Serie 10

Kuengjoe_S10/Kuengjoe_S10_Aufg3a.py

@@ -0,0 +1,58 @@
+import numpy as np
+from numpy.linalg import norm
+
+def Kuengjoe_S10_Aufg3a(A, b, x0, tol, opt):
+    dim = A.shape[0]
+
+    D_vec= np.diag(A)
+    D = np.diag(D_vec)
+    L = np.tril(A, -1)
+    U = np.triu(A, 1)
+
+    if  opt == 'Jacobi':
+        inv_D = np.diag(1.0 / D_vec)
+
+        B = -np.dot(inv_D, (L + U))
+        c = np.dot(inv_D, b)
+
+        del inv_D, L, U, D,
+
+    elif opt == 'Gauss-Seidel':
+        DL = D + L
+        inv_DL = np.linalg.inv(DL)
+
+        B = -np.dot(inv_DL, U)
+        c = np.dot(inv_DL, b)
+
+        del inv_DL, U, D, L,
+
+    else:
+        raise ValueError("Ungültige Option. Wählen Sie 'Jacobi' oder 'Gauss-Seidel'.")
+
+    norm_B = norm(B, np.inf)
+
+    x = x0.copy()
+    x1 = np.dot(B, x) + c
+    diff_x1_x0 = norm(x1 - x0, np.inf)
+
+
+    if norm_B < 1.0 and diff_x1_x0 > 0:
+        numerator = np.log((tol * (1 - norm_B)) / diff_x1_x0)
+        denominator = np.log(norm_B)
+        n2 = int(np.ceil(numerator / denominator))
+
+    else:
+        n2 = -1
+    n = 0
+    current_diff = tol +1
+
+    x = x1
+    n = 1
+
+    while current_diff > tol and n < 10000:
+        x_new = np.dot(B, x) + c
+        current_diff = norm(x_new - x, np.inf)
+        x = x_new
+        n += 1
+    xn = x
+    return xn, n, n2