def test_solve_multi_reduce(self):
A = np.random.randn(100, 60)
b = np.random.randn(100, 10)
actual = QR(A, reduce=True).solve(b)
expected = LA.lstsq(A, b, rcond=None)[0]
self.assertTrue(np.allclose(actual, expected))
def test_solve_single_complete(self):
A = np.random.randn(100, 60)
b = np.random.randn(100)
actual = QR(A, reduce=False).solve(b)
expected = LA.lstsq(A, b, rcond=None)[0]
self.assertTrue(np.allclose(actual, expected))
def test_householder_reduce(self):
T = np.random.randn(100, 60)
actual = QR(T, reduce=True).householder()
expected = LA.qr(T, mode='reduced')
self.assertTrue(np.allclose(actual[0]@actual[1], T))
self.assertTrue(all(np.allclose(a, e) for a, e in zip(actual, expected)))
def test_gram_schmidt_modified(self):
T = np.random.randn(100, 60)
actual = QR(T).gram_schmidt_modified()
# enforce uniqueness for numpy version
Q, R = LA.qr(T)
D = create_diag(np.sign(diag(R)))
Q = np.dot(Q, D)
R = np.dot(D, R)
expected = (Q, R)
self.assertTrue(all(np.allclose(a, e) for a, e in zip(actual, expected)))
def test_householder_symmetric(self):
T = np.random.randn(10, 10)
Q, R = QR(T, reduce=False).householder()
self.assertTrue(np.allclose(Q @ R, T))