def test_inverse_and_logdet():
# Test `Dense`.
a = np.random.randn(3, 3)
a = Dense(a.dot(a.T))
yield assert_allclose, B.matmul(a, B.inverse(a)), np.eye(3)
yield assert_allclose, B.matmul(B.inverse(a), a), np.eye(3)
yield assert_allclose, B.logdet(a), np.log(np.linalg.det(dense(a)))
# Test `Diagonal`.
d = Diagonal([1, 2, 3])
yield assert_allclose, B.matmul(d, B.inverse(d)), np.eye(3)
yield assert_allclose, B.matmul(B.inverse(d), d), np.eye(3)
yield assert_allclose, B.logdet(d), np.log(np.linalg.det(dense(d)))
yield eq, B.shape(B.inverse(Diagonal([1, 2], rows=2, cols=4))), (4, 2)
# Test `Woodbury`.
a = np.random.randn(3, 2)
b = np.random.randn(2, 2) + 1e-2 * np.eye(2)
wb = d + LowRank(left=a, middle=b.dot(b.T))
for _ in range(4):
yield assert_allclose, B.matmul(wb, B.inverse(wb)), np.eye(3)
yield assert_allclose, B.matmul(B.inverse(wb), wb), np.eye(3)
yield assert_allclose, B.logdet(wb), np.log(np.linalg.det(dense(wb)))
wb = B.inverse(wb)
# Test `LowRank`.
yield raises, RuntimeError, lambda: B.inverse(wb.lr)
yield raises, RuntimeError, lambda: B.logdet(wb.lr)
def test_qf():
# Generate some test inputs.
b, c = np.random.randn(5, 3), np.random.randn(5, 3)
# Generate some matrices to test.
a = np.random.randn(5, 5)
a = Dense(a.dot(a.T))
d = Diagonal(B.diag(a))
e = np.random.randn(2, 2)
wb = d + LowRank(left=np.random.randn(5, 2),
middle=e.dot(e.T))
for x in [a, d, wb]:
allclose(B.qf(x, b), np.linalg.solve(to_np(x), b).T.dot(b))
allclose(B.qf(x, b, b), B.qf(x, b))
allclose(B.qf(x, b, c), np.linalg.solve(to_np(x), b).T.dot(c))
allclose(B.qf_diag(x, b),
np.diag(np.linalg.solve(to_np(x), b).T.dot(b)))
allclose(B.qf_diag(x, b, b), B.qf_diag(x, b, b))
allclose(B.qf_diag(x, b, c),
np.diag(np.linalg.solve(to_np(x), b).T.dot(c)))
# Test `LowRank`.
lr = LowRank(np.random.randn(5, 3))
with pytest.raises(RuntimeError):
B.qf(lr, b)
with pytest.raises(RuntimeError):
B.qf(lr, b, c)
with pytest.raises(RuntimeError):
B.qf_diag(lr, b)
with pytest.raises(RuntimeError):
B.qf_diag(lr, b, c)
def test_inverse_and_logdet():
# Test `Dense`.
a = np.random.randn(3, 3)
a = Dense(a.dot(a.T))
allclose(B.matmul(a, B.inverse(a)), np.eye(3))
allclose(B.matmul(B.inverse(a), a), np.eye(3))
allclose(B.logdet(a), np.log(np.linalg.det(to_np(a))))
# Test `Diagonal`.
d = Diagonal(np.array([1, 2, 3]))
allclose(B.matmul(d, B.inverse(d)), np.eye(3))
allclose(B.matmul(B.inverse(d), d), np.eye(3))
allclose(B.logdet(d), np.log(np.linalg.det(to_np(d))))
assert B.shape(B.inverse(Diagonal(np.array([1, 2]),
rows=2, cols=4))) == (4, 2)
# Test `Woodbury`.
a = np.random.randn(3, 2)
b = np.random.randn(2, 2) + 1e-2 * np.eye(2)
wb = d + LowRank(left=a, middle=b.dot(b.T))
for _ in range(4):
allclose(B.matmul(wb, B.inverse(wb)), np.eye(3))
allclose(B.matmul(B.inverse(wb), wb), np.eye(3))
allclose(B.logdet(wb), np.log(np.linalg.det(to_np(wb))))
wb = B.inverse(wb)
# Test `LowRank`.
with pytest.raises(RuntimeError):
B.inverse(wb.lr)
with pytest.raises(RuntimeError):
B.logdet(wb.lr)
def test_root():
# Test `Dense`.
a = np.random.randn(5, 5)
a = Dense(a.dot(a.T))
yield assert_allclose, a, B.matmul(B.root(a), B.root(a))
# Test `Diagonal`.
d = Diagonal(np.array([1, 2, 3, 4, 5]))
yield assert_allclose, d, B.matmul(B.root(d), B.root(d))
def test_ratio():
a, b = np.random.randn(4, 4), np.random.randn(4, 4)
a, b = Dense(a.dot(a.T)), Dense(b.dot(b.T))
d, e = Diagonal(B.diag(a)), Diagonal(B.diag(b))
c = np.random.randn(3, 3)
lr = LowRank(left=np.random.randn(4, 3), middle=c.dot(c.T))
allclose(B.ratio(a, b), np.trace(np.linalg.solve(to_np(b), to_np(a))))
allclose(B.ratio(lr, b), np.trace(np.linalg.solve(to_np(b), to_np(lr))))
allclose(B.ratio(d, e), np.trace(np.linalg.solve(to_np(e), to_np(d))))
def test_sample():
a = np.random.randn(3, 3)
a = Dense(a.dot(a.T))
b = np.random.randn(2, 2)
wb = Diagonal(B.diag(a)) + \
LowRank(left=np.random.randn(3, 2), middle=b.dot(b.T))
# Test `Dense` and `Woodbury`.
num_samps = 500000
for cov in [a, wb]:
samps = B.sample(cov, num_samps)
cov_emp = B.matmul(samps, samps, tr_b=True) / num_samps
yield le, np.mean(np.abs(dense(cov_emp) - dense(cov))), 5e-2
