gpflow.quadrature.gauss_hermite#
Functions#
gpflow.quadrature.gauss_hermite.gh_points_and_weights#
- gpflow.quadrature.gauss_hermite.gh_points_and_weights(n_gh)[source]#
Given the number of Gauss-Hermite points n_gh, returns the points z and the weights dz to perform the following uni-dimensional gaussian quadrature:
X ~ N(mean, stddev²) E[f(X)] = ∫ f(x) p(x) dx = sum_{i=1}^{n_gh} f(mean + stddev*z_i) dz_i
- Parameters:
n_gh (
int) – Number of Gauss-Hermite points- Return type:
Tuple[Tensor,Tensor]- Returns:
return[0] has shape [N].
return[1] has shape [N].
Points z and weights dz to compute uni-dimensional gaussian expectation
gpflow.quadrature.gauss_hermite.list_to_flat_grid#
- gpflow.quadrature.gauss_hermite.list_to_flat_grid(xs)[source]#
- Parameters:
xs (
Sequence[Union[ndarray[Any,Any],Tensor,Variable,Parameter]]) –xs[all] has shape [.].
List with d rank-1 Tensors, with shapes N1, N2, …, Nd
- Return type:
Tensor- Returns:
return has shape [N_product, D].
Tensor with shape [N1*N2*…*Nd, d] representing the flattened d-dimensional grid built from the input tensors xs
gpflow.quadrature.gauss_hermite.ndgh_points_and_weights#
- gpflow.quadrature.gauss_hermite.ndgh_points_and_weights(dim, n_gh)[source]#
- Parameters:
dim (
int) – dimension of the multivariate normaln_gh (
int) – number of Gauss-Hermite points per dimension
- Return type:
Tuple[Tensor,Tensor]- Returns:
return[0] has shape [n_quad_points, D].
return[1] has shape [n_quad_points, 1].
points Z, Tensor with shape [n_gh**dim, D], and weights dZ, Tensor with shape [n_gh**dim, 1]
gpflow.quadrature.gauss_hermite.repeat_as_list#
- gpflow.quadrature.gauss_hermite.repeat_as_list(x, n)[source]#
- Parameters:
x (
Union[ndarray[Any,Any],Tensor,Variable,Parameter]) –x has shape [batch…].
Array/Tensor to be repeated
n (
int) – Integer with the number of repetitions
- Return type:
Sequence[Tensor]- Returns:
return has shape [n, batch…].
List of n repetitions of Tensor x