def _test_solve(alpha_real,
beta_real,
alpha_complex_real,
alpha_complex_imag,
beta_complex_real,
beta_complex_imag,
method,
seed=42):
solver = get_solver(method)
np.random.seed(seed)
t = np.sort(np.random.rand(500))
diag = np.random.uniform(0.1, 0.5, len(t))
b = np.random.randn(len(t))
with pytest.raises(RuntimeError):
solver.log_determinant()
with pytest.raises(RuntimeError):
solver.dot_solve(b)
solver.compute(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real, beta_complex_imag, t,
diag)
K = get_kernel_value(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t[:, None] - t[None, :])
K[np.diag_indices_from(K)] += diag
assert np.allclose(solver.solve(b).T, np.linalg.solve(K, b))
b = np.random.randn(len(t), 5)
assert np.allclose(solver.solve(b), np.linalg.solve(K, b))
def test_dot_L(seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(5))
b = np.random.randn(len(t), 5)
yerr = np.random.uniform(0.1, 0.5, len(t))
alpha_real = np.array([1.3, 0.2])
beta_real = np.array([0.5, 0.8])
alpha_complex_real = np.array([0.1])
alpha_complex_imag = np.array([0.0])
beta_complex_real = np.array([1.5])
beta_complex_imag = np.array([0.1])
K = get_kernel_value(
alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t[:, None] - t[None, :]
)
K[np.diag_indices_from(K)] += yerr**2
L = np.linalg.cholesky(K)
x0 = np.dot(L, b)
solver.compute(
0.0, alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t, yerr**2)
x = solver.dot_L(b)
assert np.allclose(x0, x)
def test_dot(with_general, seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(500))
b = np.random.randn(len(t), 5)
alpha_real = np.array([1.3, 0.2])
beta_real = np.array([0.5, 0.8])
alpha_complex_real = np.array([0.1])
alpha_complex_imag = np.array([0.0])
beta_complex_real = np.array([1.5])
beta_complex_imag = np.array([0.1])
K = get_kernel_value(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t[:, None] - t[None, :])
if with_general:
U = np.vander(t - np.mean(t), 4).T
V = U * np.random.rand(4)[:, None]
A = np.sum(U * V, axis=0) + 1e-8
K[np.diag_indices_from(K)] += A
K += np.tril(np.dot(U.T, V), -1) + np.triu(np.dot(V.T, U), 1)
else:
A = np.empty(0)
U = np.empty((0, 0))
V = np.empty((0, 0))
x0 = np.dot(K, b)
x = solver.dot(0.0, alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real, beta_complex_imag, A,
U, V, t, b)
assert np.allclose(x0, x)
def _test_log_determinant(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(5))
diag = np.random.uniform(0.1, 0.5, len(t))
solver.compute(
0.0, alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t, diag
)
K = get_kernel_value(
alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t[:, None] - t[None, :]
)
K[np.diag_indices_from(K)] += diag
assert np.allclose(solver.log_determinant(), np.linalg.slogdet(K)[1])
def _test_solve(alpha_real,
beta_real,
alpha_complex_real,
alpha_complex_imag,
beta_complex_real,
beta_complex_imag,
seed=42,
with_general=False):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(500))
diag = np.random.uniform(0.1, 0.5, len(t))
b = np.random.randn(len(t))
with pytest.raises(RuntimeError):
solver.log_determinant()
with pytest.raises(RuntimeError):
solver.dot_solve(b)
if with_general:
U = np.vander(t - np.mean(t), 4).T
V = U * np.random.rand(4)[:, None]
A = np.sum(U * V, axis=0) + 1e-8
else:
A = np.empty(0)
U = np.empty((0, 0))
V = np.empty((0, 0))
solver.compute(0.0, alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real, beta_complex_imag, A,
U, V, t, diag)
K = get_kernel_value(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t[:, None] - t[None, :])
K[np.diag_indices_from(K)] += diag
if len(A):
K[np.diag_indices_from(K)] += A
K += np.tril(np.dot(U.T, V), -1) + np.triu(np.dot(V.T, U), 1)
assert np.allclose(solver.solve(b).T, np.linalg.solve(K, b))
b = np.random.randn(len(t), 5)
assert np.allclose(solver.solve(b), np.linalg.solve(K, b))
def test_dot(method, seed=42):
solver = get_solver(method)
np.random.seed(seed)
t = np.sort(np.random.rand(300))
b = np.random.randn(len(t), 5)
alpha_real = np.array([1.3, 0.2])
beta_real = np.array([0.5, 0.8])
alpha_complex_real = np.array([0.1])
alpha_complex_imag = np.array([0.3])
beta_complex_real = np.array([0.5])
beta_complex_imag = np.array([3.0])
K = get_kernel_value(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t[:, None] - t[None, :])
x0 = np.dot(K, b)
x = solver.dot(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real, beta_complex_imag, t,
b)
assert np.allclose(x0, x)
def test_single(seed=42):
if not celerite.__with_lapack__:
with pytest.raises(RuntimeError):
solver = SingleSolver()
return
alpha_real = np.array([1.5])
beta_real = np.array([0.3])
alpha_complex_real = np.array([])
alpha_complex_imag = np.array([])
beta_complex_real = np.array([])
beta_complex_imag = np.array([])
solver = SingleSolver()
np.random.seed(seed)
t = np.sort(np.random.uniform(0, 10, 5))
diag = np.random.uniform(0.1, 0.8, len(t))
flag = solver.compute(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t, diag)
assert flag == 0
K0 = get_kernel_value(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real,
beta_complex_imag, t[:, None] - t[None, :])
K = np.array(K0)
K[np.diag_indices_from(K)] += diag
assert np.allclose(solver.log_determinant(), np.linalg.slogdet(K)[1])
b = np.random.randn(len(t), 2)
assert np.allclose(solver.solve(b), np.linalg.solve(K, b))
d1 = solver.dot(alpha_real, beta_real, alpha_complex_real,
alpha_complex_imag, beta_complex_real, beta_complex_imag,
t, b)
d2 = np.dot(K0, b)
assert np.allclose(d1, d2)
def test_dot(seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(500))
b = np.random.randn(len(t), 5)
alpha_real = np.array([1.3, 0.2])
beta_real = np.array([0.5, 0.8])
alpha_complex_real = np.array([0.1])
alpha_complex_imag = np.array([0.0])
beta_complex_real = np.array([1.5])
beta_complex_imag = np.array([0.1])
K = get_kernel_value(
alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t[:, None] - t[None, :]
)
x0 = np.dot(K, b)
x = solver.dot(
0.0, alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t, b
)
assert np.allclose(x0, x)
