From 6eb77df9b7a53a98332235575a2461c1b3aa5349 Mon Sep 17 00:00:00 2001
From: "iliya.saroukha" <iliya.saroukhanian@etu.hesge.ch>
Date: Tue, 25 Jun 2024 17:08:31 +0200
Subject: [PATCH] fix: renamed functions
---
ISC_421_Controle_4_Saroukhanian_Iliya.py | 70 ++++++++++++++++++------
1 file changed, 53 insertions(+), 17 deletions(-)
diff --git a/ISC_421_Controle_4_Saroukhanian_Iliya.py b/ISC_421_Controle_4_Saroukhanian_Iliya.py
index 8f9aa3c..a001bbe 100644
--- a/ISC_421_Controle_4_Saroukhanian_Iliya.py
+++ b/ISC_421_Controle_4_Saroukhanian_Iliya.py
@@ -156,28 +156,28 @@ print(f"valeur de la fonction en a et b: {SD.f(SD.a), SD.f(SD.b)}")
###########################################################################
-def taylor_err_max(plot_range, eval_pt):
+def errmax_taylor(plot_range, eval_pt):
return (SD.Maximal_derivatives_values[len(SD.Maximal_derivatives_values) - 1] /
math.factorial(len(SD.Maximal_derivatives_values) + 1)) * \
(plot_range - eval_pt)**(len(SD.Maximal_derivatives_values) + 1)
-def ex2_taylor_poly():
+def plot_taylor_poly():
t = np.linspace(SD.a, SD.b, Nmbre_pts)
y0 = compute_taylor_series(
t, SD.Taylor_points[0], SD.Taylor_derivatives_values[SD.Taylor_points[0]])
- err_y0 = taylor_err_max(t, SD.Taylor_points[0])
+ err_y0 = errmax_taylor(t, SD.Taylor_points[0])
y1 = compute_taylor_series(
t, SD.Taylor_points[1], SD.Taylor_derivatives_values[SD.Taylor_points[1]])
- err_y1 = taylor_err_max(t, SD.Taylor_points[1])
+ err_y1 = errmax_taylor(t, SD.Taylor_points[1])
y2 = compute_taylor_series(
t, SD.Taylor_points[2], SD.Taylor_derivatives_values[SD.Taylor_points[2]])
- err_y2 = taylor_err_max(t, SD.Taylor_points[2])
+ err_y2 = errmax_taylor(t, SD.Taylor_points[2])
fig, axs = plt.subplots(2, 2, figsize=(18, 12))
@@ -225,7 +225,7 @@ def ex2_taylor_poly():
plt.show()
-def polerr(nb_points, interpolation_pts, plot_range):
+def errmax_poly_interpolation(nb_points, interpolation_pts, plot_range):
errs_range = []
for pt in plot_range:
@@ -247,7 +247,7 @@ def chebyshev_pts(start, stop, nb_points):
np.cos(((2 * np.arange(nb_points) + 1) * np.pi) / (2 * (nb_points))))
-def ex3_lagrange_interpolation_poly():
+def plot_lagrange_poly():
nb_points = np.linspace(1, 12, 6, dtype=np.uint8)
fig, axes = plt.subplots(2, 3, figsize=(20, 12))
@@ -262,33 +262,67 @@ def ex3_lagrange_interpolation_poly():
l_poly_chebyshev_pts = lagrange(
cheb_pts, SD.f(cheb_pts))
- uniform_err = polerr(nb_points[i], interpolate_pts, t)
- chebyshev_err = polerr(nb_points[i], cheb_pts, t)
-
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, uniform_err, '--', color='red',
- label='ErrMax de $L_{f}$, intervalle équidistants')
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(cheb_pts, SD.f(cheb_pts), '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'Polynômes d\'interpolation de Lagrange de $f$ avec 2 subdivisions différentes d\'intervalle: Équidistantes (rouge) / Points de Chebyshev (bleu)')
+
+ fig.tight_layout()
+ plt.show()
+
+
+def plot_errmax_interpolation():
+ nb_points = np.linspace(1, 12, 6, dtype=np.uint8)
+ 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):
+ cheb_pts = chebyshev_pts(SD.a, SD.b, nb_points[i])
+
+ interpolate_pts = np.linspace(SD.a, SD.b, nb_points[i])
+
+ l_poly_uniform = lagrange(interpolate_pts, SD.f(interpolate_pts))
+ l_poly_chebyshev_pts = lagrange(
+ cheb_pts, SD.f(cheb_pts))
+
+ uniform_err = errmax_poly_interpolation(
+ nb_points[i], interpolate_pts, t)
+ chebyshev_err = errmax_poly_interpolation(nb_points[i], cheb_pts, t)
+
+ 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, uniform_err, '--', color='red',
+ label='ErrMax de $L_{f}$, intervalle équidistants')
+ ax.plot(t, l_poly_chebyshev_pts(t), color='blue',
+ label='$L_{f}$, points de Chebyshev')
ax.plot(t, chebyshev_err, '--', color='blue',
label='ErrMax de $L_{f}$, points de Chebyshev')
ax.plot(interpolate_pts, SD.f(interpolate_pts), 'o', color='red',
label='Points équidistants')
- ax.plot(cheb_pts[::-1],
- SD.f(cheb_pts[::-1]), 'o', color='blue',
+ ax.plot(cheb_pts, SD.f(cheb_pts), '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 Lagrange de $f$ avec 2 subdivisions différentes d\'intervalle: Équidistantes (rouge) / Points de Chebyshev (bleu)')
+ fig.suptitle(f'Erreur maximale théorique lors de l\'interpolation de $f$ avec 2 subdivisions différentes d\'intervalle: Équidistantes (rouge) / Points de Chebyshev (bleu)')
fig.tight_layout()
plt.show()
@@ -299,7 +333,9 @@ def ex3_lagrange_interpolation_poly():
# ex2_taylor_poly()
-ex3_lagrange_interpolation_poly()
+# plot_taylor_poly()
+plot_lagrange_poly()
+# plot_errmax_interpolation()
# def ex3_newton_interpolation_poly():
--
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