GaussianMeasure

class probnum.quad.integration_measures.GaussianMeasure(mean, cov, input_dim=None)

Bases: IntegrationMeasure

Gaussian measure on Euclidean space with given mean and covariance.

If mean and cov are scalars but input_dim is larger than one, mean and cov are extended to a constant vector and diagonal matrix, respectively, of appropriate dimensions.

Parameters:

• mean (Union[float, np.floating, np.ndarray]) – shape=(input_dim,) – Mean of the Gaussian measure.

• cov (Union[float, np.floating, np.ndarray]) – shape=(input_dim, input_dim) – Covariance matrix of the Gaussian measure.

• input_dim (Optional[IntLike]) – Dimension of the integration domain.

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 (FloatLike | 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