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_solve(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(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(
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.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(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_pickle(with_general, seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(500))
diag = np.random.uniform(0.1, 0.5, len(t))
y = np.sin(t)
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))
alpha_real = np.array([1.3, 1.5])
beta_real = np.array([0.5, 0.2])
alpha_complex_real = np.array([1.0])
alpha_complex_imag = np.array([0.1])
beta_complex_real = np.array([1.0])
beta_complex_imag = np.array([1.0])
def compare(solver1, solver2):
assert solver1.computed() == solver2.computed()
if not solver1.computed():
return
assert np.allclose(solver1.log_determinant(),
solver2.log_determinant())
assert np.allclose(solver1.dot_solve(y), solver2.dot_solve(y))
s = pickle.dumps(solver, -1)
solver2 = pickle.loads(s)
compare(solver, solver2)
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)
solver2 = pickle.loads(pickle.dumps(solver, -1))
compare(solver, solver2)
# Test that models can be pickled too.
kernel = terms.RealTerm(0.5, 0.1)
kernel += terms.ComplexTerm(0.6, 0.7, 1.0)
gp1 = GP(kernel)
gp1.compute(t, diag)
s = pickle.dumps(gp1, -1)
gp2 = pickle.loads(s)
assert np.allclose(gp1.log_likelihood(y), gp2.log_likelihood(y))
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_carma(seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.uniform(0, 5, 100))
yerr = 0.1 + np.zeros_like(t)
y = np.sin(t) + yerr * np.random.randn(len(t))
carma_solver = CARMASolver(-0.5, np.array([0.1, 0.05, 0.01]),
np.array([0.2, 0.1]))
carma_ll = carma_solver.log_likelihood(t, y, yerr)
params = carma_solver.get_celerite_coeffs()
solver.compute(0.0, params[0], params[1], params[2], params[3],
params[4], params[5], np.empty(0), np.empty((0, 0)),
np.empty((0, 0)), t, yerr**2)
celerite_ll = -0.5 * (solver.dot_solve(y) + solver.log_determinant() +
len(t) * np.log(2 * np.pi))
assert np.allclose(carma_ll, celerite_ll)
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_pickle(seed=42):
solver = celerite.CholeskySolver()
np.random.seed(seed)
t = np.sort(np.random.rand(500))
diag = np.random.uniform(0.1, 0.5, len(t))
y = np.sin(t)
alpha_real = np.array([1.3, 1.5])
beta_real = np.array([0.5, 0.2])
alpha_complex_real = np.array([1.0])
alpha_complex_imag = np.array([0.1])
beta_complex_real = np.array([1.0])
beta_complex_imag = np.array([1.0])
def compare(solver1, solver2):
assert solver1.computed() == solver2.computed()
if not solver1.computed():
return
assert np.allclose(solver1.log_determinant(),
solver2.log_determinant())
assert np.allclose(solver1.dot_solve(y),
solver2.dot_solve(y))
s = pickle.dumps(solver, -1)
solver2 = pickle.loads(s)
compare(solver, solver2)
solver.compute(
0.0, alpha_real, beta_real, alpha_complex_real, alpha_complex_imag,
beta_complex_real, beta_complex_imag, t, diag
)
solver2 = pickle.loads(pickle.dumps(solver, -1))
compare(solver, solver2)
# Test that models can be pickled too.
kernel = terms.RealTerm(0.5, 0.1)
kernel += terms.ComplexTerm(0.6, 0.7, 1.0)
gp1 = GP(kernel)
gp1.compute(t, diag)
s = pickle.dumps(gp1, -1)
gp2 = pickle.loads(s)
assert np.allclose(gp1.log_likelihood(y), gp2.log_likelihood(y))
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)