bayesquad_from_data¶

probnum.quad.bayesquad_from_data(nodes, fun_evals, kernel=None, domain=None, measure=None)[source]¶

Infer the value of an integral from a given set of nodes and function evaluations.

Parameters

nodes (ndarray) – shape=(n_eval, input_dim) – Locations at which the function evaluations are available as fun_evals.
fun_evals (ndarray) – shape=(n_eval,) – Function evaluations at nodes.
kernel (Optional[Kernel]) – The kernel used for the GP model.
domain (Optional[Tuple[Union[ndarray, float, Real, floating], Union[ndarray, float, Real, floating]]]) – shape=(input_dim,) – Domain of integration. Contains lower and upper bound as int or ndarray.
measure (Optional[IntegrationMeasure]) – Integration measure. Defaults to the Lebesgue measure.

Return type

Tuple[Normal, BQInfo]

Returns

integral – The integral of fun on the domain.
info – Information on the performance of the method.

Raises

ValueError – If neither a domain nor a measure are given.
ValueError – If a domain is given with a Gaussian measure.

Examples

>>> import numpy as np
>>> domain = (0, 1)
>>> nodes = np.linspace(0, 1, 15)[:, None]
>>> fun_evals = 3*nodes**2
>>> F, info = bayesquad_from_data(nodes=nodes, fun_evals=fun_evals, domain=domain)
>>> print(F.mean)
1.0001