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, degree, ...)	Create new instance of ir_custom_element(cell_type, degree, value_shape, wcoeffs, x, M, map_type, discontinuous, highest_complete_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)

class ffcx.ir.representation.Integral(integrand, integral_type, domain, subdomain_id, metadata, subdomain_data)[source]

Bases: object

An integral over a single domain.

integral_type()[source]: Return the domain type of this integral.

integrand()[source]: Return the integrand expression, which is an Expr instance.

metadata()[source]: 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)[source]: 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()[source]: Return the domain data of this integral.

subdomain_id()[source]: Return the subdomain id of this integral.

ufl_domain()[source]: Return the integration domain of this integral.

class ffcx.ir.representation.QuadratureRule(points, weights)[source]

Bases: object

id()[source]: 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)[source]

ffcx.ir.representation.compute_ir(analysis, object_names, prefix, parameters, visualise)[source]: Compute intermediate representation.

ffcx.ir.representation.create_element(element: ufl.finiteelement.finiteelementbase.FiniteElementBase) → ffcx.element_interface.BaseElement[source]

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)[source]: Create quadrature rule and return points and weights.

class ffcx.ir.representation.ir_custom_element(cell_type, degree, value_shape, wcoeffs, x, M, map_type, discontinuous, highest_complete_degree)

Bases: tuple

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

M: Alias for field number 5

cell_type: Alias for field number 0

degree: Alias for field number 1

discontinuous: Alias for field number 7

highest_complete_degree: Alias for field number 8

map_type: Alias for field number 6

value_shape: Alias for field number 2

wcoeffs: Alias for field number 3

x: Alias for field number 4

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)[source]

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)[source]