def _generate_physical_offsets(ufl_element, offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
cell = ufl_element.cell()
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
# Refer to reference if gdim == tdim. This is a hack to support
# more stuff (in particular restricted elements)
if gdim == tdim:
return _generate_reference_offsets(create_element(ufl_element))
if isinstance(ufl_element, ufl.MixedElement):
offsets = []
for e in ufl_element.sub_elements():
offsets += _generate_physical_offsets(e, offset)
# e is a ufl element, so value_size means the physical value size
offset += e.value_size()
return offsets
elif isinstance(ufl_element, ufl.EnrichedElement):
offsets = []
for e in ufl_element._elements: # TODO: Avoid private member access
offsets += _generate_physical_offsets(e, offset)
return offsets
elif isinstance(ufl_element, ufl.FiniteElement):
fiat_element = create_element(ufl_element)
return [offset] * fiat_element.space_dimension()
else:
raise NotImplementedError("This element combination is not implemented")
def compute_shapes(form: ufl.Form):
"""Computes the shapes of the cell tensor, coefficient & coordinate arrays for a form"""
# Cell tensor
elements = tuple(arg.ufl_element() for arg in form.arguments())
fiat_elements = (create_element(element) for element in elements)
element_dims = tuple(fe.space_dimension() for fe in fiat_elements)
A_shape = element_dims
# Coefficient arrays
ws_shapes = []
for coefficient in form.coefficients():
w_element = coefficient.ufl_element()
w_dim = create_element(w_element).space_dimension()
ws_shapes.append((w_dim,))
if len(ws_shapes) > 0:
max_w_dim = sorted(ws_shapes, key=lambda w_dim: np.prod(w_dim))[-1]
w_full_shape = (len(ws_shapes), ) + max_w_dim
else:
w_full_shape = (0,)
# Coordinate dofs array
num_vertices_per_cell = form.ufl_cell().num_vertices()
gdim = form.ufl_cell().geometric_dimension()
coords_shape = (num_vertices_per_cell, gdim)
return A_shape, w_full_shape, coords_shape
def _generate_physical_offsets(ufl_element, offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
offsets = []
# Refer to reference if gdim == tdim. This is a hack to support
# more stuff (in particular restricted elements)
gdim = ufl_element.cell().geometric_dimension()
tdim = ufl_element.cell().topological_dimension()
if (gdim == tdim):
return _generate_reference_offsets(create_element(ufl_element))
if isinstance(ufl_element, ufl.MixedElement):
for e in ufl_element.sub_elements():
offsets += _generate_physical_offsets(e, offset)
offset += _value_size(e)
elif isinstance(ufl_element, ufl.EnrichedElement):
for e in ufl_element._elements:
offsets += _generate_physical_offsets(e, offset)
elif isinstance(ufl_element, ufl.FiniteElement):
element = create_element(ufl_element)
offsets = [offset] * element.space_dimension()
else:
raise NotImplementedError, \
"This element combination is not implemented"
return offsets
def _generate_physical_offsets(ufl_element, offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
cell = ufl_element.cell()
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
# Refer to reference if gdim == tdim. This is a hack to support more
# stuff (in particular restricted elements)
if gdim == tdim:
return _generate_reference_offsets(create_element(ufl_element))
if isinstance(ufl_element, ufl.MixedElement):
offsets = []
for e in ufl_element.sub_elements():
offsets += _generate_physical_offsets(e, offset)
# e is a ufl element, so value_size means the physical value size
offset += e.value_size()
return offsets
elif isinstance(ufl_element, ufl.EnrichedElement):
offsets = []
for e in ufl_element._elements: # TODO: Avoid private member access
offsets += _generate_physical_offsets(e, offset)
return offsets
elif isinstance(ufl_element, ufl.FiniteElement):
fiat_element = create_element(ufl_element)
return [offset] * fiat_element.space_dimension()
else:
raise NotImplementedError(
"This element combination is not implemented")
def _generate_physical_offsets(ufl_element, offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
offsets = []
# Refer to reference if gdim == tdim. This is a hack to support
# more stuff (in particular restricted elements)
gdim = ufl_element.cell().geometric_dimension()
tdim = ufl_element.cell().topological_dimension()
if (gdim == tdim):
return _generate_reference_offsets(create_element(ufl_element))
if isinstance(ufl_element, ufl.MixedElement):
for e in ufl_element.sub_elements():
offsets += _generate_physical_offsets(e, offset)
offset += _value_size(e)
elif isinstance(ufl_element, ufl.EnrichedElement):
for e in ufl_element._elements:
offsets += _generate_physical_offsets(e, offset)
elif isinstance(ufl_element, ufl.FiniteElement):
element = create_element(ufl_element)
offsets = [offset]*element.space_dimension()
else:
raise NotImplementedError, \
"This element combination is not implemented"
return offsets
def compute_integral_ir(itg_data, form_data, form_id, element_numbers,
parameters):
"Compute intermediate represention of integral."
info("Computing uflacs representation")
# Initialise representation
ir = initialize_integral_ir("uflacs", itg_data, form_data, form_id)
# Sort integrals into a dict with quadrature degree and rule as key
sorted_integrals = sort_integrals(itg_data.integrals,
itg_data.metadata["quadrature_degree"],
itg_data.metadata["quadrature_rule"])
# TODO: Might want to create the uflacs ir first and then create the tables we need afterwards!
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quadrature_rules = \
tabulate_basis(sorted_integrals, form_data, itg_data)
# Store element numbers, needed for classnames
ir["element_numbers"] = element_numbers
# Delegate to flacs to build its intermediate representation and add to ir
uflacs_ir = compute_uflacs_integral_ir(psi_tables, ir["entitytype"],
integrals_dict, form_data,
parameters)
# Store uflacs generated part separately
ir["uflacs"] = uflacs_ir
# Create and save the optisation parameters # TODO: Define uflacs specific optimization parameters instead
#ir["optimise_parameters"] = parse_optimise_parameters(parameters)
# Save tables for quadrature weights and points
ir["quadrature_rules"] = quadrature_rules
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [
create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements
]
# Added for uflacs, not sure if this is the best way to get this:
ir["coeff_idims"] = [
create_element(ufl_element).space_dimension()
for ufl_element in form_data.coefficient_elements
]
return ir
def _compute_dofmap_ir(ufl_element, element_id, element_numbers):
"Compute intermediate representation of dofmap."
# Create FIAT element
element = create_element(ufl_element)
cell = ufl_element.cell()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(element)
facet_dofs = _tabulate_facet_dofs(element, cell)
# Store id
ir = {"id": element_id}
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["needs_mesh_entities"] = _needs_mesh_entities(element)
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["global_dimension"] = _global_dimension(element)
ir["local_dimension"] = element.space_dimension()
ir["num_facet_dofs"] = len(facet_dofs[0])
ir["num_entity_dofs"] = num_dofs_per_entity
ir["tabulate_dofs"] = _tabulate_dofs(element, cell)
ir["tabulate_facet_dofs"] = facet_dofs
ir["tabulate_entity_dofs"] = (element.entity_dofs(), num_dofs_per_entity)
ir["tabulate_coordinates"] = _tabulate_coordinates(ufl_element, element)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = _create_sub_foo(ufl_element, element_numbers)
#debug_ir(ir, "dofmap")
return ir
def _compute_element_ir(ufl_element, element_id, element_numbers):
"Compute intermediate representation of element."
# Create FIAT element
element = create_element(ufl_element)
cell = ufl_element.cell()
# Store id
ir = {"id": element_id}
# Compute data for each function
ir["signature"] = repr(ufl_element)
ir["cell_shape"] = cell.cellname()
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["space_dimension"] = element.space_dimension()
ir["value_rank"] = len(ufl_element.value_shape())
ir["value_dimension"] = ufl_element.value_shape()
ir["evaluate_basis"] = _evaluate_basis(ufl_element, element, cell)
ir["evaluate_dof"] = _evaluate_dof(ufl_element, element, cell)
ir["interpolate_vertex_values"] = _interpolate_vertex_values(ufl_element, element, cell)
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = _create_sub_foo(ufl_element, element_numbers)
#debug_ir(ir, "finite_element")
return ir
def _generate_offsets(ufl_element, reference_offset=0, physical_offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
if isinstance(ufl_element, ufl.MixedElement):
offsets = []
for e in ufl_element.sub_elements():
offsets += _generate_offsets(e, reference_offset, physical_offset)
# e is a ufl element, so value_size means the physical value size
reference_offset += e.reference_value_size()
physical_offset += e.value_size()
return offsets
elif isinstance(ufl_element, ufl.EnrichedElement):
offsets = []
for e in ufl_element._elements: # TODO: Avoid private member access
offsets += _generate_offsets(e, reference_offset, physical_offset)
return offsets
elif isinstance(ufl_element, ufl.FiniteElement):
fiat_element = create_element(ufl_element)
return [(reference_offset, physical_offset)
] * fiat_element.space_dimension()
else:
# TODO: Support RestrictedElement, QuadratureElement,
# TensorProductElement, etc.! and replace
# _generate_{physical|reference}_offsets with this
# function.
raise NotImplementedError(
"This element combination is not implemented")
def _generate_offsets(ufl_element, reference_offset=0, physical_offset=0):
"""Generate offsets: i.e value offset for each basis function
relative to a physical element representation."""
if isinstance(ufl_element, ufl.MixedElement):
offsets = []
for e in ufl_element.sub_elements():
offsets += _generate_offsets(e, reference_offset, physical_offset)
# e is a ufl element, so value_size means the physical value size
reference_offset += e.reference_value_size()
physical_offset += e.value_size()
return offsets
elif isinstance(ufl_element, ufl.EnrichedElement):
offsets = []
for e in ufl_element._elements: # TODO: Avoid private member access
offsets += _generate_offsets(e, reference_offset, physical_offset)
return offsets
elif isinstance(ufl_element, ufl.FiniteElement):
fiat_element = create_element(ufl_element)
return [(reference_offset, physical_offset)] * fiat_element.space_dimension()
else:
# TODO: Support RestrictedElement, QuadratureElement,
# TensorProductElement, etc.! and replace
# _generate_{physical|reference}_offsets with this
# function.
raise NotImplementedError("This element combination is not implemented")
def cell_vertices(self, e, mt, tabledata, num_points):
L = self.language
# Get properties of domain
domain = mt.terminal.ufl_domain()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim,)
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get dof and component
dof, = vertex_scalar_dofs[mt.component[0]]
component = mt.component[1]
expr = self.symbols.domain_dof_access(dof, component,
gdim, num_scalar_dofs,
mt.restriction)
return expr
def _extract_element_data(element_map, element_numbers):
"Extract element data for psi_tables"
# Iterate over map
element_data = {}
for elements in six.itervalues(element_map):
for ufl_element, counter in six.iteritems(elements):
# Create corresponding FIAT element
fiat_element = create_element(ufl_element)
# Compute value size
value_size = product(ufl_element.value_shape())
# Get element number
element_number = element_numbers.get(ufl_element)
if element_number is None:
# FIXME: Should not be necessary, we should always know the element number
#warning("Missing element number, likely because vector elements are not yet supported in custom integrals.")
pass
# Store data
element_data[counter] = {
"value_size": value_size,
"num_element_dofs": fiat_element.space_dimension(),
"element_number": element_number
}
return element_data
def _init_table(arguments, domain_type, points, facet0, facet1):
"""Initialize table of basis functions and their derivatives at
the given quadrature points for each element."""
# Compute maximum number of derivatives for each element
num_derivatives = {}
for v in arguments:
ufl_element = v.element
order = len(v.derivatives)
if ufl_element in num_derivatives:
num_derivatives[ufl_element] = max(order, num_derivatives[ufl_element])
else:
num_derivatives[ufl_element] = order
# Call FIAT to tabulate the basis functions for each element
table = {}
for (ufl_element, order) in num_derivatives.items():
fiat_element = create_element(ufl_element)
if domain_type == Measure.CELL:
table[(ufl_element, None)] = fiat_element.tabulate(order, points)
elif domain_type == Measure.EXTERIOR_FACET:
x = map_facet_points(points, facet0)
table[(ufl_element, None)] = fiat_element.tabulate(order, x)
elif domain_type == Measure.INTERIOR_FACET:
x0 = map_facet_points(points, facet0)
x1 = map_facet_points(points, facet1)
table[(ufl_element, "+")] = fiat_element.tabulate(order, x0)
table[(ufl_element, "-")] = fiat_element.tabulate(order, x1)
return table
def _init_table(arguments, integral_type, points, facet0, facet1):
"""Initialize table of basis functions and their derivatives at
the given quadrature points for each element."""
# Compute maximum number of derivatives for each element
num_derivatives = {}
for v in arguments:
ufl_element = v.element
order = len(v.derivatives)
if ufl_element in num_derivatives:
num_derivatives[ufl_element] = max(order,
num_derivatives[ufl_element])
else:
num_derivatives[ufl_element] = order
# Call FIAT to tabulate the basis functions for each element
table = {}
for (ufl_element, order) in num_derivatives.items():
fiat_element = create_element(ufl_element)
if integral_type == Measure.CELL:
table[(ufl_element, None)] = fiat_element.tabulate(order, points)
elif integral_type == Measure.EXTERIOR_FACET:
x = map_facet_points(points, facet0)
table[(ufl_element, None)] = fiat_element.tabulate(order, x)
elif integral_type == Measure.INTERIOR_FACET:
x0 = map_facet_points(points, facet0)
x1 = map_facet_points(points, facet1)
table[(ufl_element, "+")] = fiat_element.tabulate(order, x0)
table[(ufl_element, "-")] = fiat_element.tabulate(order, x1)
return table
def transform_component(component, offset, ufl_element):
"""
This function accounts for the fact that if the geometrical and
topological dimension does not match, then for native vector
elements, in particular the Piola-mapped ones, the physical value
dimensions and the reference value dimensions are not the
same. This has certain consequences for mixed elements, aka 'fun
with offsets'.
"""
# This code is used for tensor/monomialtransformation.py and
# quadrature/quadraturetransformerbase.py.
cell = ufl_element.cell()
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
# Do nothing if we are not in a special case: The special cases
# occur if we have piola mapped elements (for which value_shape !=
# ()), and if gdim != tdim)
if gdim == tdim:
return component, offset
all_mappings = create_element(ufl_element).mapping()
special_case = (any(['piola' in m for m in all_mappings])
and ufl_element.num_sub_elements() > 1)
if not special_case:
return component, offset
# Extract lists of reference and physical value dimensions by
# sub-element
reference_value_dims = []
physical_value_dims = []
for sub_element in ufl_element.sub_elements():
assert (len(sub_element.value_shape()) < 2), \
"Vector-valued assumption failed"
if sub_element.value_shape() == ():
reference_value_dims += [1]
physical_value_dims += [1]
else:
reference_value_dims += [sub_element.value_shape()[0]
- (gdim - tdim)]
physical_value_dims += [sub_element.value_shape()[0]]
# Figure out which sub-element number 'component' is in,
# 'sub_element_number' contains the result
tot = physical_value_dims[0]
for sub_element_number in range(len(physical_value_dims)):
if component < tot:
break
else:
tot += physical_value_dims[sub_element_number + 1]
# Compute the new reference offset:
reference_offset = sum(reference_value_dims[:sub_element_number])
physical_offset = sum(physical_value_dims[:sub_element_number])
shift = physical_offset - reference_offset
# Compute the component relative to the reference frame
reference_component = component - shift
return reference_component, reference_offset
def transform_component(component, offset, ufl_element):
"""
This function accounts for the fact that if the geometrical and
topological dimension does not match, then for native vector
elements, in particular the Piola-mapped ones, the physical value
dimensions and the reference value dimensions are not the
same. This has certain consequences for mixed elements, aka 'fun
with offsets'.
"""
# This code is used for tensor/monomialtransformation.py and
# quadrature/quadraturetransformerbase.py.
domain, = ufl_element.domains() # Assuming single domain
gdim = domain.geometric_dimension()
tdim = domain.topological_dimension()
# Do nothing if we are not in a special case: The special cases
# occur if we have piola mapped elements (for which value_shape !=
# ()), and if gdim != tdim)
if gdim == tdim:
return component, offset
all_mappings = create_element(ufl_element).mapping()
special_case = (any(['piola' in m for m in all_mappings])
and ufl_element.num_sub_elements() > 1)
if not special_case:
return component, offset
# Extract lists of reference and physical value dimensions by
# sub-element
reference_value_dims = []
physical_value_dims = []
for sub_element in ufl_element.sub_elements():
assert (len(sub_element.value_shape()) < 2), \
"Vector-valued assumption failed"
if sub_element.value_shape() == ():
reference_value_dims += [1]
physical_value_dims += [1]
else:
reference_value_dims += [sub_element.value_shape()[0]
- (gdim - tdim)]
physical_value_dims += [sub_element.value_shape()[0]]
# Figure out which sub-element number 'component' is in,
# 'sub_element_number' contains the result
tot = physical_value_dims[0]
for sub_element_number in range(len(physical_value_dims)):
if component < tot:
break
else:
tot += physical_value_dims[sub_element_number+1]
# Compute the new reference offset:
reference_offset = sum(reference_value_dims[:sub_element_number])
physical_offset = sum(physical_value_dims[:sub_element_number])
shift = physical_offset - reference_offset
# Compute the component relative to the reference frame
reference_component = component - shift
return reference_component, reference_offset
def _compute_element_ir(ufl_element, element_id, element_numbers):
"Compute intermediate representation of element."
# Create FIAT element
element = create_element(ufl_element)
cell = ufl_element.cell()
# Store id
ir = {"id": element_id}
# Compute data for each function
ir["signature"] = repr(ufl_element)
ir["cell_shape"] = cell.cellname()
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["space_dimension"] = element.space_dimension()
ir["value_rank"] = len(ufl_element.value_shape())
ir["value_dimension"] = ufl_element.value_shape()
ir["evaluate_basis"] = _evaluate_basis(ufl_element, element, cell)
ir["evaluate_dof"] = _evaluate_dof(ufl_element, element, cell)
ir["interpolate_vertex_values"] = _interpolate_vertex_values(
ufl_element, element, cell)
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = _create_sub_foo(ufl_element, element_numbers)
#debug_ir(ir, "finite_element")
return ir
def _compute_dofmap_ir(ufl_element, element_id, element_numbers):
"Compute intermediate representation of dofmap."
# Create FIAT element
element = create_element(ufl_element)
cell = ufl_element.cell()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(element)
facet_dofs = _tabulate_facet_dofs(element, cell)
# Store id
ir = {"id": element_id}
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["needs_mesh_entities"] = _needs_mesh_entities(element)
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["global_dimension"] = _global_dimension(element)
ir["local_dimension"] = element.space_dimension()
ir["num_facet_dofs"] = len(facet_dofs[0])
ir["num_entity_dofs"] = num_dofs_per_entity
ir["tabulate_dofs"] = _tabulate_dofs(element, cell)
ir["tabulate_facet_dofs"] = facet_dofs
ir["tabulate_entity_dofs"] = (element.entity_dofs(), num_dofs_per_entity)
ir["tabulate_coordinates"] = _tabulate_coordinates(ufl_element, element)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = _create_sub_foo(ufl_element, element_numbers)
#debug_ir(ir, "dofmap")
return ir
def _extract_element_data(element_map, element_numbers):
"Extract element data for psi_tables"
# Iterate over map
element_data = {}
for elements in six.itervalues(element_map):
for ufl_element, counter in six.iteritems(elements):
# Create corresponding FIAT element
fiat_element = create_element(ufl_element)
# Compute value size
value_size = product(ufl_element.value_shape())
# Get element number
element_number = element_numbers.get(ufl_element)
if element_number is None:
# FIXME: Should not be necessary, we should always know the element number
#warning("Missing element number, likely because vector elements are not yet supported in custom integrals.")
pass
# Store data
element_data[counter] = {"value_size": value_size,
"num_element_dofs": fiat_element.space_dimension(),
"element_number": element_number}
return element_data
def _compute_element_ir(ufl_element, element_numbers, classnames, parameters):
"""Compute intermediate representation of element."""
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
cellname = cell.cellname()
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = classnames["finite_element"][ufl_element]
# Compute data for each function
ir["signature"] = repr(ufl_element)
ir["cell_shape"] = cellname
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["space_dimension"] = fiat_element.space_dimension()
ir["value_shape"] = ufl_element.value_shape()
ir["reference_value_shape"] = ufl_element.reference_value_shape()
ir["degree"] = ufl_element.degree()
ir["family"] = ufl_element.family()
ir["evaluate_basis"] = _evaluate_basis(ufl_element, fiat_element,
parameters["epsilon"])
ir["evaluate_dof"] = _evaluate_dof(ufl_element, fiat_element)
ir["tabulate_dof_coordinates"] = _tabulate_dof_coordinates(
ufl_element, fiat_element)
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = [
classnames["finite_element"][e] for e in ufl_element.sub_elements()
]
return ir_element(**ir)
def _compute_dofmap_ir(ufl_element, element_numbers, classnames, parameters):
"""Compute intermediate representation of dofmap."""
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(fiat_element)
entity_dofs = fiat_element.entity_dofs()
edge_permutations, face_permutations, cell_topology = _compute_dofmap_permutation_tables(
fiat_element, cell)
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = classnames["dofmap"][ufl_element]
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["num_global_support_dofs"] = _num_global_support_dofs(fiat_element)
ir["num_element_support_dofs"] = fiat_element.space_dimension(
) - ir["num_global_support_dofs"]
ir["num_entity_dofs"] = num_dofs_per_entity
ir["tabulate_entity_dofs"] = (entity_dofs, num_dofs_per_entity)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = [
classnames["dofmap"][e] for e in ufl_element.sub_elements()
]
return ir_dofmap(**ir)
def compute_integral_ir(itg_data,
form_data,
form_id,
element_numbers,
parameters):
"Compute intermediate represention of integral."
info("Computing uflacs representation")
# Initialise representation
ir = initialize_integral_ir("uflacs", itg_data, form_data, form_id)
# Sort integrals into a dict with quadrature degree and rule as key
sorted_integrals = sort_integrals(itg_data.integrals,
itg_data.metadata["quadrature_degree"],
itg_data.metadata["quadrature_rule"])
# TODO: Might want to create the uflacs ir first and then create the tables we need afterwards!
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quadrature_rules = \
tabulate_basis(sorted_integrals, form_data, itg_data)
# Store element numbers, needed for classnames
ir["element_numbers"] = element_numbers
# Delegate to flacs to build its intermediate representation and add to ir
uflacs_ir = compute_uflacs_integral_ir(psi_tables, ir["entitytype"], integrals_dict, form_data, parameters)
# Store uflacs generated part separately
ir["uflacs"] = uflacs_ir
# Create and save the optisation parameters # TODO: Define uflacs specific optimization parameters instead
#ir["optimise_parameters"] = parse_optimise_parameters(parameters)
# Save tables for quadrature weights and points
ir["quadrature_rules"] = quadrature_rules
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements]
# Added for uflacs, not sure if this is the best way to get this:
ir["coeff_idims"] = [create_element(ufl_element).space_dimension()
for ufl_element in form_data.coefficient_elements]
return ir
def needs_oriented_jacobian(form_data):
# Check whether this form needs an oriented jacobian (only forms
# involgin contravariant piola mappings seem to need it)
for ufl_element in form_data.unique_elements:
element = create_element(ufl_element)
if "contravariant piola" in element.mapping():
return True
return False
def needs_oriented_jacobian(form_data):
# Check whether this form needs an oriented jacobian (only forms
# involgin contravariant piola mappings seem to need it)
for ufl_element in form_data.unique_elements:
element = create_element(ufl_element)
if "contravariant piola" in element.mapping():
return True
return False
def compute_integral_ir(itg_data,
form_data,
form_id,
parameters):
"Compute intermediate represention of integral."
info("Computing quadrature representation")
# Initialise representation
ir = initialize_integral_ir("quadrature", itg_data, form_data, form_id)
# Sort integrals into a dict with number of integral points as key
sorted_integrals = _sort_integrals(itg_data.integrals, itg_data.metadata, form_data)
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quad_weights = \
_tabulate_basis(sorted_integrals, itg_data.domain_type, form_data)
# Save tables for quadrature weights and points
ir["quadrature_weights"] = quad_weights
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements]
# Create and save the optisation parameters.
ir["optimise_parameters"] = _parse_optimise_parameters(parameters)
# Create transformer.
if ir["optimise_parameters"]["optimisation"]:
QuadratureTransformerClass = QuadratureTransformerOpt
else:
QuadratureTransformerClass = QuadratureTransformer
transformer = QuadratureTransformerClass(psi_tables,
quad_weights,
form_data.geometric_dimension,
form_data.topological_dimension,
ir["entitytype"],
form_data.function_replace_map,
ir["optimise_parameters"])
# Transform integrals.
ir["trans_integrals"] = _transform_integrals_by_type(ir, transformer, integrals_dict,
itg_data.domain_type, form_data.cell)
# Save tables populated by transformer
ir["name_map"] = transformer.name_map
ir["unique_tables"] = transformer.unique_tables # Basis values?
# Save tables map, to extract table names for optimisation option -O.
ir["psi_tables_map"] = transformer.psi_tables_map
ir["additional_includes_set"] = transformer.additional_includes_set
# Insert empty data which will be populated if optimization is turned on
ir["geo_consts"] = {}
return ir
def compute_integral_ir(itg_data, form_data, form_id, parameters):
"Compute intermediate represention of integral."
info("Computing uflacs representation")
# Initialise representation
ir = initialize_integral_ir("uflacs", itg_data, form_data, form_id)
# Sort integrals into a dict with number of integral points as key
sorted_integrals = _sort_integrals(itg_data.integrals, itg_data.metadata,
form_data)
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quad_weights = \
_tabulate_basis(sorted_integrals, itg_data.domain_type, form_data)
# Save tables for quadrature weights and points
ir["quadrature_weights"] = quad_weights
# Save tables for basis function values
ir["psi_tables"] = psi_tables
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [
create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements
]
# Added for uflacs, not sure if this is the best way to get this:
ir["coeff_idims"] = [
create_element(ufl_element).space_dimension()
for ufl_element in form_data.coefficient_elements
]
# Create and save the optisation parameters.
ir["optimise_parameters"] = _parse_optimise_parameters(parameters)
# Delegate to flacs to build its intermediate representation and add to ir
import uflacs.backends.ffc
uir = uflacs.backends.ffc.compute_tabulate_tensor_ir(
ir, integrals_dict, form_data, parameters)
ir.update(uir)
return ir
def compute_integral_ir(itg_data, form_data, form_id, parameters):
"Compute intermediate represention of integral."
info("Computing quadrature representation")
# Initialise representation
ir = initialize_integral_ir("quadrature", itg_data, form_data, form_id)
# Sort integrals into a dict with number of integral points as key
sorted_integrals = _sort_integrals(itg_data.integrals, itg_data.metadata,
form_data)
# Tabulate quadrature points and basis function values in these points
integrals_dict, psi_tables, quad_weights = \
_tabulate_basis(sorted_integrals, itg_data.domain_type, form_data)
# Save tables for quadrature weights and points
ir["quadrature_weights"] = quad_weights
# Create dimensions of primary indices, needed to reset the argument 'A'
# given to tabulate_tensor() by the assembler.
ir["prim_idims"] = [
create_element(ufl_element).space_dimension()
for ufl_element in form_data.argument_elements
]
# Create and save the optisation parameters.
ir["optimise_parameters"] = _parse_optimise_parameters(parameters)
# Create transformer.
if ir["optimise_parameters"]["optimisation"]:
QuadratureTransformerClass = QuadratureTransformerOpt
else:
QuadratureTransformerClass = QuadratureTransformer
transformer = QuadratureTransformerClass(psi_tables, quad_weights,
form_data.geometric_dimension,
form_data.topological_dimension,
ir["entitytype"],
form_data.function_replace_map,
ir["optimise_parameters"])
# Transform integrals.
ir["trans_integrals"] = _transform_integrals_by_type(
ir, transformer, integrals_dict, itg_data.domain_type, form_data.cell)
# Save tables populated by transformer
ir["name_map"] = transformer.name_map
ir["unique_tables"] = transformer.unique_tables # Basis values?
# Save tables map, to extract table names for optimisation option -O.
ir["psi_tables_map"] = transformer.psi_tables_map
ir["additional_includes_set"] = transformer.additional_includes_set
# Insert empty data which will be populated if optimization is turned on
ir["geo_consts"] = {}
return ir
def _get_auxiliary_variables(self,
ufl_function,
component,
derivatives):
"Helper function for both Coefficient and Argument."
# Get UFL element.
ufl_element = ufl_function.element()
# Get subelement and the relative (flattened) component (in case we have mixed elements).
local_comp, local_elem = ufl_element.extract_component(component)
ffc_assert(len(local_comp) <= 1, "Assuming there are no tensor-valued basic elements.")
local_comp = local_comp[0] if local_comp else 0
# Check that component != not () since the UFL component map will turn
# it into 0, and () does not mean zeroth component in this context.
if len(component):
# Map component using component map from UFL. (TODO: inefficient use of this function)
comp_map, comp_num = build_component_numbering(ufl_element.value_shape(), ufl_element.symmetry())
component = comp_map[component]
# Map physical components into reference components
component, dummy = transform_component(component, 0, ufl_element)
# Compute the local offset (needed for non-affine mappings).
local_offset = component - local_comp
else:
# Compute the local offset (needed for non-affine mappings).
local_offset = 0
# Create FFC element.
ffc_element = create_element(ufl_element)
# Assuming that mappings for all basisfunctions are equal
# (they should be).
ffc_sub_element = create_element(local_elem)
transformation = ffc_sub_element.mapping()[0]
# Generate FFC multi index for derivatives.
multiindices = FFCMultiIndex([range(self.tdim)]*len(derivatives)).indices
#print "in create_auxiliary"
#print "component = ", component
return (component, local_elem, local_comp, local_offset, ffc_element, transformation, multiindices)
def num_coordinate_component_dofs(coordinate_element):
"""Get the number of dofs for a coordinate component for this degree.
"""
fiat_elements = create_element(coordinate_element).elements()
# Extracting only first component degrees of freedom from FIAT
fiat_element = fiat_elements[0]
assert (all(
isinstance(element, type(fiat_element)) for element in fiat_elements))
return fiat_element.space_dimension()
def numBasisFunctions(e):
"""Return the number of basis functions. e can be a form or an element -
if e is a form, the element from the test function is used."""
if isinstance(e, FormData):
# Use the element from the first argument, which should be the TestFunction
e = e.arguments[0].element()
element = create_element(e)
if isinstance(element, FFCMixedElement):
return len(element.entity_dofs()) * element.num_components()
else:
return element.get_nodal_basis().get_num_members()
def _compute_dofmap_ir(ufl_element,
element_numbers,
classnames,
parameters,
jit=False):
"Compute intermediate representation of dofmap."
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(fiat_element)
entity_dofs = fiat_element.entity_dofs()
facet_dofs = _tabulate_facet_dofs(fiat_element, cell)
entity_closure_dofs, num_dofs_per_entity_closure = \
_tabulate_entity_closure_dofs(fiat_element, cell)
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = classnames["dofmap"][ufl_element]
# Remember jit status
ir["jit"] = jit
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["needs_mesh_entities"] = _needs_mesh_entities(fiat_element)
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["global_dimension"] = _global_dimension(fiat_element)
ir["num_global_support_dofs"] = _num_global_support_dofs(fiat_element)
ir["num_element_support_dofs"] = fiat_element.space_dimension(
) - ir["num_global_support_dofs"]
ir["num_element_dofs"] = fiat_element.space_dimension()
ir["num_facet_dofs"] = len(facet_dofs[0])
ir["num_entity_dofs"] = num_dofs_per_entity
ir["num_entity_closure_dofs"] = num_dofs_per_entity_closure
ir["tabulate_dofs"] = _tabulate_dofs(fiat_element, cell)
ir["tabulate_facet_dofs"] = facet_dofs
ir["tabulate_entity_dofs"] = (entity_dofs, num_dofs_per_entity)
ir["tabulate_entity_closure_dofs"] = (entity_closure_dofs, entity_dofs,
num_dofs_per_entity)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = [
classnames["dofmap"][e] for e in ufl_element.sub_elements()
]
return ir
def test_values(self, family, cell, degree, reference):
# Create element
element = create_element(FiniteElement(family, cell, degree))
# Get some points and check basis function values at points
points = [random_point(element_coords(cell)) for i in range(5)]
for x in points:
table = element.tabulate(0, (x,))
basis = table[list(table.keys())[0]]
for i in range(len(basis)):
if not element.value_shape():
assert round(float(basis[i]) - reference[i](x), 10) == 0.0
else:
for k in range(element.value_shape()[0]):
assert round(basis[i][k][0] - reference[i](x)[k] , 10) == 0.0
def test_values(self, family, cell, degree, reference):
# Create element
element = create_element(FiniteElement(family, cell, degree))
# Get some points and check basis function values at points
points = [random_point(element_coords(cell)) for i in range(5)]
for x in points:
table = element.tabulate(0, (x, ))
basis = table[list(table.keys())[0]]
for i in range(len(basis)):
if not element.value_shape():
assert round(float(basis[i]) - reference[i](x), 10) == 0.0
else:
for k in range(element.value_shape()[0]):
assert round(basis[i][k][0] - reference[i](x)[k],
10) == 0.0
def facet_edge_vectors(self, e, mt, tabledata, num_points):
L = self.language
# Get properties of domain
domain = mt.terminal.ufl_domain()
cellname = domain.ufl_cell().cellname()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
if cellname in ("tetrahedron", "hexahedron"):
pass
elif cellname in ("interval", "triangle", "quadrilateral"):
error(
"The physical facet edge vectors doesn't make sense for {0} cell."
.format(cellname))
else:
error("Unhandled cell types {0}.".format(cellname))
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim, )
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get edge vertices
facet = self.symbols.entity("facet", mt.restriction)
facet_edge = mt.component[0]
facet_edge_vertices = L.Symbol(
"{0}_facet_edge_vertices".format(cellname))
vertex0 = facet_edge_vertices[facet][facet_edge][0]
vertex1 = facet_edge_vertices[facet][facet_edge][1]
# Get dofs and component
component = mt.component[1]
assert coordinate_element.degree() == 1, "Assuming degree 1 element"
dof0 = vertex0
dof1 = vertex1
expr = (self.symbols.domain_dof_access(
dof0, component, gdim, num_scalar_dofs, mt.restriction) -
self.symbols.domain_dof_access(
dof1, component, gdim, num_scalar_dofs, mt.restriction))
return expr
def facet_edge_vectors(self, e, mt, tabledata, num_points):
L = self.language
# Get properties of domain
domain = mt.terminal.ufl_domain()
cellname = domain.ufl_cell().cellname()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
if cellname in ("tetrahedron", "hexahedron"):
pass
elif cellname in ("interval", "triangle", "quadrilateral"):
error("The physical facet edge vectors doesn't make sense for {0} cell.".format(cellname))
else:
error("Unhandled cell types {0}.".format(cellname))
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim,)
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get edge vertices
facet = self.symbols.entity("facet", mt.restriction)
facet_edge = mt.component[0]
facet_edge_vertices = L.Symbol("{0}_facet_edge_vertices".format(cellname))
vertex0 = facet_edge_vertices[facet][facet_edge][0]
vertex1 = facet_edge_vertices[facet][facet_edge][1]
# Get dofs and component
component = mt.component[1]
assert coordinate_element.degree() == 1, "Assuming degree 1 element"
dof0 = vertex0
dof1 = vertex1
expr = (
self.symbols.domain_dof_access(dof0, component, gdim, num_scalar_dofs,
mt.restriction)
- self.symbols.domain_dof_access(dof1, component, gdim, num_scalar_dofs,
mt.restriction)
)
return expr
def cell_edge_vectors(self, e, mt, tabledata, num_points):
L = self.language
# Get properties of domain
domain = mt.terminal.ufl_domain()
cellname = domain.ufl_cell().cellname()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
if cellname in ("triangle", "tetrahedron", "quadrilateral",
"hexahedron"):
pass
elif cellname == "interval":
error(
"The physical cell edge vectors doesn't make sense for interval cell."
)
else:
error("Unhandled cell types {0}.".format(cellname))
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim, )
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get edge vertices
edge = mt.component[0]
edge_vertices = fiat_scalar_element.get_reference_element(
).get_topology()[1][edge]
vertex0, vertex1 = edge_vertices
# Get dofs and component
dof0, = vertex_scalar_dofs[vertex0]
dof1, = vertex_scalar_dofs[vertex1]
component = mt.component[1]
expr = (self.symbols.domain_dof_access(
dof0, component, gdim, num_scalar_dofs, mt.restriction) -
self.symbols.domain_dof_access(
dof1, component, gdim, num_scalar_dofs, mt.restriction))
return expr
def _compute_dofmap_ir(ufl_element, element_numbers, classnames, parameters, jit=False):
"Compute intermediate representation of dofmap."
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(fiat_element)
entity_dofs = fiat_element.entity_dofs()
facet_dofs = _tabulate_facet_dofs(fiat_element, cell)
entity_closure_dofs, num_dofs_per_entity_closure = \
_tabulate_entity_closure_dofs(fiat_element, cell)
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = classnames["dofmap"][ufl_element]
# Remember jit status
ir["jit"] = jit
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["needs_mesh_entities"] = _needs_mesh_entities(fiat_element)
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["global_dimension"] = _global_dimension(fiat_element)
ir["num_global_support_dofs"] = _num_global_support_dofs(fiat_element)
ir["num_element_support_dofs"] = fiat_element.space_dimension() - ir["num_global_support_dofs"]
ir["num_element_dofs"] = fiat_element.space_dimension()
ir["num_facet_dofs"] = len(facet_dofs[0])
ir["num_entity_dofs"] = num_dofs_per_entity
ir["num_entity_closure_dofs"] = num_dofs_per_entity_closure
ir["tabulate_dofs"] = _tabulate_dofs(fiat_element, cell)
ir["tabulate_facet_dofs"] = facet_dofs
ir["tabulate_entity_dofs"] = (entity_dofs, num_dofs_per_entity)
ir["tabulate_entity_closure_dofs"] = (entity_closure_dofs, entity_dofs, num_dofs_per_entity)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = [classnames["dofmap"][e]
for e in ufl_element.sub_elements()]
return ir
def cell_edge_vectors(self, e, mt, tabledata, num_points):
L = self.language
# Get properties of domain
domain = mt.terminal.ufl_domain()
cellname = domain.ufl_cell().cellname()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
if cellname in ("triangle", "tetrahedron", "quadrilateral", "hexahedron"):
pass
elif cellname == "interval":
error("The physical cell edge vectors doesn't make sense for interval cell.")
else:
error("Unhandled cell types {0}.".format(cellname))
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim,)
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get edge vertices
edge = mt.component[0]
edge_vertices = fiat_scalar_element.get_reference_element().get_topology()[1][edge]
vertex0, vertex1 = edge_vertices
# Get dofs and component
dof0, = vertex_scalar_dofs[vertex0]
dof1, = vertex_scalar_dofs[vertex1]
component = mt.component[1]
expr = (
self.symbols.domain_dof_access(dof0, component, gdim, num_scalar_dofs,
mt.restriction)
- self.symbols.domain_dof_access(dof1, component, gdim, num_scalar_dofs,
mt.restriction)
)
return expr
def cell_vertices(self, e, mt, tabledata, num_points):
# Get properties of domain
domain = mt.terminal.ufl_domain()
gdim = domain.geometric_dimension()
coordinate_element = domain.ufl_coordinate_element()
# Get dimension and dofmap of scalar element
assert isinstance(coordinate_element, MixedElement)
assert coordinate_element.value_shape() == (gdim, )
ufl_scalar_element, = set(coordinate_element.sub_elements())
assert ufl_scalar_element.family() in ("Lagrange", "Q", "S")
fiat_scalar_element = create_element(ufl_scalar_element)
vertex_scalar_dofs = fiat_scalar_element.entity_dofs()[0]
num_scalar_dofs = fiat_scalar_element.space_dimension()
# Get dof and component
dof, = vertex_scalar_dofs[mt.component[0]]
component = mt.component[1]
expr = self.symbols.domain_dof_access(dof, component, gdim, num_scalar_dofs, mt.restriction)
return expr
def _compute_element_ir(ufl_element, element_numbers, classnames, parameters, jit):
"Compute intermediate representation of element."
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
cellname = cell.cellname()
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = classnames["finite_element"][ufl_element]
# Remember jit status
ir["jit"] = jit
# Compute data for each function
ir["signature"] = repr(ufl_element)
ir["cell_shape"] = cellname
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["space_dimension"] = fiat_element.space_dimension()
ir["value_shape"] = ufl_element.value_shape()
ir["reference_value_shape"] = ufl_element.reference_value_shape()
ir["degree"] = ufl_element.degree()
ir["family"] = ufl_element.family()
ir["evaluate_basis"] = _evaluate_basis(ufl_element, fiat_element, parameters["epsilon"])
ir["evaluate_dof"] = _evaluate_dof(ufl_element, fiat_element)
ir["interpolate_vertex_values"] = _interpolate_vertex_values(ufl_element,
fiat_element)
ir["tabulate_dof_coordinates"] = _tabulate_dof_coordinates(ufl_element,
fiat_element)
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = [classnames["finite_element"][e]
for e in ufl_element.sub_elements()]
# debug_ir(ir, "finite_element")
return ir
def _compute_element_ir(ufl_element, prefix, element_numbers):
"Compute intermediate representation of element."
# This hits unimplemented FIAT functionality for OPEs; the IR
# is only required for function evaluation at a point, not integrals
if isinstance(ufl_element.cell(), ufl.OuterProductCell):
return None
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
cellname = cell.cellname()
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = make_classname(prefix, "finite_element", element_numbers[ufl_element])
# Compute data for each function
ir["cell"] = cell
ir["signature"] = repr(ufl_element)
ir["cell_shape"] = cellname
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["space_dimension"] = fiat_element.space_dimension()
ir["value_rank"] = len(ufl_element.value_shape())
ir["value_dimension"] = ufl_element.value_shape()
ir["reference_value_dimension"] = ufl_element.reference_value_shape()
ir["evaluate_basis"] = _evaluate_basis(ufl_element, fiat_element)
ir["evaluate_dof"] = _evaluate_dof(ufl_element, fiat_element)
ir["interpolate_vertex_values"] = _interpolate_vertex_values(ufl_element,
fiat_element)
ir["tabulate_dof_coordinates"] = _tabulate_dof_coordinates(ufl_element,
fiat_element)
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = [make_classname(prefix, "finite_element", element_numbers[e])
for e in ufl_element.sub_elements()]
#debug_ir(ir, "finite_element")
return ir
def _compute_dofmap_ir(ufl_element, prefix, element_numbers):
"Compute intermediate representation of dofmap."
# This hits unimplemented FIAT functionality for OPEs; our
# dofmaps are not produced by FFC anyway, AFAIK
if isinstance(ufl_element.cell(), ufl.OuterProductCell):
return None
# Create FIAT element
fiat_element = create_element(ufl_element)
cell = ufl_element.cell()
cellname = cell.cellname()
# Precompute repeatedly used items
num_dofs_per_entity = _num_dofs_per_entity(fiat_element)
facet_dofs = _tabulate_facet_dofs(fiat_element, cell)
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["classname"] = make_classname(prefix, "dofmap", element_numbers[ufl_element])
# Compute data for each function
ir["signature"] = "FFC dofmap for " + repr(ufl_element)
ir["needs_mesh_entities"] = _needs_mesh_entities(fiat_element)
ir["cell"] = cell
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = cell.geometric_dimension()
ir["global_dimension"] = _global_dimension(fiat_element)
ir["num_element_dofs"] = fiat_element.space_dimension()
ir["num_facet_dofs"] = len(facet_dofs[0])
ir["num_entity_dofs"] = num_dofs_per_entity
ir["tabulate_dofs"] = _tabulate_dofs(fiat_element, cell)
ir["tabulate_facet_dofs"] = facet_dofs
ir["tabulate_entity_dofs"] = (fiat_element.entity_dofs(), num_dofs_per_entity)
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
ir["create_sub_dofmap"] = [make_classname(prefix, "dofmap", element_numbers[e])
for e in ufl_element.sub_elements()]
return ir
def _tabulate_coordinate_mapping_basis(ufl_element):
# TODO: Move this function to a table generation module?
# Get scalar element, assuming coordinates are represented
# with a VectorElement of scalar subelements
selement = ufl_element.sub_elements()[0]
fiat_element = create_element(selement)
cell = selement.cell()
tdim = cell.topological_dimension()
tables = {}
# Get points
origo = (0.0, ) * tdim
midpoint = cell_midpoint(cell)
# Tabulate basis
t0 = fiat_element.tabulate(1, [origo])
tm = fiat_element.tabulate(1, [midpoint])
# Get basis values at cell origo
tables["x0"] = t0[(0, ) * tdim][:, 0]
# Get basis values at cell midpoint
tables["xm"] = tm[(0, ) * tdim][:, 0]
# Single direction derivatives, e.g. [(1,0), (0,1)] in 2d
derivatives = [(0, ) * i + (1, ) + (0, ) * (tdim - 1 - i)
for i in range(tdim)]
# Get basis derivative values at cell origo
tables["J0"] = numpy.asarray([t0[d][:, 0] for d in derivatives])
# Get basis derivative values at cell midpoint
tables["Jm"] = numpy.asarray([tm[d][:, 0] for d in derivatives])
return tables
def _extract_element_data(element_map, classnames):
"Extract element data for psi_tables"
# Iterate over map
element_data = {}
for elements in element_map.values():
for ufl_element, counter in elements.items():
# Create corresponding FIAT element
fiat_element = create_element(ufl_element)
# Compute value size
value_size = product(ufl_element.value_shape())
# Get element classname
element_classname = classnames["finite_element"][ufl_element]
# Store data
element_data[counter] = {"physical_value_size": value_size,
"num_element_dofs": fiat_element.space_dimension(),
"classname": element_classname}
return element_data
def _tabulate_coordinate_mapping_basis(ufl_element):
# TODO: Move this function to a table generation module?
# Get scalar element, assuming coordinates are represented
# with a VectorElement of scalar subelements
selement = ufl_element.sub_elements()[0]
fiat_element = create_element(selement)
cell = selement.cell()
tdim = cell.topological_dimension()
tables = {}
# Get points
origo = (0.0,) * tdim
midpoint = cell_midpoint(cell)
# Tabulate basis
t0 = fiat_element.tabulate(1, [origo])
tm = fiat_element.tabulate(1, [midpoint])
# Get basis values at cell origo
tables["x0"] = t0[(0,) * tdim][:, 0]
# Get basis values at cell midpoint
tables["xm"] = tm[(0,) * tdim][:, 0]
# Single direction derivatives, e.g. [(1,0), (0,1)] in 2d
derivatives = [(0,) * i + (1,) + (0,) * (tdim - 1 - i) for i in range(tdim)]
# Get basis derivative values at cell origo
tables["J0"] = numpy.asarray([t0[d][:, 0] for d in derivatives])
# Get basis derivative values at cell midpoint
tables["Jm"] = numpy.asarray([tm[d][:, 0] for d in derivatives])
return tables
def get_data(ufl_element):
"Get needed data to run tests."
# Create fiat element.
element = create_element(ufl_element)
# The derivative order that we are interested in is the degree of the element.
if isinstance(element, FFCMixedElement):
deriv_order = max([e.degree() for e in element.elements()])
else:
deriv_order = element.degree()
# Get coordinates of the reference cell.
cell = ufl_element.cell()
ref_coords = reference_cell(cell.cellname()).get_vertices()
# Get the locations of the fiat element dofs.
elem_points = [list(L.pt_dict.keys())[0] for L in element.dual_basis()]
# Add some random points.
geo_dim = cell.geometric_dimension()
points = elem_points + random_points[geo_dim]
return (element, points, geo_dim, ref_coords, deriv_order)
def get_data(ufl_element):
"Get needed data to run tests."
# Create fiat element.
element = create_element(ufl_element)
# The derivative order that we are interested in is the degree of the element.
if isinstance(element, FFCMixedElement):
deriv_order = max([e.degree() for e in element.elements()])
else:
deriv_order = element.degree()
# Get coordinates of the reference cell.
cell = ufl_element.cell()
ref_coords = reference_cell(cell.cellname()).get_vertices()
# Get the locations of the fiat element dofs.
elem_points = [list(L.pt_dict.keys())[0] for L in element.dual_basis()]
# Add some random points.
geo_dim = cell.geometric_dimension()
points = elem_points + random_points[geo_dim]
return (element, points, geo_dim, ref_coords, deriv_order)
def test_continuous_lagrange_quadrilateral(degree, expected_dim):
"Test space dimensions of continuous TensorProduct elements (quadrilateral)."
P = create_element(FiniteElement("Lagrange", "quadrilateral", degree))
assert P.space_dimension() == expected_dim
def test_discontinuous_lagrange(degree, expected_dim):
"Test space dimensions of discontinuous Lagrange elements."
P = create_element(FiniteElement("DG", "triangle", degree))
assert P.space_dimension() == expected_dim
def test_hhj(degree, expected_dim):
"Test space dimensions of Hellan-Herrmann-Johnson element."
P = create_element(FiniteElement("HHJ", "triangle", degree))
assert P.space_dimension() == expected_dim
def __init__(self, monomial):
"Create transformed monomial from given monomial."
# Reset monomial data
self.float_value = monomial.float_value
self.determinants = []
self.coefficients = []
self.transforms = []
self.arguments = []
# Reset index counters
_reset_indices()
# Initialize index map
index_map = {}
# Iterate over factors
for f in monomial.factors:
# Create FIAT element
ufl_element = f.element()
fiat_element = create_element(ufl_element)
# Note nifty aspect here: when gdim != tdim, it might be
# (in particular, is for H(div)/H(curl), that the value
# dimension is different for the physical and reference
# elements.
# Get number of components
# FIXME: Can't handle tensor-valued elements: vdim = shape[0]
shape = ufl_element.value_shape()
assert(len(shape) <= 1), \
"MonomialTransformation does not handle tensor-valued elements"
if len(shape) == 0:
vdim = 1
else:
vdim = shape[0]
# Extract dimensions
sdim = fiat_element.space_dimension()
cell = ufl_element.cell()
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
# Extract basis function index and coefficients
if isinstance(f.function, Argument):
vindex = MonomialIndex(index_type=MonomialIndex.PRIMARY,
index_range=list(range(sdim)),
index_id=f.index())
elif isinstance(f.function, Coefficient):
vindex = MonomialIndex(index_range=list(range(sdim)))
coefficient = MonomialCoefficient(vindex, f.index())
self.coefficients.append(coefficient)
# Extract components
components = self._extract_components(f, index_map, vdim)
if len(components) > 1:
raise MonomialException("Can only handle rank 0 or rank 1 tensors.")
# Handle non-affine mappings (Piola)
if len(components) > 0:
# We can only handle rank 1 elements for now
component = components[0]
# Get mapping (all need to be equal)
mappings = []
for i in component.index_range:
(offset, ufl_sub_element) = ufl_element.extract_component(i)
fiat_sub_element = create_element(ufl_sub_element)
mappings.extend(fiat_sub_element.mapping())
if not all_equal(mappings):
raise MonomialException("Mappings differ: " + str(mappings))
mapping = mappings[0]
# Get component index relative to its sub element and its sub element
(component_index, sub_element) = ufl_element.extract_component(component.index_range[0])
# Get offset
if len(component_index) == 0:
offset = 0
else:
offset = component.index_range[0] - component_index[0]
# MER: Need to handle mappings in special ways if gdim
# != tdim and some Piolas are present. This could
# probably be merged with the offset code above, but I
# was not able to wrap my head around the offsets
# always referring to component.index_range[0].
if (gdim != tdim):
assert len(component.index_range) == 1, \
"Component transform not implemented for this case. Please request this feature."
component, offset = transform_component(component.index_range[0], offset, ufl_element)
component = MonomialIndex(index_type=MonomialIndex.FIXED,
index_range=[component], index_id=None)
components = [component, ]
# Add transforms where appropriate
if mapping == "contravariant piola":
# phi(x) = (det J)^{-1} J Phi(X)
index0 = component
index1 = MonomialIndex(index_range=list(range(tdim))) + offset
transform = MonomialTransform(index0, index1,
MonomialTransform.J,
f.restriction, offset)
self.transforms.append(transform)
determinant = MonomialDeterminant(power=-1,
restriction=f.restriction)
self.determinants.append(determinant)
components[0] = index1
elif mapping == "covariant piola":
# phi(x) = J^{-T} Phi(X)
index0 = MonomialIndex(index_range=list(range(tdim))) + offset
index1 = component
transform = MonomialTransform(index0, index1,
MonomialTransform.JINV,
f.restriction, offset)
self.transforms.append(transform)
components[0] = index0
# Extract derivatives / transforms
derivatives = []
for d in f.derivatives:
index0 = MonomialIndex(index_range=list(range(tdim)))
if d in index_map:
index1 = index_map[d]
elif isinstance(d, FixedIndex):
index1 = MonomialIndex(index_type=MonomialIndex.FIXED,
index_range=[int(d)],
index_id=int(d))
else:
index1 = MonomialIndex(index_range=list(range(gdim)))
index_map[d] = index1
transform = MonomialTransform(index0, index1, MonomialTransform.JINV, f.restriction, 0)
self.transforms.append(transform)
derivatives.append(index0)
# Extract restriction
restriction = f.restriction
# Create basis function
v = MonomialArgument(ufl_element, vindex, components, derivatives, restriction)
self.arguments.append(v)
# Figure out secondary and auxiliary indices
internal_indices = self._extract_internal_indices(None)
external_indices = self._extract_external_indices(None)
for i in internal_indices + external_indices:
# Skip already visited indices
if not i.index_type is None:
continue
# Set index type and id
num_internal = len([j for j in internal_indices if j == i])
num_external = len([j for j in external_indices if j == i])
if num_internal == 1 and num_external == 1:
i.index_type = MonomialIndex.SECONDARY
i.index_id = _next_secondary_index()
elif num_internal == 2 and num_external == 0:
i.index_type = MonomialIndex.INTERNAL
i.index_id = _next_internal_index()
elif num_internal == 0 and num_external == 2:
i.index_type = MonomialIndex.EXTERNAL
i.index_id = _next_external_index()
else:
raise Exception("Summation index does not appear exactly twice: %s" % str(i))
def test_regge(degree, expected_dim):
"Test space dimensions of generalized Regge element."
P = create_element(FiniteElement("Regge", "triangle", degree))
assert P.space_dimension() == expected_dim
def test_discontinuous_lagrange(degree, expected_dim):
"Test space dimensions of discontinuous Lagrange elements."
P = create_element(FiniteElement("DG", "triangle", degree))
assert P.space_dimension() == expected_dim
def test_continuous_lagrange_quadrilateral(degree, expected_dim):
"Test space dimensions of continuous TensorProduct elements (quadrilateral)."
P = create_element(FiniteElement("Lagrange", "quadrilateral", degree))
assert P.space_dimension() == expected_dim
def test_regge(degree, expected_dim):
"Test space dimensions of generalized Regge element."
P = create_element(FiniteElement("Regge", "triangle", degree))
assert P.space_dimension() == expected_dim
def create_dof_models(element):
"Create Soya3D models for dofs."
# Flags for whether to flip and center arrows
directional = {"PointScaledNormalEval": (True, False),
"PointEdgeTangent": (False, True),
"PointFaceTangent": (False, True)}
# Elements not supported fully by FIAT
unsupported = {"Argyris": argyris_dofs,
"Arnold-Winther": arnold_winther_dofs,
"Hermite": hermite_dofs,
"Mardal-Tai-Winther": mardal_tai_winther_dofs,
"Morley": morley_dofs}
# Check if element is supported
family = element.family()
if not family in unsupported:
# Create FIAT element and get dofs
fiat_element = create_element(element)
dofs = [(dof.get_type_tag(), dof.get_point_dict()) for dof in fiat_element.dual_basis()]
else:
# Bybass FIAT and set the dofs ourselves
dofs = unsupported[family](element)
# Iterate over dofs and add models
models = []
num_moments = 0
for (dof_type, L) in dofs:
# Check type of dof
if dof_type == "PointEval":
# Point evaluation, just get point
points = list(L.keys())
if not len(points) == 1:
error("Strange dof, single point expected.")
x = points[0]
# Generate model
models.append(PointEvaluation(x))
elif dof_type == "PointDeriv":
# Evaluation of derivatives at point
points = list(L.keys())
if not len(points) == 1:
error("Strange dof, single point expected.")
x = points[0]
# Generate model
models.append(PointDerivative(x))
elif dof_type == "PointSecondDeriv":
# Evaluation of derivatives at point
points = list(L.keys())
if not len(points) == 1:
error("Strange dof, single point expected.")
x = points[0]
# Generate model
models.append(PointSecondDerivative(x))
elif dof_type in directional:
# Normal evaluation, get point and normal
points = list(L.keys())
if not len(points) == 1:
error("Strange dof, single point expected.")
x = points[0]
n = [xx[0] for xx in L[x]]
# Generate model
flip, center = directional[dof_type]
models.append(DirectionalEvaluation(x, n, flip, center))
elif dof_type == "PointNormalDeriv":
# Evaluation of derivatives at point
points = list(L.keys())
if not len(points) == 1:
error("Strange dof, single point expected.")
x = points[0]
n = [xx[0] for xx in L[x]]
# Generate model
models.append(DirectionalDerivative(x, n))
elif dof_type in ("FrobeniusIntegralMoment", "IntegralMoment", "ComponentPointEval"):
# Generate model
models.append(IntegralMoment(element.cell().cellname(), num_moments))
# Count the number of integral moments
num_moments += 1
else:
error("Unable to plot dof, unhandled dof type: %s" % str(dof_type))
return models, num_moments
def test_hhj(degree, expected_dim):
"Test space dimensions of Hellan-Herrmann-Johnson element."
P = create_element(FiniteElement("HHJ", "triangle", degree))
assert P.space_dimension() == expected_dim
def tabulate_basis(sorted_integrals, form_data, itg_data):
"Tabulate the basisfunctions and derivatives."
# MER: Note to newbies: this code assumes that each integral in
# the dictionary of sorted_integrals that enters here, has a
# unique number of quadrature points ...
# Initialise return values.
quadrature_rules = {}
psi_tables = {}
integrals = {}
avg_elements = {"cell": [], "facet": []}
# Get some useful variables in short form
integral_type = itg_data.integral_type
cell = itg_data.domain.ufl_cell()
cellname = cell.cellname()
tdim = itg_data.domain.topological_dimension()
entity_dim = integral_type_to_entity_dim(integral_type, tdim)
num_entities = num_cell_entities[cellname][entity_dim]
# Create canonical ordering of quadrature rules
rules = sorted(sorted_integrals.keys())
# Loop the quadrature points and tabulate the basis values.
for rule in rules:
scheme, degree = rule
# --------- Creating quadrature rule
# Make quadrature rule and get points and weights.
(points, weights) = create_quadrature_points_and_weights(integral_type,
cell, degree,
scheme)
# The TOTAL number of weights/points
num_points = None if weights is None else len(weights)
# Add points and rules to dictionary
if num_points in quadrature_rules:
error("This number of points is already present in the weight table: " + repr(quadrature_rules))
quadrature_rules[num_points] = (weights, points)
# --------- Store integral
# Add the integral with the number of points as a key to the
# return integrals.
integral = sorted_integrals[rule]
if num_points in integrals:
error("This number of points is already present in the integrals: " + repr(integrals))
integrals[num_points] = integral
# --------- Analyse UFL elements in integral
# Get all unique elements in integral.
ufl_elements = [form_data.element_replace_map[e]
for e in extract_unique_elements(integral)]
# Insert elements for x and J
domain = integral.ufl_domain() # FIXME: For all domains to be sure? Better to rewrite though.
x_element = domain.ufl_coordinate_element()
if x_element not in ufl_elements:
if integral_type in custom_integral_types:
# FIXME: Not yet implemented, in progress
# warning("Vector elements not yet supported in custom integrals so element for coordinate function x will not be generated.")
pass
else:
ufl_elements.append(x_element)
# Find all CellAvg and FacetAvg in integrals and extract
# elements
for avg, AvgType in (("cell", CellAvg), ("facet", FacetAvg)):
expressions = extract_type(integral, AvgType)
avg_elements[avg] = [form_data.element_replace_map[e]
for expr in expressions
for e in extract_unique_elements(expr)]
# Find the highest number of derivatives needed for each element
num_derivatives = _find_element_derivatives(integral.integrand(),
ufl_elements,
form_data.element_replace_map)
# Need at least 1 for the Jacobian
num_derivatives[x_element] = max(num_derivatives.get(x_element, 0), 1)
# --------- Evaluate FIAT elements in quadrature points and
# --------- store in tables
# Add the number of points to the psi tables dictionary
if num_points in psi_tables:
error("This number of points is already present in the psi table: " + repr(psi_tables))
psi_tables[num_points] = {}
# Loop FIAT elements and tabulate basis as usual.
for ufl_element in ufl_elements:
fiat_element = create_element(ufl_element)
# Tabulate table of basis functions and derivatives in
# points
psi_table = _tabulate_psi_table(integral_type, cellname, tdim,
fiat_element,
num_derivatives[ufl_element],
points)
# Insert table into dictionary based on UFL elements
# (None=not averaged)
avg = None
psi_tables[num_points][ufl_element] = { avg: psi_table }
# Loop over elements found in CellAvg and tabulate basis averages
num_points = 1
for avg in ("cell", "facet"):
# Doesn't matter if it's exterior or interior
if avg == "cell":
avg_integral_type = "cell"
elif avg == "facet":
avg_integral_type = "exterior_facet"
for element in avg_elements[avg]:
fiat_element = create_element(element)
# Make quadrature rule and get points and weights.
(points, weights) = create_quadrature_points_and_weights(avg_integral_type, cell, element.degree(), "default")
wsum = sum(weights)
# Tabulate table of basis functions and derivatives in
# points
entity_psi_tables = _tabulate_psi_table(avg_integral_type,
cellname, tdim,
fiat_element, 0, points)
rank = len(element.value_shape())
# Hack, duplicating table with per-cell values for each
# facet in the case of cell_avg(f) in a facet integral
if num_entities > len(entity_psi_tables):
assert len(entity_psi_tables) == 1
assert avg_integral_type == "cell"
assert "facet" in integral_type
v, = sorted(entity_psi_tables.values())
entity_psi_tables = dict((e, v) for e in range(num_entities))
for entity, deriv_table in sorted(entity_psi_tables.items()):
deriv, = sorted(deriv_table.keys()) # Not expecting derivatives of averages
psi_table = deriv_table[deriv]
if rank:
# Compute numeric integral
num_dofs, num_components, num_points = psi_table.shape
if num_points != len(weights):
error("Weights and table shape does not match.")
avg_psi_table = numpy.asarray([[[numpy.dot(psi_table[j, k, :], weights) / wsum]
for k in range(num_components)]
for j in range(num_dofs)])
else:
# Compute numeric integral
num_dofs, num_points = psi_table.shape
if num_points != len(weights):
error("Weights and table shape does not match.")
avg_psi_table = numpy.asarray([[numpy.dot(psi_table[j, :],
weights) / wsum] for j in range(num_dofs)])
# Insert table into dictionary based on UFL elements
insert_nested_dict(psi_tables, (num_points, element, avg,
entity, deriv), avg_psi_table)
return (integrals, psi_tables, quadrature_rules)
