4.1.3.1 pde.backends.numba_mpi.backend module

Defines a numba backend class that support MPI parallelism.

class NumbaMPIBackend(config: MutableMapping[str, Any] | Config | None, *, name: str | None = None)

Bases: NumbaBackend

Defines MPI-compatible numba backend.

Initialize the backend.

Parameters:

• config (Config) – Configuration data for the backend

• name (str) – The name of the backend

compile_function(func: TFunc, **kwargs) → TFunc

General method that compiles a user function.

Parameters:

• func (callable) – The function that needs to be compiled for this backend

• **kwargs – Additional arguments forwarded to pde.backends.numba.utils.jit()

classmethod from_args(config: MutableMapping[str, Any] | Config | None, args: str = '', *, name: str | None = None) → Self

Initialize backend with extra arguments.

Parameters:

• config (Config) – Configuration data for the backend

• args (str) – Additional arguments that determine how the backend is initialized

• name (str) – The name of the backend

get_operator_info(grid: GridBase, operator: str | OperatorInfo) → OperatorInfo

Return the operator defined for this backend.

Parameters:

• grid (GridBase) – Grid for which the operator is needed

• operator (str) – Identifier for the operator. Some examples are ‘laplace’, ‘gradient’, or ‘divergence’. The registered operators for this grid can be obtained from the operators attribute.

Returns:

information for the operator

Return type:

OperatorInfo

get_registered_operators(grid_id: GridBase | type[GridBase]) → set[str]

Returns all operators defined for a backend.

Parameters:

grid_id (GridBase or its type) – Grid for which the operator need to be returned

property info: dict[str, Any]

relevant information about the backend

Type:

dict

make_data_setter(grid: GridBase, rank: int, bcs: BoundariesBase | None = None) → DataSetter

Create a function to set the valid part of a full data array.

Parameters:

• grid (GridBase) – Grid for which the data setter is defined

• rank (int) – Rank of the data represented on the grid

• bcs (BoundariesBase, optional) – If supplied, the returned function also enforces boundary conditions by setting the ghost cells to the correct values

Returns:

Takes two numpy arrays, setting the valid data in the first one, using the second array. The arrays need to be allocated already and they need to have the correct dimensions, which are not checked. If bcs are given, a third argument is allowed, which sets arguments for the BCs.

Return type:

callable

make_expression_function(expression: ExpressionBase, *, single_arg: bool = False, user_funcs: dict[str, Callable] | None = None) → Callable[..., NumberOrArray]

Return a function evaluating an expression.

Parameters:

• expression (ExpressionBase) – The expression that is converted to a function

• single_arg (bool) – Determines whether the returned function accepts all variables in a single argument as an array or whether all variables need to be supplied separately.

• user_funcs (dict) – Additional functions that can be used in the expression.

Returns:

the function

Return type:

function

make_full_data_setter(bcs: BoundariesBase) → DataSetter

Create a function to set the valid part of a full data array.

Parameters:

bcs (BoundariesBase, optional) – If supplied, the returned function also enforces boundary conditions by setting the ghost cells to the correct values

Returns:

Takes two numpy arrays, setting the valid data in the first one, using the second array. The arrays need to be allocated already and they need to have the correct dimensions, which are not checked. If bcs are given, a third argument is allowed, which sets arguments for the BCs.

Return type:

callable

make_gaussian_noise(field: TField, *, rng: np.random.Generator) → Callable[[], NumericArray]

Create a function generating Gaussian white noise.

Parameters:

• field (FieldBase) – An example for the state from which the grid and other information can be extracted.

• rng (Generator) – Random number generator (default: default_rng()). Not used in this numba backend.

make_ghost_cell_setter(bcs: BoundariesBase) → GhostCellSetter

Return function that sets the ghost cells on a full array.

Parameters:

bcs (BoundariesBase) – Defines the boundary conditions for a particular grid, for which the setter should be defined.

Returns:

Callable with signature (data_full: NumericArray, args=None), which sets the ghost cells of the full data, potentially using additional information in args (e.g., the time t during solving a PDE)

make_inner_prod_operator(field: DataFieldBase, *, conjugate: bool = True) → _BinaryOperatorImplType

Return operator calculating the dot product between two fields.

This supports both products between two vectors as well as products between a vector and a tensor.

Parameters:

• field (DataFieldBase) – Field for which the inner product is defined

• conjugate (bool) – Whether to use the complex conjugate for the second operand

Returns:

function that takes two instance of ndarray, which contain the discretized data of the two operands. An optional third argument can specify the output array to which the result is written.

make_inserter(grid: GridBase, *, with_ghost_cells: bool = False) → Callable[[InexactArray, FloatingArray, NumberOrArray], None]

Return a compiled function to insert values at interpolated positions.

Parameters:

• grid (GridBase) – Grid for which the integrator is defined

• with_ghost_cells (bool) – Flag indicating that the interpolator should work on the full data array that includes values for the grid points. If this is the case, the boundaries are not checked and the coordinates are used as is.

Returns:

A function with signature (data, position, amount), where data is the numpy array containing the field data, position is denotes the position in grid coordinates, and amount is the that is to be added to the field.

Return type:

callable

make_integrator(grid: GridBase) → Callable[[NumericArray], NumberOrArray]

Return function that integrates discretized data over a grid.

If this function is used in a multiprocessing run (using MPI), the integrals are performed on all subgrids and then accumulated. Each process then receives the same value representing the global integral.

Parameters:

grid (GridBase) – Grid for which the integrator is defined

Returns:

A function that takes a numpy array and returns the integral with the correct weights given by the cell volumes.

make_interpolator(field: DataFieldBase, *, fill: Number | None = None, with_ghost_cells: bool = False) → Callable[[FloatingArray, NumericArray], NumberOrArray]

Returns a function that can be used to interpolate values.

Parameters:

• field (DataFieldBase) – Field for which the interpolator is defined

• fill (Number, optional) – Determines how values out of bounds are handled. If None, a ValueError is raised when out-of-bounds points are requested. Otherwise, the given value is returned.

• with_ghost_cells (bool) – Flag indicating that the interpolator should work on the full data array that includes values for the ghost points. If this is the case, the boundaries are not checked and the coordinates are used as is.

Returns:

A function which returns interpolated values when called with arbitrary positions within the space of the grid.

make_mpi_synchronizer(operator: int | str = 'MAX') → Callable[[float], float]

Return function that synchronizes values between multiple MPI processes.

Warning

The default implementation does not synchronize anything. This is simply a hook, which can be used by backends that support MPI

Parameters:

operator (str or int) – Flag determining how the value from multiple nodes is combined. Possible values include “MAX”, “MIN”, and “SUM”.

Returns:

Function that can be used to synchronize values across nodes

make_operator(grid: GridBase, operator: str | OperatorInfo, *, bcs: BoundariesBase, dtype: DTypeLike | None = None, **kwargs) → OperatorType

Return a compiled function applying an operator with boundary conditions.

Parameters:

• grid (GridBase) – Grid for which the operator is needed

• operator (str) – Identifier for the operator. Some examples are ‘laplace’, ‘gradient’, or ‘divergence’. The registered operators for this grid can be obtained from the operators attribute.

• bcs (BoundariesBase, optional) – The boundary conditions used before the operator is applied

• dtype (numpy dtype) – The data type of the field.

• **kwargs – Specifies extra arguments influencing how the operator is created.

The returned function takes the discretized data on the grid as an input and returns the data to which the operator operator has been applied. The function only takes the valid grid points and allocates memory for the ghost points internally to apply the boundary conditions specified as bc. Note that the function supports an optional argument out, which if given should provide space for the valid output array without the ghost cells. The result of the operator is then written into this output array.

The function also accepts an optional parameter args, which is forwarded to set_ghost_cells. This allows setting boundary conditions based on external parameters, like time. Note that since the returned operator will always be compiled by Numba, the arguments need to be compatible with Numba. The following example shows how to pass the current time t:

The internal raw operator implementation is expected to use the in-place signature operator_raw(arr_full, out[, args]).

Returns:

the function that applies the operator. This function has the signature (arr: NumericArray, out: NumericArray = None, args=None).

Return type:

callable

make_operator_no_bc(grid: GridBase, operator: str | OperatorInfo, *, dtype: DTypeLike | None = None, **kwargs) → OperatorType

Return a compiled function applying an operator without boundary conditions.

The returned function has public signature (arr, out=None, args=None) -> result.

Note

The resulting function does not check whether the ghost cells of the input array have been supplied with sensible values. It is the responsibility of the user to set the values of the ghost cells beforehand. Use this function only if you absolutely know what you’re doing. In all other cases, make_operator() is probably the better choice.

Backends can choose whether their internal operator implementation uses a functional style op(arr, *, args=None) -> result or an in-place style op(arr, out, *, args=None). This wrapper normalizes both styles to the public signature above.

Parameters:

• grid (GridBase) – Grid for which the operator is needed

• operator (str) – Identifier for the operator. Some examples are ‘laplace’, ‘gradient’, or ‘divergence’. The registered operators for this grid can be obtained from the operators attribute.

• dtype (numpy dtype) – The data type of the field.

• **kwargs – Specifies extra arguments influencing how the operator is created.

Returns:

the function that applies the operator. This function has the signature (arr: NumericArray, out: NumericArray=None, args=None).

Return type:

callable

Internally, raw operator implementations are expected to use the functional signature operator_raw(arr_full, out[, args]).

make_outer_prod_operator(field: DataFieldBase) → _BinaryOperatorImplType

Return operator calculating the outer product between two fields.

This supports typically only supports products between two vector fields.

Parameters:

field (DataFieldBase) – Field for which the outer product is defined

Returns:

function that takes two instance of ndarray, which contain the discretized data of the two operands. An optional third argument can specify the output array to which the result is written.

make_pde_rhs(eq: PDEBase, state: TField) → Callable[[NumericArray, float], NumericArray]

Return a function for evaluating the right hand side of the PDE.

Parameters:

• eq (PDEBase) – The object describing the differential equation

• state (FieldBase) – An example for the state from which information can be extracted

Returns:

Function returning deterministic part of the right hand side of the PDE

make_stepper(solver: SolverBase, state: TField) → StepperType

Create a field-based stepping function for a given solver.

Parameters:

• solver (SolverBase) – The solver instance, which determines how the stepper is constructed

• state (FieldBase) – An example for the state from which the grid and other information can be extracted

Returns:

Function that can be called to advance the state from time t_start to time t_end. The function call signature is (state: numpy.ndarray, t_start: float, t_end: float)

make_valid_data_setter(grid: GridBase, rank: int) → DataSetter

Create a function to set the valid part of a full data array.

Parameters:

• grid (GridBase) – The grid for which the data setter is created

• rank (int) – Rank of the data represented on the grid.

Returns:

Takes two numpy arrays, setting the valid data in the first one, using the second array. The arrays need to be allocated already and they need to have the correct dimensions, which are not checked. If bcs are given, a third argument is allowed, which sets arguments for the BCs.

Return type:

callable

native_to_numpy(value: Any) → Any

Convert native values to numpy representation.

Parameters:

value – The value to convert to numpy representation

numpy_to_native(value: Any) → Any

Convert values from numpy to native representation.

Parameters:

value – The value to convert from numpy representation

classmethod register_operator(grid_cls: type[GridBase], name: str, factory_func: OperatorFactory | None = None, *, rank_in: int = 0, rank_out: int = 0)

Register an operator for a particular grid.

Example

The method can either be used directly:

BackendClass.register_operator(grid_class, "operator", make_operator)

or as a decorator for the factory function:

@BackendClass.register_operator(grid_class, "operator")
def make_operator(grid: GridBase): ...

Parameters:

• grid_cls (GridBase) – Grid class for which the operator is defined

• name (str) – The name of the operator to register

• factory_func (callable) – A function with signature (grid: GridBase, **kwargs), which takes a grid object and optional keyword arguments and returns an implementation of the given operator. This implementation is a function that takes a ndarray of discretized values as arguments and returns the resulting discretized data in a ndarray after applying the operator.

• rank_in (int) – The rank of the input field for the operator

• rank_out (int) – The rank of the field that is returned by the operator

use_multithreading() → bool

Determine whether multithreading should be used in numba-compiled code.

This method checks the configuration setting for numba.multithreading and determines whether multithreading should be enabled based on the value of this setting. The possible values for numba.multithreading are: - ‘always’: Multithreading is always enabled. - ‘never’: Multithreading is never enabled. - ‘only_local’: Multithreading is enabled only if the code is not running in a high-performance computing (HPC) environment.

Returns:

True if multithreading should be enabled, False otherwise.

Return type:

bool

Raises:

• ValueError – If the numba.multithreading setting is not one of the expected

• values ('always', 'never', 'only_local'). –