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FENICSFORMCOMPILERX(1) FEniCS Form Compiler X FENICSFORMCOMPILERX(1)

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.

Return (a copy of) the merged parameter values for FFCX.
priority_parameters – take priority over all other parameter values (see notes)
dict
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.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, parameters) Analyze ufl object(s).

Classes

ufl_data(form_data, unique_elements, ...) Create new instance of ufl_data(form_data, unique_elements, element_numbers, unique_coordinate_elements, expressions)
Analyze ufl object(s).
  • ufl_objects –
  • parameters – FFCx parameters. These parameters take priority over all other set parameters.

  • form_datas – Form_data objects
  • unique_elements – Unique elements across all forms
  • element_numbers – Mapping to unique numbers for all elements
  • unique_coordinate_elements



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)

Bases: tuple

Create new instance of ufl_data(form_data, unique_elements, element_numbers, unique_coordinate_elements, expressions)

Alias for field number 2

Alias for field number 4

Alias for field number 0

Alias for field number 3

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.
Analyze ufl object(s).
  • ufl_objects –
  • parameters – FFCx parameters. These parameters take priority over all other set parameters.

  • form_datas – Form_data objects
  • unique_elements – Unique elements across all forms
  • element_numbers – Mapping to unique numbers for all elements
  • unique_coordinate_elements



Generate UFC code for a given UFL objects.
ufl_objects (@param) – Objects to be compiled. Accepts elements, forms, integrals or coordinate mappings.


Compute intermediate representation.

Format given code in UFC format. Returns two strings with header and source file contents.

Generate code blocks from intermediate representation.

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, cell_type, ...) Create a basix element.
create_element(element) Create an FFCx element from a UFL element.
create_quadrature(cellname, degree, rule) Create a quadrature rule.
map_facet_points(points, facet, cellname) Map points from a reference 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, block_size[, ...]) An element with a block size that contains multiple copies of a sub element.
ComponentElement(element, component) An element representing one component of a BasixElement.
MixedElement(sub_elements) A mixed element that combines two or more elements.
QuadratureElement(ufl_element) A quadrature element.
Bases: object

Helper class that provides a standard way to create an ABC using inheritance.


Bases: abc.ABC

An abstract element class.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

Element type.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


True if the element is a custom Basix element.

Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


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 (,).



Value size of the element.

Equal to numpy.prod(value_shape).



Bases: ffcx.element_interface.BaseElement

An element defined by Basix.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

Element type.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


True if the element is a custom Basix element.

Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


Get the value shape of the element.

Value size of the element.

Equal to numpy.prod(value_shape).



Bases: ffcx.element_interface.BaseElement

An element with a block size that contains multiple copies of a sub element.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

Element type.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


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 (,).



Value size of the element.

Equal to numpy.prod(value_shape).



Bases: ffcx.element_interface.BaseElement

An element representing one component of a BasixElement.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


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 (,).



Value size of the element.

Equal to numpy.prod(value_shape).



Bases: ffcx.element_interface.BaseElement

A mixed element that combines two or more elements.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

Get the element type.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


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 (,).



Value size of the element.

Equal to numpy.prod(value_shape).



Bases: ffcx.element_interface.BaseElement

A quadrature element.

Basix cell type used to initialise the element.

Number of DOFs the element has.

True if the discontinuous version of the element is used.

Basix DPC variant used to initialise the element.

Basix element family used to initialise the element.

Element type.

DOF numbers associated with the closure of each entity.

DOF numbers associated with each entity.

Family name of the element.

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.

flat_component – The component
component element, offset of the component, stride of the component


Basix Lagrange variant used to initialise the element.

Number of DOFs associated with the closure of each entity.

Number of DOFs associated with each entity.


Geometry of the reference element.

Topology of the reference element.

Tabulate the basis functions of the element.
  • nderivs – Number of derivatives to tabulate.
  • points – Points to tabulate at

Tabulated basis functions


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 (,).



Value size of the element.

Equal to numpy.prod(value_shape).



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:

@abstractmethod def my_abstract_method(self, …):
…






Get the Basix index of a derivative.

Create a basix element.

Create an FFCx element from a UFL element.
element – A UFL finite element
A FFCx finite element


Create a quadrature rule.

Map points from a reference facet to a physical facet.

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)
Format given code in UFC format. Returns two strings with header and source file contents.


FFCX.MAIN

Command-line interface to FFCx.

Parse command-line arguments and generate code from input UFL form files.

Functions

main([args])
Return (a copy of) the merged parameter values for FFCX.
priority_parameters – take priority over all other parameter values (see notes)
dict
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.NAMING

Functions

cdtype_to_numpy(cdtype) Map a C data type string NumPy datatype string.
compute_signature(ufl_objects, tag) Compute the signature hash.
dofmap_name(ufl_element, prefix)
expression_name(expression, prefix)
finite_element_name(ufl_element, prefix)
form_name(original_form, form_id, prefix)
integral_name(original_form, integral_type, ...)
Map a C data type string NumPy datatype string.

Compute the signature hash.

Based on the UFL type of the objects and an additional optional ‘tag’.







FFCX.CODEGENERATION

Functions

get_include_path() Return location of UFC header files.
get_signature() Return SHA-1 hash of the contents of ufcx.h.
Return location of UFC header files.

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.
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.

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.


Change the permissions of the path, like os.chmod().

Return a new path pointing to the current working directory (as returned by os.getcwd()).

Whether this path exists.

Return a new path with expanded ~ and ~user constructs (as returned by os.path.expanduser)

Iterate over this subtree and yield all existing files (of any kind, including directories) matching the given relative pattern.

Return the group name of the file gid.

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.


Return a new path pointing to the user’s home directory (as returned by os.path.expanduser(‘~’)).

Whether this path is a block device.

Whether this path is a character device.

Whether this path is a directory.

Whether this path is a FIFO.

Whether this path is a regular file (also True for symlinks pointing to regular files).

Check if this path is a POSIX mount point

Whether this path is a socket.

Whether this path is a symbolic link.

Iterate over the files in this directory. Does not yield any result for the special paths ‘.’ and ‘..’.

Like chmod(), except if the path points to a symlink, the symlink’s permissions are changed, rather than its target’s.

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.


Like stat(), except if the path points to a symlink, the symlink’s status information is returned, rather than its target’s.

Create a new directory at this given path.

Open the file pointed by this path and return a file object, as the built-in open() function does.

Return the login name of the file owner.

Open the file in bytes mode, read it, and close the file.

Open the file in text mode, read it, and close the file.

Return the path to which the symbolic link points.

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.


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.


Make the path absolute, resolving all symlinks on the way and also normalizing it (for example turning slashes into backslashes under Windows).

Recursively yield all existing files (of any kind, including directories) matching the given relative pattern, anywhere in this subtree.

Remove this directory. The directory must be empty.

Return whether other_path is the same or not as this file (as returned by os.path.samefile()).

Return the result of the stat() system call on this path, like os.stat() does.

Make this path a symlink pointing to the target path. Note the order of arguments (link, target) is the reverse of os.symlink.

Create this file with the given access mode, if it doesn’t exist.

Remove this file or link. If the path is a directory, use rmdir() instead.

Open the file in bytes mode, write to it, and close the file.

Open the file in text mode, write to it, and close the file.


Return (a copy of) the merged parameter values for FFCX.
priority_parameters – take priority over all other parameter values (see notes)
dict
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, object_names, prefix, ...) Compute intermediate representation.

Classes

ir_custom_element(cell_type, value_shape, ...) Create new instance of ir_custom_element(cell_type, value_shape, wcoeffs, x, M, map_type, discontinuous, highest_complete_degree, highest_degree)
ir_data(elements, dofmaps, integrals, forms, ...) Create new instance of 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, cell_shape, ...) 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)
ir_expression(name, element_dimensions, ...) 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)
ir_form(id, name, signature, rank, ...) 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)
ir_integral(integral_type, subdomain_id, ...) 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)
Bases: object

An integral over a single domain.

Return the domain type of this integral.

Return the integrand expression, which is an Expr instance.

Return the compiler metadata this integral has been annotated with.

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})



Return the domain data of this integral.

Return the subdomain id of this integral.

Return the integration domain of this integral.


Bases: object
Return unique deterministic identifier.

NOTE:

This identifier is used to provide unique names to tables and symbols in generated code.





Compute intermediate representation.

Create an FFCx element from a UFL element.
element – A UFL finite element
A FFCx finite element


Create quadrature rule and return points and weights.

Bases: tuple

Create new instance of ir_custom_element(cell_type, value_shape, wcoeffs, x, M, map_type, discontinuous, highest_complete_degree, highest_degree)

Alias for field number 4

Alias for field number 0

Alias for field number 6

Alias for field number 7

Alias for field number 8

Alias for field number 5

Alias for field number 1

Alias for field number 2

Alias for field number 3


Bases: tuple

Create new instance of ir_data(elements, dofmaps, integrals, forms, expressions)

Alias for field number 1

Alias for field number 0

Alias for field number 4

Alias for field number 3

Alias for field number 2


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)

Alias for field number 11

Alias for field number 0

Alias for field number 1

Alias for field number 4

Alias for field number 7

Alias for field number 5

Alias for field number 3

Alias for field number 9

Alias for field number 2

Alias for field number 10

Alias for field number 8

Alias for field number 6


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)

Alias for field number 19

Alias for field number 18

Alias for field number 12

Alias for field number 3

Alias for field number 21

Alias for field number 9

Alias for field number 20

Alias for field number 17

Alias for field number 14

Alias for field number 15

Alias for field number 10

Alias for field number 5

Alias for field number 0

Alias for field number 16

Alias for field number 1

Alias for field number 11

Alias for field number 8

Alias for field number 2

Alias for field number 6

Alias for field number 13

Alias for field number 4

Alias for field number 7


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)

Alias for field number 16

Alias for field number 7

Alias for field number 8

Alias for field number 17

Alias for field number 1

Alias for field number 10

Alias for field number 12

Alias for field number 19

Alias for field number 9

Alias for field number 5

Alias for field number 0

Alias for field number 20

Alias for field number 18

Alias for field number 14

Alias for field number 13

Alias for field number 2

Alias for field number 15

Alias for field number 6

Alias for field number 11

Alias for field number 4

Alias for field number 3


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)

Alias for field number 9

Alias for field number 10

Alias for field number 12

Alias for field number 11

Alias for field number 7

Alias for field number 0

Alias for field number 13

Alias for field number 1

Alias for field number 6

Alias for field number 4

Alias for field number 5

Alias for field number 8

Alias for field number 3

Alias for field number 2

Alias for field number 14


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)

Alias for field number 16

Alias for field number 12

Alias for field number 13

Alias for field number 24

Alias for field number 9

Alias for field number 10

Alias for field number 8

Alias for field number 5

Alias for field number 3

Alias for field number 0

Alias for field number 20

Alias for field number 21

Alias for field number 23

Alias for field number 6

Alias for field number 7

Alias for field number 14

Alias for field number 15

Alias for field number 22

Alias for field number 2

Alias for field number 1

Alias for field number 19

Alias for field number 11

Alias for field number 4

Alias for field number 18

Alias for field number 17


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.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, tdim) Given integral_type and domain 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)
Bases: object
Return unique deterministic identifier.

NOTE:

This identifier is used to provide unique names to tables and symbols in generated code.




Create a quadrature rule.

Create quadrature rule and return points and weights.

Given integral_type and domain tdim, return the tdim of the integration entity.

Map points from a reference facet to a physical facet.

Map points from reference entity to its parent reference cell.

Get the vertices of a reference cell.

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AUTHOR

FEniCS Project

COPYRIGHT

2022, FEniCS Project

June 16, 2022 0.4.2