fenicsformcompilerx(1)

FEniCS Form Compiler X Documentation

Section 1 python3-ffcx bookworm source

Description

FENICSFORMCOMPILERX

NAME

fenicsformcompilerx - FEniCS Form Compiler X Documentation

The is an experimental version of the FEniCS Form Compiler. It is developed at https://github.com/FEniCS/ffcx.

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FFCX

FEniCS Form Compiler (FFCx).

FFCx compiles finite element variational forms into C code.
ffcx.get_parameters(priority_parameters: Optional[dict] = None) -> dict

Return (a copy of) the merged parameter values for FFCX.
Parameters

priority_parameters â take priority over all other parameter values (see notes)

Returns

dict

Return type

merged parameter values

Notes

This function sets the log level from the merged parameter values prior to returning.

The ffcx_parameters.json files are cached on the first call. Subsequent calls to this function use this cache.

Priority ordering of parameters from highest to lowest is:

	•		priority_parameters (API and command line parameters)
	•		$PWD/ffcx_parameters.json (local parameters)
	•		$XDG_CONFIG_HOME/ffcx/ffcx_parameters.json (user parameters)
	•		FFCX_DEFAULT_PARAMETERS in ffcx.parameters

XDG_CONFIG_HOME is ˜/.config/ if the environment variable is not set.

Example ffcx_parameters.json file:

{ âassume_alignedâ: 32, âepsilonâ: 1e-7 }

FFCX.MAIN

ffcx.__main__.main(args=None)

FFCX.ANALYSIS

Compiler stage 1: Analysis.

This module implements the analysis/preprocessing of variational forms, including automatic selection of elements, degrees and form representation type.

Functions

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Classes

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class ffcx.analysis.UFLData(form_data, unique_elements, element_numbers,
unique_coordinate_elements, expressions)

Bases: NamedTuple

Create new instance of UFLData(form_data, unique_elements, element_numbers, unique_coordinate_elements, expressions)
element_numbers: Dict[_BasixElementBase, int]

Alias for field number 2

expressions: List[Tuple[Expr, ndarray[Any, dtype[float64]], Expr]]

Alias for field number 4

form_data: Tuple[FormData, ...]

Alias for field number 0

unique_coordinate_elements: List[_BasixElementBase]

Alias for field number 3

unique_elements: List[_BasixElementBase]

Alias for field number 1

ffcx.analysis.analyze_ufl_objects(ufl_objects: List, parameters: Dict) ->
UFLData

Analyze ufl object(s).
Parameters

	•		ufl_objects â
	•		parameters â FFCx parameters. These parameters take priority over all other set parameters.
	•		holding (Returns a data structure) â
	•		------- â
	•		form_datas â Form_data objects
	•		unique_elements â Unique elements across all forms and expressions
	•		element_numbers â Mapping to unique numbers for all elements
	•		unique_coordinate_elements â Unique coordinate elements across all forms and expressions
	•		expressions â List of all expressions after post-processing, with its evaluation points and the original expression

ffcx.analysis.convert_element(element: FiniteElementBase) ->
_BasixElementBase

Convert and element to a FFCx element.

FFCX.COMPILER

Main interface for compilation of forms.

Breaks the compilation into several sequential stages. The output of each stage is the input of the next stage.

Compiler stages

Language, parsing

•

			Input: Python code or .ufl file
	•		Output: UFL form

This stage consists of parsing and expressing a form in the UFL form language. This stage is handled by UFL.

Analysis

•

			Input: UFL form
	•		Output: Preprocessed UFL form and FormData (metadata)

This stage preprocesses the UFL form and extracts form metadata. It may also perform simplifications on the form.

Code representation

•

			Input: Preprocessed UFL form and FormData (metadata)
	•		Output: Intermediate Representation (IR)

This stage examines the input and generates all data needed for code generation. This includes generation of finite element basis functions, extraction of data for mapping of degrees of freedom and possible precomputation of integrals. Most of the complexity of compilation is handled in this stage.

The IR is stored as a dictionary, mapping names of UFC functions to data needed for generation of the corresponding code.

Code generation

•

			Input: Intermediate Representation (IR)
	•		Output: C code

This stage examines the IR and generates the actual C code for the body of each UFC function.

The code is stored as a dictionary, mapping names of UFC functions to strings containing the C code of the body of each function.

Code formatting

•

			Input: C code
	•		Output: C code files

This stage examines the generated C++ code and formats it according to the UFC format, generating as output one or more .h/.c files conforming to the UFC format.

Functions

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ffcx.compiler.analyze_ufl_objects(ufl_objects: List, parameters: Dict) ->
UFLData

Analyze ufl object(s).
Parameters

	•		ufl_objects â
	•		parameters â FFCx parameters. These parameters take priority over all other set parameters.
	•		holding (Returns a data structure) â
	•		------- â
	•		form_datas â Form_data objects
	•		unique_elements â Unique elements across all forms and expressions
	•		element_numbers â Mapping to unique numbers for all elements
	•		unique_coordinate_elements â Unique coordinate elements across all forms and expressions
	•		expressions â List of all expressions after post-processing, with its evaluation points and the original expression

ffcx.compiler.compile_ufl_objects(ufl_objects: List[Any], object_names:
Dict = {}, prefix: str = None, parameters: Dict = {}, visualise: bool =
False)

Generate UFC code for a given UFL objects.
Parameters

ufl_objects (@param) â Objects to be compiled. Accepts elements, forms, integrals or coordinate mappings.

ffcx.compiler.compute_ir(analysis: UFLData, object_names, prefix,
parameters, visualise)

Compute intermediate representation.

ffcx.compiler.format_code(code, parameters: dict)

Format given code in UFC format. Returns two strings with header and source file contents.

ffcx.compiler.generate_code(ir, parameters) -> CodeBlocks

Generate code blocks from intermediate representation.

ffcx.compiler.time() -> floating point number

Return the current time in seconds since the Epoch. Fractions of a second may be present if the system clock provides them.

FFCX.ELEMENT_INTERFACE

Finite element interface.

Functions

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Classes

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class ffcx.element_interface.QuadratureElement(element: FiniteElementBase)

Bases: _BasixElementBase

A quadrature element.

Initialise the element.
property cell_type: CellType

Basix cell type used to initialise the element.

property dim: int

Number of DOFs the element has.

property discontinuous: bool

True if the discontinuous version of the element is used.

property dpc_variant: DPCVariant

Basix DPC variant used to initialise the element.

property element_family: ElementFamily

Basix element family used to initialise the element.

property entity_closure_dofs: List[List[List[int]]]

DOF numbers associated with the closure of each entity.

property entity_dofs: List[List[List[int]]]

DOF numbers associated with each entity.

property family_name: str

Family name of the element.

get_component_element(flat_component: int) ->
Tuple[_BasixElementBase, int, int]

Get element that represents a component of the element, and the offset and stride of the component.
Parameters

flat_component â The component

Returns

component element, offset of the component, stride of the component

property interpolation_nderivs: int

The number of derivatives needed when interpolating.

property lagrange_variant: LagrangeVariant

Basix Lagrange variant used to initialise the element.

property num_entity_closure_dofs: List[List[int]]

Number of DOFs associated with the closure of each entity.

property num_entity_dofs: List[List[int]]

Number of DOFs associated with each entity.

property num_global_support_dofs: int

Get the number of global support DOFs.

property reference_geometry: ndarray[Any, dtype[float64]]

Geometry of the reference element.

property reference_topology: List[List[List[int]]]

Topology of the reference element.

tabulate(nderivs: int, points: ndarray[Any, dtype[float64]]) ->
ndarray[Any, dtype[float64]]

Tabulate the basis functions of the element.
Parameters

	•		nderivs â Number of derivatives to tabulate.
	•		points â Points to tabulate at

Returns

Tabulated basis functions

property ufcx_element_type: str

Element type.

ffcx.element_interface.basix_index(indices: Tuple[int]) -> int

Get the Basix index of a derivative.

ffcx.element_interface.convert_element(element: FiniteElementBase) ->
_BasixElementBase

Convert and element to a FFCx element.

ffcx.element_interface.create_element(element: FiniteElementBase) ->
_BasixElementBase

Create an FFCx element from a UFL element.
Parameters

element â A UFL finite element

Returns

A Basix finite element

ffcx.element_interface.create_quadrature(cellname, degree, rule) ->
Tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]]

Create a quadrature rule.

ffcx.element_interface.lru_cache(maxsize=128, typed=False)

Least-recently-used cache decorator.

If maxsize is set to None, the LRU features are disabled and the cache can grow without bound.

If typed is True, arguments of different types will be cached separately. For example, f(3.0) and f(3) will be treated as distinct calls with distinct results.

Arguments to the cached function must be hashable.

View the cache statistics named tuple (hits, misses, maxsize, currsize) with f.cache_info(). Clear the cache and statistics with f.cache_clear(). Access the underlying function with f.__wrapped__.

See: https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU)

ffcx.element_interface.map_facet_points(points: ndarray[Any,
dtype[float64]], facet: int, cellname: str) -> ndarray[Any, dtype[float64]]

Map points from a reference facet to a physical facet.

ffcx.element_interface.reference_cell_vertices(cellname: str) -> ndarray[-
Any, dtype[float64]]

Get the vertices of a reference cell.

FFCX.FORMATTING

Compiler stage 5: Code formatting.

This module implements the formatting of UFC code from a given dictionary of generated C++ code for the body of each UFC function.

It relies on templates for UFC code available as part of the module ufcx_utils.

Functions

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ffcx.formatting.format_code(code, parameters: dict)

Format given code in UFC format. Returns two strings with header and source file contents.

ffcx.formatting.write_code(code_h, code_c, prefix, output_dir)

FFCX.MAIN

Command-line interface to FFCx.

Parse command-line arguments and generate code from input UFL form files.

Functions

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ffcx.main.get_parameters(priority_parameters: Optional[dict] = None) ->
dict

Return (a copy of) the merged parameter values for FFCX.
Parameters

priority_parameters â take priority over all other parameter values (see notes)

Returns

dict

Return type

merged parameter values

Notes

This function sets the log level from the merged parameter values prior to returning.

The ffcx_parameters.json files are cached on the first call. Subsequent calls to this function use this cache.

Priority ordering of parameters from highest to lowest is:

	•		priority_parameters (API and command line parameters)
	•		$PWD/ffcx_parameters.json (local parameters)
	•		$XDG_CONFIG_HOME/ffcx/ffcx_parameters.json (user parameters)
	•		FFCX_DEFAULT_PARAMETERS in ffcx.parameters

XDG_CONFIG_HOME is ˜/.config/ if the environment variable is not set.

Example ffcx_parameters.json file:

{ âassume_alignedâ: 32, âepsilonâ: 1e-7 }

ffcx.main.main(args=None)

FFCX.NAMING

Functions

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ffcx.naming.cdtype_to_numpy(cdtype: str)

Map a C data type string NumPy datatype string.

ffcx.naming.compute_signature(ufl_objects: List[Union[Form,
FiniteElementBase, Tuple[Expr, ndarray[Any, dtype[float64]]]]], tag: str)
-> str

Compute the signature hash.

Based on the UFL type of the objects and an additional optional âtagâ.

ffcx.naming.convert_element(element: FiniteElementBase) ->
_BasixElementBase

Convert and element to a FFCx element.

ffcx.naming.dofmap_name(ufl_element, prefix)
ffcx.naming.expression_name(expression, prefix)
ffcx.naming.finite_element_name(ufl_element, prefix)
ffcx.naming.form_name(original_form, form_id, prefix)
ffcx.naming.integral_name(original_form, integral_type, form_id,
subdomain_id, prefix)
ffcx.naming.scalar_to_value_type(scalar_type: str) -> str

The C value type associated with a C scalar type.
Parameters

scalar_type â A C type.

Returns

The value type associated with scalar_type. E.g., if scalar_type is float _Complex the return value is âfloatâ.

FFCX.CODEGENERATION

Functions

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ffcx.codegeneration.get_include_path()

Return location of UFC header files.

ffcx.codegeneration.get_signature()

Return SHA-1 hash of the contents of ufcx.h.

In this implementation, the value is computed on import.

FFCX.PARAMETERS

Functions

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class ffcx.parameters.Any(*args, **kwargs)

Bases: object

Special type indicating an unconstrained type.

	•		Any is compatible with every type.
	•		Any assumed to have all methods.
	•		All values assumed to be instances of Any.

Note that all the above statements are true from the point of view of static type checkers. At runtime, Any should not be used with instance checks.

class ffcx.parameters.Path(*args, **kwargs)

Bases: PurePath

PurePath subclass that can make system calls.

Path represents a filesystem path but unlike PurePath, also offers methods to do system calls on path objects. Depending on your system, instantiating a Path will return either a PosixPath or a WindowsPath object. You can also instantiate a PosixPath or WindowsPath directly, but cannot instantiate a WindowsPath on a POSIX system or vice versa.

Construct a PurePath from one or several strings and or existing PurePath objects. The strings and path objects are combined so as to yield a canonicalized path, which is incorporated into the new PurePath object.
absolute()

Return an absolute version of this path by prepending the current working directory. No normalization or symlink resolution is performed.

Use resolve() to get the canonical path to a file.

chmod(mode, *, follow_symlinks=True)

Change the permissions of the path, like os.chmod().

classmethod cwd()

Return a new path pointing to the current working directory (as returned by os.getcwd()).

exists()

Whether this path exists.

expanduser()

Return a new path with expanded ˜ and ˜user constructs (as returned by os.path.expanduser)

glob(pattern)

Iterate over this subtree and yield all existing files (of any kind, including directories) matching the given relative pattern.

group()

Return the group name of the file gid.

hardlink_to(target)

Make this path a hard link pointing to the same file as target.

Note the order of arguments (self, target) is the reverse of os.linkâs.

classmethod home()

Return a new path pointing to the userâs home directory (as returned by os.path.expanduser(â˜â)).

is_block_device()

Whether this path is a block device.

is_char_device()

Whether this path is a character device.

is_dir()

Whether this path is a directory.

is_fifo()

Whether this path is a FIFO.

is_file()

Whether this path is a regular file (also True for symlinks pointing to regular files).

is_mount()

Check if this path is a POSIX mount point

is_socket()

Whether this path is a socket.

is_symlink()

Whether this path is a symbolic link.

iterdir()

Iterate over the files in this directory. Does not yield any result for the special paths â.â and â..â.

lchmod(mode)

Like chmod(), except if the path points to a symlink, the symlinkâs permissions are changed, rather than its targetâs.

link_to(target)

Make the target path a hard link pointing to this path.

Note this function does not make this path a hard link to target, despite the implication of the function and argument names. The order of arguments (target, link) is the reverse of Path.symlink_to, but matches that of os.link.

Deprecated since Python 3.10 and scheduled for removal in Python 3.12. Use hardlink_to() instead.

lstat()

Like stat(), except if the path points to a symlink, the symlinkâs status information is returned, rather than its targetâs.

mkdir(mode=511, parents=False, exist_ok=False)

Create a new directory at this given path.

open(mode='r', buffering=-1, encoding=None, errors=None,
newline=None)

Open the file pointed by this path and return a file object, as the built-in open() function does.

owner()

Return the login name of the file owner.

read_bytes()

Open the file in bytes mode, read it, and close the file.

read_text(encoding=None, errors=None)

Open the file in text mode, read it, and close the file.

readlink()

Return the path to which the symbolic link points.

rename(target)

Rename this path to the target path.

The target path may be absolute or relative. Relative paths are interpreted relative to the current working directory, not the directory of the Path object.

Returns the new Path instance pointing to the target path.

replace(target)

Rename this path to the target path, overwriting if that path exists.

The target path may be absolute or relative. Relative paths are interpreted relative to the current working directory, not the directory of the Path object.

Returns the new Path instance pointing to the target path.

resolve(strict=False)

Make the path absolute, resolving all symlinks on the way and also normalizing it.

rglob(pattern)

Recursively yield all existing files (of any kind, including directories) matching the given relative pattern, anywhere in this subtree.

rmdir()

Remove this directory. The directory must be empty.

samefile(other_path)

Return whether other_path is the same or not as this file (as returned by os.path.samefile()).

stat(*, follow_symlinks=True)

Return the result of the stat() system call on this path, like os.stat() does.

symlink_to(target, target_is_directory=False)

Make this path a symlink pointing to the target path. Note the order of arguments (link, target) is the reverse of os.symlink.

touch(mode=438, exist_ok=True)

Create this file with the given access mode, if it doesnât exist.

unlink(missing_ok=False)

Remove this file or link. If the path is a directory, use rmdir() instead.

write_bytes(data)

Open the file in bytes mode, write to it, and close the file.

write_text(data, encoding=None, errors=None, newline=None)

Open the file in text mode, write to it, and close the file.

ffcx.parameters.get_parameters(priority_parameters: Optional[dict] = None)
-> dict

Return (a copy of) the merged parameter values for FFCX.
Parameters

priority_parameters â take priority over all other parameter values (see notes)

Returns

dict

Return type

merged parameter values

Notes

This function sets the log level from the merged parameter values prior to returning.

The ffcx_parameters.json files are cached on the first call. Subsequent calls to this function use this cache.

Priority ordering of parameters from highest to lowest is:

	•		priority_parameters (API and command line parameters)
	•		$PWD/ffcx_parameters.json (local parameters)
	•		$XDG_CONFIG_HOME/ffcx/ffcx_parameters.json (user parameters)
	•		FFCX_DEFAULT_PARAMETERS in ffcx.parameters

XDG_CONFIG_HOME is ˜/.config/ if the environment variable is not set.

Example ffcx_parameters.json file:

{ âassume_alignedâ: 32, âepsilonâ: 1e-7 }

FFCX.IR.REPRESENTATION

Compiler stage 2: Code representation.

Module computes intermediate representations of forms, elements and dofmaps. For each UFC function, we extract the data needed for code generation at a later stage.

The representation should conform strictly to the naming and order of functions in UFC. Thus, for code generation of the function âfooâ, one should only need to use the data stored in the intermediate representation under the key âfooâ.

Functions

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Classes

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class ffcx.ir.representation.CustomElementIR(cell_type, value_shape,
wcoeffs, x, M, map_type, interpolation_nderivs, discontinuous,
highest_complete_degree, highest_degree)

Bases: NamedTuple

Create new instance of CustomElementIR(cell_type, value_shape, wcoeffs, x, M, map_type, interpolation_nderivs, discontinuous, highest_complete_degree, highest_degree)
M: List[List[ndarray[Any, dtype[float64]]]]

Alias for field number 4

cell_type: CellType

Alias for field number 0

discontinuous: bool

Alias for field number 7

highest_complete_degree: int

Alias for field number 8

highest_degree: int

Alias for field number 9

interpolation_nderivs: int

Alias for field number 6

map_type: MapType

Alias for field number 5

value_shape: Tuple[int, ...]

Alias for field number 1

wcoeffs: ndarray[Any, dtype[float64]]

Alias for field number 2

x: List[List[ndarray[Any, dtype[float64]]]]

Alias for field number 3

class ffcx.ir.representation.DataIR(elements, dofmaps, integrals, forms,
expressions)

Bases: NamedTuple

Create new instance of DataIR(elements, dofmaps, integrals, forms, expressions)
dofmaps: List[DofMapIR]

Alias for field number 1

elements: List[ElementIR]

Alias for field number 0

expressions: List[ExpressionIR]

Alias for field number 4

forms: List[FormIR]

Alias for field number 3

integrals: List[IntegralIR]

Alias for field number 2

class ffcx.ir.representation.DofMapIR(id, name, signature,
num_global_support_dofs, num_element_support_dofs, entity_dofs,
num_entity_dofs, entity_closure_dofs, num_entity_closure_dofs,
num_sub_dofmaps, sub_dofmaps, block_size)

Bases: NamedTuple

Create new instance of DofMapIR(id, name, signature, num_global_support_dofs, num_element_support_dofs, entity_dofs, num_entity_dofs, entity_closure_dofs, num_entity_closure_dofs, num_sub_dofmaps, sub_dofmaps, block_size)
block_size: int

Alias for field number 11

entity_closure_dofs: List[List[List[int]]]

Alias for field number 7

entity_dofs: List[List[List[int]]]

Alias for field number 5

id: int

Alias for field number 0

name: str

Alias for field number 1

num_element_support_dofs: int

Alias for field number 4

num_entity_closure_dofs: List[List[int]]

Alias for field number 8

num_entity_dofs: List[List[int]]

Alias for field number 6

num_global_support_dofs: int

Alias for field number 3

num_sub_dofmaps: int

Alias for field number 9

signature: str

Alias for field number 2

sub_dofmaps: List[str]

Alias for field number 10

class ffcx.ir.representation.ElementIR(id, name, signature, cell_shape,
topological_dimension, geometric_dimension, space_dimension, value_shape,
reference_value_shape, degree, family, num_sub_elements, block_size,
sub_elements, element_type, entity_dofs, lagrange_variant, dpc_variant,
basix_family, basix_cell, discontinuous, custom_element)

Bases: NamedTuple

Create new instance of ElementIR(id, name, signature, cell_shape, topological_dimension, geometric_dimension, space_dimension, value_shape, reference_value_shape, degree, family, num_sub_elements, block_size, sub_elements, element_type, entity_dofs, lagrange_variant, dpc_variant, basix_family, basix_cell, discontinuous, custom_element)
basix_cell: CellType

Alias for field number 19

basix_family: ElementFamily

Alias for field number 18

block_size: int

Alias for field number 12

cell_shape: str

Alias for field number 3

custom_element: CustomElementIR

Alias for field number 21

degree: int

Alias for field number 9

discontinuous: bool

Alias for field number 20

dpc_variant: DPCVariant

Alias for field number 17

element_type: str

Alias for field number 14

entity_dofs: List[List[List[int]]]

Alias for field number 15

family: str

Alias for field number 10

geometric_dimension: int

Alias for field number 5

id: int

Alias for field number 0

lagrange_variant: LagrangeVariant

Alias for field number 16

name: str

Alias for field number 1

num_sub_elements: int

Alias for field number 11

reference_value_shape: Tuple[int, ...]

Alias for field number 8

signature: str

Alias for field number 2

space_dimension: int

Alias for field number 6

sub_elements: List[str]

Alias for field number 13

topological_dimension: int

Alias for field number 4

value_shape: Tuple[int, ...]

Alias for field number 7

class ffcx.ir.representation.ExpressionIR(name, element_dimensions, params,
unique_tables, unique_table_types, integrand, coefficient_numbering,
coefficient_offsets, integral_type, entitytype, tensor_shape,
expression_shape, original_constant_offsets, points, coefficient_names,
constant_names, needs_facet_permutations, function_spaces,
name_from_uflfile, original_coefficient_positions)

Bases: NamedTuple

Create new instance of ExpressionIR(name, element_dimensions, params, unique_tables, unique_table_types, integrand, coefficient_numbering, coefficient_offsets, integral_type, entitytype, tensor_shape, expression_shape, original_constant_offsets, points, coefficient_names, constant_names, needs_facet_permutations, function_spaces, name_from_uflfile, original_coefficient_positions)
coefficient_names: List[str]

Alias for field number 14

coefficient_numbering: Dict[Coefficient, int]

Alias for field number 6

coefficient_offsets: Dict[Coefficient, int]

Alias for field number 7

constant_names: List[str]

Alias for field number 15

element_dimensions: Dict[FiniteElementBase, int]

Alias for field number 1

entitytype: str

Alias for field number 9

expression_shape: List[int]

Alias for field number 11

function_spaces: Dict[str, Tuple[str, str, str, int, CellType,
LagrangeVariant]]

Alias for field number 17

integral_type: str

Alias for field number 8

integrand: Dict[QuadratureRule, dict]

Alias for field number 5

name: str

Alias for field number 0

name_from_uflfile: str

Alias for field number 18

needs_facet_permutations: bool

Alias for field number 16

original_coefficient_positions: List[int]

Alias for field number 19

original_constant_offsets: Dict[Constant, int]

Alias for field number 12

params: dict

Alias for field number 2

points: ndarray[Any, dtype[float64]]

Alias for field number 13

tensor_shape: List[int]

Alias for field number 10

unique_table_types: Dict[str, str]

Alias for field number 4

unique_tables: Dict[str, ndarray[Any, dtype[float64]]]

Alias for field number 3

class ffcx.ir.representation.FormIR(id, name, signature, rank,
num_coefficients, num_constants, name_from_uflfile, function_spaces,
original_coefficient_position, coefficient_names, constant_names,
finite_elements, dofmaps, integral_names, subdomain_ids)

Bases: NamedTuple

Create new instance of FormIR(id, name, signature, rank, num_coefficients, num_constants, name_from_uflfile, function_spaces, original_coefficient_position, coefficient_names, constant_names, finite_elements, dofmaps, integral_names, subdomain_ids)
coefficient_names: List[str]

Alias for field number 9

constant_names: List[str]

Alias for field number 10

dofmaps: List[str]

Alias for field number 12

finite_elements: List[str]

Alias for field number 11

function_spaces: Dict[str, Tuple[str, str, str, int, CellType,
LagrangeVariant]]

Alias for field number 7

id: int

Alias for field number 0

integral_names: Dict[str, List[str]]

Alias for field number 13

name: str

Alias for field number 1

name_from_uflfile: str

Alias for field number 6

num_coefficients: int

Alias for field number 4

num_constants: int

Alias for field number 5

original_coefficient_position: List[int]

Alias for field number 8

rank: int

Alias for field number 3

signature: str

Alias for field number 2

subdomain_ids: Dict[str, List[int]]

Alias for field number 14

class ffcx.ir.representation.Integral(integrand, integral_type, domain,
subdomain_id, metadata, subdomain_data)

Bases: object

An integral over a single domain.
integral_type()

Return the domain type of this integral.

integrand()

Return the integrand expression, which is an Expr instance.

metadata()

Return the compiler metadata this integral has been annotated with.

reconstruct(integrand=None, integral_type=None, domain=None,
subdomain_id=None, metadata=None, subdomain_data=None)

Construct a new Integral object with some properties replaced with new values.

Example:

<a = Integral instance> b = a.reconstruct(expand_compounds(a.integrand())) c = a.reconstruct(metadata={âquadrature_degreeâ:2})

subdomain_data()

Return the domain data of this integral.

subdomain_id()

Return the subdomain id of this integral.

ufl_domain()

Return the integration domain of this integral.

class ffcx.ir.representation.IntegralIR(integral_type, subdomain_id, rank,
geometric_dimension, topological_dimension, entitytype, num_facets,
num_vertices, enabled_coefficients, element_dimensions, element_ids,
tensor_shape, coefficient_numbering, coefficient_offsets,
original_constant_offsets, params, cell_shape, unique_tables,
unique_table_types, integrand, name, precision, needs_facet_permutations,
coordinate_element)

Bases: NamedTuple

Create new instance of IntegralIR(integral_type, subdomain_id, rank, geometric_dimension, topological_dimension, entitytype, num_facets, num_vertices, enabled_coefficients, element_dimensions, element_ids, tensor_shape, coefficient_numbering, coefficient_offsets, original_constant_offsets, params, cell_shape, unique_tables, unique_table_types, integrand, name, precision, needs_facet_permutations, coordinate_element)
cell_shape: str

Alias for field number 16

coefficient_numbering: Dict[Coefficient, int]

Alias for field number 12

coefficient_offsets: Dict[Coefficient, int]

Alias for field number 13

coordinate_element: str

Alias for field number 23

element_dimensions: Dict[FiniteElementBase, int]

Alias for field number 9

element_ids: Dict[FiniteElementBase, int]

Alias for field number 10

enabled_coefficients: List[bool]

Alias for field number 8

entitytype: str

Alias for field number 5

geometric_dimension: int

Alias for field number 3

integral_type: str

Alias for field number 0

integrand: Dict[QuadratureRule, dict]

Alias for field number 19

name: str

Alias for field number 20

needs_facet_permutations: bool

Alias for field number 22

num_facets: int

Alias for field number 6

num_vertices: int

Alias for field number 7

original_constant_offsets: Dict[Constant, int]

Alias for field number 14

params: dict

Alias for field number 15

precision: int

Alias for field number 21

rank: int

Alias for field number 2

subdomain_id: Union[str, Tuple[int, ...], int]

Alias for field number 1

tensor_shape: List[int]

Alias for field number 11

topological_dimension: int

Alias for field number 4

unique_table_types: Dict[str, str]

Alias for field number 18

unique_tables: Dict[str, ndarray[Any, dtype[float64]]]

Alias for field number 17

class ffcx.ir.representation.QuadratureRule(points, weights)

Bases: object

id()

Return unique deterministic identifier.

NOTE:

This identifier is used to provide unique names to tables and symbols in generated code.

class ffcx.ir.representation.UFLData(form_data, unique_elements,
element_numbers, unique_coordinate_elements, expressions)

Bases: NamedTuple

Create new instance of UFLData(form_data, unique_elements, element_numbers, unique_coordinate_elements, expressions)
element_numbers: Dict[_BasixElementBase, int]

Alias for field number 2

expressions: List[Tuple[Expr, ndarray[Any, dtype[float64]], Expr]]

Alias for field number 4

form_data: Tuple[FormData, ...]

Alias for field number 0

unique_coordinate_elements: List[_BasixElementBase]

Alias for field number 3

unique_elements: List[_BasixElementBase]

Alias for field number 1

ffcx.ir.representation.compute_integral_ir(cell, integral_type, entitytype,
integrands, argument_shape, p, visualise)
ffcx.ir.representation.compute_ir(analysis: UFLData, object_names, prefix,
parameters, visualise)

Compute intermediate representation.

ffcx.ir.representation.convert_element(element: FiniteElementBase) ->
_BasixElementBase

Convert and element to a FFCx element.

ffcx.ir.representation.create_quadrature_points_and_weights(integral_type,
cell, degree, rule)

Create quadrature rule and return points and weights.

ffcx.ir.representation.sorted_expr_sum(seq)

FFCX.IR.REPRESENTATIONUTILS

Utility functions for some code shared between representations.

Functions

Image grohtml-71520-14.png

Classes

Image grohtml-71520-15.png

class ffcx.ir.representationutils.QuadratureRule(points, weights)

Bases: object

id()

Return unique deterministic identifier.

NOTE:

This identifier is used to provide unique names to tables and symbols in generated code.

ffcx.ir.representationutils.create_quadrature(cellname, degree, rule) ->
Tuple[ndarray[Any, dtype[float64]], ndarray[Any, dtype[float64]]]

Create a quadrature rule.

ffcx.ir.representationutils.create_quadrature_points_and_weights(integral_type,
cell, degree, rule)

Create quadrature rule and return points and weights.

ffcx.ir.representationutils.integral_type_to_entity_dim(integral_type,
tdim)

Given integral_type and domain tdim, return the tdim of the integration entity.

ffcx.ir.representationutils.map_facet_points(points: ndarray[Any,
dtype[float64]], facet: int, cellname: str) -> ndarray[Any, dtype[float64]]

Map points from a reference facet to a physical facet.

ffcx.ir.representationutils.map_integral_points(points, integral_type,
cell, entity)

Map points from reference entity to its parent reference cell.

ffcx.ir.representationutils.reference_cell_vertices(cellname: str) ->
ndarray[Any, dtype[float64]]

Get the vertices of a reference cell.

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AUTHOR

FEniCS Project

COPYRIGHT

2023, FEniCS Project

Description

FENICSFORMCOMPILERX

NAME

FFCX

FFCX.__MAIN__

FFCX.ANALYSIS

FFCX.COMPILER

Compiler stages

FFCX.ELEMENT_INTERFACE

FFCX.FORMATTING

FFCX.MAIN

FFCX.NAMING

FFCX.CODEGENERATION

FFCX.PARAMETERS

FFCX.IR.REPRESENTATION

Example:

FFCX.IR.REPRESENTATIONUTILS

AUTHOR

COPYRIGHT

FFCX.MAIN