def compile_ufl(expression, interior_facet=False, **kwargs):
context = Context(**kwargs)
# Abs-simplification
expression = simplify_abs(expression)
# Collect modified terminals
modified_terminals = []
map_expr_dag(CollectModifiedTerminals(modified_terminals), expression)
# Collect maximal derivatives that needs tabulation
max_derivs = collections.defaultdict(int)
for mt in map(analyse_modified_terminal, modified_terminals):
if isinstance(mt.terminal, FormArgument):
ufl_element = mt.terminal.ufl_element()
max_derivs[ufl_element] = max(mt.local_derivatives, max_derivs[ufl_element])
# Collect tabulations for all components and derivatives
tabulation_manager = TabulationManager(context.points, context.integration_dim, context.entity_ids, context.epsilon)
for ufl_element, max_deriv in max_derivs.items():
if ufl_element.family() != 'Real':
tabulation_manager.tabulate(ufl_element, max_deriv)
if interior_facet:
expressions = []
for rs in itertools.product(("+", "-"), repeat=len(context.argument_indices)):
expressions.append(map_expr_dag(PickRestriction(*rs), expression))
else:
expressions = [expression]
# Translate UFL to GEM, lowering finite element specific nodes
translator = Translator(tabulation_manager, context)
return map_expr_dags(translator, expressions)
def to_reference_coordinates(ufl_coordinate_element):
# Set up UFL form
cell = ufl_coordinate_element.cell()
domain = ufl.Mesh(ufl_coordinate_element)
K = ufl.JacobianInverse(domain)
x = ufl.SpatialCoordinate(domain)
x0_element = ufl.VectorElement("Real", cell, 0)
x0 = ufl.Coefficient(ufl.FunctionSpace(domain, x0_element))
expr = ufl.dot(K, x - x0)
# Translation to GEM
C = ufl_utils.coordinate_coefficient(domain)
expr = ufl_utils.preprocess_expression(expr)
expr = ufl_utils.replace_coordinates(expr, C)
expr = ufl_utils.simplify_abs(expr)
builder = firedrake_interface.KernelBuilderBase()
builder._coefficient(C, "C")
builder._coefficient(x0, "x0")
dim = cell.topological_dimension()
point = gem.Variable('X', (dim, ))
context = tsfc.fem.GemPointContext(
interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
)
translator = tsfc.fem.Translator(context)
ir = map_expr_dag(translator, expr)
# Unroll result
ir = [gem.Indexed(ir, alpha) for alpha in numpy.ndindex(ir.shape)]
# Unroll IndexSums
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
ir = gem.optimise.unroll_indexsum(ir, predicate=predicate)
# Translate to COFFEE
ir = impero_utils.preprocess_gem(ir)
return_variable = gem.Variable('dX', (dim, ))
assignments = [(gem.Indexed(return_variable, (i, )), e)
for i, e in enumerate(ir)]
impero_c = impero_utils.compile_gem(assignments, ())
body = tsfc.coffee.generate(impero_c, {}, parameters["precision"])
body.open_scope = False
return body
def to_reference_coordinates(ufl_coordinate_element, parameters):
# Set up UFL form
cell = ufl_coordinate_element.cell()
domain = ufl.Mesh(ufl_coordinate_element)
K = ufl.JacobianInverse(domain)
x = ufl.SpatialCoordinate(domain)
x0_element = ufl.VectorElement("Real", cell, 0)
x0 = ufl.Coefficient(ufl.FunctionSpace(domain, x0_element))
expr = ufl.dot(K, x - x0)
# Translation to GEM
C = ufl.Coefficient(ufl.FunctionSpace(domain, ufl_coordinate_element))
expr = ufl_utils.preprocess_expression(expr)
expr = ufl_utils.simplify_abs(expr)
builder = firedrake_interface.KernelBuilderBase()
builder.domain_coordinate[domain] = C
builder._coefficient(C, "C")
builder._coefficient(x0, "x0")
dim = cell.topological_dimension()
point = gem.Variable('X', (dim,))
context = tsfc.fem.GemPointContext(
interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
)
translator = tsfc.fem.Translator(context)
ir = map_expr_dag(translator, expr)
# Unroll result
ir = [gem.Indexed(ir, alpha) for alpha in numpy.ndindex(ir.shape)]
# Unroll IndexSums
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
ir = gem.optimise.unroll_indexsum(ir, predicate=predicate)
# Translate to COFFEE
ir = impero_utils.preprocess_gem(ir)
return_variable = gem.Variable('dX', (dim,))
assignments = [(gem.Indexed(return_variable, (i,)), e)
for i, e in enumerate(ir)]
impero_c = impero_utils.compile_gem(assignments, ())
body = tsfc.coffee.generate(impero_c, {}, parameters["precision"])
body.open_scope = False
return body
def compile_ufl(expression, interior_facet=False, point_sum=False, **kwargs):
context = PointSetContext(**kwargs)
# Abs-simplification
expression = simplify_abs(expression)
if interior_facet:
expressions = []
for rs in itertools.product(("+", "-"), repeat=len(context.argument_multiindices)):
expressions.append(map_expr_dag(PickRestriction(*rs), expression))
else:
expressions = [expression]
# Translate UFL to GEM, lowering finite element specific nodes
result = map_expr_dags(context.translator, expressions)
if point_sum:
result = [gem.index_sum(expr, context.point_indices) for expr in result]
return result
