Provided by: python3-ffcx_0.5.0-3_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.parameters │ │
├────────────────────────────┼──────────────────────────────────┤
│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_parameters(priority_parameters: Optional[dict] = None) -> dict
Return (a copy of) the merged parameter values for FFCX.
Parameters
priority_parameters – 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:
{ “assume_aligned”: 32, “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). │
│parameters) │ │
└─────────────────────────────────┴────────────────────────┘
Classes
┌──────────────────────┬──────────────────────────────────┐
│UFLData(form_data, │ Create new instance of │
│unique_elements, ...) │ 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[_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 –
• parameters – FFCx parameters. These parameters take priority over all
other set parameters.
• holding (Returns a data structure) –
• ------- –
• 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) -> _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
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, parameters: Dict) -> UFLData
Analyze ufl object(s).
Parameters
• ufl_objects –
• parameters – FFCx parameters. These parameters take priority over all
other set parameters.
• holding (Returns a data structure) –
• ------- –
• 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, parameters: Dict = {}, visualise: bool = False)
Generate UFC code for a given UFL objects.
Parameters
ufl_objects (@param) – 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
┌──────────────────────────────────┬──────────────────────────────────┐
│basix_index(indices) │ Get the Basix index of a │
│ │ derivative. │
├──────────────────────────────────┼──────────────────────────────────┤
│convert_element(element) │ Convert and element to a FFCx │
│ │ element. │
├──────────────────────────────────┼──────────────────────────────────┤
│create_element(element) │ Create an FFCx element from a │
│ │ UFL element. │
├──────────────────────────────────┼──────────────────────────────────┤
│create_quadrature(cellname, │ Create a quadrature rule. │
│degree, rule) │ │
├──────────────────────────────────┼──────────────────────────────────┤
│map_facet_points(points, facet, │ Map points from a reference │
│cellname) │ facet to a physical facet. │
├──────────────────────────────────┼──────────────────────────────────┤
│reference_cell_vertices(cellname) │ Get the vertices of a reference │
│ │ cell. │
└──────────────────────────────────┴──────────────────────────────────┘
Classes
┌───────────────────────────┬───────────────────────┐
│QuadratureElement(element) │ A quadrature element. │
└───────────────────────────┴───────────────────────┘
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 – 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 – Number of derivatives to tabulate.
• points – 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 – 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
┌─────────────────────────────────┬──────────────────────────────────┐
│format_code(code, parameters) │ Format given code in UFC format. │
├─────────────────────────────────┼──────────────────────────────────┤
│write_code(code_h, code_c, │ │
│prefix, output_dir) │ │
└─────────────────────────────────┴──────────────────────────────────┘
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
┌─────────────┬───┐
│main([args]) │ │
└─────────────┴───┘
ffcx.main.get_parameters(priority_parameters: Optional[dict] = None) -> dict
Return (a copy of) the merged parameter values for FFCX.
Parameters
priority_parameters – 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:
{ “assume_aligned”: 32, “epsilon”: 1e-7 }
ffcx.main.main(args=None)
FFCX.NAMING
Functions
┌──────────────────────────────────┬──────────────────────────────────┐
│cdtype_to_numpy(cdtype) │ Map a C data type string NumPy │
│ │ datatype string. │
├──────────────────────────────────┼──────────────────────────────────┤
│compute_signature(ufl_objects, │ Compute the signature hash. │
│tag) │ │
├──────────────────────────────────┼──────────────────────────────────┤
│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, ...) │ │
├──────────────────────────────────┼──────────────────────────────────┤
│scalar_to_value_type(scalar_type) │ The C value type associated with │
│ │ a C scalar type. │
└──────────────────────────────────┴──────────────────────────────────┘
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 ‘tag’.
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 – A C type.
Returns
The value type associated with scalar_type. E.g., if scalar_type is float
_Complex the return value is ‘float’.
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.PARAMETERS
Functions
┌──────────────────────────────────────┬──────────────────────────────────┐
│get_parameters([priority_parameters]) │ Return (a copy of) the merged │
│ │ parameter values for FFCX. │
└──────────────────────────────────────┴──────────────────────────────────┘
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.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_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 ‘.’ and ‘..’.
lchmod(mode)
Like chmod(), except if the path points to a symlink, the symlink’s
permissions are changed, rather than its target’s.
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 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)
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.
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 – 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:
{ “assume_aligned”: 32, “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, │ Compute intermediate │
│object_names, prefix, ...) │ representation. │
└───────────────────────────┴──────────────────────────────────┘
Classes
┌─────────────────────────────────┬──────────────────────────────────┐
│CustomElementIR(cell_type, │ Create new instance of │
│value_shape, ...) │ CustomElementIR(cell_type, │
│ │ value_shape, wcoeffs, x, M, │
│ │ map_type, interpolation_nderivs, │
│ │ discontinuous, │
│ │ highest_complete_degree, │
│ │ highest_degree) │
├─────────────────────────────────┼──────────────────────────────────┤
│DataIR(elements, dofmaps, │ Create new instance of │
│integrals, 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 │
│cell_shape, ...) │ 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) │
└─────────────────────────────────┴──────────────────────────────────┘
│ExpressionIR(name, │ Create new instance of │
│element_dimensions, ...) │ 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) │
├─────────────────────────────────┼──────────────────────────────────┤
│FormIR(id, name, signature, │ Create new instance of │
│rank, ...) │ 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, │
│ │ params, cell_shape, │
│ │ unique_tables, │
│ │ unique_table_types, integrand, │
│ │ name, precision, │
│ │ needs_facet_permutations, │
│ │ coordinate_element) │
└─────────────────────────────────┴──────────────────────────────────┘
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={‘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, 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
┌───────────────────────────────────────────┬──────────────────────────────────┐
│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, 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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FEniCS Project
COPYRIGHT
2023, FEniCS Project