def test_gradient(solver, white_noise, seed=123, N=305, ndim=3, eps=1.32e-3):
np.random.seed(seed)
# Set up the solver.
kernel = 1.0 * kernels.ExpSquaredKernel(0.5, ndim=ndim)
kwargs = dict()
if white_noise is not None:
kwargs = dict(white_noise=white_noise, fit_white_noise=True)
if solver == HODLRSolver:
kwargs["tol"] = 1e-8
gp = GP(kernel, solver=solver, **kwargs)
# Sample some data.
x = np.random.rand(N, ndim)
x = x[np.argsort(x[:, 0])]
y = gp.sample(x)
gp.compute(x, yerr=0.1)
# Compute the initial gradient.
grad0 = gp.grad_log_likelihood(y)
vector = gp.get_parameter_vector()
for i, v in enumerate(vector):
# Compute the centered finite difference approximation to the gradient.
vector[i] = v + eps
gp.set_parameter_vector(vector)
lp = gp.lnlikelihood(y)
vector[i] = v - eps
gp.set_parameter_vector(vector)
lm = gp.lnlikelihood(y)
vector[i] = v
gp.set_parameter_vector(vector)
grad = 0.5 * (lp - lm) / eps
assert np.abs(grad - grad0[i]) < 5 * eps, \
"Gradient computation failed in dimension {0} ({1})\n{2}" \
.format(i, solver.__name__, np.abs(grad - grad0[i]))
