LebesgueMeasure

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

Bases: probnum.quad.IntegrationMeasure

Lebesgue measure on a hyper-rectangle.

Parameters

• domain (Union[Tuple[Union[float, Real, floating], Union[float, Real, floating]], Tuple[ndarray, ndarray]]) –

  shape=(input_dim,) – Domain of integration. Contains lower and upper bound as

  scalars or np.ndarray.

• input_dim (Union[int, Integral, integer, None]) – Dimension of the integration domain. If not given, inferred from domain.

• normalized (Optional[bool]) – Boolean which controls whether or not the measure is normalized (i.e., integral over the domain is one).

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=Generator(PCG64) at 0x7FD6AE243900)

Sample n_sample points from the integration measure.

Parameters

• n_sample (Union[int, Integral, integer]) – Number of points to be sampled

• rng (Optional[Generator]) – Random number generator. Optional. Default is np.random.default_rng().

Returns

shape=(n_sample,input_dim) – Sampled points

Return type

points