Serie 11 and 12

Kuengjoe_S12/Kuengjoe_S12_Aufg4.py

@@ -0,0 +1,48 @@
+import numpy as np
+
+def Kuengjoe_S12_Aufg4(in_matrix: np.ndarray, iteration: int):
+    current_iteration = np.array(in_matrix, dtype=float)
+    dimension = current_iteration.shape[0]
+    acc_orthogonal_matrix = np.eye(dimension, dtype=float)
+
+    for iteration in range(iteration):
+        q_matrix, r_matrix = np.linalg.qr(current_iteration)
+        current_iteration = r_matrix @ q_matrix
+        acc_orthogonal_matrix = acc_orthogonal_matrix @ q_matrix
+    return current_iteration, acc_orthogonal_matrix
+
+
+if __name__ == "__main__":
+    #4a)
+    test_matrix = np.array([
+        [1, -2, 0],
+        [2, 0, 1],
+        [0, -2, 1]
+    ], dtype=float)
+
+    ak_1, pk_1 = Kuengjoe_S12_Aufg4(test_matrix, 1)
+    print("A1 =\n", np.round(ak_1, 6))
+    print("P1 =\n", np.round(pk_1, 6))
+
+    #4b)
+    symmetric_matrix = np.array([
+        [6, 1, 2, 1, 2],
+        [1, 5, 0, 2, -1],
+        [2, 0, 5, -1, 0],
+        [1, 2, -1, 6, 1],
+        [2, -1, 0, 1, 7]
+    ], dtype=float)
+
+    ak_100, pk_100 = Kuengjoe_S12_Aufg4(symmetric_matrix, 100)
+
+    orthogonality_residual = np.linalg.norm(pk_100.T @ pk_100 - np.eye(5))
+    print("||P^T P - I|| =", orthogonality_residual)
+
+    approx_eigenvalues_from_qr = np.diag(ak_100)
+    print("Eigenvalues approx (diag(Ak)) =", approx_eigenvalues_from_qr)
+
+    #4c)
+
+    eigenvalues_numpy, eigenvectors_numpy = np.linalg.eig(symmetric_matrix)
+    print(eigenvalues_numpy)
+