def convert_finiteelement(element, **kwargs):
cell = as_fiat_cell(element.cell())
if element.family() == "Quadrature":
degree = element.degree()
scheme = element.quadrature_scheme()
if degree is None or scheme is None:
raise ValueError("Quadrature scheme and degree must be specified!")
return finat.QuadratureElement(cell, degree, scheme), set()
lmbda = supported_elements[element.family()]
if lmbda is None:
if element.cell().cellname() != "quadrilateral":
raise ValueError("%s is supported, but handled incorrectly" %
element.family())
# Handle quadrilateral short names like RTCF and RTCE.
element = element.reconstruct(cell=quad_tpc)
finat_elem, deps = _create_element(element, **kwargs)
return finat.QuadrilateralElement(finat_elem), deps
kind = element.variant()
if kind is None:
kind = 'equispaced' # default variant
if element.family() == "Lagrange":
if kind == 'equispaced':
lmbda = finat.Lagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLobattoLegendre
else:
raise ValueError("Variant %r not supported on %s" % (kind, element.cell()))
elif element.family() == "Discontinuous Lagrange":
kind = element.variant() or 'equispaced'
if kind == 'equispaced':
lmbda = finat.DiscontinuousLagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLegendre
else:
raise ValueError("Variant %r not supported on %s" % (kind, element.cell()))
return lmbda(cell, element.degree()), set()
def compile_integral(integral_data, form_data, prefix, parameters,
interface=firedrake_interface):
"""Compiles a UFL integral into an assembly kernel.
:arg integral_data: UFL integral data
:arg form_data: UFL form data
:arg prefix: kernel name will start with this string
:arg parameters: parameters object
:arg interface: backend module for the kernel interface
:returns: a kernel constructed by the kernel interface
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Remove these here, they're handled below.
if parameters.get("quadrature_degree") in ["auto", "default", None, -1, "-1"]:
del parameters["quadrature_degree"]
if parameters.get("quadrature_rule") in ["auto", "default", None]:
del parameters["quadrature_rule"]
integral_type = integral_data.integral_type
interior_facet = integral_type.startswith("interior_facet")
mesh = integral_data.domain
cell = integral_data.domain.ufl_cell()
arguments = form_data.preprocessed_form.arguments()
kernel_name = "%s_%s_integral_%s" % (prefix, integral_type, integral_data.subdomain_id)
# Handle negative subdomain_id
kernel_name = kernel_name.replace("-", "_")
fiat_cell = as_fiat_cell(cell)
integration_dim, entity_ids = lower_integral_type(fiat_cell, integral_type)
quadrature_indices = []
# Dict mapping domains to index in original_form.ufl_domains()
domain_numbering = form_data.original_form.domain_numbering()
builder = interface.KernelBuilder(integral_type, integral_data.subdomain_id,
domain_numbering[integral_data.domain])
argument_multiindices = tuple(builder.create_element(arg.ufl_element()).get_indices()
for arg in arguments)
return_variables = builder.set_arguments(arguments, argument_multiindices)
builder.set_coordinates(mesh)
builder.set_coefficients(integral_data, form_data)
# Map from UFL FiniteElement objects to multiindices. This is
# so we reuse Index instances when evaluating the same coefficient
# multiple times with the same table.
#
# We also use the same dict for the unconcatenate index cache,
# which maps index objects to tuples of multiindices. These two
# caches shall never conflict as their keys have different types
# (UFL finite elements vs. GEM index objects).
index_cache = {}
kernel_cfg = dict(interface=builder,
ufl_cell=cell,
integral_type=integral_type,
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
argument_multiindices=argument_multiindices,
index_cache=index_cache)
mode_irs = collections.OrderedDict()
for integral in integral_data.integrals:
params = parameters.copy()
params.update(integral.metadata()) # integral metadata overrides
if params.get("quadrature_rule") == "default":
del params["quadrature_rule"]
mode = pick_mode(params["mode"])
mode_irs.setdefault(mode, collections.OrderedDict())
integrand = ufl.replace(integral.integrand(), form_data.function_replace_map)
integrand = ufl_utils.split_coefficients(integrand, builder.coefficient_split)
# Check if the integral has a quad degree attached, otherwise use
# the estimated polynomial degree attached by compute_form_data
quadrature_degree = params.get("quadrature_degree",
params["estimated_polynomial_degree"])
try:
quadrature_degree = params["quadrature_degree"]
except KeyError:
quadrature_degree = params["estimated_polynomial_degree"]
functions = list(arguments) + [builder.coordinate(mesh)] + list(integral_data.integral_coefficients)
function_degrees = [f.ufl_function_space().ufl_element().degree() for f in functions]
if all((asarray(quadrature_degree) > 10 * asarray(degree)).all()
for degree in function_degrees):
logger.warning("Estimated quadrature degree %s more "
"than tenfold greater than any "
"argument/coefficient degree (max %s)",
quadrature_degree, max_degree(function_degrees))
try:
quad_rule = params["quadrature_rule"]
except KeyError:
integration_cell = fiat_cell.construct_subelement(integration_dim)
quad_rule = make_quadrature(integration_cell, quadrature_degree)
if not isinstance(quad_rule, AbstractQuadratureRule):
raise ValueError("Expected to find a QuadratureRule object, not a %s" %
type(quad_rule))
quadrature_multiindex = quad_rule.point_set.indices
quadrature_indices.extend(quadrature_multiindex)
config = kernel_cfg.copy()
config.update(quadrature_rule=quad_rule)
expressions = fem.compile_ufl(integrand,
interior_facet=interior_facet,
**config)
reps = mode.Integrals(expressions, quadrature_multiindex,
argument_multiindices, params)
for var, rep in zip(return_variables, reps):
mode_irs[mode].setdefault(var, []).append(rep)
# Finalise mode representations into a set of assignments
assignments = []
for mode, var_reps in mode_irs.items():
assignments.extend(mode.flatten(var_reps.items(), index_cache))
if assignments:
return_variables, expressions = zip(*assignments)
else:
return_variables = []
expressions = []
# Need optimised roots for COFFEE
options = dict(reduce(operator.and_,
[mode.finalise_options.items()
for mode in mode_irs.keys()]))
expressions = impero_utils.preprocess_gem(expressions, **options)
assignments = list(zip(return_variables, expressions))
# Look for cell orientations in the IR
if builder.needs_cell_orientations(expressions):
builder.require_cell_orientations()
# Construct ImperoC
split_argument_indices = tuple(chain(*[var.index_ordering()
for var in return_variables]))
index_ordering = tuple(quadrature_indices) + split_argument_indices
try:
impero_c = impero_utils.compile_gem(assignments, index_ordering, remove_zeros=True)
except impero_utils.NoopError:
# No operations, construct empty kernel
return builder.construct_empty_kernel(kernel_name)
# Generate COFFEE
index_names = []
def name_index(index, name):
index_names.append((index, name))
if index in index_cache:
for multiindex, suffix in zip(index_cache[index],
string.ascii_lowercase):
name_multiindex(multiindex, name + suffix)
def name_multiindex(multiindex, name):
if len(multiindex) == 1:
name_index(multiindex[0], name)
else:
for i, index in enumerate(multiindex):
name_index(index, name + str(i))
name_multiindex(quadrature_indices, 'ip')
for multiindex, name in zip(argument_multiindices, ['j', 'k']):
name_multiindex(multiindex, name)
# Construct kernel
body = generate_coffee(impero_c, index_names, parameters["precision"], expressions, split_argument_indices)
return builder.construct_kernel(kernel_name, body)
def compile_integral(integral_data,
form_data,
prefix,
parameters,
interface=firedrake_interface):
"""Compiles a UFL integral into an assembly kernel.
:arg integral_data: UFL integral data
:arg form_data: UFL form data
:arg prefix: kernel name will start with this string
:arg parameters: parameters object
:arg interface: backend module for the kernel interface
:returns: a kernel constructed by the kernel interface
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Remove these here, they're handled below.
if parameters.get("quadrature_degree") in [
"auto", "default", None, -1, "-1"
]:
del parameters["quadrature_degree"]
if parameters.get("quadrature_rule") in ["auto", "default", None]:
del parameters["quadrature_rule"]
integral_type = integral_data.integral_type
interior_facet = integral_type.startswith("interior_facet")
mesh = integral_data.domain
cell = integral_data.domain.ufl_cell()
arguments = form_data.preprocessed_form.arguments()
kernel_name = "%s_%s_integral_%s" % (prefix, integral_type,
integral_data.subdomain_id)
fiat_cell = as_fiat_cell(cell)
integration_dim, entity_ids = lower_integral_type(fiat_cell, integral_type)
argument_multiindices = tuple(
create_element(arg.ufl_element()).get_indices() for arg in arguments)
argument_indices = tuple(chain(*argument_multiindices))
quadrature_indices = []
# Dict mapping domains to index in original_form.ufl_domains()
domain_numbering = form_data.original_form.domain_numbering()
builder = interface.KernelBuilder(integral_type,
integral_data.subdomain_id,
domain_numbering[integral_data.domain])
return_variables = builder.set_arguments(arguments, argument_multiindices)
coordinates = ufl_utils.coordinate_coefficient(mesh)
builder.set_coordinates(coordinates)
builder.set_coefficients(integral_data, form_data)
# Map from UFL FiniteElement objects to multiindices. This is
# so we reuse Index instances when evaluating the same coefficient
# multiple times with the same table.
index_cache = {}
kernel_cfg = dict(interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
argument_multiindices=argument_multiindices,
index_cache=index_cache)
kernel_cfg["facetarea"] = facetarea_generator(mesh, coordinates,
kernel_cfg, integral_type)
kernel_cfg["cellvolume"] = cellvolume_generator(mesh, coordinates,
kernel_cfg)
mode_irs = collections.OrderedDict()
for integral in integral_data.integrals:
params = parameters.copy()
params.update(integral.metadata()) # integral metadata overrides
if params.get("quadrature_rule") == "default":
del params["quadrature_rule"]
mode = pick_mode(params["mode"])
mode_irs.setdefault(mode, collections.OrderedDict())
integrand = ufl_utils.replace_coordinates(integral.integrand(),
coordinates)
integrand = ufl.replace(integrand, form_data.function_replace_map)
integrand = ufl_utils.split_coefficients(integrand,
builder.coefficient_split)
# Check if the integral has a quad degree attached, otherwise use
# the estimated polynomial degree attached by compute_form_data
quadrature_degree = params.get("quadrature_degree",
params["estimated_polynomial_degree"])
try:
quad_rule = params["quadrature_rule"]
except KeyError:
integration_cell = fiat_cell.construct_subelement(integration_dim)
quad_rule = make_quadrature(integration_cell, quadrature_degree)
if not isinstance(quad_rule, AbstractQuadratureRule):
raise ValueError(
"Expected to find a QuadratureRule object, not a %s" %
type(quad_rule))
quadrature_multiindex = quad_rule.point_set.indices
quadrature_indices.extend(quadrature_multiindex)
config = kernel_cfg.copy()
config.update(quadrature_rule=quad_rule)
expressions = fem.compile_ufl(integrand,
interior_facet=interior_facet,
**config)
reps = mode.Integrals(expressions, quadrature_multiindex,
argument_multiindices, params)
for var, rep in zip(return_variables, reps):
mode_irs[mode].setdefault(var, []).append(rep)
# Finalise mode representations into a set of assignments
assignments = []
for mode, var_reps in iteritems(mode_irs):
assignments.extend(mode.flatten(viewitems(var_reps)))
if assignments:
return_variables, expressions = zip(*assignments)
else:
return_variables = []
expressions = []
# Need optimised roots for COFFEE
options = dict(
reduce(
operator.and_,
[viewitems(mode.finalise_options) for mode in iterkeys(mode_irs)]))
expressions = impero_utils.preprocess_gem(expressions, **options)
assignments = list(zip(return_variables, expressions))
# Look for cell orientations in the IR
if builder.needs_cell_orientations(expressions):
builder.require_cell_orientations()
# Construct ImperoC
index_ordering = tuple(quadrature_indices) + argument_indices
try:
impero_c = impero_utils.compile_gem(assignments,
index_ordering,
remove_zeros=True)
except impero_utils.NoopError:
# No operations, construct empty kernel
return builder.construct_empty_kernel(kernel_name)
# Generate COFFEE
index_names = [(si, name + str(n))
for index, name in zip(argument_multiindices, ['j', 'k'])
for n, si in enumerate(index)]
if len(quadrature_indices) == 1:
index_names.append((quadrature_indices[0], 'ip'))
else:
for i, quadrature_index in enumerate(quadrature_indices):
index_names.append((quadrature_index, 'ip_%d' % i))
# Construct kernel
body = generate_coffee(impero_c, index_names, parameters["precision"],
expressions, argument_indices)
return builder.construct_kernel(kernel_name, body)
def compile_integral(integral_data,
form_data,
prefix,
parameters,
interface,
coffee,
*,
diagonal=False):
"""Compiles a UFL integral into an assembly kernel.
:arg integral_data: UFL integral data
:arg form_data: UFL form data
:arg prefix: kernel name will start with this string
:arg parameters: parameters object
:arg interface: backend module for the kernel interface
:arg diagonal: Are we building a kernel for the diagonal of a rank-2 element tensor?
:returns: a kernel constructed by the kernel interface
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
if interface is None:
if coffee:
import tsfc.kernel_interface.firedrake as firedrake_interface_coffee
interface = firedrake_interface_coffee.KernelBuilder
else:
# Delayed import, loopy is a runtime dependency
import tsfc.kernel_interface.firedrake_loopy as firedrake_interface_loopy
interface = firedrake_interface_loopy.KernelBuilder
# Remove these here, they're handled below.
if parameters.get("quadrature_degree") in [
"auto", "default", None, -1, "-1"
]:
del parameters["quadrature_degree"]
if parameters.get("quadrature_rule") in ["auto", "default", None]:
del parameters["quadrature_rule"]
integral_type = integral_data.integral_type
interior_facet = integral_type.startswith("interior_facet")
mesh = integral_data.domain
cell = integral_data.domain.ufl_cell()
arguments = form_data.preprocessed_form.arguments()
kernel_name = "%s_%s_integral_%s" % (prefix, integral_type,
integral_data.subdomain_id)
# Handle negative subdomain_id
kernel_name = kernel_name.replace("-", "_")
fiat_cell = as_fiat_cell(cell)
integration_dim, entity_ids = lower_integral_type(fiat_cell, integral_type)
quadrature_indices = []
# Dict mapping domains to index in original_form.ufl_domains()
domain_numbering = form_data.original_form.domain_numbering()
builder = interface(integral_type,
integral_data.subdomain_id,
domain_numbering[integral_data.domain],
parameters["scalar_type"],
diagonal=diagonal)
argument_multiindices = tuple(
builder.create_element(arg.ufl_element()).get_indices()
for arg in arguments)
if diagonal:
# Error checking occurs in the builder constructor.
# Diagonal assembly is obtained by using the test indices for
# the trial space as well.
a, _ = argument_multiindices
argument_multiindices = (a, a)
return_variables = builder.set_arguments(arguments, argument_multiindices)
builder.set_coordinates(mesh)
builder.set_cell_sizes(mesh)
builder.set_coefficients(integral_data, form_data)
# Map from UFL FiniteElement objects to multiindices. This is
# so we reuse Index instances when evaluating the same coefficient
# multiple times with the same table.
#
# We also use the same dict for the unconcatenate index cache,
# which maps index objects to tuples of multiindices. These two
# caches shall never conflict as their keys have different types
# (UFL finite elements vs. GEM index objects).
index_cache = {}
kernel_cfg = dict(interface=builder,
ufl_cell=cell,
integral_type=integral_type,
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
argument_multiindices=argument_multiindices,
index_cache=index_cache)
mode_irs = collections.OrderedDict()
for integral in integral_data.integrals:
params = parameters.copy()
params.update(integral.metadata()) # integral metadata overrides
if params.get("quadrature_rule") == "default":
del params["quadrature_rule"]
mode = pick_mode(params["mode"])
mode_irs.setdefault(mode, collections.OrderedDict())
integrand = ufl.replace(integral.integrand(),
form_data.function_replace_map)
integrand = ufl_utils.split_coefficients(integrand,
builder.coefficient_split)
# Check if the integral has a quad degree attached, otherwise use
# the estimated polynomial degree attached by compute_form_data
quadrature_degree = params.get("quadrature_degree",
params["estimated_polynomial_degree"])
try:
quadrature_degree = params["quadrature_degree"]
except KeyError:
quadrature_degree = params["estimated_polynomial_degree"]
functions = list(arguments) + [builder.coordinate(mesh)] + list(
integral_data.integral_coefficients)
function_degrees = [
f.ufl_function_space().ufl_element().degree()
for f in functions
]
if all((asarray(quadrature_degree) > 10 * asarray(degree)).all()
for degree in function_degrees):
logger.warning(
"Estimated quadrature degree %s more "
"than tenfold greater than any "
"argument/coefficient degree (max %s)", quadrature_degree,
max_degree(function_degrees))
try:
quad_rule = params["quadrature_rule"]
except KeyError:
integration_cell = fiat_cell.construct_subelement(integration_dim)
quad_rule = make_quadrature(integration_cell, quadrature_degree)
if not isinstance(quad_rule, AbstractQuadratureRule):
raise ValueError(
"Expected to find a QuadratureRule object, not a %s" %
type(quad_rule))
quadrature_multiindex = quad_rule.point_set.indices
quadrature_indices.extend(quadrature_multiindex)
config = kernel_cfg.copy()
config.update(quadrature_rule=quad_rule)
expressions = fem.compile_ufl(integrand,
interior_facet=interior_facet,
**config)
reps = mode.Integrals(expressions, quadrature_multiindex,
argument_multiindices, params)
for var, rep in zip(return_variables, reps):
mode_irs[mode].setdefault(var, []).append(rep)
# Finalise mode representations into a set of assignments
assignments = []
for mode, var_reps in mode_irs.items():
assignments.extend(mode.flatten(var_reps.items(), index_cache))
if assignments:
return_variables, expressions = zip(*assignments)
else:
return_variables = []
expressions = []
# Need optimised roots
options = dict(
reduce(operator.and_,
[mode.finalise_options.items() for mode in mode_irs.keys()]))
expressions = impero_utils.preprocess_gem(expressions, **options)
assignments = list(zip(return_variables, expressions))
# Let the kernel interface inspect the optimised IR to register
# what kind of external data is required (e.g., cell orientations,
# cell sizes, etc.).
builder.register_requirements(expressions)
# Construct ImperoC
split_argument_indices = tuple(
chain(*[var.index_ordering() for var in return_variables]))
index_ordering = tuple(quadrature_indices) + split_argument_indices
try:
impero_c = impero_utils.compile_gem(assignments,
index_ordering,
remove_zeros=True)
except impero_utils.NoopError:
# No operations, construct empty kernel
return builder.construct_empty_kernel(kernel_name)
# Generate COFFEE
index_names = []
def name_index(index, name):
index_names.append((index, name))
if index in index_cache:
for multiindex, suffix in zip(index_cache[index],
string.ascii_lowercase):
name_multiindex(multiindex, name + suffix)
def name_multiindex(multiindex, name):
if len(multiindex) == 1:
name_index(multiindex[0], name)
else:
for i, index in enumerate(multiindex):
name_index(index, name + str(i))
name_multiindex(quadrature_indices, 'ip')
for multiindex, name in zip(argument_multiindices, ['j', 'k']):
name_multiindex(multiindex, name)
return builder.construct_kernel(kernel_name, impero_c,
parameters["precision"], index_names,
quad_rule)
def fiat_cell(self):
return as_fiat_cell(self.ufl_cell)
def convert_finiteelement(element, **kwargs):
cell = as_fiat_cell(element.cell())
if element.family() == "Quadrature":
degree = element.degree()
scheme = element.quadrature_scheme()
if degree is None or scheme is None:
raise ValueError("Quadrature scheme and degree must be specified!")
return finat.QuadratureElement(cell, degree, scheme), set()
elif element.family() == "Bernstein":
return fiat_compat(element), set()
lmbda = supported_elements[element.family()]
if lmbda is None:
if element.cell().cellname() == "quadrilateral":
# Handle quadrilateral short names like RTCF and RTCE.
element = element.reconstruct(cell=quadrilateral_tpc)
elif element.cell().cellname() == "hexahedron":
# Handle hexahedron short names like NCF and NCE.
element = element.reconstruct(cell=hexahedron_tpc)
else:
raise ValueError("%s is supported, but handled incorrectly" %
element.family())
finat_elem, deps = _create_element(element, **kwargs)
return finat.FlattenedDimensions(finat_elem), deps
kind = element.variant()
if kind is None:
kind = 'spectral' if element.cell().cellname(
) == 'interval' else 'equispaced' # default variant
if element.family() == "Lagrange":
if kind == 'equispaced':
lmbda = finat.Lagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLobattoLegendre
elif kind in ['mgd', 'feec', 'qb', 'mse']:
degree = element.degree()
shift_axes = kwargs["shift_axes"]
restriction = kwargs["restriction"]
deps = {"shift_axes", "restriction"}
return finat.RuntimeTabulated(cell,
degree,
variant=kind,
shift_axes=shift_axes,
restriction=restriction), deps
else:
raise ValueError("Variant %r not supported on %s" %
(kind, element.cell()))
elif element.family() in [
"Discontinuous Lagrange", "Discontinuous Lagrange L2"
]:
if kind == 'equispaced':
lmbda = finat.DiscontinuousLagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLegendre
elif kind in ['mgd', 'feec', 'qb', 'mse']:
degree = element.degree()
shift_axes = kwargs["shift_axes"]
restriction = kwargs["restriction"]
deps = {"shift_axes", "restriction"}
return finat.RuntimeTabulated(cell,
degree,
variant=kind,
shift_axes=shift_axes,
restriction=restriction,
continuous=False), deps
else:
raise ValueError("Variant %r not supported on %s" %
(kind, element.cell()))
elif element.family() == ["DPC", "DPC L2"]:
if element.cell().geometric_dimension() == 2:
element = element.reconstruct(cell=ufl.cell.hypercube(2))
elif element.cell().geometric_dimension() == 3:
element = element.reconstruct(cell=ufl.cell.hypercube(3))
elif element.family() == "S":
if element.cell().geometric_dimension() == 2:
element = element.reconstruct(cell=ufl.cell.hypercube(2))
elif element.cell().geometric_dimension() == 3:
element = element.reconstruct(cell=ufl.cell.hypercube(3))
return lmbda(cell, element.degree()), set()
def compile_integral(integral_data, form_data, prefix, parameters,
interface=firedrake_interface):
"""Compiles a UFL integral into an assembly kernel.
:arg integral_data: UFL integral data
:arg form_data: UFL form data
:arg prefix: kernel name will start with this string
:arg parameters: parameters object
:arg interface: backend module for the kernel interface
:returns: a kernel constructed by the kernel interface
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Remove these here, they're handled below.
if parameters.get("quadrature_degree") in ["auto", "default", None, -1, "-1"]:
del parameters["quadrature_degree"]
if parameters.get("quadrature_rule") in ["auto", "default", None]:
del parameters["quadrature_rule"]
integral_type = integral_data.integral_type
interior_facet = integral_type.startswith("interior_facet")
mesh = integral_data.domain
cell = integral_data.domain.ufl_cell()
arguments = form_data.preprocessed_form.arguments()
fiat_cell = as_fiat_cell(cell)
integration_dim, entity_ids = lower_integral_type(fiat_cell, integral_type)
argument_indices = tuple(gem.Index(name=name) for arg, name in zip(arguments, ['j', 'k']))
quadrature_indices = []
# Dict mapping domains to index in original_form.ufl_domains()
domain_numbering = form_data.original_form.domain_numbering()
builder = interface.KernelBuilder(integral_type, integral_data.subdomain_id,
domain_numbering[integral_data.domain])
return_variables = builder.set_arguments(arguments, argument_indices)
coordinates = ufl_utils.coordinate_coefficient(mesh)
if ufl_utils.is_element_affine(mesh.ufl_coordinate_element()):
# For affine mesh geometries we prefer code generation that
# composes well with optimisations.
builder.set_coordinates(coordinates, mode='list_tensor')
else:
# Otherwise we use the approach that might be faster (?)
builder.set_coordinates(coordinates)
builder.set_coefficients(integral_data, form_data)
# Map from UFL FiniteElement objects to Index instances. This is
# so we reuse Index instances when evaluating the same coefficient
# multiple times with the same table. Occurs, for example, if we
# have multiple integrals here (and the affine coordinate
# evaluation can be hoisted).
index_cache = collections.defaultdict(gem.Index)
kernel_cfg = dict(interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
argument_indices=argument_indices,
index_cache=index_cache)
kernel_cfg["facetarea"] = facetarea_generator(mesh, coordinates, kernel_cfg, integral_type)
kernel_cfg["cellvolume"] = cellvolume_generator(mesh, coordinates, kernel_cfg)
irs = []
for integral in integral_data.integrals:
params = {}
# Record per-integral parameters
params.update(integral.metadata())
if params.get("quadrature_rule") == "default":
del params["quadrature_rule"]
# parameters override per-integral metadata
params.update(parameters)
# Check if the integral has a quad degree attached, otherwise use
# the estimated polynomial degree attached by compute_form_data
quadrature_degree = params.get("quadrature_degree",
params["estimated_polynomial_degree"])
integration_cell = fiat_cell.construct_subelement(integration_dim)
quad_rule = params.get("quadrature_rule",
create_quadrature(integration_cell,
quadrature_degree))
if not isinstance(quad_rule, QuadratureRule):
raise ValueError("Expected to find a QuadratureRule object, not a %s" %
type(quad_rule))
integrand = ufl_utils.replace_coordinates(integral.integrand(), coordinates)
integrand = ufl_utils.split_coefficients(integrand, builder.coefficient_split)
quadrature_index = gem.Index(name='ip')
quadrature_indices.append(quadrature_index)
config = kernel_cfg.copy()
config.update(quadrature_rule=quad_rule, point_index=quadrature_index)
ir = fem.compile_ufl(integrand, interior_facet=interior_facet, **config)
if parameters["unroll_indexsum"]:
ir = opt.unroll_indexsum(ir, max_extent=parameters["unroll_indexsum"])
irs.append([(gem.IndexSum(expr, quadrature_index)
if quadrature_index in expr.free_indices
else expr)
for expr in ir])
# Sum the expressions that are part of the same restriction
ir = list(reduce(gem.Sum, e, gem.Zero()) for e in zip(*irs))
# Need optimised roots for COFFEE
ir = opt.remove_componenttensors(ir)
# Look for cell orientations in the IR
if builder.needs_cell_orientations(ir):
builder.require_cell_orientations()
impero_c = impero_utils.compile_gem(return_variables, ir,
tuple(quadrature_indices) + argument_indices,
remove_zeros=True)
# Generate COFFEE
index_names = [(index, index.name) for index in argument_indices]
if len(quadrature_indices) == 1:
index_names.append((quadrature_indices[0], 'ip'))
else:
for i, quadrature_index in enumerate(quadrature_indices):
index_names.append((quadrature_index, 'ip_%d' % i))
body = generate_coffee(impero_c, index_names, parameters["precision"], ir, argument_indices)
kernel_name = "%s_%s_integral_%s" % (prefix, integral_type, integral_data.subdomain_id)
return builder.construct_kernel(kernel_name, body)
