Feat: Ajoute l'exercice 1 de l'interpolation & extrapolation

tp6.py

@@ -0,0 +1,83 @@
+from dataclasses import dataclass
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+@dataclass
+class Point:
+    x: float
+    y: float
+
+
+def interpolation_lagrange(points: list[Point], x: float, show_polynome: bool=False) -> float:
+    """
+
+    :param points: Les points de la courbe représentant une fonction
+    :param x: le x en entrée de la fonction où on veut interpoler
+    :return: L'interpolation
+    """
+
+    interpolation: float = 0.
+    n = len(points) # nombre de points
+    for i in range(n):
+        term: float = 1. # 0.0 will always give 0, it's a product ! So lets put 1
+        # Lagrange L(x)
+        for k in range(n):
+            if k != i:
+                term *= ((x - points[k].x) / (points[i].x - points[k].x))
+
+            # erreur ici, voir le chat
+            if show_polynome:
+                print(f'P(x) = (({x} - {points[k].x}) / ({points[i].x} - {points[k].x}))')
+
+        # interpolation with a piece of Lagrange (y_i)
+        interpolation += term * points[i].y
+
+    return interpolation
+
+
+def interpolation_newton(points: list[Point], x: float) -> float:
+    interpolation = 0. # alpha sum
+    n = len(points)
+    for i in range(n):
+        a_i = 1.
+        for k in range(n-1):
+            a_i *= (points[k+1].y - points[k].y) / (points[k+1].x - points[k].x)
+
+    return interpolation
+
+
+def interpolation_moindre_carree(points: list[Point], x: float) -> float:
+    interpolation = 0.
+
+    pass
+
+
+def test() -> None:
+    points = [Point(0, 1), Point(1, 3), Point(2, 2)]
+    x = 1.5
+    result = interpolation_lagrange(points, x)
+    print(f"P({x}) = {result}")  # Doit afficher 2.875
+
+
+def exercice1() -> None:
+    points = [Point(-1,0), Point(0,-1), Point(1,0), Point(3,70)]
+
+    inter_x2 = interpolation_lagrange(points, 2, True)
+    inter_x3 = interpolation_lagrange(points, 3, True)
+    print(f"X2={inter_x2}, X3={inter_x3}")
+
+    x = np.linspace(0, 4, 300)
+    y = [interpolation_lagrange(points, x[i]) for i in range(len(x))]
+
+    # extrapolation
+    plt.plot(x, y)
+    plt.title('fonction f(x) ex 1')
+    plt.show()
+
+
+def exercice2() -> None:
+    pass
+
+if __name__ == '__main__':
+    exercice1()