Feat: Ajoute la méthode des moindres carrés

tp6.py

@@ -74,10 +74,6 @@ def P_newton(x_i: list[float], y_i: list[float], x: float) -> float:
 
     return p
 
-def interpolation_moindre_carree(points: list[Point], x: float) -> float:
-    interpolation = 0.
-
-    pass
 
 def exercice1() -> None:
     points = [Point(-1,0), Point(0,-1), Point(1,0), Point(3,70)]
@@ -126,17 +122,33 @@ def exercice2() -> None:
     plt.show()
 
 
+def moindre_carre(points: list[Point]) -> np.ndarray[np.float64]:
+    # Construction de la matrice A et du vecteur y
+    T = np.array([p.x for p in points])
+    Y = np.array([p.y for p in points])
+
+    A = np.column_stack((T**2, T, np.ones(len(T))))
+
+    # Équations normales
+    X = np.linalg.inv(A.T @ A) @ A.T @ Y
+
+    return X
+
+
 def exercice3() -> None:
     t = [1.5, 3.5, 4.5, 11, 12, 13]
     h = [80, 160, 184, 184, 149, 116]
 
+    points = [Point(t[i], h[i]) for i in range(len(t))]
+
     # fonction de calcul de h
     f_h = lambda a, b, c, t: a * (t ** 2) + b * t + c
 
-    print(f'{f_h(1,2,3,t[0])}')
+    a, b, c = moindre_carre(points)
+    print(a,b,c)
 
 
 if __name__ == '__main__':
     #exercice1()
-    exercice2()
-    #exercice3()
+    #exercice2()
+    exercice3()