def _compute_element_ir(ufl_element, element_numbers, finite_element_names,
epsilon):
"""Compute intermediate representation of element."""
logger.info(f"Computing IR for element {ufl_element}")
# Create basix elements
basix_element = create_basix_element(ufl_element)
cell = ufl_element.cell()
cellname = cell.cellname()
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["name"] = finite_element_names[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"] = basix_element.dim
ir["degree"] = ufl_element.degree()
ir["family"] = basix_element.family_name
ir["value_shape"] = ufl_element.value_shape()
ir["reference_value_shape"] = ufl_element.reference_value_shape()
ir["num_sub_elements"] = ufl_element.num_sub_elements()
ir["create_sub_element"] = [
finite_element_names[e] for e in ufl_element.sub_elements()
]
if hasattr(basix_element, "block_size"):
ir["block_size"] = basix_element.block_size
ufl_element = ufl_element.sub_elements()[0]
basix_element = create_basix_element(ufl_element)
else:
ir["block_size"] = 1
im = basix_element.interpolation_matrix
if im.shape[0] == im.shape[1] and numpy.allclose(
im, numpy.identity(im.shape[0])):
ir["interpolation_is_identity"] = 1
else:
ir["interpolation_is_identity"] = 0
ir["base_transformations"] = basix_element.base_transformations
ir["needs_transformation_data"] = 0
for p in basix_element.base_transformations:
if not numpy.allclose(p, numpy.identity(len(p))):
ir["needs_transformation_data"] = 1
ir["entity_dofs"] = basix_element.entity_dof_numbers
return ir_element(**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]
basix_element = create_basix_element(selement)
cell = selement.cell()
tdim = cell.topological_dimension()
tables = {}
# Get points
origin = (0.0, ) * tdim
midpoint = cell_midpoint(cell)
# Tabulate basis
t0 = basix_element.tabulate(1, [origin])
tm = basix_element.tabulate(1, [midpoint])
# Get basis values at cell origin
tables["x0"] = t0[0][:, 0]
# Get basis values at cell midpoint
tables["xm"] = tm[0][:, 0]
# Get basis derivative values at cell origin
tables["J0"] = numpy.asarray([t0[d][:, 0] for d in range(1, 1 + tdim)])
# Get basis derivative values at cell midpoint
tables["Jm"] = numpy.asarray([tm[d][:, 0] for d in range(1, 1 + tdim)])
return tables
def test_values(self, family, cell, degree, reference):
# Create element
element = create_basix_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[0]
if sum(element.value_shape) == 1:
for i, value in enumerate(basis[0]):
assert numpy.isclose(value, reference[i](x))
else:
for i, ref in enumerate(reference):
assert numpy.allclose(basis[0][i::len(reference)], ref(x))
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"):
raise RuntimeError(
f"The physical facet edge vectors doesn't make sense for {cellname} cell."
)
else:
raise RuntimeError(f"Unhandled cell types {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")
basix_scalar_element = create_basix_element(ufl_scalar_element)
num_scalar_dofs = basix_scalar_element.dim
# Get edge vertices
facet = self.symbols.entity("facet", mt.restriction)
facet_edge = mt.component[0]
facet_edge_vertices = L.Symbol(f"{cellname}_facet_edge_vertices")
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 _compute_dofmap_ir(ufl_element, element_numbers, dofmap_names):
"""Compute intermediate representation of dofmap."""
logger.info(f"Computing IR for dofmap of {ufl_element}")
# Create basix elements
basix_element = create_basix_element(ufl_element)
# Store id
ir = {"id": element_numbers[ufl_element]}
ir["name"] = dofmap_names[ufl_element]
# Compute data for each function
ir["signature"] = "FFCX dofmap for " + repr(ufl_element)
ir["create_sub_dofmap"] = [
dofmap_names[e] for e in ufl_element.sub_elements()
]
ir["num_sub_dofmaps"] = ufl_element.num_sub_elements()
if hasattr(basix_element, "block_size"):
ir["block_size"] = basix_element.block_size
basix_element = basix_element.sub_element
else:
ir["block_size"] = 1
ir["base_transformations"] = basix_element.base_transformations
# Precompute repeatedly used items
for i in basix_element.entity_dofs:
if max(i) != min(i):
raise RuntimeError(
"Elements with different numbers of DOFs on subentities of the same dimension"
" are not yet supported in FFCx.")
num_dofs_per_entity = [i[0] for i in basix_element.entity_dofs]
ir["num_entity_dofs"] = num_dofs_per_entity
ir["tabulate_entity_dofs"] = (basix_element.entity_dof_numbers,
num_dofs_per_entity)
ir["num_global_support_dofs"] = basix_element.num_global_support_dofs
ir["num_element_support_dofs"] = basix_element.dim - ir[
"num_global_support_dofs"]
return ir_dofmap(**ir)
def cell_edge_vectors(self, e, mt, tabledata, num_points):
# 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":
raise RuntimeError(
"The physical cell edge vectors doesn't make sense for interval cell."
)
else:
raise RuntimeError(f"Unhandled cell types {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")
basix_scalar_element = create_basix_element(ufl_scalar_element)
vertex_scalar_dofs = basix_scalar_element.entity_dof_numbers[0]
num_scalar_dofs = basix_scalar_element.dim
# Get edge vertices
edge = mt.component[0]
vertex0, vertex1 = basix_scalar_element.reference_topology[1][edge]
# Get dofs and component
dof0, = vertex_scalar_dofs[vertex0]
dof1, = vertex_scalar_dofs[vertex1]
component = mt.component[1]
return 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)
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")
basix_scalar_element = create_basix_element(ufl_scalar_element)
vertex_scalar_dofs = basix_scalar_element.entity_dof_numbers[0]
num_scalar_dofs = basix_scalar_element.dim
# 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 num_coordinate_component_dofs(coordinate_element):
"""Get the number of dofs for a coordinate component for this degree."""
return create_basix_element(coordinate_element).sub_element.dim
def xtest_hhj(degree, expected_dim):
"Test space dimensions of Hellan-Herrmann-Johnson element."
P = create_basix_element(FiniteElement("HHJ", "triangle", degree))
assert P.dim == expected_dim
def test_regge(degree, expected_dim):
"Test space dimensions of generalized Regge element."
P = create_basix_element(FiniteElement("Regge", "triangle", degree))
assert P.dim == expected_dim
def xtest_continuous_lagrange_quadrilateral_spectral(degree, expected_dim):
"Test space dimensions of continuous TensorProduct elements (quadrilateral)."
P = create_basix_element(
FiniteElement("Lagrange", "quadrilateral", degree, variant="spectral"))
assert P.dim == expected_dim
def _compute_expression_ir(expression, index, prefix, analysis, parameters,
visualise):
logger.info(f"Computing IR for expression {index}")
# Compute representation
ir = {}
original_expression = (expression[2], expression[1])
sig = naming.compute_signature([original_expression], "", parameters)
ir["name"] = "expression_{!s}".format(sig)
original_expression = expression[2]
points = expression[1]
expression = expression[0]
try:
cell = expression.ufl_domain().ufl_cell()
except AttributeError:
# This case corresponds to a spatially constant expression without any dependencies
cell = None
# Prepare dimensions of all unique element in expression, including
# elements for arguments, coefficients and coordinate mappings
ir["element_dimensions"] = {
ufl_element: create_basix_element(ufl_element).dim
for ufl_element in analysis.unique_elements
}
# Extract dimensions for elements of arguments only
arguments = ufl.algorithms.extract_arguments(expression)
argument_elements = tuple(f.ufl_element() for f in arguments)
argument_dimensions = [
ir["element_dimensions"][ufl_element]
for ufl_element in argument_elements
]
tensor_shape = argument_dimensions
ir["tensor_shape"] = tensor_shape
ir["expression_shape"] = list(expression.ufl_shape)
coefficients = ufl.algorithms.extract_coefficients(expression)
coefficient_numbering = {}
for i, coeff in enumerate(coefficients):
coefficient_numbering[coeff] = i
# Add coefficient numbering to IR
ir["coefficient_numbering"] = coefficient_numbering
original_coefficient_positions = []
original_coefficients = ufl.algorithms.extract_coefficients(
original_expression)
for coeff in coefficients:
original_coefficient_positions.append(
original_coefficients.index(coeff))
ir["original_coefficient_positions"] = original_coefficient_positions
coefficient_elements = tuple(f.ufl_element() for f in coefficients)
offsets = {}
_offset = 0
for i, el in enumerate(coefficient_elements):
offsets[coefficients[i]] = _offset
_offset += ir["element_dimensions"][el]
# Copy offsets also into IR
ir["coefficient_offsets"] = offsets
ir["integral_type"] = "expression"
ir["entitytype"] = "cell"
# Build offsets for Constants
original_constant_offsets = {}
_offset = 0
for constant in ufl.algorithms.analysis.extract_constants(expression):
original_constant_offsets[constant] = _offset
_offset += numpy.product(constant.ufl_shape, dtype=int)
ir["original_constant_offsets"] = original_constant_offsets
ir["points"] = points
weights = numpy.array([1.0] * points.shape[0])
rule = QuadratureRule(points, weights)
integrands = {rule: expression}
if cell is None:
assert len(ir["original_coefficient_positions"]) == 0 and len(
ir["original_constant_offsets"]) == 0
expression_ir = compute_integral_ir(cell, ir["integral_type"],
ir["entitytype"], integrands,
tensor_shape, parameters, visualise)
ir.update(expression_ir)
return ir_expression(**ir)
def _compute_integral_ir(form_data, form_index, prefix, element_numbers,
integral_names, parameters, visualise):
"""Compute intermediate represention for form integrals."""
_entity_types = {
"cell": "cell",
"exterior_facet": "facet",
"interior_facet": "facet",
"vertex": "vertex",
"custom": "cell"
}
# Iterate over groups of integrals
irs = []
for itg_data_index, itg_data in enumerate(form_data.integral_data):
logger.info(
f"Computing IR for integral in integral group {itg_data_index}")
# Compute representation
entitytype = _entity_types[itg_data.integral_type]
cell = itg_data.domain.ufl_cell()
cellname = cell.cellname()
tdim = cell.topological_dimension()
assert all(tdim == itg.ufl_domain().topological_dimension()
for itg in itg_data.integrals)
ir = {
"integral_type": itg_data.integral_type,
"subdomain_id": itg_data.subdomain_id,
"rank": form_data.rank,
"geometric_dimension": form_data.geometric_dimension,
"topological_dimension": tdim,
"entitytype": entitytype,
"num_facets": cell.num_facets(),
"num_vertices": cell.num_vertices(),
"enabled_coefficients": itg_data.enabled_coefficients,
"cell_shape": cellname
}
# Get element space dimensions
unique_elements = element_numbers.keys()
ir["element_dimensions"] = {
ufl_element: create_basix_element(ufl_element).dim
for ufl_element in unique_elements
}
ir["element_ids"] = {
ufl_element: i
for i, ufl_element in enumerate(unique_elements)
}
# Create dimensions of primary indices, needed to reset the argument
# 'A' given to tabulate_tensor() by the assembler.
argument_dimensions = [
ir["element_dimensions"][ufl_element]
for ufl_element in form_data.argument_elements
]
# Compute shape of element tensor
if ir["integral_type"] == "interior_facet":
ir["tensor_shape"] = [2 * dim for dim in argument_dimensions]
else:
ir["tensor_shape"] = argument_dimensions
integral_type = itg_data.integral_type
cell = itg_data.domain.ufl_cell()
# Group integrands with the same quadrature rule
grouped_integrands = {}
for integral in itg_data.integrals:
md = integral.metadata() or {}
scheme = md["quadrature_rule"]
degree = md["quadrature_degree"]
if scheme == "custom":
points = md["quadrature_points"]
weights = md["quadrature_weights"]
elif scheme == "vertex":
# FIXME: Could this come from basix?
# The vertex scheme, i.e., averaging the function value in the
# vertices and multiplying with the simplex volume, is only of
# order 1 and inferior to other generic schemes in terms of
# error reduction. Equation systems generated with the vertex
# scheme have some properties that other schemes lack, e.g., the
# mass matrix is a simple diagonal matrix. This may be
# prescribed in certain cases.
if degree > 1:
warnings.warn(
"Explicitly selected vertex quadrature (degree 1), but requested degree is {}."
.format(degree))
if cellname == "tetrahedron":
points, weights = (numpy.array([[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]]),
numpy.array([
1.0 / 24.0, 1.0 / 24.0, 1.0 / 24.0,
1.0 / 24.0
]))
elif cellname == "triangle":
points, weights = (numpy.array([[0.0, 0.0], [1.0, 0.0],
[0.0, 1.0]]),
numpy.array(
[1.0 / 6.0, 1.0 / 6.0, 1.0 / 6.0]))
elif cellname == "interval":
# Trapezoidal rule
return (numpy.array([[0.0], [1.0]]),
numpy.array([1.0 / 2.0, 1.0 / 2.0]))
else:
points, weights = create_quadrature_points_and_weights(
integral_type, cell, degree, scheme)
points = numpy.asarray(points)
weights = numpy.asarray(weights)
rule = QuadratureRule(points, weights)
if rule not in grouped_integrands:
grouped_integrands[rule] = []
grouped_integrands[rule].append(integral.integrand())
sorted_integrals = {}
for rule, integrands in grouped_integrands.items():
integrands_summed = sorted_expr_sum(integrands)
integral_new = Integral(integrands_summed, itg_data.integral_type,
itg_data.domain, itg_data.subdomain_id, {},
None)
sorted_integrals[rule] = integral_new
# TODO: See if coefficient_numbering can be removed
# Build coefficient numbering for UFC interface here, to avoid
# renumbering in UFL and application of replace mapping
coefficient_numbering = {}
for i, f in enumerate(form_data.reduced_coefficients):
coefficient_numbering[f] = i
# Add coefficient numbering to IR
ir["coefficient_numbering"] = coefficient_numbering
index_to_coeff = sorted([(v, k)
for k, v in coefficient_numbering.items()])
offsets = {}
width = 2 if integral_type in ("interior_facet") else 1
_offset = 0
for k, el in zip(index_to_coeff, form_data.coefficient_elements):
offsets[k[1]] = _offset
_offset += width * ir["element_dimensions"][el]
# Copy offsets also into IR
ir["coefficient_offsets"] = offsets
# Build offsets for Constants
original_constant_offsets = {}
_offset = 0
for constant in form_data.original_form.constants():
original_constant_offsets[constant] = _offset
_offset += numpy.product(constant.ufl_shape, dtype=int)
ir["original_constant_offsets"] = original_constant_offsets
ir["precision"] = itg_data.metadata["precision"]
# Create map from number of quadrature points -> integrand
integrands = {
rule: integral.integrand()
for rule, integral in sorted_integrals.items()
}
# Build more specific intermediate representation
integral_ir = compute_integral_ir(itg_data.domain.ufl_cell(),
itg_data.integral_type,
ir["entitytype"], integrands,
ir["tensor_shape"], parameters,
visualise)
ir.update(integral_ir)
# Fetch name
ir["name"] = integral_names[(form_index, itg_data_index)]
irs.append(ir_integral(**ir))
return irs
def _compute_coordinate_mapping_ir(ufl_coordinate_element, prefix,
element_numbers, coordinate_mapping_names,
dofmap_names, finite_element_names):
"""Compute intermediate representation of coordinate mapping."""
logger.info(
f"Computing IR for coordinate mapping {ufl_coordinate_element}")
cell = ufl_coordinate_element.cell()
cellname = cell.cellname()
assert ufl_coordinate_element.value_shape() == (
cell.geometric_dimension(), )
# Compute element values
tables = _tabulate_coordinate_mapping_basis(ufl_coordinate_element)
# Store id
ir = {"id": element_numbers[ufl_coordinate_element]}
ir["prefix"] = prefix
ir["name"] = coordinate_mapping_names[ufl_coordinate_element]
# Compute data for each function
ir["signature"] = "FFCX coordinate_mapping from " + repr(
ufl_coordinate_element)
ir["cell_shape"] = cellname
ir["topological_dimension"] = cell.topological_dimension()
ir["geometric_dimension"] = ufl_coordinate_element.value_size()
ir["compute_physical_coordinates"] = None # currently unused, corresponds to function name
ir["compute_reference_coordinates"] = None # currently unused, corresponds to function name
ir["compute_jacobians"] = None # currently unused, corresponds to function name
ir["compute_jacobian_determinants"] = None # currently unused, corresponds to function name
ir["compute_jacobian_inverses"] = None # currently unused, corresponds to function name
ir["compute_geometry"] = None # currently unused, corresponds to function name
# NB! The entries below breaks the pattern of using ir keywords == code keywords,
# which I personally don't find very useful anyway (martinal).
basix_element = create_basix_element(ufl_coordinate_element)
ir["needs_transformation_data"] = 0
for p in basix_element.base_transformations:
if not numpy.allclose(p, numpy.identity(len(p))):
ir["needs_transformation_data"] = 1
ir["base_transformations"] = basix_element.sub_element.base_transformations
# Store tables and other coordinate element data
ir["tables"] = tables
ir["coordinate_element_degree"] = ufl_coordinate_element.degree()
ir["coordinate_element_family"] = basix_element.family_name
ir["num_scalar_coordinate_element_dofs"] = tables["x0"].shape[0]
ir["is_affine"] = ir["coordinate_element_degree"] == 1 and cellname in (
"interval", "triangle", "tetrahedron")
# Get classnames for coordinate element
ir["coordinate_finite_element_classname"] = finite_element_names[
ufl_coordinate_element]
# Get classnames for finite element and dofmap of scalar subelement
scalar_element = ufl_coordinate_element.sub_elements()[0]
ir["scalar_coordinate_finite_element_classname"] = finite_element_names[
scalar_element]
ir["scalar_dofmap_name"] = dofmap_names[scalar_element]
return ir_coordinate_map(**ir)
def get_ffcx_table_values(points, cell, integral_type, ufl_element, avg,
entitytype, derivative_counts, flat_component):
"""Extract values from ffcx element table.
Returns a 3D numpy array with axes
(entity number, quadrature point number, dof number)
"""
deriv_order = sum(derivative_counts)
if integral_type in ufl.custom_integral_types:
# Use quadrature points on cell for analysis in custom integral types
integral_type = "cell"
assert not avg
if integral_type == "expression":
# FFCX tables for expression are generated as interior cell points
integral_type = "cell"
if avg in ("cell", "facet"):
# Redefine points to compute average tables
# Make sure this is not called with points, that doesn't make sense
# assert points is None
# Not expecting derivatives of averages
assert not any(derivative_counts)
assert deriv_order == 0
# Doesn't matter if it's exterior or interior facet integral,
# just need a valid integral type to create quadrature rule
if avg == "cell":
integral_type = "cell"
elif avg == "facet":
integral_type = "exterior_facet"
# Make quadrature rule and get points and weights
points, weights = create_quadrature_points_and_weights(
integral_type, cell, ufl_element.degree(), "default")
# Tabulate table of basis functions and derivatives in points for each entity
tdim = cell.topological_dimension()
entity_dim = integral_type_to_entity_dim(integral_type, tdim)
num_entities = ufl.cell.num_cell_entities[cell.cellname()][entity_dim]
numpy.set_printoptions(suppress=True, precision=2)
basix_element = create_basix_element(ufl_element)
# Extract arrays for the right scalar component
component_tables = []
sh = ufl_element.value_shape()
if sh == ():
# Scalar valued element
for entity in range(num_entities):
entity_points = map_integral_points(points, integral_type, cell,
entity)
# basix
tbl = basix_element.tabulate(deriv_order, entity_points)
index = basix_index(*derivative_counts)
tbl = tbl[index].transpose()
component_tables.append(tbl)
elif len(sh) > 0 and ufl_element.num_sub_elements() == 0:
# 2-tensor-valued elements, not a tensor product
# mapping flat_component back to tensor component
(_, f2t) = ufl.permutation.build_component_numbering(
sh, ufl_element.symmetry())
t_comp = f2t[flat_component]
for entity in range(num_entities):
entity_points = map_integral_points(points, integral_type, cell,
entity)
tbl = basix_element.tabulate(deriv_order, entity_points)
tbl = tbl[basix_index(*derivative_counts)]
sum_sh = sum(sh)
bshape = (tbl.shape[0], ) + sh + (tbl.shape[1] // sum_sh, )
tbl = tbl.reshape(bshape).transpose()
if len(sh) == 1:
component_tables.append(tbl[:, t_comp[0], :])
elif len(sh) == 2:
component_tables.append(tbl[:, t_comp[0], t_comp[1], :])
else:
raise RuntimeError(
"Cannot tabulate tensor valued element with rank > 2")
else:
# Vector-valued or mixed element
sub_dims = [0] + [e.dim for e in basix_element.sub_elements]
sub_cmps = [0] + [e.value_size for e in basix_element.sub_elements]
irange = numpy.cumsum(sub_dims)
crange = numpy.cumsum(sub_cmps)
# Find index of sub element which corresponds to the current flat component
component_element_index = numpy.where(
crange <= flat_component)[0].shape[0] - 1
ir = irange[component_element_index:component_element_index + 2]
cr = crange[component_element_index:component_element_index + 2]
component_element = basix_element.sub_elements[component_element_index]
# Get the block size to switch XXYYZZ ordering to XYZXYZ
if isinstance(ufl_element, ufl.VectorElement) or isinstance(
ufl_element, ufl.TensorElement):
block_size = basix_element.block_size
ir = [ir[0] * block_size // irange[-1], irange[-1], block_size]
def slice_size(r):
if len(r) == 1:
return r[0]
if len(r) == 2:
return r[1] - r[0]
if len(r) == 3:
return 1 + (r[1] - r[0] - 1) // r[2]
for entity in range(num_entities):
entity_points = map_integral_points(points, integral_type, cell,
entity)
# basix
tbl = component_element.tabulate(deriv_order, entity_points)
index = basix_index(*derivative_counts)
tbl = tbl[index].transpose()
# Prepare a padded table with zeros
padded_shape = (
basix_element.dim, ) + basix_element.value_shape + (
len(entity_points), )
padded_tbl = numpy.zeros(padded_shape, dtype=tbl.dtype)
tab = tbl.reshape(slice_size(ir), slice_size(cr), -1)
padded_tbl[slice(*ir), slice(*cr)] = tab
component_tables.append(padded_tbl[:, flat_component, :])
if avg in ("cell", "facet"):
# Compute numeric integral of the each component table
wsum = sum(weights)
for entity, tbl in enumerate(component_tables):
num_dofs = tbl.shape[0]
tbl = numpy.dot(tbl, weights) / wsum
tbl = numpy.reshape(tbl, (num_dofs, 1))
component_tables[entity] = tbl
# Loop over entities and fill table blockwise (each block = points x dofs)
# Reorder axes as (points, dofs) instead of (dofs, points)
assert len(component_tables) == num_entities
num_dofs, num_points = component_tables[0].shape
shape = (num_entities, num_points, num_dofs)
res = numpy.zeros(shape)
for entity in range(num_entities):
res[entity, :, :] = numpy.transpose(component_tables[entity])
return res
def build_optimized_tables(quadrature_rule,
cell,
integral_type,
entitytype,
modified_terminals,
existing_tables,
rtol=default_rtol,
atol=default_atol):
# Build tables needed by all modified terminals
tables, mt_table_names, table_origins = build_element_tables(
quadrature_rule,
cell,
integral_type,
entitytype,
modified_terminals,
rtol=rtol,
atol=atol)
# Optimize tables and get table name and dofrange for each modified terminal
unique_tables, unique_table_origins, table_unames, table_ranges, table_dofmaps, table_permuted, \
table_original_num_dofs = optimize_element_tables(
tables, table_origins, rtol=rtol, atol=atol)
# Get num_dofs for all tables before they can be deleted later
unique_table_num_dofs = {
uname: tbl.shape[-1]
for uname, tbl in unique_tables.items()
}
# Analyze tables for properties useful for optimization
unique_table_ttypes = analyse_table_types(unique_tables,
rtol=rtol,
atol=atol)
# Compress tables that are constant along num_entities or num_points
for uname, tabletype in unique_table_ttypes.items():
if tabletype in piecewise_ttypes:
# Reduce table to dimension 1 along num_points axis in generated code
unique_tables[uname] = unique_tables[uname][:, :, :1, :]
if tabletype in uniform_ttypes:
# Reduce table to dimension 1 along num_entities axis in generated code
unique_tables[uname] = unique_tables[uname][:, :1, :, :]
if not table_permuted[uname]:
# Reduce table to dimenstion 2 along num_perms axis in generated code
unique_tables[uname] = unique_tables[uname][:1, :, :, :]
# Delete tables not referenced by modified terminals
used_unames = set(table_unames[name] for name in mt_table_names.values())
unused_unames = set(unique_tables.keys()) - used_unames
for uname in unused_unames:
del unique_table_ttypes[uname]
del unique_tables[uname]
# Change tables to point to existing optimized tables
# (i.e. tables from other contexts that have been compressed to look the same)
name_map = {}
existing_names = sorted(existing_tables)
for uname in sorted(unique_tables):
utbl = unique_tables[uname]
for i, ename in enumerate(existing_names):
etbl = existing_tables[ename]
if equal_tables(utbl, etbl, rtol=rtol, atol=atol):
# Setup table name mapping
name_map[uname] = ename
# Don't visit this table again (just to avoid the processing)
existing_names.pop(i)
break
# Replace unique table names
for uname, ename in name_map.items():
unique_tables[ename] = existing_tables[ename]
del unique_tables[uname]
unique_table_ttypes[ename] = unique_table_ttypes[uname]
del unique_table_ttypes[uname]
needs_transformation_data = False
# Build mapping from modified terminal to unique table with metadata
# { mt: (unique name,
# (table dof range begin, table dof range end),
# [top parent element dof index for each local index],
# ttype, original_element_dim) }
mt_unique_table_reference = {}
for mt, name in list(mt_table_names.items()):
# Get metadata for the original table (name is not the unique name!)
dofrange = table_ranges[name]
dofmap = table_dofmaps[name]
original_dim = table_original_num_dofs[name]
is_permuted = table_permuted[name]
if is_permuted:
needs_transformation_data = True
# Map name -> uname
uname = table_unames[name]
# Map uname -> ename
ename = name_map.get(uname, uname)
# Some more metadata stored under the ename
ttype = unique_table_ttypes[ename]
offset = 0
# Add offset to dofmap and dofrange for restricted terminals
if mt.restriction and isinstance(mt.terminal,
ufl.classes.FormArgument):
# offset = 0 or number of dofs before table optimization
offset = ufc_restriction_offset(mt.restriction, original_dim)
(b, e) = dofrange
dofrange = (b + offset, e + offset)
dofmap = tuple(i + offset for i in dofmap)
base_transformations = [[[
p[i - offset][j - offset] for j in dofmap
] for i in dofmap] for p in create_basix_element(
table_origins[name][0]).base_transformations]
needs_transformation_data = False
for p in base_transformations:
if not numpy.allclose(p, numpy.identity(len(p))):
needs_transformation_data = True
# Store reference to unique table for this mt
mt_unique_table_reference[mt] = unique_table_reference_t(
ename, unique_tables[ename], dofrange, dofmap, original_dim, ttype,
ttype in piecewise_ttypes, ttype in uniform_ttypes, is_permuted,
base_transformations, needs_transformation_data)
return (unique_tables, unique_table_ttypes, unique_table_num_dofs,
mt_unique_table_reference)
def test_discontinuous_lagrange(degree, expected_dim):
"Test space dimensions of discontinuous Lagrange elements."
P = create_basix_element(FiniteElement("DG", "triangle", degree))
assert P.dim == expected_dim