Prior Builder

builder

Builders for prior objects from lower-level components.

Classes:

Name	Description
BilaplacianPriorSettings	Settings for the bilaplacian prior builder.
BilaplacianPriorBuilder	Builder for a Bilaplacian prior.

ls_prior.builder.BilaplacianPriorSettings dataclass

Settings for the bilaplacian prior builder.

This dataclass collects all configuration options required to set up a biplaplacian prior using the BilaplacianPriorBuilder class. The builder distributes these settings to the respective components that are assembled within the builder.

Attributes:

Name	Type	Description
mesh	dlx.mesh.Mesh	Dolfinx mesh on which the prior is defined.
mean_vector	np.ndarray[tuple[int], np.dtype[np.float64]]	Mean vector of the prior, vertex-based representation.
kappa	Real	Parameter \(\kappa\) in the SPDE formulation of the prior
tau	Real	Parameter \(\tau\) in the SPDE formulation of the prior
robin_const	Real | None	Robin boundary condition constant. If None, homogeneous Neumann boundary conditions are applied. Defaults to None.
seed	int	Random seed for the internal random number generator. Defaults to 0.
fe_data	tuple[str, int]	Finite element type and degree used for the function space setup. Defaults to ("CG", 1).
cg_relative_tolerance	Real | None	Relative tolerance for the CG solver used in the application of the precision operator. If None, the default PETSc tolerance is used. Defaults to None.
cg_absolute_tolerance	Real | None	Absolute tolerance for the CG solver used in the application of the precision operator. If None, the default PETSc tolerance is used. Defaults to None.
cg_max_iterations	int | None	Maximum number of iterations for the CG solver used in the application of the precision operator. If None, the default PETSc value is used Defaults to None.
amg_relative_tolerance	Real | None	Relative tolerance for the AMG solver used in the application of the covariance operator and its factorization. If None, the default PETSc tolerance is used. Defaults to None.
amg_absolute_tolerance	Real | None	Absolute tolerance for the AMG solver used in the application of the covariance operator and its factorization. If None, the default PETSc tolerance is used. Defaults to None.
amg_max_iterations	int | None	Maximum number of iterations for the AMG solver used in the application of the covariance operator and its factorization. If None, the default PETSc value is used. Defaults to None.

ls_prior.builder.BilaplacianPriorBuilder

Builder for a Bilaplacian prior.

Specific builder class for a bilaplacian prior, i.e. the distribution that arises from solving the SPDE \(\tau(\kappa^2 - \Delta)^2 m = W\).

Methods:

Name	Description
build	Build the Bilaplacian prior.

__init__

__init__(settings: BilaplacianPriorSettings) -> None

Initialize the builder with the given settings.

Parameters:

Name	Type	Description	Default
settings	BilaplacianPriorSettings	Settings for the Bilaplacian prior.	required

build

build() -> prior.Prior

Build the Bilaplacian prior.

Internally, this method assembles all dolfinx structures, composes a hierarchy of PETScComponents, wraps them in InterfaceComponents and hands them to the Prior class.

Returns:

Type	Description
prior.Prior	prior.Prior: The constructed Bilaplacian prior.

_build_fem_structures

_build_fem_structures() -> tuple[PETSc.Mat, PETSc.Mat, PETSc.Mat, PETSc.Mat, fem.FEMConverter]

Assemble FEM data structures, i.e. FEM Matrices and FEMConverter object.

Returns:

Type	Description
tuple[PETSc.Mat, PETSc.Mat, PETSc.Mat, PETSc.Mat, fem.FEMConverter]	tuple[PETSc.Mat, PETSc.Mat, PETSc.Mat, fem.FEMConverter]: mass matrix \(M\), SPDE matrix \(A\), block-diagonal matrix \(\widehat{M}_w\), DoF map matrix \(L\), FEMConverter object.

_build_components

_build_components(
    mass_matrix: PETSc.Mat,
    spde_matrix: PETSc.Mat,
    block_diagonal_matrix: PETSc.Mat,
    dof_map_matrix: PETSc.Mat,
) -> tuple[components.PETScComponent, components.PETScComponent, components.PETScComponent]

Build PETSc components for bilaplacian prior from FEM matrices.

The main components for the prior are:

1. Precision operator: \(\mathcal{C}^{-1} = A M^{-1} A\)
2. Covariance operator: \(\mathcal{C} = A^{-1} M A^{-1}\)
3. Sampling factor: \(\widehat{\mathcal{C}} = A^{-1} L^T \widehat{M}_e\)

Parameters:

Name	Type	Description	Default
mass_matrix	PETSc.Mat	Mass matrix \(M\).	required
spde_matrix	PETSc.Mat	SPDE matrix \(A\).	required
block_diagonal_matrix	PETSc.Mat	Block-diagonal matrix \(\widehat{M}_e\).	required
dof_map_matrix	PETSc.Mat	DoF map matrix \(L\).	required

Returns:

Type	Description
tuple[components.PETScComponent, components.PETScComponent, components.PETScComponent]	tuple[components.PETScComponent, components.PETScComponent, components.PETScComponent]: Precision operator \(\mathcal{C}^{-1}\), covariance operator \(\mathcal{C}\), sampling factor \(\widehat{\mathcal{C}}\).

_build_interfaces

_build_interfaces(
    precision_operator: components.PETScComponent,
    covariance_operator: components.PETScComponent,
    sampling_factor: components.PETScComponent,
) -> tuple[
    components.InterfaceComponent, components.InterfaceComponent, components.InterfaceComponent
]

Wrap PETSc components in interface components.

Parameters:

Name	Type	Description	Default
precision_operator	components.PETScComponent	Precision operator \(\mathcal{C}^{-1}\).	required
covariance_operator	components.PETScComponent	SPDE matrix \(A\).	required
sampling_factor	components.PETScComponent	Sampling factor \(\widehat{\mathcal{C}}\).	required

Returns:

Type	Description
tuple[components.InterfaceComponent, components.InterfaceComponent, components.InterfaceComponent]	tuple[components.InterfaceComponent, components.InterfaceComponent, components.InterfaceComponent]: Wrapped interface components.