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, │ 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[_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, │ 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. │
└──────────────────────────────────┴──────────────────────────────────┘
ffcx.element_interface.QuadratureElement(cellname: str, value_shape: Tuple[int, ...],
scheme: str | None = None, degree: int | None = None, points: ndarray[Any, dtype[float64]]
| None = None, weights: ndarray[Any, dtype[float64]] | None = None, mapname: str =
'identity') -> _ElementBase
ffcx.element_interface.RealElement(element: FiniteElementBase) -> _ElementBase
ffcx.element_interface.basix_index(indices: Tuple[int]) -> int
Get the Basix index of a derivative.
ffcx.element_interface.convert_element(element: FiniteElementBase) -> _ElementBase
Convert and element to a FFCx element.
ffcx.element_interface.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.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, options) │ Format given code in UFC format. │
├─────────────────────────────────┼──────────────────────────────────┤
│write_code(code_h, code_c, │ │
│prefix, output_dir) │ │
└─────────────────────────────────┴──────────────────────────────────┘
ffcx.formatting.format_code(code, options: 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_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.main(args=None)
FFCX.NAMING
Functions
┌─────────────────────────────────┬─────────────────────────────┐
│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, ...) │ │
└─────────────────────────────────┴─────────────────────────────┘
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, │ 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, sobolev_space, │
│ │ interpolation_nderivs, │
│ │ discontinuous, │
│ │ highest_complete_degree, │
│ │ highest_degree, polyset_type) │
├─────────────────────────────────┼──────────────────────────────────┤
│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, 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, │ 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, │
│ │ options, cell_shape, │
│ │ unique_tables, │
│ │ unique_table_types, integrand, │
│ │ name, needs_facet_permutations, │
│ │ coordinate_element) │
└─────────────────────────────────┴──────────────────────────────────┘
class ffcx.ir.representation.CustomElementIR(cell_type, value_shape, wcoeffs, x, M,
map_type, sobolev_space, interpolation_nderivs, discontinuous, highest_complete_degree,
highest_degree, polyset_type)
Bases: NamedTuple
Create new instance of CustomElementIR(cell_type, value_shape, wcoeffs, x, M,
map_type, sobolev_space, interpolation_nderivs, discontinuous,
highest_complete_degree, highest_degree, 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
highest_complete_degree: int
Alias for field number 9
highest_degree: 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, 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, 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)
Bases: NamedTuple
Create new instance of 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)
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
options: dict
Alias for field number 2
original_coefficient_positions: List[int]
Alias for field number 19
original_constant_offsets: Dict[Constant, int]
Alias for field number 12
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.
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, 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)
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, options,
cell_shape, unique_tables, unique_table_types, integrand, name,
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 22
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 21
num_facets: int
Alias for field number 6
num_vertices: int
Alias for field number 7
options: dict
Alias for field number 15
original_constant_offsets: Dict[Constant, int]
Alias for field number 14
rank: int
Alias for field number 2
subdomain_id: 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[_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)
ffcx.ir.representation.compute_ir(analysis: UFLData, object_names, prefix, options,
visualise)
Compute intermediate representation.
ffcx.ir.representation.convert_element(element: FiniteElementBase) -> _ElementBase
Convert and element to a FFCx element.
ffcx.ir.representation.create_quadrature_points_and_weights(integral_type, cell, degree,
rule, elements)
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) │ │
└────────────────────────────────┴───┘
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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FEniCS Project
COPYRIGHT
2024, FEniCS Project