Feat: Add tp5

ex2.py

@@ -0,0 +1,54 @@
+"""
+Ici, on implémente gauss
+"""
+import numpy as np
+from ex1 import resolve_up
+
+
+def gauss(A: np.array, b: np.array) -> (np.array, np.array):
+    n = len(A)
+    for k in range(n): # k = pivot
+        for i in range(k+1, n): # i = ligne en dessous du pivot
+            g = A[i, k] / A[k, k] # multiplication pour éliminer A[i, k]
+            A[i, k:] -= g * A[k, k:] # row operation on A
+            b[i] -= g * b[k] # same row operation on b
+
+    return A, b # matrice triangularisé et le b modifié
+
+
+def cholesky(A: np.array) -> np.array:
+    L = np.zeros(A)
+    L = np.sqrt(A[0, 0])
+    m = len(A)
+    # first column
+    for i in range(1, m):
+        L[i, 0] = A[i, 0] / L[0, 0]
+
+    # généralisation k = 2, ..., m
+    for k in range(1, m):
+        # diagonale
+        L[k, k] = np.sqrt(A[k, k] - np.sum(L[k, :k]**2))
+        for i in range(k+1, m):
+            for j in range(k-1):
+                L[i,k] = (A[i,k] - np.sum(L[i, j] * L[k, j])) / L[k, k]
+    return L
+
+
+if __name__ == '__main__':
+    A = np.array([
+        [1, 1, 1, 1],
+        [1, 5, 5, 5],
+        [1, 5, 14, 14],
+        [1, 5, 14, 15]
+    ], dtype=np.float64)
+
+    b = np.array([1, 0, 0, 0], dtype=np.float64)
+
+    A_triangle, b_gauss = gauss(A, b)
+    print(f"A triangulsarisée:\n {A_triangle}")
+
+    x = resolve_up(A, b_gauss)
+    print(f"x={x}")
+
+    L = cholesky(A)
+    print(f"L\n {L}")