def test_apply_inverse(solver, seed=1234, N=201, yerr=0.1):
np.random.seed(seed)
# Set up the solver.
kernel = 1.0 * kernels.ExpSquaredKernel(0.5)
kwargs = dict()
if solver == HODLRSolver:
kwargs["tol"] = 1e-10
gp = GP(kernel, solver=solver, **kwargs)
# Sample some data.
x = np.sort(np.random.rand(N))
y = gp.sample(x)
gp.compute(x, yerr=yerr)
K = gp.get_matrix(x)
K[np.diag_indices_from(K)] += yerr**2
b1 = np.linalg.solve(K, y)
b2 = gp.apply_inverse(y)
assert np.allclose(b1, b2)
y = gp.sample(x, size=5).T
b1 = np.linalg.solve(K, y)
b2 = gp.apply_inverse(y)
assert np.allclose(b1, b2)
def _general_metric(metric, N=100, ndim=3):
kernel = 0.1 * kernels.ExpSquaredKernel(metric, ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = np.empty((N, N))
for i in range(N):
for j in range(N):
r = x[i] - x[j]
r2 = np.dot(r, np.linalg.solve(metric, r))
M2[i, j] = 0.1 * np.exp(-0.5 * r2)
if not np.allclose(M0, M2):
print(M0)
print()
print(M2)
print()
print(M0 - M2)
print()
print(M0 / M2)
L = np.linalg.cholesky(metric)
i = N - 1
j = N - 2
r = x[j] - x[i]
print(x[i], x[j])
print("r = ", r)
print("L.r = ", np.dot(L, r))
assert np.allclose(M0, M2)
def _general_metric(metric, N=100, ndim=3):
kernel = 0.1 * kernels.ExpSquaredKernel(metric, ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = np.empty((N, N))
for i in range(N):
for j in range(N):
r = x[i] - x[j]
r2 = np.dot(r, np.linalg.solve(metric, r))
M2[i, j] = 0.1 * np.exp(-0.5*r2)
if not np.allclose(M0, M2):
print(M0)
print()
print(M2)
print()
print(M0 - M2)
print()
print(M0 / M2)
L = np.linalg.cholesky(metric)
i = N - 1
j = N - 2
r = x[j] - x[i]
print(x[i], x[j])
print("r = ", r)
print("L.r = ", np.dot(L, r))
assert np.allclose(M0, M2)
def test_prediction(solver, seed=42):
"""Basic sanity checks for GP regression."""
np.random.seed(seed)
kernel = kernels.ExpSquaredKernel(1.0)
kwargs = dict()
if solver == HODLRSolver:
kwargs["tol"] = 1e-8
gp = GP(kernel, solver=solver, white_noise=0.0, **kwargs)
x0 = np.linspace(-10, 10, 500)
x = np.sort(np.random.uniform(-10, 10, 300))
gp.compute(x)
y = np.sin(x)
mu, cov = gp.predict(y, x0)
Kstar = gp.get_matrix(x0, x)
K = gp.get_matrix(x)
K[np.diag_indices_from(K)] += 1.0
mu0 = np.dot(Kstar, np.linalg.solve(K, y))
print(np.abs(mu - mu0).max())
assert np.allclose(mu, mu0)
def test_axis_algined_metric(seed=1234, N=100, ndim=3):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(np.ones(ndim), ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = 0.1*np.exp(-0.5*np.sum((x[None, :, :] - x[:, None, :])**2, axis=-1))
assert np.allclose(M0, M2)
def test_axis_algined_metric(seed=1234, N=100, ndim=3):
np.random.seed(seed)
kernel = 0.1 * kernels.ExpSquaredKernel(np.ones(ndim), ndim=ndim)
x = np.random.rand(N, ndim)
M0 = kernel.get_value(x)
gp = GP(kernel)
M1 = gp.get_matrix(x)
assert np.allclose(M0, M1)
# Compute the expected matrix.
M2 = 0.1 * np.exp(-0.5 * np.sum(
(x[None, :, :] - x[:, None, :])**2, axis=-1))
assert np.allclose(M0, M2)
