def test_updating_qr_with_linear_dependence():
np.random.seed(0)
m = 10
n = 5
assert n >= 3
X = np.random.normal(size=(n, m)).T
X[:, 2] = X[:, 0] + 3 * X[:, 1]
Q = np.linalg.qr(X, mode='reduced')[0]
u = UpdatingQT.alloc(m, n, 1e-14)
u2 = UpdatingQT.alloc(m, n, 1e-14)
u.update(X[:, 0])
u2.update(X[:, 0])
# u2.update(X[:,0])
u.update(X[:, 1])
u2.update(X[:, 1])
# u2.update(X[:,1])
u.update(X[:, 2])
assert np.max(
np.abs(np.abs(u.Q_t[:2, :]) - np.abs(Q[:, :2].T))) < .0000000000001
assert np.max(np.abs(u.Q_t[2, :])) == 0.
# Make sure you can downdate a dependent column safely
u.downdate()
u.update(X[:, 2])
assert np.max(
np.abs(np.abs(u.Q_t[:2, :]) - np.abs(Q[:, :2].T))) < .0000000000001
assert np.max(np.abs(u.Q_t[2, :])) == 0.
for j in range(3, n):
u.update(X[:, j])
u2.update(X[:, j])
# Q_t is orthonormal except for its zero column
Q_nonzero = np.concatenate([u.Q_t[:2, :].T, u.Q_t[3:, :].T], axis=1)
np.testing.assert_array_almost_equal(np.dot(Q_nonzero.T, Q_nonzero),
np.eye(n - 1))
# Q_t.T is in the column space of X
b = np.linalg.lstsq(X, u.Q_t.T)[0]
Q_hat = np.dot(X, b)
np.testing.assert_array_almost_equal(Q_hat, u.Q_t.T)
# X is in the column space of Q_t.T
a = np.linalg.lstsq(u.Q_t.T, X)[0]
X_hat = np.dot(u.Q_t.T, a)
np.testing.assert_array_almost_equal(X_hat, X)
# u and u2 should have the same householder
np.testing.assert_array_almost_equal(
u.householder.V[:, :u.householder.k],
u2.householder.V[:, :u2.householder.k])
np.testing.assert_array_almost_equal(
u.householder.T[:u.householder.k, :u.householder.k],
u2.householder.T[:u2.householder.k, :u2.householder.k])
# u should have one more column than u2
assert u.k == u2.k + 1
def test_updating_qr_with_linear_dependence():
np.random.seed(0)
m = 10
n = 5
assert n >= 3
X = np.random.normal(size=(n, m)).T
X[:, 2] = X[:, 0] + 3 * X[:, 1]
Q = np.linalg.qr(X, mode='reduced')[0]
u = UpdatingQT.alloc(m, n, 1e-14)
u2 = UpdatingQT.alloc(m, n, 1e-14)
u.update(X[:, 0])
u2.update(X[:, 0])
# u2.update(X[:,0])
u.update(X[:, 1])
u2.update(X[:, 1])
# u2.update(X[:,1])
u.update(X[:, 2])
assert np.max(
np.abs(np.abs(u.Q_t[:2, :]) - np.abs(Q[:, :2].T))) < .0000000000001
assert np.max(np.abs(u.Q_t[2, :])) == 0.
# Make sure you can downdate a dependent column safely
u.downdate()
u.update(X[:, 2])
assert np.max(
np.abs(np.abs(u.Q_t[:2, :]) - np.abs(Q[:, :2].T))) < .0000000000001
assert np.max(np.abs(u.Q_t[2, :])) == 0.
for j in range(3, n):
u.update(X[:, j])
u2.update(X[:, j])
# Q_t is orthonormal except for its zero column
Q_nonzero = np.concatenate([u.Q_t[:2, :].T, u.Q_t[3:, :].T], axis=1)
np.testing.assert_array_almost_equal(
np.dot(Q_nonzero.T, Q_nonzero), np.eye(n - 1))
# Q_t.T is in the column space of X
b = np.linalg.lstsq(X, u.Q_t.T)[0]
Q_hat = np.dot(X, b)
np.testing.assert_array_almost_equal(Q_hat, u.Q_t.T)
# X is in the column space of Q_t.T
a = np.linalg.lstsq(u.Q_t.T, X)[0]
X_hat = np.dot(u.Q_t.T, a)
np.testing.assert_array_almost_equal(X_hat, X)
# u and u2 should have the same householder
np.testing.assert_array_almost_equal(
u.householder.V[:, :u.householder.k],
u2.householder.V[:, :u2.householder.k])
np.testing.assert_array_almost_equal(
u.householder.T[:u.householder.k, :u.householder.k],
u2.householder.T[:u2.householder.k, :u2.householder.k])
# u should have one more column than u2
assert u.k == u2.k + 1
def test_updating_qt():
np.random.seed(0)
m = 10
n = 3
X = np.random.normal(size=(n, m)).T
u = UpdatingQT.alloc(m, n, 1e-14)
# u2 = UpdatingQT(m, n)
Q = np.linalg.qr(X, mode='reduced')[0]
u.update(X[:, 0])
# u2.update(X[:,0])
u.update(X[:, 1])
# u2.update(X[:,1])
u.update(X[:, 2])
# u2.update(X[:,2])
# assert np.max(np.abs(np.abs(u2.Q_t) - np.abs(Q.T))) < .0000000000001
assert np.max(np.abs(np.abs(u.Q_t) - np.abs(Q.T))) < .0000000000001
X2 = X.copy()
X2[:, 2] = np.random.normal(size=m)
u.downdate()
u.update(X2[:, 2])
Q2 = np.linalg.qr(X2, mode='reduced')[0]
assert np.max(np.abs(np.abs(u.Q_t) - np.abs(Q2.T))) < .0000000000001
def test_updating_qt():
np.random.seed(0)
m = 10
n = 3
X = np.random.normal(size=(n, m)).T
u = UpdatingQT.alloc(m, n, 1e-14)
# u2 = UpdatingQT(m, n)
Q = np.linalg.qr(X, mode='reduced')[0]
u.update(X[:, 0])
# u2.update(X[:,0])
u.update(X[:, 1])
# u2.update(X[:,1])
u.update(X[:, 2])
# u2.update(X[:,2])
# assert np.max(np.abs(np.abs(u2.Q_t) - np.abs(Q.T))) < .0000000000001
assert np.max(np.abs(np.abs(u.Q_t) - np.abs(Q.T))) < .0000000000001
X2 = X.copy()
X2[:, 2] = np.random.normal(size=m)
u.downdate()
u.update(X2[:, 2])
Q2 = np.linalg.qr(X2, mode='reduced')[0]
assert np.max(np.abs(np.abs(u.Q_t) - np.abs(Q2.T))) < .0000000000001
