Provided by: python3-ffcx_0.7.0-3_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__ │ │
├─────────────────────────────┼───────────────────────────────────────┤
│ 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 │ │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.codegeneration │ │
├─────────────────────────────┼───────────────────────────────────────┤
│ ffcx.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 | None = None) -> dict
Return (a copy of) the merged option values for FFCX.
Options
priority_options:
take priority over all other option values (see notes)
returns
dict
rtype merged option values
Notes
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__
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
┌──────────────────────────────────┬────────────────────────┐
│ analyze_ufl_objects(ufl_objects, │ Analyze ufl object(s). │
│ options) │ │
└──────────────────────────────────┴────────────────────────┘
Classes
┌───────────────────────────────────────┬───────────────────────────────────────┐
│ UFLData(form_data, unique_elements, │ Create new instance of │
│ ...) │ UFLData(form_data, unique_elements, │
│ │ element_numbers, │
│ │ unique_coordinate_elements, │
│ │ expressions) │
└───────────────────────────────────────┴───────────────────────────────────────┘
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[_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, options: Dict) -> UFLData
Analyze ufl object(s).
Options
ufl_objects options
FFCx options. These options take priority over all other set options.
Returns a data structure holding
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
ffcx.analysis.convert_element(element: FiniteElementBase) -> _ElementBase
Convert and element to a FFCx element.
ffcx.analysis.warn()
Issue a warning, or maybe ignore it or raise an exception.
message
Text of the warning message.
category
The Warning category subclass. Defaults to UserWarning.
stacklevel
How far up the call stack to make this warning appear. A value of 2 for example attributes
the warning to the caller of the code calling warn().
source If supplied, the destroyed object which emitted a ResourceWarning
skip_file_prefixes
An optional tuple of module filename prefixes indicating frames to skip during stacklevel
computations for stack frame attribution.
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 │
│ ...]) │ objects. │
└───────────────────────────────────┴───────────────────────────────────────┘
ffcx.compiler.analyze_ufl_objects(ufl_objects: List, options: Dict) -> UFLData
Analyze ufl object(s).
Options
ufl_objects options
FFCx options. These options take priority over all other set options.
Returns a data structure holding
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
ffcx.compiler.compile_ufl_objects(ufl_objects: List[Any], object_names: Dict = {}, prefix: str | None =
None, options: Dict = {}, visualise: bool = False)
Generate UFC code for a given UFL objects.
Options
@param ufl_objects:
Objects to be compiled. Accepts elements, forms, integrals or coordinate mappings.
ffcx.compiler.compute_ir(analysis: UFLData, object_names, prefix, options, visualise)
Compute intermediate representation.
ffcx.compiler.format_code(code, options: dict)
Format given code in UFC format. Returns two strings with header and source file contents.
ffcx.compiler.generate_code(ir, options) -> 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
─────────────────────────────────────────────────────────────────────────────────
QuadratureElement(cellname,
value_shape[, ...])
─────────────────────────────────────────────────────────────────────────────────
RealElement(element)
─────────────────────────────────────────────────────────────────────────────────
basix_index(indices) Get the Basix index of a derivative.
─────────────────────────────────────────────────────────────────────────────────
convert_element(element) Convert and element to a FFCx
element.
─────────────────────────────────────────────────────────────────────────────────
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 │ │ │
--
FFCX.NAMING
Functions
┌───────────────────────────────────────┬─────────────────────────────┐
│ compute_signature(ufl_objects, tag) │ Compute the signature hash. │
├───────────────────────────────────────┼─────────────────────────────┤
│ dofmap_name(ufl_element, prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ expression_name(expression, prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ finite_element_name(ufl_element, │ │
│ prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ form_name(original_form, form_id, │ │
│ prefix) │ │
├───────────────────────────────────────┼─────────────────────────────┤
│ integral_name(original_form, │ │
│ integral_type, ...) │ │
└───────────────────────────────────────┴─────────────────────────────┘
ffcx.naming.compute_signature(ufl_objects: List[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 ‘tag’.
ffcx.naming.convert_element(element: FiniteElementBase) -> _ElementBase
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.CODEGENERATION
Functions
┌────────────────────┬───────────────────────────────────────┐
│ get_include_path() │ Return location of UFC header files. │
├────────────────────┼───────────────────────────────────────┤
│ get_signature() │ Return SHA-1 hash of the contents of │
│ │ ufcx.h. │
└────────────────────┴───────────────────────────────────────┘
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.OPTIONS
Functions
┌─────────────────────────────────┬───────────────────────────────────────┐
│ get_options([priority_options]) │ Return (a copy of) the merged option │
│ │ values for FFCX. │
└─────────────────────────────────┴───────────────────────────────────────┘
class ffcx.options.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.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 | None = None) -> dict
Return (a copy of) the merged option values for FFCX.
Options
priority_options:
take priority over all other option values (see notes)
returns
dict
rtype merged option values
Notes
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, Create new instance of
value_shape, ...) CustomElementIR(cell_type,
value_shape, wcoeffs, x, M, map_type,
sobolev_space, interpolation_nderivs,
discontinuous,
highest_complete_degree,
highest_degree, polyset_type)
─────────────────────────────────────────────────────────────────────────────────
DataIR(elements, dofmaps, integrals, Create new instance of
forms, ...) DataIR(elements, dofmaps, integrals,
forms, expressions)
─────────────────────────────────────────────────────────────────────────────────
DofMapIR(id, name, signature, ...) 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)
─────────────────────────────────────────────────────────────────────────────────
ElementIR(id, name, signature, Create new instance of ElementIR(id,
cell_shape, ...) 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)
─────────────────────────────────────────────────────────────────────────────────
ExpressionIR(name, Create new instance of
element_dimensions, ...) ExpressionIR(name,
element_dimensions, 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)
─────────────────────────────────────────────────────────────────────────────────
FormIR(id, name, signature, rank, 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)
─────────────────────────────────────────────────────────────────────────────────
IntegralIR(integral_type, Create new instance of
subdomain_id, ...) 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, options,
cell_shape, unique_tables,
unique_table_types, integrand, name,
needs_facet_permutations,
coordinate_element)
┌───────────────────────────────────────┬───────────────────────────────────────┐
│ │ │
--
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) │ │
└─────────────────────────────────┴───┘
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: 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)
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
0.7.0 Feb 25, 2024 FENICSFORMCOMPILERX(1)