TransportMaps.Maps.Defaults

Module Contents

Functions

assemble_IsotropicIntegratedExponentialTriangularTransportMap(...)	Generate a triangular transport map with default settings.
assemble_IsotropicIntegratedExponentialDiagonalTransportMap(...)	Generate a diagonal transport map with default settings.
assemble_IsotropicIntegratedSquaredTriangularTransportMap(...)	Generate a triangular transport map with default settings.
assemble_IsotropicIntegratedSquaredDiagonalTransportMap(...)	Generate a diagonal transport map with default settings.
assemble_IsotropicLinearSpanTriangularTransportMap(...)	Generate a triangular transport map with default settings.
assemble_IsotropicLinearSpanTriangularMap(dim, order)	Generate a triangular transport map with default settings.
assemble_LinearSpanTriangularMap(dim, sl_list, active_vars)	Generate a linear span triangular transport map with default settings and user defined sparsity and orders.

TransportMaps.Maps.Defaults.assemble_IsotropicIntegratedExponentialTriangularTransportMap(dim, order, span='total', SemilatticeConstructor=LinearSpanSemilattice, active_vars=None, btype='poly', common_basis_flag=True)

Generate a triangular transport map with default settings.

Parameters:

• dim (int) – dimension \(d\) of the map

• order (int) – isotropic order of the map

• span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component \(T^{(k)}\).

• SemilatticeConstructor (class) – constructor for the semilattices of each function approximation. It must be a sub-class of LinearSpanSemilattice.

• active_vars (list) – list of \(d\) lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map.

• btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component \(T^{(k)}\).

• common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements).

Returns:

(IntegratedExponentialTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_IsotropicIntegratedExponentialDiagonalTransportMap(dim, order, *args, **kwargs)

Generate a diagonal transport map with default settings.

Parameters:

• dim (int) – dimension \(d\) of the map

• order (int) – isotropic order of the map

Returns:

(IntegratedExponentialTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_IsotropicIntegratedSquaredTriangularTransportMap(dim, order, span='total', SemilatticeConstructor=LinearSpanSemilattice, active_vars=None, btype='poly', common_basis_flag=False)

Generate a triangular transport map with default settings.

Parameters:

• dim (int) – dimension \(d\) of the map

• order (int) – isotropic order of the map

• span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component \(T^{(k)}\).

• SemilatticeConstructor (class) – constructor for the semilattices of each function approximation. It must be a sub-class of LinearSpanSemilattice.

• active_vars (list) – list of \(d\) lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map.

• btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component \(T^{(k)}\).

• common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements).

Returns:

(IntegratedSquaredTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_IsotropicIntegratedSquaredDiagonalTransportMap(dim, order, *args, **kwargs)

Generate a diagonal transport map with default settings.

Parameters:

• dim (int) – dimension \(d\) of the map

• order (int) – isotropic order of the map

Returns:

(IntegratedSquaredTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_IsotropicLinearSpanTriangularTransportMap(dim, order, span='total', SemilatticeConstructor=LinearSpanSemilattice, active_vars=None, btype='poly', common_basis_flag=True)

Generate a triangular transport map with default settings.

Parameters:

• dim (int) – dimension of the map

• order (int) – isotropic order of the map

• span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component \(T^{(k)}\).

• SemilatticeConstructor (class) – constructor for the semilattices of each function approximation. It must be a sub-class of LinearSpanSemilattice.

• active_vars (list) – list of \(d\) lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map.

• btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component \(T^{(k)}\).

• common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements).

Returns:

(LinearSpanTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_IsotropicLinearSpanTriangularMap(dim, order, span='total', SemilatticeConstructor=LinearSpanSemilattice, active_vars=None, btype='poly', common_basis_flag=True, monotone=False)

Generate a triangular transport map with default settings.

Parameters:

• dim (int) – dimension of the map

• order (int) – isotropic order of the map

• span (str) – ‘full’ for full order approximations, ‘total’ for total order approximations. If a list of dim strings is provided, these will define the approximation type fore each component \(T^{(k)}\).

• SemilatticeConstructor (class) – constructor for the semilattices of each function approximation. It must be a sub-class of LinearSpanSemilattice.

• active_vars (list) – list of \(d\) lists containing the row sparsity pattern of the transport, i.e. the active variables for each component. Default None will generate a full triangular map.

• btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component \(T^{(k)}\).

• common_basis_flag (bool) – use acceleration provided by common basis among the components (span and btype must be a string or a list with all equal elements).

Returns:

(LinearSpanTriangularTransportMap) – the constructed transport map

TransportMaps.Maps.Defaults.assemble_LinearSpanTriangularMap(dim, sl_list: List[semilattices.CoordinateSemilattice], active_vars, btype='poly', common_basis_flag=True)

Generate a linear span triangular transport map with default settings and user defined sparsity and orders.

Parameters:

• dim (int) – dimension of the map

• sl_list (list) – list of CoordinateSemilattice, one for each component of the linear map.

• active_vars (list) – list of \(d\) lists containing the row sparsity pattern of the transport, i.e. the active variables for each component.

• btype (string) – poly uses Hermite polynomials, fun uses Hermite functions, rbf uses radial basis functions. If a list of dim strings is provided, these will define the basis type fore each component \(T^{(k)}\).

• common_basis_flag (bool) – use acceleration provided by common basis among the components (btype must be a string or a list with all equal elements).

Returns:

(LinearSpanTriangularTransportMap) – the constructed transport map