Fix: Correct gauss-seidel

ex3.py

@@ -39,28 +39,18 @@ def jacobi(A, b, epsilon=1e-6, max_iter=100_000):
     return x_new
 
 
-def gauss_seidel(A, b):
-    x0 = np.array([0, 0, 0])
-
+def gauss_seidel(A, b, epsilon=1e-6, max_iter=100_000):
     D = np.diag(np.diag(A))
     L = np.tril(A, k=-1)
     U = np.triu(A, k=1)
-    epsilon = 1e-6
-    max_iter = 100_000
-
-    # Pré-calcul de l'inverse de (D - L) pour éviter de le recalculer à chaque itération
-    inv_D_minus_L = np.linalg.inv(D - L)
-
-    x = x0
-
+    x = np.zeros_like(b, dtype=float)
     for _ in range(max_iter):
-        x_new = inv_D_minus_L @ (-U @ x) + inv_D_minus_L @ b
-
-        if np.linalg.norm(x_new - x, ord=2) < epsilon:
-            return x_new
-        x = x_new
-
-    raise RuntimeError('Gauss-Seidel')
+        x_old = x.copy()
+        # Résolution de (D - L) x = U x_old + b
+        x = np.linalg.solve(D - L, -U @ x_old + b)
+        if np.linalg.norm(x - x_old, ord=2) < epsilon:
+            return x
+    raise RuntimeError('Gauss-Seidel : convergence non atteinte')
 
 
 def relaxation(A, b, omega=1.0, epsilon=1e-6, max_iter=100_000):