot(t, taylor_poly(t), label=f"Polynôme de Taylor en x={pt}")
-# ax.legend()
-# ax.set_title(f"Polynôme de Taylor en x={pt}")
-# plt.show()
+#
+# for i, ax in enumerate(axes.flat):
+# chebyshev_points = np.cos(
+# (2 * np.arange(nb_points[i]) + 1) / (2 * nb_points[i]) * np.pi)
+#
+# chebyshev_points_mapped = 0.5 * \
+# (SD.b - SD.a) * (chebyshev_points + 1) + SD.a
+#
+# interpolate_pts = np.linspace(SD.a, SD.b, nb_points[i])
+#
+# y_points_uni = SD.f(interpolate_pts)
+#
+# coef_uni = divided_differences(interpolate_pts, y_points_uni)
+# y_plot_uni = newton_polynomial(t, interpolate_pts, coef_uni)
+#
+# y_points_cheb = SD.f(chebyshev_points_mapped)
+#
+# coef_cheb = divided_differences(chebyshev_points_mapped, y_points_cheb)
+# y_plot_cheb = newton_polynomial(t, chebyshev_points_mapped, coef_cheb)
+#
+# ax.plot(t, SD.f(t), color='black', label='f')
+# ax.plot(t, y_plot_uni, color='red',
+# label='$N_{f}$, intervalle équidistants')
+# ax.plot(t, y_plot_cheb, color='blue',
+# label='$N_{f}$, points de Chebyshev')
+# ax.plot(interpolate_pts, SD.f(interpolate_pts), 'o', color='red',
+# label='Points équidistants')
+# ax.plot(chebyshev_points_mapped[::-1],
+# SD.f(chebyshev_points_mapped[::-1]), 'o', color='blue',
+# label='Points de Chebyshev')
+# ax.set_title(f'n = {nb_points[i]}')
+# ax.set_ylim([-1.2, 1.2])
+#
+# ax.legend()
+#
+# fig.suptitle(f'Polynôme d\'interpolation de Newton de $f$ avec 2 subdivisions différentes d\'intervalle: Équidistantes (rouge) / Points de Chebyshev (bleu)')
+#
+# fig.tight_layout()
+# plt.show()