Fix: Correct jacobi, gauss, cholesky

ex3.py

@@ -5,81 +5,62 @@ import numpy as np
 # D_inv = np.diag(1 / np.diag(A))
 
 
-def to_D(A: np.array) -> np.array:
-    D = np.zeros_like(A)
-    for i in range(len(A)):
-        D[i, i] = A[i, i]
-    return D
-
-
-def to_L(A: np.array) -> np.array:
-    L = np.zeros_like(A)
-    for i in range(len(A)):
-        for j in range(len(A)):
-            if i < j:
-                L[i, j] = A[i, j]
-    return L
-
-
-def to_U(A: np.array) -> np.array:
-    U = np.zeros_like(A)
-    for i in range(len(A)):
-        for j in range(len(A)):
-            if i > j:
-                U[i, j] = A[i, j]
-    return U
-
-
 def diag_strict_dominante(A) -> bool:
-    diag_sum = 0
-    for i in range(len(A)):
-        diag_sum += A[i, i]
-    other_sum = 0
-    for i in range(len(A)):
-        for j in range(len(A)):
-            if i != j:
-                other_sum += A[i, j]
-    return diag_sum > other_sum
+    """
+    Pour chaque ligne, il faut que la somme des coefs non-diagonaux soit inférieure au coef diagonal
+    TOUT EST EN VALEUR ABSOLUE.
+    :param A:
+    :return:
+    """
+    A = np.array(A)
+    n = len(A)
+    for i in range(n):
+        diag = abs(A[i,i])
+        row_sum = np.sum(np.abs(A[i,:])) - diag # On fait la somme de toute la ligne puis on soustrait le coef diagonal
+        if diag <= row_sum:
+            return False
+    return True
 
 
-def jacobi(A, b):
+def jacobi(A, b, epsilon=1e-6, max_iter=100_000):
     if not diag_strict_dominante(A):
-        raise Exception('A doit être à diagnonale strictement dominante')
+        raise ValueError("A doit être à diagonale strictement dominante")
 
-    L = to_L(A)
-    U = to_U(A)
-    x0 = np.array([0,0,0])
-    epsilon = 1e-6
-    max_iter = 100_000
+    x = np.zeros_like(b, dtype=float)
+    L = np.tril(A, k=-1)     # Partie triangulaire inférieure (sans diagonale)
+    U = np.triu(A, k=1)      # Partie triangulaire supérieure (sans diagonale)
 
-    x = x0
-    for k in range(max_iter):
-        x_new = np.diag(1 / np.diag(A)) @ ((L + U) @ x) + np.diag(1 / np.diag(A)) @ b
-        if np.linalg.norm(x_new - x, ord=2) < epsilon or np.linalg.norm(b - A @ x_new, ord=2) < epsilon:
+    for _ in range(max_iter):
+        x_new = np.diag(1 / np.diag(A)) @ (b - (L + U) @ x)
+        if np.linalg.norm(x_new - x, ord=2) < epsilon:
             break
         x = x_new
 
-    return x
+    return x_new
 
 
 def gauss_seidel(A, b):
     x0 = np.array([0, 0, 0])
 
-    D = to_D(A)
-    L = to_L(A)
-    U = to_U(A)
+    D = np.diag(np.diag(A))
+    L = np.tril(A, k=-1)
+    U = np.triu(A, k=1)
     epsilon = 1e-6
-    done = False
+    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
 
-    while not done:
-        x_new = np.linalg.inv(D - L) @ U @ x + np.linalg.inv(D - L) @ b
+    for _ in range(max_iter):
+        x_new = inv_D_minus_L @ (-U @ x) + inv_D_minus_L @ b
 
-        done: bool = np.linalg.norm(x_new - x, ord=2) < epsilon
+        if np.linalg.norm(x_new - x, ord=2) < epsilon:
+            return x_new
         x = x_new
 
-    return x
+    raise RuntimeError('Gauss-Seidel')
 
 
 def relaxation(A, b, omega=1.0, epsilon=1e-6, max_iter=100_000):
@@ -113,9 +94,9 @@ if __name__ == '__main__':
 
     b = np.array([1,0,0])
 
-    D = to_D(A)
-    L = to_L(A)
-    U = to_U(A)
+    D = np.diag(A)
+    L = np.tril(A)
+    U = np.triu(A)
 
     res_jacobi = jacobi(A, b)
     print(res_jacobi)