Provided by: python3-ffcx_0.4.2-2_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
┌──────────────────────┬──────────────────────────────────┐
│ufl_data(form_data, │ Create new instance of │
│unique_elements, ...) │ ufl_data(form_data, │
│ │ unique_elements, │
│ │ element_numbers, │
│ │ unique_coordinate_elements, │
│ │ expressions) │
└──────────────────────┴──────────────────────────────────┘
ffcx.analysis.analyze_ufl_objects(ufl_objects: List, parameters: Dict) ->
ffcx.analysis.ufl_data
Analyze ufl object(s).
Parameters
• ufl_objects –
• parameters – FFCx parameters. These parameters take priority over all
other set parameters.
Returns
• form_datas – Form_data objects
• unique_elements – Unique elements across all forms
• element_numbers – Mapping to unique numbers for all elements
• unique_coordinate_elements
ffcx.analysis.namedtuple(typename, field_names, *, rename=False, defaults=None,
module=None)
Returns a new subclass of tuple with named fields.
>>> Point = namedtuple('Point', ['x', 'y'])
>>> Point.__doc__ # docstring for the new class
'Point(x, y)'
>>> p = Point(11, y=22) # instantiate with positional args or keywords
>>> p[0] + p[1] # indexable like a plain tuple
33
>>> x, y = p # unpack like a regular tuple
>>> x, y
(11, 22)
>>> p.x + p.y # fields also accessible by name
33
>>> d = p._asdict() # convert to a dictionary
>>> d['x']
11
>>> Point(**d) # convert from a dictionary
Point(x=11, y=22)
>>> p._replace(x=100) # _replace() is like str.replace() but targets named fields
Point(x=100, y=22)
class ffcx.analysis.ufl_data(form_data, unique_elements, element_numbers,
unique_coordinate_elements, expressions)
Bases: tuple
Create new instance of ufl_data(form_data, unique_elements, element_numbers,
unique_coordinate_elements, expressions)
element_numbers
Alias for field number 2
expressions
Alias for field number 4
form_data
Alias for field number 0
unique_coordinate_elements
Alias for field number 3
unique_elements
Alias for field number 1
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) ->
ffcx.analysis.ufl_data
Analyze ufl object(s).
Parameters
• ufl_objects –
• parameters – FFCx parameters. These parameters take priority over all
other set parameters.
Returns
• form_datas – Form_data objects
• unique_elements – Unique elements across all forms
• element_numbers – Mapping to unique numbers for all elements
• unique_coordinate_elements
ffcx.compiler.compile_ufl_objects(ufl_objects: List[Any], object_names: Dict = {}, prefix:
Optional[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, object_names, prefix, parameters, visualise)
Compute intermediate representation.
ffcx.compiler.format_code(code, parameters)
Format given code in UFC format. Returns two strings with header and source file
contents.
ffcx.compiler.generate_code(ir, parameters)
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(*args) │ Get the Basix index of a │
│ │ derivative. │
├──────────────────────────────────┼──────────────────────────────────┤
│create_basix_element(family_type, │ Create a basix element. │
│cell_type, ...) │ │
├──────────────────────────────────┼──────────────────────────────────┤
│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
┌───────────────────────────────┬──────────────────────────────────┐
│BaseElement() │ An abstract element class. │
├───────────────────────────────┼──────────────────────────────────┤
│BasixElement(element) │ An element defined by Basix. │
├───────────────────────────────┼──────────────────────────────────┤
│BlockedElement(sub_element, │ An element with a block size │
│block_size[, ...]) │ that contains multiple copies of │
│ │ a sub element. │
├───────────────────────────────┼──────────────────────────────────┤
│ComponentElement(element, │ An element representing one │
│component) │ component of a BasixElement. │
├───────────────────────────────┼──────────────────────────────────┤
│MixedElement(sub_elements) │ A mixed element that combines │
│ │ two or more elements. │
├───────────────────────────────┼──────────────────────────────────┤
│QuadratureElement(ufl_element) │ A quadrature element. │
└───────────────────────────────┴──────────────────────────────────┘
class ffcx.element_interface.ABC
Bases: object
Helper class that provides a standard way to create an ABC using inheritance.
class ffcx.element_interface.BaseElement
Bases: abc.ABC
An abstract element class.
abstract property cell_type
Basix cell type used to initialise the element.
abstract property dim: int
Number of DOFs the element has.
abstract property discontinuous: bool
True if the discontinuous version of the element is used.
abstract property dpc_variant
Basix DPC variant used to initialise the element.
abstract property element_family
Basix element family used to initialise the element.
property element_type
Element type.
abstract property entity_closure_dofs
DOF numbers associated with the closure of each entity.
abstract property entity_dofs
DOF numbers associated with each entity.
abstract property family_name: str
Family name of the element.
abstract get_component_element(flat_component: int) -> tuple[‐
ffcx.element_interface.BaseElement, int, int]
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property is_custom_element: bool
True if the element is a custom Basix element.
abstract property lagrange_variant
Basix Lagrange variant used to initialise the element.
abstract property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
abstract property num_entity_dofs
Number of DOFs associated with each entity.
abstract property num_global_support_dofs
abstract property reference_geometry
Geometry of the reference element.
abstract property reference_topology
Topology of the reference element.
abstract tabulate(nderivs: int, points: numpy.ndarray)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
abstract property value_shape: Tuple[int, ...]
Value shape of the element basis function.
NOTE:
For scalar elements, (1,) is returned. This is different from Basix where
the value shape for scalar elements is (,).
abstract property value_size: int
Value size of the element.
Equal to numpy.prod(value_shape).
class ffcx.element_interface.BasixElement(element)
Bases: ffcx.element_interface.BaseElement
An element defined by Basix.
property cell_type
Basix cell type used to initialise the element.
property dim
Number of DOFs the element has.
property discontinuous
True if the discontinuous version of the element is used.
property dpc_variant
Basix DPC variant used to initialise the element.
property element_family
Basix element family used to initialise the element.
property element_type: str
Element type.
property entity_closure_dofs
DOF numbers associated with the closure of each entity.
property entity_dofs
DOF numbers associated with each entity.
property family_name
Family name of the element.
get_component_element(flat_component)
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property is_custom_element: bool
True if the element is a custom Basix element.
property lagrange_variant
Basix Lagrange variant used to initialise the element.
property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
property num_entity_dofs
Number of DOFs associated with each entity.
property num_global_support_dofs
property reference_geometry
Geometry of the reference element.
property reference_topology
Topology of the reference element.
tabulate(nderivs, points)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
property value_shape
Get the value shape of the element.
property value_size
Value size of the element.
Equal to numpy.prod(value_shape).
class ffcx.element_interface.BlockedElement(sub_element, block_size, block_shape=None)
Bases: ffcx.element_interface.BaseElement
An element with a block size that contains multiple copies of a sub element.
property cell_type
Basix cell type used to initialise the element.
property dim
Number of DOFs the element has.
property discontinuous
True if the discontinuous version of the element is used.
property dpc_variant
Basix DPC variant used to initialise the element.
property element_family
Basix element family used to initialise the element.
property element_type
Element type.
property entity_closure_dofs
DOF numbers associated with the closure of each entity.
property entity_dofs
DOF numbers associated with each entity.
property family_name
Family name of the element.
get_component_element(flat_component)
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property lagrange_variant
Basix Lagrange variant used to initialise the element.
property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
property num_entity_dofs
Number of DOFs associated with each entity.
property num_global_support_dofs
property reference_geometry
Geometry of the reference element.
property reference_topology
Topology of the reference element.
tabulate(nderivs, points)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
property value_shape
Value shape of the element basis function.
NOTE:
For scalar elements, (1,) is returned. This is different from Basix where
the value shape for scalar elements is (,).
property value_size
Value size of the element.
Equal to numpy.prod(value_shape).
class ffcx.element_interface.ComponentElement(element, component)
Bases: ffcx.element_interface.BaseElement
An element representing one component of a BasixElement.
property cell_type
Basix cell type used to initialise the element.
property dim
Number of DOFs the element has.
property discontinuous
True if the discontinuous version of the element is used.
property dpc_variant
Basix DPC variant used to initialise the element.
property element_family
Basix element family used to initialise the element.
property entity_closure_dofs
DOF numbers associated with the closure of each entity.
property entity_dofs
DOF numbers associated with each entity.
property family_name: str
Family name of the element.
get_component_element(flat_component)
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property lagrange_variant
Basix Lagrange variant used to initialise the element.
property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
property num_entity_dofs
Number of DOFs associated with each entity.
property num_global_support_dofs
property reference_geometry
Geometry of the reference element.
property reference_topology
Topology of the reference element.
tabulate(nderivs, points)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
property value_shape
Value shape of the element basis function.
NOTE:
For scalar elements, (1,) is returned. This is different from Basix where
the value shape for scalar elements is (,).
property value_size
Value size of the element.
Equal to numpy.prod(value_shape).
class ffcx.element_interface.MixedElement(sub_elements)
Bases: ffcx.element_interface.BaseElement
A mixed element that combines two or more elements.
property cell_type
Basix cell type used to initialise the element.
property dim
Number of DOFs the element has.
property discontinuous
True if the discontinuous version of the element is used.
property dpc_variant
Basix DPC variant used to initialise the element.
property element_family
Basix element family used to initialise the element.
property element_type: str
Get the element type.
property entity_closure_dofs
DOF numbers associated with the closure of each entity.
property entity_dofs
DOF numbers associated with each entity.
property family_name
Family name of the element.
get_component_element(flat_component)
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property lagrange_variant
Basix Lagrange variant used to initialise the element.
property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
property num_entity_dofs
Number of DOFs associated with each entity.
property num_global_support_dofs
property reference_geometry
Geometry of the reference element.
property reference_topology
Topology of the reference element.
tabulate(nderivs, points)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
property value_shape
Value shape of the element basis function.
NOTE:
For scalar elements, (1,) is returned. This is different from Basix where
the value shape for scalar elements is (,).
property value_size
Value size of the element.
Equal to numpy.prod(value_shape).
class ffcx.element_interface.QuadratureElement(ufl_element)
Bases: ffcx.element_interface.BaseElement
A quadrature element.
property cell_type: None
Basix cell type used to initialise the element.
property dim
Number of DOFs the element has.
property discontinuous
True if the discontinuous version of the element is used.
property dpc_variant
Basix DPC variant used to initialise the element.
property element_family
Basix element family used to initialise the element.
property element_type: str
Element type.
property entity_closure_dofs
DOF numbers associated with the closure of each entity.
property entity_dofs
DOF numbers associated with each entity.
property family_name
Family name of the element.
get_component_element(flat_component)
Get element that represents a component of the element, and the offset and
stride of the component.
For example, for a MixedElement, this will return the sub-element that
represents the given component, the offset of that sub-element, and a stride
of 1. For a BlockedElement, this will return the sub-element, an offset
equal to the component number, and a stride equal to the block size. For
vector-valued element (eg H(curl) and H(div) elements), this returns a
ComponentElement (and as offset of 0 and a stride of 1). When tabulate is
called on the ComponentElement, only the part of the table for the given
component is returned.
Parameters
flat_component – The component
Returns
component element, offset of the component, stride of the component
property lagrange_variant
Basix Lagrange variant used to initialise the element.
property num_entity_closure_dofs
Number of DOFs associated with the closure of each entity.
property num_entity_dofs
Number of DOFs associated with each entity.
property num_global_support_dofs
property reference_geometry
Geometry of the reference element.
property reference_topology
Topology of the reference element.
tabulate(nderivs, points)
Tabulate the basis functions of the element.
Parameters
• nderivs – Number of derivatives to tabulate.
• points – Points to tabulate at
Returns
Tabulated basis functions
property value_shape
Value shape of the element basis function.
NOTE:
For scalar elements, (1,) is returned. This is different from Basix where
the value shape for scalar elements is (,).
property value_size
Value size of the element.
Equal to numpy.prod(value_shape).
ffcx.element_interface.abstractmethod(funcobj)
A decorator indicating abstract methods.
Requires that the metaclass is ABCMeta or derived from it. A class that has a
metaclass derived from ABCMeta cannot be instantiated unless all of its abstract
methods are overridden. The abstract methods can be called using any of the normal
‘super’ call mechanisms. abstractmethod() may be used to declare abstract methods
for properties and descriptors.
Usage:
class C(metaclass=ABCMeta):
@abstractmethod def my_abstract_method(self, …):
…
ffcx.element_interface.basix_index(*args)
Get the Basix index of a derivative.
ffcx.element_interface.create_basix_element(family_type, cell_type, degree, variant_info,
discontinuous)
Create a basix element.
ffcx.element_interface.create_element(element:
ufl.finiteelement.finiteelementbase.FiniteElementBase) ->
ffcx.element_interface.BaseElement
Create an FFCx element from a UFL element.
Parameters
element – A UFL finite element
Returns
A FFCx finite element
ffcx.element_interface.create_quadrature(cellname, degree, rule)
Create a quadrature rule.
ffcx.element_interface.map_facet_points(points, facet, cellname)
Map points from a reference facet to a physical facet.
ffcx.element_interface.reference_cell_vertices(cellname)
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)
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, ...) │ │
└─────────────────────────────────┴──────────────────────────────────┘
ffcx.naming.cdtype_to_numpy(cdtype)
Map a C data type string NumPy datatype string.
ffcx.naming.compute_signature(ufl_objects, tag)
Compute the signature hash.
Based on the UFL type of the objects and an additional optional ‘tag’.
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.PARAMETERS
Functions
┌──────────────────────────────────────┬──────────────────────────────────┐
│get_parameters([priority_parameters]) │ Return (a copy of) the merged │
│ │ parameter values for FFCX. │
└──────────────────────────────────────┴──────────────────────────────────┘
class ffcx.parameters.Path(*args, **kwargs)
Bases: pathlib.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. This function works even if the
path doesn’t point to anything.
No normalization is done, i.e. all ‘.’ and ‘..’ will be kept along. 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 (for example turning slashes into backslashes under Windows).
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
┌─────────────────────────────────┬──────────────────────────────────┐
│ir_custom_element(cell_type, │ Create new instance of │
│value_shape, ...) │ ir_custom_element(cell_type, │
│ │ value_shape, wcoeffs, x, M, │
│ │ map_type, discontinuous, │
│ │ highest_complete_degree, │
│ │ highest_degree) │
├─────────────────────────────────┼──────────────────────────────────┤
│ir_data(elements, dofmaps, │ Create new instance of │
│integrals, forms, ...) │ ir_data(elements, dofmaps, │
│ │ integrals, forms, expressions) │
├─────────────────────────────────┼──────────────────────────────────┤
│ir_dofmap(id, name, signature, │ Create new instance of │
│...) │ ir_dofmap(id, name, signature, │
│ │ num_global_support_dofs, │
│ │ num_element_support_dofs, │
│ │ num_entity_dofs, │
│ │ tabulate_entity_dofs, │
│ │ num_entity_closure_dofs, │
│ │ tabulate_entity_closure_dofs, │
│ │ num_sub_dofmaps, sub_dofmaps, │
│ │ block_size) │
└─────────────────────────────────┴──────────────────────────────────┘
│ir_element(id, name, signature, │ Create new instance of │
│cell_shape, ...) │ ir_element(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) │
├─────────────────────────────────┼──────────────────────────────────┤
│ir_expression(name, │ Create new instance of │
│element_dimensions, ...) │ ir_expression(name, │
│ │ element_dimensions, params, │
│ │ unique_tables, │
│ │ unique_table_types, integrand, │
│ │ table_dofmaps, │
│ │ coefficient_numbering, │
│ │ coefficient_offsets, │
│ │ integral_type, entitytype, │
│ │ tensor_shape, expression_shape, │
│ │ original_constant_offsets, │
│ │ original_coefficient_positions, │
│ │ points, coefficient_names, │
│ │ constant_names, │
│ │ needs_facet_permutations, │
│ │ function_spaces, │
│ │ name_from_uflfile) │
├─────────────────────────────────┼──────────────────────────────────┤
│ir_form(id, name, signature, │ Create new instance of │
│rank, ...) │ ir_form(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) │
├─────────────────────────────────┼──────────────────────────────────┤
│ir_integral(integral_type, │ Create new instance of │
│subdomain_id, ...) │ ir_integral(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, │
│ │ table_dofmaps, integrand, name, │
│ │ precision, │
│ │ needs_facet_permutations, │
│ │ coordinate_element) │
└─────────────────────────────────┴──────────────────────────────────┘
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.
<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.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.representation.compute_integral_ir(cell, integral_type, entitytype, integrands,
argument_shape, p, visualise)
ffcx.ir.representation.compute_ir(analysis, object_names, prefix, parameters, visualise)
Compute intermediate representation.
ffcx.ir.representation.create_element(element:
ufl.finiteelement.finiteelementbase.FiniteElementBase) ->
ffcx.element_interface.BaseElement
Create an FFCx element from a UFL element.
Parameters
element – A UFL finite element
Returns
A FFCx finite element
ffcx.ir.representation.create_quadrature_points_and_weights(integral_type, cell, degree,
rule)
Create quadrature rule and return points and weights.
class ffcx.ir.representation.ir_custom_element(cell_type, value_shape, wcoeffs, x, M,
map_type, discontinuous, highest_complete_degree, highest_degree)
Bases: tuple
Create new instance of ir_custom_element(cell_type, value_shape, wcoeffs, x, M,
map_type, discontinuous, highest_complete_degree, highest_degree)
M Alias for field number 4
cell_type
Alias for field number 0
discontinuous
Alias for field number 6
highest_complete_degree
Alias for field number 7
highest_degree
Alias for field number 8
map_type
Alias for field number 5
value_shape
Alias for field number 1
wcoeffs
Alias for field number 2
x Alias for field number 3
class ffcx.ir.representation.ir_data(elements, dofmaps, integrals, forms, expressions)
Bases: tuple
Create new instance of ir_data(elements, dofmaps, integrals, forms, expressions)
dofmaps
Alias for field number 1
elements
Alias for field number 0
expressions
Alias for field number 4
forms Alias for field number 3
integrals
Alias for field number 2
class ffcx.ir.representation.ir_dofmap(id, name, signature, num_global_support_dofs,
num_element_support_dofs, num_entity_dofs, tabulate_entity_dofs, num_entity_closure_dofs,
tabulate_entity_closure_dofs, num_sub_dofmaps, sub_dofmaps, block_size)
Bases: tuple
Create new instance of ir_dofmap(id, name, signature, num_global_support_dofs,
num_element_support_dofs, num_entity_dofs, tabulate_entity_dofs,
num_entity_closure_dofs, tabulate_entity_closure_dofs, num_sub_dofmaps,
sub_dofmaps, block_size)
block_size
Alias for field number 11
id Alias for field number 0
name Alias for field number 1
num_element_support_dofs
Alias for field number 4
num_entity_closure_dofs
Alias for field number 7
num_entity_dofs
Alias for field number 5
num_global_support_dofs
Alias for field number 3
num_sub_dofmaps
Alias for field number 9
signature
Alias for field number 2
sub_dofmaps
Alias for field number 10
tabulate_entity_closure_dofs
Alias for field number 8
tabulate_entity_dofs
Alias for field number 6
class ffcx.ir.representation.ir_element(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: tuple
Create new instance of ir_element(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
Alias for field number 19
basix_family
Alias for field number 18
block_size
Alias for field number 12
cell_shape
Alias for field number 3
custom_element
Alias for field number 21
degree Alias for field number 9
discontinuous
Alias for field number 20
dpc_variant
Alias for field number 17
element_type
Alias for field number 14
entity_dofs
Alias for field number 15
family Alias for field number 10
geometric_dimension
Alias for field number 5
id Alias for field number 0
lagrange_variant
Alias for field number 16
name Alias for field number 1
num_sub_elements
Alias for field number 11
reference_value_shape
Alias for field number 8
signature
Alias for field number 2
space_dimension
Alias for field number 6
sub_elements
Alias for field number 13
topological_dimension
Alias for field number 4
value_shape
Alias for field number 7
class ffcx.ir.representation.ir_expression(name, element_dimensions, params,
unique_tables, unique_table_types, integrand, table_dofmaps, coefficient_numbering,
coefficient_offsets, integral_type, entitytype, tensor_shape, expression_shape,
original_constant_offsets, original_coefficient_positions, points, coefficient_names,
constant_names, needs_facet_permutations, function_spaces, name_from_uflfile)
Bases: tuple
Create new instance of ir_expression(name, element_dimensions, params,
unique_tables, unique_table_types, integrand, table_dofmaps, coefficient_numbering,
coefficient_offsets, integral_type, entitytype, tensor_shape, expression_shape,
original_constant_offsets, original_coefficient_positions, points,
coefficient_names, constant_names, needs_facet_permutations, function_spaces,
name_from_uflfile)
coefficient_names
Alias for field number 16
coefficient_numbering
Alias for field number 7
coefficient_offsets
Alias for field number 8
constant_names
Alias for field number 17
element_dimensions
Alias for field number 1
entitytype
Alias for field number 10
expression_shape
Alias for field number 12
function_spaces
Alias for field number 19
integral_type
Alias for field number 9
integrand
Alias for field number 5
name Alias for field number 0
name_from_uflfile
Alias for field number 20
needs_facet_permutations
Alias for field number 18
original_coefficient_positions
Alias for field number 14
original_constant_offsets
Alias for field number 13
params Alias for field number 2
points Alias for field number 15
table_dofmaps
Alias for field number 6
tensor_shape
Alias for field number 11
unique_table_types
Alias for field number 4
unique_tables
Alias for field number 3
class ffcx.ir.representation.ir_form(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: tuple
Create new instance of ir_form(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
Alias for field number 9
constant_names
Alias for field number 10
dofmaps
Alias for field number 12
finite_elements
Alias for field number 11
function_spaces
Alias for field number 7
id Alias for field number 0
integral_names
Alias for field number 13
name Alias for field number 1
name_from_uflfile
Alias for field number 6
num_coefficients
Alias for field number 4
num_constants
Alias for field number 5
original_coefficient_position
Alias for field number 8
rank Alias for field number 3
signature
Alias for field number 2
subdomain_ids
Alias for field number 14
class ffcx.ir.representation.ir_integral(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, table_dofmaps, integrand, name, precision,
needs_facet_permutations, coordinate_element)
Bases: tuple
Create new instance of ir_integral(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, table_dofmaps, integrand, name,
precision, needs_facet_permutations, coordinate_element)
cell_shape
Alias for field number 16
coefficient_numbering
Alias for field number 12
coefficient_offsets
Alias for field number 13
coordinate_element
Alias for field number 24
element_dimensions
Alias for field number 9
element_ids
Alias for field number 10
enabled_coefficients
Alias for field number 8
entitytype
Alias for field number 5
geometric_dimension
Alias for field number 3
integral_type
Alias for field number 0
integrand
Alias for field number 20
name Alias for field number 21
needs_facet_permutations
Alias for field number 23
num_facets
Alias for field number 6
num_vertices
Alias for field number 7
original_constant_offsets
Alias for field number 14
params Alias for field number 15
precision
Alias for field number 22
rank Alias for field number 2
subdomain_id
Alias for field number 1
table_dofmaps
Alias for field number 19
tensor_shape
Alias for field number 11
topological_dimension
Alias for field number 4
unique_table_types
Alias for field number 18
unique_tables
Alias for field number 17
ffcx.ir.representation.namedtuple(typename, field_names, *, rename=False, defaults=None,
module=None)
Returns a new subclass of tuple with named fields.
>>> Point = namedtuple('Point', ['x', 'y'])
>>> Point.__doc__ # docstring for the new class
'Point(x, y)'
>>> p = Point(11, y=22) # instantiate with positional args or keywords
>>> p[0] + p[1] # indexable like a plain tuple
33
>>> x, y = p # unpack like a regular tuple
>>> x, y
(11, 22)
>>> p.x + p.y # fields also accessible by name
33
>>> d = p._asdict() # convert to a dictionary
>>> d['x']
11
>>> Point(**d) # convert from a dictionary
Point(x=11, y=22)
>>> p._replace(x=100) # _replace() is like str.replace() but targets named fields
Point(x=100, y=22)
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)
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, facet, cellname)
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)
Get the vertices of a reference cell.
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AUTHOR
FEniCS Project
COPYRIGHT
2022, FEniCS Project