LebesgueMeasure

class probnum.quad.integration_measures.LebesgueMeasure(domain, input_dim=None, normalized=False)

Bases: IntegrationMeasure

Lebesgue measure on a hyper-rectangle.

Parameters:

• domain (DomainLike) – Domain of integration. Contains lower and upper bound as a scalar or np.ndarray.

• input_dim (Optional[IntLike]) – Dimension of the integration domain. If not given, inferred from domain.

• normalized (bool) – Boolean which controls whether the measure is normalized (i.e., integral over the domain is one). Defaults to False.

Methods Summary

__call__(points)	Evaluate the density function of the integration measure.
sample(n_sample, rng)	Sample n_sample points from the integration measure.

Methods Documentation

__call__(points)

Evaluate the density function of the integration measure.

Parameters:

points (ndarray) – shape=(n_points, input_dim) – Input locations.

Returns:

shape=(n_points,) – Density evaluated at given locations.

Return type:

density_evals

sample(n_sample, rng)

Sample n_sample points from the integration measure.

Parameters:

• n_sample (IntLike) – Number of points to be sampled

• rng (Generator) – A Random number generator.

Returns:

shape=(n_sample,input_dim) – Sampled points

Return type:

points