scimba_torch.numerical_solvers.preconditioner_solvers¶

Matrix preconditioner for solvers.

Functions

`default_pre_processing`(*args)	Default pre-processing function that concatenates input tensors.
`functional_operator_id`(func, *args)	Identity functional operator that directly calls the input function.

Classes

MatrixPreconditionerSolver(space, pde, **kwargs)

Matrix-based preconditioner solver.

functional_operator_id(func, *args)[source]¶

Identity functional operator that directly calls the input function.

Parameters:

func (VarArgAnyCallable) – The function to be called.
*args (Tensor | dict[str, Parameter]) – Arguments to be passed to the function.

Return type:

Tensor

Returns:

The result of calling the input function with the provided arguments.

default_pre_processing(*args)[source]¶

Default pre-processing function that concatenates input tensors.

Parameters:: *args (Tensor) – Input tensors to be concatenated.
Return type:: Tensor
Returns:: The concatenated tensor.

class MatrixPreconditionerSolver(space, pde, **kwargs)[source]¶

Bases: AbstractPreconditioner

Matrix-based preconditioner solver.

Parameters:

space (AbstractApproxSpace) – The approximation space.
pde (EllipticPDE | TemporalPDE | KineticPDE | LinearOrder2PDE | RitzFormEllipticPDE | DivAGradUPDE) – The PDE to be solved.
**kwargs –
Additional keyword arguments:
- functional_post_processing: A function to be applied after the main processing.
- functional_pre_processing: A function to be applied before the main processing.

abstract compute_preconditioning_matrix(labels, *args, **kwargs)[source]¶

Abstract method for computing the preconditioning matrix.

Parameters:

labels (Tensor) – The labels tensor.
*args (Tensor) – Additional arguments.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The preconditioning matrix.

abstract compute_preconditioning_matrix_bc(labels, *args, **kwargs)[source]¶

Abstract method for computing the boundary condition preconditioning matrix.

Parameters:

labels (Tensor) – The labels tensor.
*args (Tensor) – Additional arguments.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The boundary condition preconditioning matrix.

abstract compute_preconditioning_matrix_ic(labels, *args, **kwargs)[source]¶

Abstract method for computing the initial condition preconditioning matrix.

Parameters:

labels (Tensor) – The labels tensor.
*args (Tensor) – Additional arguments.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The initial condition preconditioning matrix.

get_args_for_operator(data, **kwargs)[source]¶

Get arguments for the main operator based on the type of space.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

list[Tensor]

Returns:

A list of tensors to be used as arguments for the operator.

Raises:

NotImplementedError – If the type_space is ‘phase_space’.

get_preconditioning_matrix(data, **kwargs)[source]¶

Get the preconditioning matrix using the main operator.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The preconditioning matrix.

get_args_for_operator_bc(data, **kwargs)[source]¶

Get arguments for the boundary condition operator based on the type of space.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

list[Tensor]

Returns:

A list of tensors to be used as arguments for the boundary condition operator.

Raises:

NotImplementedError – If the type_space is ‘phase_space’.

get_preconditioning_matrix_bc(data, **kwargs)[source]¶

Get the preconditioning matrix using the boundary condition operator.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The preconditioning matrix.

get_args_for_operator_ic(data, **kwargs)[source]¶

Get arguments for the initial condition operator based on the type of space.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

list[Tensor]

Returns:

A list of tensors to be used as arguments for the initial condition operator.

Raises:

ValueError – If the type_space is ‘space’.
NotImplementedError – If the type_space is ‘phase_space’.

get_preconditioning_matrix_ic(data, **kwargs)[source]¶

Get the preconditioning matrix using the initial condition operator.

Parameters:

data (tuple[LabelTensor, ...] | dict[str, tuple[LabelTensor, ...]]) – Input data, either as a tuple or a dictionary.
**kwargs – Additional keyword arguments.

Return type:

Tensor

Returns:

The preconditioning matrix.

vectorize_along_physical_variables(dict_of_funcs)[source]¶

Vectorize functions along physical variables based on the type of space.

Parameters:: dict_of_funcs (OrderedDict[int | tuple[int], VarArgAnyCallable]) – A dictionary of functions to be vectorized.
Return type:: OrderedDict[int | tuple[int], VarArgAnyCallable]
Returns:: A dictionary of vectorized functions.
Raises:: NotImplementedError – If the type_space is ‘phase_space’.

vectorize_along_physical_variables_bc(dict_of_funcs)[source]¶

Vectorize functions along physical variables for boundary conditions.

Parameters:: dict_of_funcs (OrderedDict[int | tuple[int], VarArgAnyCallable]) – A dictionary of functions to be vectorized.
Return type:: OrderedDict[int | tuple[int], VarArgAnyCallable]
Returns:: A dictionary of vectorized functions.
Raises:: NotImplementedError – If the type_space is ‘phase_space’.

vectorize_along_physical_variables_ic(dict_of_funcs)[source]¶

Vectorize functions along physical variables for initial conditions.

Parameters:

dict_of_funcs (OrderedDict[int | tuple[int], VarArgAnyCallable]) – A dictionary of functions to be vectorized.

Return type:

OrderedDict[int | tuple[int], VarArgAnyCallable]

Returns:

A dictionary of vectorized functions.

Raises:

NotImplementedError – If the type_space is ‘phase_space’.
ValueError – If the type_space is ‘space’.

get_formatted_current_theta()[source]¶

Get the current parameters of the approximation space.

Return type:: dict[str, Parameter]
Returns:: A dictionary of the current parameters of the approximation space.

eval_network(*args)[source]¶

Evaluate the network with pre-processing.

Parameters:: *args (Tensor | dict[str, Parameter]) – Arguments to be passed to the network, with the last argument being the parameters of the network.
Return type:: Tensor
Returns:: The output of the network after applying pre-processing.

eval_func(*args)[source]¶

Evaluate the network with pre-processing and post-processing.

Parameters:: *args (Tensor | dict[str, Parameter]) – Arguments to be passed to the network, with the last argument being the parameters of the network.
Return type:: Tensor
Returns:: The output of the network after applying pre-processing and post-processing.