def test_QR_MGS_Q_orthogonal(): 'verify the orthogonality of the computed Q' np.random.seed(1) M = 6 N = 5 A = np.random.rand(M,N) Q1, R1 = qra.QR_MGS(A) aae(np.identity(N), np.dot(Q1.T,Q1), decimal=10)
def test_QR_MGS_decomposition(): 'verify the computed Q and R matrices' np.random.seed(6) M = 6 N = 5 A = np.random.rand(M,N) Q1, R1 = qra.QR_MGS(A) aae(A, np.dot(Q1, R1), decimal=10)
def test_QR_MCS_Cholesky(): 'verify that R is the transpose of the Cholesky factor of ATA' np.random.seed(98) M = 6 N = 5 A = np.random.rand(M,N) ATA = np.dot(A.T,A) Q1, R1 = qra.QR_MGS(A) aae(ATA, np.dot(R1.T,R1), decimal=10)