def form_info(form):
ufl_assert(isinstance(form, Form), "Expecting a Form.")
bf = extract_arguments(form)
cf = extract_coefficients(form)
ci = form.integrals(Measure.CELL)
ei = form.integrals(Measure.EXTERIOR_FACET)
ii = form.integrals(Measure.INTERIOR_FACET)
pi = form.integrals(Measure.POINT)
mi = form.integrals(Measure.MACRO_CELL)
s = "Form info:\n"
s += " rank: %d\n" % len(bf)
s += " num_coefficients: %d\n" % len(cf)
s += " num_cell_integrals: %d\n" % len(ci)
s += " num_exterior_facet_integrals: %d\n" % len(ei)
s += " num_interior_facet_integrals: %d\n" % len(ii)
s += " num_point_integrals: %d\n" % len(pi)
s += " num_macro_cell_integrals: %d\n" % len(mi)
for f in cf:
if f._name:
s += "\n"
s += " Coefficient %d is named '%s'" % (f._count, f._name)
s += "\n"
for itg in ci:
s += "\n"
s += integral_info(itg)
for itg in ei:
s += "\n"
s += integral_info(itg)
for itg in ii:
s += "\n"
s += integral_info(itg)
for itg in mi:
s += "\n"
s += integral_info(itg)
return s
def form_info(form):
ufl_assert(isinstance(form, Form), "Expecting a Form.")
bf = extract_arguments(form)
cf = extract_coefficients(form)
ci = form.integrals(Measure.CELL)
ei = form.integrals(Measure.EXTERIOR_FACET)
ii = form.integrals(Measure.INTERIOR_FACET)
pi = form.integrals(Measure.POINT)
mi = form.integrals(Measure.MACRO_CELL)
s = "Form info:\n"
s += " rank: %d\n" % len(bf)
s += " num_coefficients: %d\n" % len(cf)
s += " num_cell_integrals: %d\n" % len(ci)
s += " num_exterior_facet_integrals: %d\n" % len(ei)
s += " num_interior_facet_integrals: %d\n" % len(ii)
s += " num_point_integrals: %d\n" % len(pi)
s += " num_macro_cell_integrals: %d\n" % len(mi)
for f in cf:
if f._name:
s += "\n"
s += " Coefficient %d is named '%s'" % (f._count, f._name)
s += "\n"
for itg in ci:
s += "\n"
s += integral_info(itg)
for itg in ei:
s += "\n"
s += integral_info(itg)
for itg in ii:
s += "\n"
s += integral_info(itg)
for itg in mi:
s += "\n"
s += integral_info(itg)
return s
def compile_element(expression,
dual_space=None,
parameters=None,
name="evaluate"):
"""Generate code for point evaluations.
:arg expression: A UFL expression (may contain up to one coefficient, or one argument)
:arg dual_space: if the expression has an argument, should we also distribute residual data?
:returns: Some coffee AST
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
expression = tsfc.ufl_utils.preprocess_expression(expression)
# # Collect required coefficients
try:
arg, = extract_coefficients(expression)
argument_multiindices = ()
coefficient = True
if expression.ufl_shape:
tensor_indices = tuple(gem.Index() for s in expression.ufl_shape)
else:
tensor_indices = ()
except ValueError:
arg, = extract_arguments(expression)
finat_elem = create_element(arg.ufl_element())
argument_multiindices = (finat_elem.get_indices(), )
argument_multiindex, = argument_multiindices
value_shape = finat_elem.value_shape
if value_shape:
tensor_indices = argument_multiindex[-len(value_shape):]
else:
tensor_indices = ()
coefficient = False
# Replace coordinates (if any)
builder = firedrake_interface.KernelBuilderBase(scalar_type=ScalarType_c)
domain = expression.ufl_domain()
# Translate to GEM
cell = domain.ufl_cell()
dim = cell.topological_dimension()
point = gem.Variable('X', (dim, ))
point_arg = ast.Decl(ScalarType_c, ast.Symbol('X', rank=(dim, )))
config = dict(interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
argument_multiindices=argument_multiindices)
context = tsfc.fem.GemPointContext(**config)
# Abs-simplification
expression = tsfc.ufl_utils.simplify_abs(expression)
# Translate UFL -> GEM
if coefficient:
assert dual_space is None
f_arg = [builder._coefficient(arg, "f")]
else:
f_arg = []
translator = tsfc.fem.Translator(context)
result, = map_expr_dags(translator, [expression])
b_arg = []
if coefficient:
if expression.ufl_shape:
return_variable = gem.Indexed(
gem.Variable('R', expression.ufl_shape), tensor_indices)
result_arg = ast.Decl(ScalarType_c,
ast.Symbol('R', rank=expression.ufl_shape))
result = gem.Indexed(result, tensor_indices)
else:
return_variable = gem.Indexed(gem.Variable('R', (1, )), (0, ))
result_arg = ast.Decl(ScalarType_c, ast.Symbol('R', rank=(1, )))
else:
return_variable = gem.Indexed(
gem.Variable('R', finat_elem.index_shape), argument_multiindex)
result = gem.Indexed(result, tensor_indices)
if dual_space:
elem = create_element(dual_space.ufl_element())
if elem.value_shape:
var = gem.Indexed(gem.Variable("b", elem.value_shape),
tensor_indices)
b_arg = [
ast.Decl(ScalarType_c,
ast.Symbol("b", rank=elem.value_shape))
]
else:
var = gem.Indexed(gem.Variable("b", (1, )), (0, ))
b_arg = [ast.Decl(ScalarType_c, ast.Symbol("b", rank=(1, )))]
result = gem.Product(result, var)
result_arg = ast.Decl(ScalarType_c,
ast.Symbol('R', rank=finat_elem.index_shape))
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
result, = gem.optimise.unroll_indexsum([result], predicate=predicate)
# Translate GEM -> COFFEE
result, = gem.impero_utils.preprocess_gem([result])
impero_c = gem.impero_utils.compile_gem([(return_variable, result)],
tensor_indices)
body = generate_coffee(impero_c, {}, parameters["precision"], ScalarType_c)
# Build kernel tuple
kernel_code = builder.construct_kernel(
"pyop2_kernel_" + name, [result_arg] + b_arg + f_arg + [point_arg],
body)
return kernel_code
def compute_form_data(
form,
# Default arguments configured to behave the way old FFC expects it:
do_apply_function_pullbacks=False,
do_apply_integral_scaling=False,
do_apply_geometry_lowering=False,
preserve_geometry_types=(),
do_apply_default_restrictions=True,
do_apply_restrictions=True,
do_estimate_degrees=True,
):
# TODO: Move this to the constructor instead
self = FormData()
# --- Store untouched form for reference.
# The user of FormData may get original arguments,
# original coefficients, and form signature from this object.
# But be aware that the set of original coefficients are not
# the same as the ones used in the final UFC form.
# See 'reduced_coefficients' below.
self.original_form = form
# --- Pass form integrands through some symbolic manipulation
# Note: Default behaviour here will process form the way that is
# currently expected by vanilla FFC
# Lower abstractions for tensor-algebra types into index notation,
# reducing the number of operators later algorithms and form
# compilers need to handle
form = apply_algebra_lowering(form)
# Apply differentiation before function pullbacks, because for
# example coefficient derivatives are more complicated to derive
# after coefficients are rewritten, and in particular for
# user-defined coefficient relations it just gets too messy
form = apply_derivatives(form)
# --- Group form integrals
# TODO: Refactor this, it's rather opaque what this does
# TODO: Is self.original_form.ufl_domains() right here?
# It will matter when we start including 'num_domains' in ufc form.
form = group_form_integrals(form, self.original_form.ufl_domains())
# Estimate polynomial degree of integrands now, before applying
# any pullbacks and geometric lowering. Otherwise quad degrees
# blow up horrifically.
if do_estimate_degrees:
form = attach_estimated_degrees(form)
if do_apply_function_pullbacks:
# Rewrite coefficients and arguments in terms of their
# reference cell values with Piola transforms and symmetry
# transforms injected where needed.
# Decision: Not supporting grad(dolfin.Expression) without a
# Domain. Current dolfin works if Expression has a
# cell but this should be changed to a mesh.
form = apply_function_pullbacks(form)
# Scale integrals to reference cell frames
if do_apply_integral_scaling:
form = apply_integral_scaling(form)
# Apply default restriction to fully continuous terminals
if do_apply_default_restrictions:
form = apply_default_restrictions(form)
# Lower abstractions for geometric quantities into a smaller set
# of quantities, allowing the form compiler to deal with a smaller
# set of types and treating geometric quantities like any other
# expressions w.r.t. loop-invariant code motion etc.
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Apply differentiation again, because the algorithms above can
# generate new derivatives or rewrite expressions inside
# derivatives
if do_apply_function_pullbacks or do_apply_geometry_lowering:
form = apply_derivatives(form)
# Neverending story: apply_derivatives introduces new Jinvs,
# which needs more geometry lowering
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Lower derivatives that may have appeared
form = apply_derivatives(form)
# Propagate restrictions to terminals
if do_apply_restrictions:
form = apply_restrictions(form)
# --- Group integrals into IntegralData objects
# Most of the heavy lifting is done above in group_form_integrals.
self.integral_data = build_integral_data(form.integrals())
# --- Create replacements for arguments and coefficients
# Figure out which form coefficients each integral should enable
for itg_data in self.integral_data:
itg_coeffs = set()
# Get all coefficients in integrand
for itg in itg_data.integrals:
itg_coeffs.update(extract_coefficients(itg.integrand()))
# Store with IntegralData object
itg_data.integral_coefficients = itg_coeffs
# Figure out which coefficients from the original form are
# actually used in any integral (Differentiation may reduce the
# set of coefficients w.r.t. the original form)
reduced_coefficients_set = set()
for itg_data in self.integral_data:
reduced_coefficients_set.update(itg_data.integral_coefficients)
self.reduced_coefficients = sorted(reduced_coefficients_set,
key=lambda c: c.count())
self.num_coefficients = len(self.reduced_coefficients)
self.original_coefficient_positions = [
i for i, c in enumerate(self.original_form.coefficients())
if c in self.reduced_coefficients
]
# Store back into integral data which form coefficients are used
# by each integral
for itg_data in self.integral_data:
itg_data.enabled_coefficients = [
bool(coeff in itg_data.integral_coefficients)
for coeff in self.reduced_coefficients
]
# --- Collect some trivial data
# Get rank of form from argument list (assuming not a mixed arity form)
self.rank = len(self.original_form.arguments())
# Extract common geometric dimension (topological is not common!)
self.geometric_dimension = self.original_form.integrals()[0].ufl_domain(
).geometric_dimension()
# --- Build mapping from old incomplete element objects to new
# well defined elements. This is to support the Expression
# construct in dolfin which subclasses Coefficient but doesn't
# provide an element, and the Constant construct that doesn't
# provide the domain that a Coefficient is supposed to have. A
# future design iteration in UFL/UFC/FFC/DOLFIN may allow removal
# of this mapping with the introduction of UFL types for
# Expression-like functions that can be evaluated in quadrature
# points.
self.element_replace_map = _compute_element_mapping(self.original_form)
# Mappings from elements and coefficients that reside in form to
# objects with canonical numbering as well as completed cells and
# elements
renumbered_coefficients, function_replace_map = \
_build_coefficient_replace_map(self.reduced_coefficients,
self.element_replace_map)
self.function_replace_map = function_replace_map
# --- Store various lists of elements and sub elements (adds
# members to self)
_compute_form_data_elements(self, self.original_form.arguments(),
renumbered_coefficients,
self.original_form.ufl_domains())
# --- Store number of domains for integral types
# TODO: Group this by domain first. For now keep a backwards
# compatible data structure.
self.max_subdomain_ids = _compute_max_subdomain_ids(self.integral_data)
# --- Checks
_check_elements(self)
_check_facet_geometry(self.integral_data)
# TODO: This is a very expensive check... Replace with something
# faster!
preprocessed_form = reconstruct_form_from_integral_data(self.integral_data)
check_form_arity(
preprocessed_form,
self.original_form.arguments()) # Currently testing how fast this is
# TODO: This member is used by unit tests, change the tests to
# remove this!
self.preprocessed_form = preprocessed_form
return self
def compute_form_data(form,
# Default arguments configured to behave the way old FFC expects it:
do_apply_function_pullbacks=False,
do_apply_integral_scaling=False,
do_apply_geometry_lowering=False,
preserve_geometry_types=(),
do_apply_default_restrictions=True,
do_apply_restrictions=True,
do_estimate_degrees=True,
complex_mode=False,
):
# TODO: Move this to the constructor instead
self = FormData()
# --- Store untouched form for reference.
# The user of FormData may get original arguments,
# original coefficients, and form signature from this object.
# But be aware that the set of original coefficients are not
# the same as the ones used in the final UFC form.
# See 'reduced_coefficients' below.
self.original_form = form
# --- Pass form integrands through some symbolic manipulation
# Note: Default behaviour here will process form the way that is
# currently expected by vanilla FFC
# Check that the form does not try to compare complex quantities:
# if the quantites being compared are 'provably' real, wrap them
# with Real, otherwise throw an error.
if complex_mode:
form = do_comparison_check(form)
# Lower abstractions for tensor-algebra types into index notation,
# reducing the number of operators later algorithms and form
# compilers need to handle
form = apply_algebra_lowering(form)
# After lowering to index notation, remove any complex nodes that
# have been introduced but are not wanted when working in real mode,
# allowing for purely real forms to be written
if not complex_mode:
form = remove_complex_nodes(form)
# Apply differentiation before function pullbacks, because for
# example coefficient derivatives are more complicated to derive
# after coefficients are rewritten, and in particular for
# user-defined coefficient relations it just gets too messy
form = apply_derivatives(form)
# strip the coordinate derivatives away from the integral as they
# interfere with the integral grouping
(form, coordinate_derivatives) = strip_coordinate_derivatives(form)
# --- Group form integrals
# TODO: Refactor this, it's rather opaque what this does
# TODO: Is self.original_form.ufl_domains() right here?
# It will matter when we start including 'num_domains' in ufc form.
form = group_form_integrals(form, self.original_form.ufl_domains())
# attach coordinate derivatives again
form = attach_coordinate_derivatives(form, coordinate_derivatives)
# Estimate polynomial degree of integrands now, before applying
# any pullbacks and geometric lowering. Otherwise quad degrees
# blow up horrifically.
if do_estimate_degrees:
form = attach_estimated_degrees(form)
if do_apply_function_pullbacks:
# Rewrite coefficients and arguments in terms of their
# reference cell values with Piola transforms and symmetry
# transforms injected where needed.
# Decision: Not supporting grad(dolfin.Expression) without a
# Domain. Current dolfin works if Expression has a
# cell but this should be changed to a mesh.
form = apply_function_pullbacks(form)
# Scale integrals to reference cell frames
if do_apply_integral_scaling:
form = apply_integral_scaling(form)
# Apply default restriction to fully continuous terminals
if do_apply_default_restrictions:
form = apply_default_restrictions(form)
# Lower abstractions for geometric quantities into a smaller set
# of quantities, allowing the form compiler to deal with a smaller
# set of types and treating geometric quantities like any other
# expressions w.r.t. loop-invariant code motion etc.
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Apply differentiation again, because the algorithms above can
# generate new derivatives or rewrite expressions inside
# derivatives
if do_apply_function_pullbacks or do_apply_geometry_lowering:
form = apply_derivatives(form)
# Neverending story: apply_derivatives introduces new Jinvs,
# which needs more geometry lowering
if do_apply_geometry_lowering:
form = apply_geometry_lowering(form, preserve_geometry_types)
# Lower derivatives that may have appeared
form = apply_derivatives(form)
form = apply_coordinate_derivatives(form)
# Propagate restrictions to terminals
if do_apply_restrictions:
form = apply_restrictions(form)
# --- Group integrals into IntegralData objects
# Most of the heavy lifting is done above in group_form_integrals.
self.integral_data = build_integral_data(form.integrals())
# --- Create replacements for arguments and coefficients
# Figure out which form coefficients each integral should enable
for itg_data in self.integral_data:
itg_coeffs = set()
# Get all coefficients in integrand
for itg in itg_data.integrals:
itg_coeffs.update(extract_coefficients(itg.integrand()))
# Store with IntegralData object
itg_data.integral_coefficients = itg_coeffs
# Figure out which coefficients from the original form are
# actually used in any integral (Differentiation may reduce the
# set of coefficients w.r.t. the original form)
reduced_coefficients_set = set()
for itg_data in self.integral_data:
reduced_coefficients_set.update(itg_data.integral_coefficients)
self.reduced_coefficients = sorted(reduced_coefficients_set,
key=lambda c: c.count())
self.num_coefficients = len(self.reduced_coefficients)
self.original_coefficient_positions = [i for i, c in enumerate(self.original_form.coefficients())
if c in self.reduced_coefficients]
# Store back into integral data which form coefficients are used
# by each integral
for itg_data in self.integral_data:
itg_data.enabled_coefficients = [bool(coeff in itg_data.integral_coefficients)
for coeff in self.reduced_coefficients]
# --- Collect some trivial data
# Get rank of form from argument list (assuming not a mixed arity form)
self.rank = len(self.original_form.arguments())
# Extract common geometric dimension (topological is not common!)
self.geometric_dimension = self.original_form.integrals()[0].ufl_domain().geometric_dimension()
# --- Build mapping from old incomplete element objects to new
# well defined elements. This is to support the Expression
# construct in dolfin which subclasses Coefficient but doesn't
# provide an element, and the Constant construct that doesn't
# provide the domain that a Coefficient is supposed to have. A
# future design iteration in UFL/UFC/FFC/DOLFIN may allow removal
# of this mapping with the introduction of UFL types for
# Expression-like functions that can be evaluated in quadrature
# points.
self.element_replace_map = _compute_element_mapping(self.original_form)
# Mappings from elements and coefficients that reside in form to
# objects with canonical numbering as well as completed cells and
# elements
renumbered_coefficients, function_replace_map = \
_build_coefficient_replace_map(self.reduced_coefficients,
self.element_replace_map)
self.function_replace_map = function_replace_map
# --- Store various lists of elements and sub elements (adds
# members to self)
_compute_form_data_elements(self,
self.original_form.arguments(),
renumbered_coefficients,
self.original_form.ufl_domains())
# --- Store number of domains for integral types
# TODO: Group this by domain first. For now keep a backwards
# compatible data structure.
self.max_subdomain_ids = _compute_max_subdomain_ids(self.integral_data)
# --- Checks
_check_elements(self)
_check_facet_geometry(self.integral_data)
# TODO: This is a very expensive check... Replace with something
# faster!
preprocessed_form = reconstruct_form_from_integral_data(self.integral_data)
# If in real mode, remove complex nodes entirely.
if not complex_mode:
preprocessed_form = remove_complex_nodes(preprocessed_form)
check_form_arity(preprocessed_form, self.original_form.arguments(), complex_mode) # Currently testing how fast this is
# TODO: This member is used by unit tests, change the tests to
# remove this!
self.preprocessed_form = preprocessed_form
return self
def compile_element(expression, dual_space=None, parameters=None,
name="evaluate"):
"""Generate code for point evaluations.
:arg expression: A UFL expression (may contain up to one coefficient, or one argument)
:arg dual_space: if the expression has an argument, should we also distribute residual data?
:returns: Some coffee AST
"""
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
expression = tsfc.ufl_utils.preprocess_expression(expression)
# # Collect required coefficients
try:
arg, = extract_coefficients(expression)
argument_multiindices = ()
coefficient = True
if expression.ufl_shape:
tensor_indices = tuple(gem.Index() for s in expression.ufl_shape)
else:
tensor_indices = ()
except ValueError:
arg, = extract_arguments(expression)
finat_elem = create_element(arg.ufl_element())
argument_multiindices = (finat_elem.get_indices(), )
argument_multiindex, = argument_multiindices
value_shape = finat_elem.value_shape
if value_shape:
tensor_indices = argument_multiindex[-len(value_shape):]
else:
tensor_indices = ()
coefficient = False
# Replace coordinates (if any)
builder = firedrake_interface.KernelBuilderBase()
domain = expression.ufl_domain()
# Translate to GEM
cell = domain.ufl_cell()
dim = cell.topological_dimension()
point = gem.Variable('X', (dim,))
point_arg = ast.Decl(SCALAR_TYPE, ast.Symbol('X', rank=(dim,)))
config = dict(interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
argument_multiindices=argument_multiindices)
context = tsfc.fem.GemPointContext(**config)
# Abs-simplification
expression = tsfc.ufl_utils.simplify_abs(expression)
# Translate UFL -> GEM
if coefficient:
assert dual_space is None
f_arg = [builder._coefficient(arg, "f")]
else:
f_arg = []
translator = tsfc.fem.Translator(context)
result, = map_expr_dags(translator, [expression])
b_arg = []
if coefficient:
if expression.ufl_shape:
return_variable = gem.Indexed(gem.Variable('R', expression.ufl_shape), tensor_indices)
result_arg = ast.Decl(SCALAR_TYPE, ast.Symbol('R', rank=expression.ufl_shape))
result = gem.Indexed(result, tensor_indices)
else:
return_variable = gem.Indexed(gem.Variable('R', (1,)), (0,))
result_arg = ast.Decl(SCALAR_TYPE, ast.Symbol('R', rank=(1,)))
else:
return_variable = gem.Indexed(gem.Variable('R', finat_elem.index_shape), argument_multiindex)
result = gem.Indexed(result, tensor_indices)
if dual_space:
elem = create_element(dual_space.ufl_element())
if elem.value_shape:
var = gem.Indexed(gem.Variable("b", elem.value_shape),
tensor_indices)
b_arg = [ast.Decl(SCALAR_TYPE, ast.Symbol("b", rank=elem.value_shape))]
else:
var = gem.Indexed(gem.Variable("b", (1, )), (0, ))
b_arg = [ast.Decl(SCALAR_TYPE, ast.Symbol("b", rank=(1, )))]
result = gem.Product(result, var)
result_arg = ast.Decl(SCALAR_TYPE, ast.Symbol('R', rank=finat_elem.index_shape))
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
result, = gem.optimise.unroll_indexsum([result], predicate=predicate)
# Translate GEM -> COFFEE
result, = gem.impero_utils.preprocess_gem([result])
impero_c = gem.impero_utils.compile_gem([(return_variable, result)], tensor_indices)
body = generate_coffee(impero_c, {}, parameters["precision"])
# Build kernel tuple
kernel_code = builder.construct_kernel("pyop2_kernel_" + name, [result_arg] + b_arg + f_arg + [point_arg], body)
return kernel_code