def accumulate_integrals(itg_data, quadrature_rule_sizes):
"""Group and accumulate integrals according to the number of quadrature points in their rules."""
if not itg_data.integrals:
return {}
# Group integrands by quadrature rule
sorted_integrands = collections.defaultdict(list)
if itg_data.integral_type in custom_integral_types:
# Should only be one size here, ignoring irrelevant metadata and parameters
num_points, = quadrature_rule_sizes.values()
for integral in itg_data.integrals:
sorted_integrands[num_points].append(integral.integrand())
else:
default_scheme = itg_data.metadata["quadrature_degree"]
default_degree = itg_data.metadata["quadrature_rule"]
for integral in itg_data.integrals:
md = integral.metadata() or {}
scheme = md.get("quadrature_rule", default_scheme)
degree = md.get("quadrature_degree", default_degree)
rule = (scheme, degree)
num_points = quadrature_rule_sizes[rule]
sorted_integrands[num_points].append(integral.integrand())
# Accumulate integrands in a canonical ordering defined by UFL
sorted_integrals = {
num_points:
Integral(sorted_expr_sum(integrands), itg_data.integral_type,
itg_data.domain, itg_data.subdomain_id, {}, None)
for num_points, integrands in list(sorted_integrands.items())
}
return sorted_integrals
def _sort_integrals(integrals, metadata, form_data):
"""Sort integrals according to the number of quadrature points needed per axis.
Only consider those integrals defined on the given domain."""
# Get domain type and id
if integrals:
domain_type = integrals[0].domain_type()
domain_id = integrals[0].domain_id()
ffc_assert(all(domain_type == itg.domain_type() for itg in integrals),
"Expecting only integrals on the same subdomain.")
ffc_assert(all(domain_id == itg.domain_id() for itg in integrals),
"Expecting only integrals on the same subdomain.")
sorted_integrands = {}
# TODO: We might want to take into account that a form like
# a = f*g*h*v*u*dx(0, quadrature_order=4) + f*v*u*dx(0, quadrature_order=2),
# although it involves two integrals of different order, will most
# likely be integrated faster if one does
# a = (f*g*h + f)*v*u*dx(0, quadrature_order=4)
# It will of course only work for integrals defined on the same
# subdomain and representation.
for integral in integrals:
# Get default degree and rule.
degree = metadata["quadrature_degree"]
rule = metadata["quadrature_rule"]
# Override if specified in integral metadata
integral_compiler_data = integral.compiler_data()
if not integral_compiler_data is None:
if "quadrature_degree" in integral_compiler_data:
degree = integral_compiler_data["quadrature_degree"]
if "quadrature_rule" in integral_compiler_data:
rule = integral_compiler_data["quadrature_rule"]
# Add integrand to dictionary according to degree and rule.
if not (degree, rule) in sorted_integrands:
sorted_integrands[(degree, rule)] = [integral.integrand()]
else:
sorted_integrands[(degree, rule)] += [integral.integrand()]
# Create integrals from accumulated integrands.
sorted_integrals = {}
for key, integrands in sorted_integrands.items():
# Summing integrands in a canonical ordering defined by UFL
integrand = sorted_expr_sum(integrands)
sorted_integrals[key] = Integral(integrand, domain_type, domain_id, {},
None)
return sorted_integrals
def _sort_integrals(integrals, metadata, form_data):
"""Sort integrals according to the number of quadrature points needed per axis.
Only consider those integrals defined on the given domain."""
# Get domain type and id
if integrals:
domain_type = integrals[0].domain_type()
domain_id = integrals[0].domain_id()
ffc_assert(all(domain_type == itg.domain_type() for itg in integrals),
"Expecting only integrals on the same subdomain.")
ffc_assert(all(domain_id == itg.domain_id() for itg in integrals),
"Expecting only integrals on the same subdomain.")
sorted_integrands = {}
# TODO: We might want to take into account that a form like
# a = f*g*h*v*u*dx(0, quadrature_order=4) + f*v*u*dx(0, quadrature_order=2),
# although it involves two integrals of different order, will most
# likely be integrated faster if one does
# a = (f*g*h + f)*v*u*dx(0, quadrature_order=4)
# It will of course only work for integrals defined on the same
# subdomain and representation.
for integral in integrals:
# Get default degree and rule.
degree = metadata["quadrature_degree"]
rule = metadata["quadrature_rule"]
# Override if specified in integral metadata
integral_compiler_data = integral.compiler_data()
if not integral_compiler_data is None:
if "quadrature_degree" in integral_compiler_data:
degree = integral_compiler_data["quadrature_degree"]
if "quadrature_rule" in integral_compiler_data:
rule = integral_compiler_data["quadrature_rule"]
# Add integrand to dictionary according to degree and rule.
if not (degree, rule) in sorted_integrands:
sorted_integrands[(degree, rule)] = [integral.integrand()]
else:
sorted_integrands[(degree, rule)] += [integral.integrand()]
# Create integrals from accumulated integrands.
sorted_integrals = {}
for key, integrands in sorted_integrands.items():
# Summing integrands in a canonical ordering defined by UFL
integrand = sorted_expr_sum(integrands)
sorted_integrals[key] = Integral(integrand, domain_type, domain_id, {}, None)
return sorted_integrals
def sort_integrals(integrals, default_quadrature_degree,
default_quadrature_rule):
"""Sort and accumulate integrals according to the number of quadrature points needed per axis.
All integrals should be over the same (sub)domain.
"""
if not integrals:
return {}
# Get domain properties from first integral, assuming all are the same
integral_type = integrals[0].integral_type()
subdomain_id = integrals[0].subdomain_id()
domain_label = integrals[0].domain().label()
domain = integrals[0].domain() # FIXME: Is this safe? Get as input?
ffc_assert(all(integral_type == itg.integral_type() for itg in integrals),
"Expecting only integrals of the same type.")
ffc_assert(all(domain_label == itg.domain().label() for itg in integrals),
"Expecting only integrals on the same domain.")
ffc_assert(all(subdomain_id == itg.subdomain_id() for itg in integrals),
"Expecting only integrals on the same subdomain.")
sorted_integrands = collections.defaultdict(list)
for integral in integrals:
# Override default degree and rule if specified in integral metadata
integral_metadata = integral.metadata() or {}
degree = integral_metadata.get("quadrature_degree",
default_quadrature_degree)
rule = integral_metadata.get("quadrature_rule",
default_quadrature_rule)
assert isinstance(degree, int)
# Add integrand to dictionary according to degree and rule.
key = (degree, rule)
sorted_integrands[key].append(integral.integrand())
# Create integrals from accumulated integrands.
sorted_integrals = {}
for key, integrands in list(sorted_integrands.items()):
# Summing integrands in a canonical ordering defined by UFL
integrand = sorted_expr_sum(integrands)
sorted_integrals[key] = Integral(integrand, integral_type, domain,
subdomain_id, {}, None)
return sorted_integrals
def sort_integrals(integrals, default_scheme, default_degree):
"""Sort and accumulate integrals according to the number of quadrature
points needed per axis.
All integrals should be over the same (sub)domain.
"""
if not integrals:
return {}
# Get domain properties from first integral, assuming all are the
# same
integral_type = integrals[0].integral_type()
subdomain_id = integrals[0].subdomain_id()
domain = integrals[0].ufl_domain()
ffc_assert(all(integral_type == itg.integral_type() for itg in integrals),
"Expecting only integrals of the same type.")
ffc_assert(all(domain == itg.ufl_domain() for itg in integrals),
"Expecting only integrals on the same domain.")
ffc_assert(all(subdomain_id == itg.subdomain_id() for itg in integrals),
"Expecting only integrals on the same subdomain.")
sorted_integrands = collections.defaultdict(list)
for integral in integrals:
# Override default degree and rule if specified in integral
# metadata
integral_metadata = integral.metadata() or {}
degree = integral_metadata.get("quadrature_degree", default_degree)
scheme = integral_metadata.get("quadrature_rule", default_scheme)
assert isinstance(degree, int)
# Add integrand to dictionary according to degree and scheme.
rule = (scheme, degree)
sorted_integrands[rule].append(integral.integrand())
# Create integrals from accumulated integrands.
sorted_integrals = {}
for rule, integrands in list(sorted_integrands.items()):
# Summing integrands in a canonical ordering defined by UFL
integrand = sorted_expr_sum(integrands)
sorted_integrals[rule] = Integral(integrand, integral_type, domain,
subdomain_id, {}, None)
return sorted_integrals
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("Computing IR for integral in integral group {}".format(
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(),
"needs_oriented": form_needs_oriented_jacobian(form_data),
"enabled_coefficients": itg_data.enabled_coefficients,
"cell_shape": cellname
}
# Get element space dimensions
unique_elements = element_numbers.keys()
ir["element_dimensions"] = {
ufl_element: create_element(ufl_element).space_dimension()
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 FIAT?
#
# 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=numpy.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