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)