def test_QR_House_Q_from_QR_House_orthogonal():
'verify the orthogonality of the computed Q'
np.random.seed(78)
M = 6
N = 5
A = np.random.rand(M,N)
qra.QR_House(A)
Q = qra.Q_from_QR_House(A=A)
aae(np.identity(M), np.dot(Q.T,Q), decimal=10)
def test_QR_House_Q_from_QR_House_decomposition():
'verify the computed Q and R matrices'
np.random.seed(7)
M = 6
N = 5
A = np.random.rand(M,N)
A2 = A.copy()
qra.QR_House(A2)
Q = qra.Q_from_QR_House(A=A2)
R = np.triu(A2)
aae(A, np.dot(Q, R), decimal=10)