Provided by: python3-ffcx_0.8.0-1_all 
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.
┌─────────────────────────────┬───────────────────────────────────────┐
│ ffcx │ FEniCS Form Compiler (FFCx). │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.__main__ │ Run ffcx on a UFL file. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.analysis │ Compiler stage 1: Analysis. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.compiler │ Main interface for compilation of │
│ │ forms. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.element_interface │ Finite element interface. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.formatting │ Compiler stage 5: Code formatting. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.main │ Command-line interface to FFCx. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.naming │ Naming. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.codegeneration │ FFCx code generation. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.options │ Options. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.ir.representation │ Compiler stage 2: Code │
│ │ representation. │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.ir.representationutils │ Utility functions for some code │
│ │ shared between representations. │
└─────────────────────────────┴───────────────────────────────────────┘
FFCX
FEniCS Form Compiler (FFCx).
FFCx compiles finite element variational forms into C code.
ffcx.get_options(priority_options: dict[str, dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] |
str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict |
tuple[Any, Any] | int | float] | None = None) -> dict[str, int | float | dtype[Any] | None | type[Any] |
_SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]]
| list[Any] | _DTypeDict | tuple[Any, Any]]
Return (a copy of) the merged option values for FFCX.
Parameters
priority_options – take priority over all other option values (see notes)
Returns
merged option values
NOTE:
This function sets the log level from the merged option values prior to returning.
The ffcx_options.json files are cached on the first call. Subsequent calls to this function use
this cache.
Priority ordering of options from highest to lowest is:
• priority_options (API and command line options)
• $PWD/ffcx_options.json (local options)
• $XDG_CONFIG_HOME/ffcx/ffcx_options.json (user options)
• FFCX_DEFAULT_OPTIONS in ffcx.options
XDG_CONFIG_HOME is ~/.config/ if the environment variable is not set.
Example ffcx_options.json file:
{ “epsilon”: 1e-7 }
FFCX.__MAIN__
Run ffcx on a UFL file.
ffcx.__main__.main(args=None)
Run ffcx on a UFL file.
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
┌──────────────────────────────────┬────────────────────────┐
│ analyze_ufl_objects(ufl_objects, │ Analyze ufl object(s). │
│ scalar_type) │ │
└──────────────────────────────────┴────────────────────────┘
Classes
┌───────────────────────────────────────┬───────────┐
│ UFLData(form_data, unique_elements, │ UFL data. │
│ ...) │ │
└───────────────────────────────────────┴───────────┘
class ffcx.analysis.UFLData(form_data: tuple[ufl.algorithms.formdata.FormData, ...], unique_elements:
list[basix.ufl._ElementBase], element_numbers: dict[basix.ufl._ElementBase, int],
unique_coordinate_elements: list[basix.ufl._ElementBase], expressions: list[tuple[ufl.core.expr.Expr,
npt.NDArray[np.float64], ufl.core.expr.Expr]])
Bases: NamedTuple
UFL data.
Create new instance of UFLData(form_data, unique_elements, element_numbers,
unique_coordinate_elements, expressions)
element_numbers: dict[_ElementBase, 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[_ElementBase]
Alias for field number 3
unique_elements: list[_ElementBase]
Alias for field number 1
ffcx.analysis.analyze_ufl_objects(ufl_objects: list[Form | AbstractFiniteElement | Mesh | tuple[Expr,
ndarray[Any, dtype[floating]]]], scalar_type: dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]]
| str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict |
tuple[Any, Any]) -> UFLData
Analyze ufl object(s).
Parameters
• ufl_objects – UFL objects
• scalar_type – Scalar type that should be used for the analysis
Returns
form_datas: Form_data objects unique_elements: Unique elements across all forms and
expressions element_numbers: Mapping to unique numbers for all elements
unique_coordinate_elements: Unique coordinate elements across all forms and expressions
expressions: List of all expressions after post-processing, with its evaluation points
and the original expression
Return type
A data structure holding
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
0. 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.
1. 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.
2. 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.
3. 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.
4. 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
┌──────────────────────────────────┬───────────────────────────────────────┐
│ compile_ufl_objects(ufl_objects, │ Generate UFC code for a given UFL │
│ options[, ...]) │ objects. │
└──────────────────────────────────┴───────────────────────────────────────┘
ffcx.compiler.analyze_ufl_objects(ufl_objects: list[Form | AbstractFiniteElement | Mesh | tuple[Expr,
ndarray[Any, dtype[floating]]]], scalar_type: dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]]
| str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict |
tuple[Any, Any]) -> UFLData
Analyze ufl object(s).
Parameters
• ufl_objects – UFL objects
• scalar_type – Scalar type that should be used for the analysis
Returns
form_datas: Form_data objects unique_elements: Unique elements across all forms and
expressions element_numbers: Mapping to unique numbers for all elements
unique_coordinate_elements: Unique coordinate elements across all forms and expressions
expressions: List of all expressions after post-processing, with its evaluation points
and the original expression
Return type
A data structure holding
ffcx.compiler.compile_ufl_objects(ufl_objects: list[Any], options: dict[str, int | float | dtype[Any] |
None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex |
Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any]], object_names: dict[int, str] | None
= None, prefix: str | None = None, visualise: bool = False) -> tuple[str, str]
Generate UFC code for a given UFL objects.
Parameters
• ufl_objects – Objects to be compiled. Accepts elements, forms, integrals or coordinate
mappings.
• object_names – Map from object Python id to object name
• prefix – Prefix
• options – Options
• visualise – Toggle visualisation
ffcx.compiler.compute_ir(analysis: UFLData, object_names: dict[int, str], prefix: str, options: dict[str,
dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any,
SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any] | int | float],
visualise: bool) -> DataIR
Compute intermediate representation.
ffcx.compiler.format_code(code: CodeBlocks) -> tuple[str, str]
Format given code in UFC format. Returns two strings with header and source file contents.
ffcx.compiler.generate_code(ir: DataIR, options: dict[str, int | float | dtype[Any] | None | type[Any] |
_SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]]
| list[Any] | _DTypeDict | tuple[Any, Any]]) -> 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
─────────────────────────────────────────────────────────────────────────────────
basix_index(indices) Get the Basix index of a derivative.
─────────────────────────────────────────────────────────────────────────────────
create_quadrature(cellname, degree, Create a quadrature rule.
rule, ...)
─────────────────────────────────────────────────────────────────────────────────
map_facet_points(points, facet, Map points from a reference facet to
cellname) a physical facet.
─────────────────────────────────────────────────────────────────────────────────
reference_cell_vertices(cellname) Get the vertices of a reference cell.
┌───────────────────────────────────────┬───────────────────────────────────────┐
│ │ │
--
FFCX.FORMATTING │ │ │
--
FFCX.MAIN
Command-line interface to FFCx.
Parse command-line arguments and generate code from input UFL form files.
Functions
┌──────────────┬─────────────────────────┐
│ main([args]) │ Run ffcx on a UFL file. │
└──────────────┴─────────────────────────┘
ffcx.main.arg_type
alias of int
ffcx.main.get_options(priority_options: dict[str, dtype[Any] | None | type[Any] |
_SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]]
| list[Any] | _DTypeDict | tuple[Any, Any] | int | float] | None = None) -> dict[str, int | float |
dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any,
SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any]]
Return (a copy of) the merged option values for FFCX.
Parameters
priority_options – take priority over all other option values (see notes)
Returns
merged option values
NOTE:
This function sets the log level from the merged option values prior to returning.
The ffcx_options.json files are cached on the first call. Subsequent calls to this function use
this cache.
Priority ordering of options from highest to lowest is:
• priority_options (API and command line options)
• $PWD/ffcx_options.json (local options)
• $XDG_CONFIG_HOME/ffcx/ffcx_options.json (user options)
• FFCX_DEFAULT_OPTIONS in ffcx.options
XDG_CONFIG_HOME is ~/.config/ if the environment variable is not set.
Example ffcx_options.json file:
{ “epsilon”: 1e-7 }
ffcx.main.main(args=None)
Run ffcx on a UFL file.
FFCX.NAMING
Naming.
Functions
┌───────────────────────────────────────┬─────────────────────────────┐
│ compute_signature(ufl_objects, tag) │ Compute the signature hash. │
├───────────────────────────────────────┼─────────────────────────────┤
│ dofmap_name(ufl_element, prefix) │ Get DOF map name. │
├───────────────────────────────────────┼─────────────────────────────┤
│ expression_name(expression, prefix) │ Get expression name. │
├───────────────────────────────────────┼─────────────────────────────┤
│ finite_element_name(ufl_element, │ Get finite element name. │
│ prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ form_name(original_form, form_id, │ Get form name. │
│ prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ integral_name(original_form, │ Get integral name. │
│ integral_type, ...) │ │
└───────────────────────────────────────┴─────────────────────────────┘
ffcx.naming.compute_signature(ufl_objects: list[Form | _ElementBase | 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 ‘tag’.
ffcx.naming.dofmap_name(ufl_element: _ElementBase, prefix: str) -> str
Get DOF map name.
ffcx.naming.expression_name(expression: tuple[Expr, ndarray[Any, dtype[floating]]], prefix: str) -> str
Get expression name.
ffcx.naming.finite_element_name(ufl_element: _ElementBase, prefix: str) -> str
Get finite element name.
ffcx.naming.form_name(original_form: Form, form_id: int, prefix: str) -> str
Get form name.
ffcx.naming.integral_name(original_form: Form, integral_type: str, form_id: int, subdomain_id: tuple[int,
...] | tuple[str], prefix: str) -> str
Get integral name.
FFCX.CODEGENERATION
FFCx code generation.
Functions
┌────────────────────┬───────────────────────────────────────┐
│ get_include_path() │ Return location of UFCx header files. │
├────────────────────┼───────────────────────────────────────┤
│ get_signature() │ Return SHA-1 hash of the contents of │
│ │ ufcx.h. │
└────────────────────┴───────────────────────────────────────┘
ffcx.codegeneration.get_include_path()
Return location of UFCx 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.OPTIONS
Options.
Functions
┌─────────────────────────────────┬───────────────────────────────────────┐
│ get_options([priority_options]) │ Return (a copy of) the merged option │
│ │ values for FFCX. │
└─────────────────────────────────┴───────────────────────────────────────┘
class ffcx.options.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.
exists(*, follow_symlinks=True)
Whether this path exists.
This method normally follows symlinks; to check whether a symlink exists, add the argument
follow_symlinks=False.
expanduser()
Return a new path with expanded ~ and ~user constructs (as returned by os.path.expanduser)
glob(pattern, *, case_sensitive=None)
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.link’s.
classmethod home()
Return a new path pointing to the user’s home directory (as returned by
os.path.expanduser(‘~’)).
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_junction()
Whether this path is a junction.
is_mount()
Check if this path is a mount point
is_socket()
Whether this path is a socket.
is_symlink()
Whether this path is a symbolic link.
iterdir()
Yield path objects of the directory contents.
The children are yielded in arbitrary order, and the special entries ‘.’ and ‘..’ are not
included.
lchmod(mode)
Like chmod(), except if the path points to a symlink, the symlink’s permissions are
changed, rather than its target’s.
lstat()
Like stat(), except if the path points to a symlink, the symlink’s status information is
returned, rather than its target’s.
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, *, case_sensitive=None)
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 doesn’t exist.
unlink(missing_ok=False)
Remove this file or link. If the path is a directory, use rmdir() instead.
walk(top_down=True, on_error=None, follow_symlinks=False)
Walk the directory tree from this directory, similar to os.walk().
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.options.get_options(priority_options: dict[str, dtype[Any] | None | type[Any] |
_SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any, SupportsIndex | Sequence[SupportsIndex]]
| list[Any] | _DTypeDict | tuple[Any, Any] | int | float] | None = None) -> dict[str, int | float |
dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any,
SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any]]
Return (a copy of) the merged option values for FFCX.
Parameters
priority_options – take priority over all other option values (see notes)
Returns
merged option values
NOTE:
This function sets the log level from the merged option values prior to returning.
The ffcx_options.json files are cached on the first call. Subsequent calls to this function use
this cache.
Priority ordering of options from highest to lowest is:
• priority_options (API and command line options)
• $PWD/ffcx_options.json (local options)
• $XDG_CONFIG_HOME/ffcx/ffcx_options.json (user options)
• FFCX_DEFAULT_OPTIONS in ffcx.options
XDG_CONFIG_HOME is ~/.config/ if the environment variable is not set.
Example ffcx_options.json file:
{ “epsilon”: 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 “foo”, one should only need to use the data stored in the intermediate
representation under the key “foo”.
Functions
┌───────────────────────────────────────┬──────────────────────────────────────┐
│ compute_ir(analysis, object_names, │ Compute intermediate representation. │
│ prefix, ...) │ │
└───────────────────────────────────────┴──────────────────────────────────────┘
Classes
┌───────────────────────────────────────┬───────────────────────────────────────┐
│ CustomElementIR(cell_type, │ Intermediate representation of a │
│ value_shape, ...) │ custom element. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ DataIR(elements, dofmaps, integrals, │ Intermediate representation of data. │
│ forms, ...) │ │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ DofMapIR(id, name, signature, ...) │ Intermediate representation of a DOF │
│ │ map. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ ElementIR(id, name, signature, │ Intermediate representation of an │
│ cell_shape, ...) │ element. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ ExpressionIR(name, options, │ Intermediate representation of an │
│ unique_tables, ...) │ expression. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ FormIR(id, name, signature, rank, │ Intermediate representation of a │
│ ...) │ form. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ IntegralIR(integral_type, rank, │ Intermediate representation of an │
│ entitytype, ...) │ integral. │
├───────────────────────────────────────┼───────────────────────────────────────┤
│ QuadratureIR(cell_shape, points, │ Intermediate representation of a │
│ weights) │ quadrature rule. │
└───────────────────────────────────────┴───────────────────────────────────────┘
class ffcx.ir.representation.CustomElementIR(cell_type: basix.CellType, value_shape: tuple[int, ...],
wcoeffs: npt.NDArray[np.float64], x: list[list[npt.NDArray[np.float64]]], M:
list[list[npt.NDArray[np.float64]]], map_type: basix.MapType, sobolev_space: basix.SobolevSpace,
interpolation_nderivs: int, discontinuous: bool, embedded_subdegree: int, embedded_superdegree: int,
polyset_type: basix.PolysetType)
Bases: NamedTuple
Intermediate representation of a custom element.
Create new instance of CustomElementIR(cell_type, value_shape, wcoeffs, x, M, map_type,
sobolev_space, interpolation_nderivs, discontinuous, embedded_subdegree, embedded_superdegree,
polyset_type)
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 8
embedded_subdegree: int
Alias for field number 9
embedded_superdegree: int
Alias for field number 10
interpolation_nderivs: int
Alias for field number 7
map_type: MapType
Alias for field number 5
polyset_type: PolysetType
Alias for field number 11
sobolev_space: SobolevSpace
Alias for field number 6
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: list[ElementIR], dofmaps: list[DofMapIR], integrals: list[‐
IntegralIR], forms: list[FormIR], expressions: list[ExpressionIR])
Bases: NamedTuple
Intermediate representation of data.
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: int, name: str, signature: str, num_global_support_dofs: int,
num_element_support_dofs: int, entity_dofs: list[list[list[int]]], entity_closure_dofs:
list[list[list[int]]], num_entity_closure_dofs: list[list[int]], num_sub_dofmaps: int, sub_dofmaps:
list[str], block_size: int)
Bases: NamedTuple
Intermediate representation of a DOF map.
Create new instance of DofMapIR(id, name, signature, num_global_support_dofs,
num_element_support_dofs, entity_dofs, entity_closure_dofs, num_entity_closure_dofs,
num_sub_dofmaps, sub_dofmaps, block_size)
block_size: int
Alias for field number 10
entity_closure_dofs: list[list[list[int]]]
Alias for field number 6
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 7
num_global_support_dofs: int
Alias for field number 3
num_sub_dofmaps: int
Alias for field number 8
signature: str
Alias for field number 2
sub_dofmaps: list[str]
Alias for field number 9
class ffcx.ir.representation.ElementIR(id: int, name: str, signature: str, cell_shape: str,
topological_dimension: int, space_dimension: int, reference_value_shape: tuple[int, ...], degree: int,
symmetric: bool, num_sub_elements: int, block_size: int, sub_elements: list[str], element_type: str,
entity_dofs: list[list[list[int]]], lagrange_variant: basix.LagrangeVariant, dpc_variant:
basix.DPCVariant, basix_family: basix.ElementFamily, basix_cell: basix.CellType, discontinuous: bool,
custom_element: CustomElementIR, custom_quadrature: QuadratureIR)
Bases: NamedTuple
Intermediate representation of an element.
Create new instance of ElementIR(id, name, signature, cell_shape, topological_dimension,
space_dimension, reference_value_shape, degree, symmetric, num_sub_elements, block_size,
sub_elements, element_type, entity_dofs, lagrange_variant, dpc_variant, basix_family, basix_cell,
discontinuous, custom_element, custom_quadrature)
basix_cell: CellType
Alias for field number 17
basix_family: ElementFamily
Alias for field number 16
block_size: int
Alias for field number 10
cell_shape: str
Alias for field number 3
custom_element: CustomElementIR
Alias for field number 19
custom_quadrature: QuadratureIR
Alias for field number 20
degree: int
Alias for field number 7
discontinuous: bool
Alias for field number 18
dpc_variant: DPCVariant
Alias for field number 15
element_type: str
Alias for field number 12
entity_dofs: list[list[list[int]]]
Alias for field number 13
id: int
Alias for field number 0
lagrange_variant: LagrangeVariant
Alias for field number 14
name: str
Alias for field number 1
num_sub_elements: int
Alias for field number 9
reference_value_shape: tuple[int, ...]
Alias for field number 6
signature: str
Alias for field number 2
space_dimension: int
Alias for field number 5
sub_elements: list[str]
Alias for field number 11
symmetric: bool
Alias for field number 8
topological_dimension: int
Alias for field number 4
class ffcx.ir.representation.ExpressionIR(name: str, options: dict, unique_tables: dict[str,
npt.NDArray[np.float64]], unique_table_types: dict[str, str], integrand: dict[QuadratureRule, dict],
coefficient_numbering: dict[ufl.Coefficient, int], coefficient_offsets: dict[ufl.Coefficient, int],
integral_type: str, entitytype: str, tensor_shape: list[int], expression_shape: list[int],
original_constant_offsets: dict[ufl.Constant, int], points: npt.NDArray[np.float64], coefficient_names:
list[str], constant_names: list[str], needs_facet_permutations: bool, function_spaces: dict[str,
tuple[str, str, str, int, basix.CellType, basix.LagrangeVariant, tuple[int]]], name_from_uflfile: str,
original_coefficient_positions: list[int])
Bases: NamedTuple
Intermediate representation of an expression.
Create new instance of ExpressionIR(name, options, 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 13
coefficient_numbering: dict[Coefficient, int]
Alias for field number 5
coefficient_offsets: dict[Coefficient, int]
Alias for field number 6
constant_names: list[str]
Alias for field number 14
entitytype: str
Alias for field number 8
expression_shape: list[int]
Alias for field number 10
function_spaces: dict[str, tuple[str, str, str, int, CellType, LagrangeVariant, tuple[int]]]
Alias for field number 16
integral_type: str
Alias for field number 7
integrand: dict[QuadratureRule, dict]
Alias for field number 4
name: str
Alias for field number 0
name_from_uflfile: str
Alias for field number 17
needs_facet_permutations: bool
Alias for field number 15
options: dict
Alias for field number 1
original_coefficient_positions: list[int]
Alias for field number 18
original_constant_offsets: dict[Constant, int]
Alias for field number 11
points: ndarray[Any, dtype[float64]]
Alias for field number 12
tensor_shape: list[int]
Alias for field number 9
unique_table_types: dict[str, str]
Alias for field number 3
unique_tables: dict[str, ndarray[Any, dtype[float64]]]
Alias for field number 2
class ffcx.ir.representation.FormIR(id: int, name: str, signature: str, rank: int, num_coefficients: int,
num_constants: int, name_from_uflfile: str, function_spaces: dict[str, tuple[str, str, str, int,
basix.CellType, basix.LagrangeVariant, tuple[int]]], original_coefficient_position: list[int],
coefficient_names: list[str], constant_names: list[str], finite_elements: list[str], dofmaps: list[str],
integral_names: dict[str, list[str]], subdomain_ids: dict[str, list[int]])
Bases: NamedTuple
Intermediate representation of a form.
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, tuple[int]]]
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.
Initialise.
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={‘quadrature_degree’: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: str, rank: int, entitytype: str,
enabled_coefficients: list[bool], tensor_shape: list[int], coefficient_numbering: dict[ufl.Coefficient,
int], coefficient_offsets: dict[ufl.Coefficient, int], original_constant_offsets: dict[ufl.Constant,
int], unique_tables: dict[str, npt.NDArray[np.float64]], unique_table_types: dict[str, str], integrand:
dict[QuadratureRule, dict], name: str, needs_facet_permutations: bool, coordinate_element: str)
Bases: NamedTuple
Intermediate representation of an integral.
Create new instance of IntegralIR(integral_type, rank, entitytype, enabled_coefficients,
tensor_shape, coefficient_numbering, coefficient_offsets, original_constant_offsets,
unique_tables, unique_table_types, integrand, name, needs_facet_permutations, coordinate_element)
coefficient_numbering: dict[Coefficient, int]
Alias for field number 5
coefficient_offsets: dict[Coefficient, int]
Alias for field number 6
coordinate_element: str
Alias for field number 13
enabled_coefficients: list[bool]
Alias for field number 3
entitytype: str
Alias for field number 2
integral_type: str
Alias for field number 0
integrand: dict[QuadratureRule, dict]
Alias for field number 10
name: str
Alias for field number 11
needs_facet_permutations: bool
Alias for field number 12
original_constant_offsets: dict[Constant, int]
Alias for field number 7
rank: int
Alias for field number 1
tensor_shape: list[int]
Alias for field number 4
unique_table_types: dict[str, str]
Alias for field number 9
unique_tables: dict[str, ndarray[Any, dtype[float64]]]
Alias for field number 8
class ffcx.ir.representation.QuadratureIR(cell_shape: str, points: npt.NDArray[np.float64], weights:
npt.NDArray[np.float64])
Bases: NamedTuple
Intermediate representation of a quadrature rule.
Create new instance of QuadratureIR(cell_shape, points, weights)
cell_shape: str
Alias for field number 0
points: ndarray[Any, dtype[float64]]
Alias for field number 1
weights: ndarray[Any, dtype[float64]]
Alias for field number 2
class ffcx.ir.representation.QuadratureRule(points, weights, tensor_factors=None)
Bases: object
A quadrature rule.
Initialise.
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: tuple[ufl.algorithms.formdata.FormData, ...],
unique_elements: list[basix.ufl._ElementBase], element_numbers: dict[basix.ufl._ElementBase, int],
unique_coordinate_elements: list[basix.ufl._ElementBase], expressions: list[tuple[ufl.core.expr.Expr,
npt.NDArray[np.float64], ufl.core.expr.Expr]])
Bases: NamedTuple
UFL data.
Create new instance of UFLData(form_data, unique_elements, element_numbers,
unique_coordinate_elements, expressions)
element_numbers: dict[_ElementBase, 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[_ElementBase]
Alias for field number 3
unique_elements: list[_ElementBase]
Alias for field number 1
ffcx.ir.representation.compute_integral_ir(cell, integral_type, entitytype, integrands, argument_shape,
p, visualise)
Compute intermediate representation for an integral.
ffcx.ir.representation.compute_ir(analysis: UFLData, object_names: dict[int, str], prefix: str, options:
dict[str, dtype[Any] | None | type[Any] | _SupportsDType[dtype[Any]] | str | tuple[Any, int] | tuple[Any,
SupportsIndex | Sequence[SupportsIndex]] | list[Any] | _DTypeDict | tuple[Any, Any] | int | float],
visualise: bool) -> DataIR
Compute intermediate representation.
ffcx.ir.representation.create_quadrature_points_and_weights(integral_type, cell, degree, rule, elements,
use_tensor_product=False)
Create quadrature rule and return points and weights.
ffcx.ir.representation.sorted_expr_sum(seq)
Sorted expr sum.
FFCX.IR.REPRESENTATIONUTILS
Utility functions for some code shared between representations.
Functions
┌────────────────────────────────────────────┬───────────────────────────────────────┐
│ create_quadrature_points_and_weights(...[, │ Create quadrature rule and return │
│ ...]) │ points and weights. │
├────────────────────────────────────────────┼───────────────────────────────────────┤
│ integral_type_to_entity_dim(integral_type, │ Given integral_type and domain tdim, │
│ tdim) │ return the tdim of the integration │
│ │ entity. │
├────────────────────────────────────────────┼───────────────────────────────────────┤
│ map_integral_points(points, integral_type, │ Map points from reference entity to │
│ ...) │ its parent reference cell. │
└────────────────────────────────────────────┴───────────────────────────────────────┘
Classes
┌───────────────────────────────────────┬────────────────────┐
│ QuadratureRule(points, weights[, │ A quadrature rule. │
│ tensor_factors]) │ │
└───────────────────────────────────────┴────────────────────┘
class ffcx.ir.representationutils.QuadratureRule(points, weights, tensor_factors=None)
Bases: object
A quadrature rule.
Initialise.
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: str, degree: int, rule: str, elements:
list[_ElementBase]) -> 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,
elements, use_tensor_product=False)
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
2024, FEniCS Project
0.8.0 Apr 25, 2024 FENICSFORMCOMPILERX(1)