def test_no_domain_or_measure_raises_error(input_dim):
"""Test that errors are correctly raised when both domain and a Gaussian measure is
given."""
fun = lambda x: x
nodes = np.linspace(0, 1, 3)
fun_evals = fun(nodes)
with pytest.raises(ValueError):
bayesquad(fun=fun, input_dim=input_dim)
with pytest.raises(ValueError):
bayesquad_from_data(nodes=nodes, fun_evals=fun_evals)
def test_domain_and_gaussian_measure_raises_error(measure, input_dim):
"""Test that errors are correctly raised when both domain and a Gaussian measure is
given."""
domain = (0, 1)
fun = lambda x: x
with pytest.raises(ValueError):
bayesquad(fun=fun, input_dim=input_dim, domain=domain, measure=measure)
nodes = np.linspace(0, 1, 3)
fun_evals = fun(nodes)
with pytest.raises(ValueError):
bayesquad_from_data(nodes=nodes,
fun_evals=fun_evals,
domain=domain,
measure=measure)
def test_integral_values_x2_gaussian(kernel, measure, input_dim):
"""Test numerical integration of x**2 in higher dimensions."""
# pylint: disable=invalid-name
c = np.linspace(0.1, 2.2, input_dim)
fun = lambda x: np.sum(c * x**2, 1)
true_integral = np.sum(c * (measure.mean**2 + np.diag(measure.cov)))
n_gh = 8 # Be very careful about increasing this - yields huge kernel matrices
nodes, _ = gauss_hermite_tensor(n_points=n_gh,
input_dim=input_dim,
mean=measure.mean,
cov=measure.cov)
fun_evals = fun(nodes)
bq_integral, _ = bayesquad_from_data(nodes=nodes,
fun_evals=fun_evals,
kernel=kernel,
measure=measure)
np.testing.assert_almost_equal(bq_integral.mean, true_integral, decimal=2)
def test_domain_ignored_if_lebesgue(input_dim, measure):
domain = (0, 1)
fun = lambda x: x
# standard BQ
bq_integral, _ = bayesquad(fun=fun,
input_dim=input_dim,
domain=domain,
measure=measure)
assert isinstance(bq_integral, Normal)
# fixed nodes BQ
nodes = np.linspace(0, 1, 3).reshape((3, 1))
fun_evals = fun(nodes)
bq_integral, _ = bayesquad_from_data(nodes=nodes,
fun_evals=fun_evals,
domain=domain,
measure=measure)
assert isinstance(bq_integral, Normal)
def test_integral_values_sin_lebesgue(kernel, measure, input_dim):
"""Test numerical integration of products of sinusoids."""
# pylint: disable=invalid-name
c = np.linspace(0.1, 0.5, input_dim)
(a, b) = measure.domain
fun = lambda x: np.prod(np.sin(c * x), 1)
true_integral = (np.prod(
(np.cos(c * a) - np.cos(c * b)) / c) * measure.normalization_constant)
n_gl = 8 # Be very careful about increasing this - yields huge kernel matrices
nodes, _ = gauss_legendre_tensor(
n_points=n_gl,
input_dim=input_dim,
domain=measure.domain,
normalized=measure.normalized,
)
fun_evals = fun(nodes)
bq_integral, _ = bayesquad_from_data(nodes=nodes,
fun_evals=fun_evals,
kernel=kernel,
measure=measure)
np.testing.assert_almost_equal(bq_integral.mean, true_integral, decimal=2)