4.1.4.1 pde.backends.numpy.backend module

Defines base class of backends that implement computations.

class NumpyBackend(config, *, name=None)[source]

Bases: BackendBase[ndarray[Any, dtype[number]]]

Defines numpy backend, from which all other backends inherit.

Initialize the backend.

Parameters:

  • config (Config) – Configuration data for the backend

  • name (str) – The name of the backend

compile_function(func, **kwargs)[source]

General method that compiles a user function.

Parameters:

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

Return type:

TFunc

implementation = 'numpy'

The name of the python module that is used to implement this backend. This information can be used to distinguish the general implementation of backends.

Type:

str

make_expression_function(expression, *, single_arg=False, user_funcs=None)[source]

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)[source]

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, *, rng)[source]

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()).

Return type:

Callable[[], NumericArray]

make_ghost_cell_setter(bcs)[source]

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)

Return type:

GhostCellSetter

make_inner_prod_operator(field, *, conjugate=True)[source]

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.

Return type:

BinaryOperatorImplType

make_integrator(grid)[source]

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 operator is needed

Returns:

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

Return type:

Callable[[NumericArray], NumberOrArray]

make_operator(grid, operator, *, bcs, dtype=None, **kwargs)[source]

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.

Return type:

OperatorType

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.

Returns:

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

Return type:

callable

Parameters:
make_outer_prod_operator(field)[source]

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.

Return type:

BinaryOperatorImplType

make_pde_rhs(eq, state)[source]

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

Return type:

Callable[[NumericArray, float], NumericArray]

make_valid_data_setter(grid, rank)[source]

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