def test_expressions():
x = gem.Variable("x", (3, 4))
y = gem.Variable("y", (4, ))
i, j = gem.indices(2)
xij = x[i, j]
yj = y[j]
assert xij == gem.Indexed(x, (i, j))
assert yj == gem.Indexed(y, (j, ))
assert xij + yj == gem.Sum(xij, yj)
assert xij * yj == gem.Product(xij, yj)
assert xij - yj == gem.Sum(xij, gem.Product(gem.Literal(-1), yj))
assert xij / yj == gem.Division(xij, yj)
assert xij + 1 == gem.Sum(xij, gem.Literal(1))
assert 1 + xij == gem.Sum(gem.Literal(1), xij)
assert (xij + y).shape == (4, )
assert (x @ y).shape == (3, )
assert x.T.shape == (4, 3)
with pytest.raises(ValueError):
xij.T @ y
with pytest.raises(ValueError):
xij + "foo"
def _entity_support_dofs(self):
esd = {}
for entity_dim in self.cell.sub_entities.keys():
beta = self.get_indices()
zeta = self.get_value_indices()
entity_cell = self.cell.construct_subelement(entity_dim)
quad = make_quadrature(entity_cell,
(2 * numpy.array(self.degree)).tolist())
eps = 1.e-8 # Is this a safe value?
result = {}
for f in self.entity_dofs()[entity_dim].keys():
# Tabulate basis functions on the facet
vals, = self.basis_evaluation(0,
quad.point_set,
entity=(entity_dim, f)).values()
# Integrate the square of the basis functions on the facet.
ints = gem.IndexSum(
gem.Product(
gem.IndexSum(
gem.Product(gem.Indexed(vals, beta + zeta),
gem.Indexed(vals, beta + zeta)), zeta),
quad.weight_expression), quad.point_set.indices)
evaluation, = evaluate([gem.ComponentTensor(ints, beta)])
ints = evaluation.arr.flatten()
assert evaluation.fids == ()
result[f] = [dof for dof, i in enumerate(ints) if i > eps]
esd[entity_dim] = result
return esd
def compile_to_gem(expr, translator):
"""Compile a single pointwise expression to GEM.
:arg expr: The expression to compile.
:arg translator: a :class:`Translator` instance.
:returns: A (lvalue, rvalue) pair of preprocessed GEM."""
if not isinstance(expr, Assign):
raise ValueError(
f"Don't know how to assign expression of type {type(expr)}")
spaces = tuple(c.function_space() for c in expr.coefficients)
if any(
type(s.ufl_element()) is ufl.MixedElement for s in spaces
if s is not None):
raise ValueError("Not expecting a mixed space at this point, "
"did you forget to index a function with .sub(...)?")
if len(set(s.ufl_element() for s in spaces if s is not None)) != 1:
raise ValueError("All coefficients must be defined on the same space")
lvalue = expr.lvalue
rvalue = expr.rvalue
broadcast = all(
isinstance(c, firedrake.Constant)
for c in expr.rcoefficients) and rvalue.ufl_shape == ()
if not broadcast and lvalue.ufl_shape != rvalue.ufl_shape:
try:
rvalue = reshape(rvalue, lvalue.ufl_shape)
except ValueError:
raise ValueError(
"Mismatching shapes between lvalue and rvalue in pointwise assignment"
)
rvalue, = map_expr_dags(LowerCompoundAlgebra(), [rvalue])
try:
lvalue, rvalue = map_expr_dags(translator, [lvalue, rvalue])
except (AssertionError, ValueError):
raise ValueError("Mismatching shapes in pointwise assignment. "
"For intrinsically vector-/tensor-valued spaces make "
"sure you're not using shaped Constants or literals.")
indices = gem.indices(len(lvalue.shape))
if not broadcast:
if rvalue.shape != lvalue.shape:
raise ValueError(
"Mismatching shapes in pointwise assignment. "
"For intrinsically vector-/tensor-valued spaces make "
"sure you're not using shaped Constants or literals.")
rvalue = gem.Indexed(rvalue, indices)
lvalue = gem.Indexed(lvalue, indices)
if isinstance(expr, IAdd):
rvalue = gem.Sum(lvalue, rvalue)
elif isinstance(expr, ISub):
rvalue = gem.Sum(lvalue, gem.Product(gem.Literal(-1), rvalue))
elif isinstance(expr, IMul):
rvalue = gem.Product(lvalue, rvalue)
elif isinstance(expr, IDiv):
rvalue = gem.Division(lvalue, rvalue)
return preprocess_gem([lvalue, rvalue])
def basis_evaluation(self, order, ps, entity=None):
r"""Produce the recipe for basis function evaluation at a set of points :math:`q`:
.. math::
\boldsymbol\phi_{(\gamma \epsilon) (i \alpha \beta) q} = \delta_{\alpha \gamma}\delta{\beta \epsilon}\phi_{i q}
\nabla\boldsymbol\phi_{(\epsilon \gamma \zeta) (i \alpha \beta) q} = \delta_{\alpha \epsilon} \deta{\beta \gamma}\nabla\phi_{\zeta i q}
"""
# Old basis function and value indices
scalar_i = self._base_element.get_indices()
scalar_vi = self._base_element.get_value_indices()
# New basis function and value indices
tensor_i = tuple(gem.Index(extent=d) for d in self._shape)
tensor_vi = tuple(gem.Index(extent=d) for d in self._shape)
# Couple new basis function and value indices
deltas = reduce(gem.Product,
(gem.Delta(j, k) for j, k in zip(tensor_i, tensor_vi)))
scalar_result = self._base_element.basis_evaluation(order, ps, entity)
result = {}
for alpha, expr in iteritems(scalar_result):
result[alpha] = gem.ComponentTensor(
gem.Product(deltas, gem.Indexed(expr, scalar_i + scalar_vi)),
scalar_i + tensor_i + scalar_vi + tensor_vi)
return result
def translate_coefficient(terminal, mt, ctx):
vec = ctx.coefficient(terminal, mt.restriction)
if terminal.ufl_element().family() == 'Real':
assert mt.local_derivatives == 0
return vec
element = ctx.create_element(terminal.ufl_element())
# Collect FInAT tabulation for all entities
per_derivative = collections.defaultdict(list)
for entity_id in ctx.entity_ids:
finat_dict = ctx.basis_evaluation(element, mt.local_derivatives, entity_id)
for alpha, table in finat_dict.items():
# Filter out irrelevant derivatives
if sum(alpha) == mt.local_derivatives:
# A numerical hack that FFC used to apply on FIAT
# tables still lives on after ditching FFC and
# switching to FInAT.
table = ffc_rounding(table, ctx.epsilon)
per_derivative[alpha].append(table)
# Merge entity tabulations for each derivative
if len(ctx.entity_ids) == 1:
def take_singleton(xs):
x, = xs # asserts singleton
return x
per_derivative = {alpha: take_singleton(tables)
for alpha, tables in per_derivative.items()}
else:
f = ctx.entity_number(mt.restriction)
per_derivative = {alpha: gem.select_expression(tables, f)
for alpha, tables in per_derivative.items()}
# Coefficient evaluation
ctx.index_cache.setdefault(terminal.ufl_element(), element.get_indices())
beta = ctx.index_cache[terminal.ufl_element()]
zeta = element.get_value_indices()
vec_beta, = gem.optimise.remove_componenttensors([gem.Indexed(vec, beta)])
value_dict = {}
for alpha, table in per_derivative.items():
table_qi = gem.Indexed(table, beta + zeta)
summands = []
for var, expr in unconcatenate([(vec_beta, table_qi)], ctx.index_cache):
value = gem.IndexSum(gem.Product(expr, var), var.index_ordering())
summands.append(gem.optimise.contraction(value))
optimised_value = gem.optimise.make_sum(summands)
value_dict[alpha] = gem.ComponentTensor(optimised_value, zeta)
# Change from FIAT to UFL arrangement
result = fiat_to_ufl(value_dict, mt.local_derivatives)
assert result.shape == mt.expr.ufl_shape
assert set(result.free_indices) <= set(ctx.point_indices)
# Detect Jacobian of affine cells
if not result.free_indices and all(numpy.count_nonzero(node.array) <= 2
for node in traversal((result,))
if isinstance(node, gem.Literal)):
result = gem.optimise.aggressive_unroll(result)
return result
def _tensorise(self, scalar_evaluation):
# Old basis function and value indices
scalar_i = self._base_element.get_indices()
scalar_vi = self._base_element.get_value_indices()
# New basis function and value indices
tensor_i = tuple(gem.Index(extent=d) for d in self._shape)
tensor_vi = tuple(gem.Index(extent=d) for d in self._shape)
# Couple new basis function and value indices
deltas = reduce(gem.Product, (gem.Delta(j, k)
for j, k in zip(tensor_i, tensor_vi)))
if self._transpose:
index_ordering = tensor_i + scalar_i + tensor_vi + scalar_vi
else:
index_ordering = scalar_i + tensor_i + tensor_vi + scalar_vi
result = {}
for alpha, expr in scalar_evaluation.items():
result[alpha] = gem.ComponentTensor(
gem.Product(deltas, gem.Indexed(expr, scalar_i + scalar_vi)),
index_ordering
)
return result
def test_refactorise():
f = gem.Variable('f', (3,))
u = gem.Variable('u', (3,))
v = gem.Variable('v', ())
i = gem.Index()
f_i = gem.Indexed(f, (i,))
u_i = gem.Indexed(u, (i,))
def classify(atomics_set, expression):
if expression in atomics_set:
return ATOMIC
for node in traversal([expression]):
if node in atomics_set:
return COMPOUND
return OTHER
classifier = partial(classify, {u_i, v})
# \sum_i 5*(2*u_i + -1*v)*(u_i + v*f)
expr = gem.IndexSum(
gem.Product(
gem.Literal(5),
gem.Product(
gem.Sum(gem.Product(gem.Literal(2), u_i),
gem.Product(gem.Literal(-1), v)),
gem.Sum(u_i, gem.Product(v, f_i))
)
),
(i,)
)
expected = [
Monomial((i,),
(u_i, u_i),
gem.Literal(10)),
Monomial((i,),
(u_i, v),
gem.Product(gem.Literal(5),
gem.Sum(gem.Product(f_i, gem.Literal(2)),
gem.Literal(-1)))),
Monomial((),
(v, v),
gem.Product(gem.Literal(5),
gem.IndexSum(gem.Product(f_i, gem.Literal(-1)),
(i,)))),
]
actual, = collect_monomials([expr], classifier)
assert expected == list(actual)
def point_evaluation_ciarlet(fiat_element, order, refcoords, entity):
# Coordinates on the reference entity (SymPy)
esd, = refcoords.shape
Xi = sp.symbols('X Y Z')[:esd]
# Coordinates on the reference cell
cell = fiat_element.get_reference_element()
X = cell.get_entity_transform(*entity)(Xi)
# Evaluate expansion set at SymPy point
poly_set = fiat_element.get_nodal_basis()
degree = poly_set.get_embedded_degree()
base_values = poly_set.get_expansion_set().tabulate(degree, [X])
m = len(base_values)
assert base_values.shape == (m, 1)
base_values_sympy = np.array(list(base_values.flat))
# Find constant polynomials
def is_const(expr):
try:
float(expr)
return True
except TypeError:
return False
const_mask = np.array(list(map(is_const, base_values_sympy)))
# Convert SymPy expression to GEM
mapper = gem.node.Memoizer(sympy2gem)
mapper.bindings = {
s: gem.Indexed(refcoords, (i, ))
for i, s in enumerate(Xi)
}
base_values = gem.ListTensor(list(map(mapper, base_values.flat)))
# Populate result dict, creating precomputed coefficient
# matrices for each derivative tuple.
result = {}
for i in range(order + 1):
for alpha in mis(cell.get_spatial_dimension(), i):
D = form_matrix_product(poly_set.get_dmats(), alpha)
table = np.dot(poly_set.get_coeffs(), np.transpose(D))
assert table.shape[-1] == m
zerocols = np.isclose(
abs(table).max(axis=tuple(range(table.ndim - 1))), 0.0)
if all(np.logical_or(const_mask, zerocols)):
# Casting is safe by assertion of is_const
vals = base_values_sympy[const_mask].astype(np.float64)
result[alpha] = gem.Literal(table[..., const_mask].dot(vals))
else:
beta = tuple(gem.Index() for s in table.shape[:-1])
k = gem.Index()
result[alpha] = gem.ComponentTensor(
gem.IndexSum(
gem.Product(
gem.Indexed(gem.Literal(table), beta + (k, )),
gem.Indexed(base_values, (k, ))), (k, )), beta)
return result
def select_hdiv_transformer(element):
# Assume: something x interval
assert len(element.factors) == 2
assert element.factors[1].cell.get_shape() == LINE
# Globally consistent edge orientations of the reference
# quadrilateral: rightward horizontally, upward vertically.
# Their rotation by 90 degrees anticlockwise is interpreted as the
# positive direction for normal vectors.
ks = tuple(fe.formdegree for fe in element.factors)
if ks == (0, 1):
# Make the scalar value the leftward-pointing normal on the
# y-aligned edges.
return lambda v: [gem.Product(gem.Literal(-1), v), gem.Zero()]
elif ks == (1, 0):
# Make the scalar value the upward-pointing normal on the
# x-aligned edges.
return lambda v: [gem.Zero(), v]
elif ks == (2, 0):
# Same for 3D, so z-plane.
return lambda v: [gem.Zero(), gem.Zero(), v]
elif ks == (1, 1):
if element.mapping == "contravariant piola":
# Pad the 2-vector normal on the "base" cell into a
# 3-vector, maintaining direction.
return lambda v: [
gem.Indexed(v, (0, )),
gem.Indexed(v, (1, )),
gem.Zero()
]
elif element.mapping == "covariant piola":
# Rotate the 2-vector tangential component on the "base"
# cell 90 degrees anticlockwise into a 3-vector and pad.
return lambda v: [
gem.Indexed(v, (1, )),
gem.Product(gem.Literal(-1), gem.Indexed(v, (0, ))),
gem.Zero()
]
else:
assert False, "Unexpected original mapping!"
else:
assert False, "Unexpected form degree combination!"
def entity_support_dofs(elem, entity_dim):
"""Return the map of entity id to the degrees of freedom for which
the corresponding basis functions take non-zero values.
:arg elem: FInAT finite element
:arg entity_dim: Dimension of the cell subentity.
"""
if not hasattr(elem, "_entity_support_dofs"):
elem._entity_support_dofs = {}
cache = elem._entity_support_dofs
try:
return cache[entity_dim]
except KeyError:
pass
beta = elem.get_indices()
zeta = elem.get_value_indices()
entity_cell = elem.cell.construct_subelement(entity_dim)
quad = make_quadrature(entity_cell,
(2 * numpy.array(elem.degree)).tolist())
eps = 1.e-8 # Is this a safe value?
result = {}
for f in elem.entity_dofs()[entity_dim].keys():
# Tabulate basis functions on the facet
vals, = itervalues(
elem.basis_evaluation(0, quad.point_set, entity=(entity_dim, f)))
# Integrate the square of the basis functions on the facet.
ints = gem.IndexSum(
gem.Product(
gem.IndexSum(
gem.Product(gem.Indexed(vals, beta + zeta),
gem.Indexed(vals, beta + zeta)), zeta),
quad.weight_expression), quad.point_set.indices)
ints = aggressive_unroll(gem.ComponentTensor(ints,
beta)).array.flatten()
result[f] = [dof for dof, i in enumerate(ints) if i > eps]
cache[entity_dim] = result
return result
def test_pickle_gem(protocol):
f = gem.VariableIndex(gem.Indexed(gem.Variable('facet', (2, )), (1, )))
q = gem.Index()
r = gem.Index()
_1 = gem.Indexed(gem.Literal(numpy.random.rand(3, 6, 8)), (f, q, r))
_2 = gem.Indexed(
gem.view(gem.Variable('w', (None, None)), slice(8), slice(1)), (r, 0))
expr = gem.ComponentTensor(gem.IndexSum(gem.Product(_1, _2), (r, )), (q, ))
unpickled = pickle.loads(pickle.dumps(expr, protocol))
assert repr(expr) == repr(unpickled)
def translate_cell_edge_vectors(terminal, mt, ctx):
# WARNING: Assumes straight edges!
coords = CellVertices(terminal.ufl_domain())
ufl_expr = construct_modified_terminal(mt, coords)
cell_vertices = ctx.translator(ufl_expr)
e = gem.Index()
c = gem.Index()
expr = gem.ListTensor([
gem.Sum(
gem.Indexed(cell_vertices, (u, c)),
gem.Product(gem.Literal(-1), gem.Indexed(cell_vertices, (v, c))))
for _, (u, v) in sorted(ctx.fiat_cell.get_topology()[1].items())
])
return gem.ComponentTensor(gem.Indexed(expr, (e, )), (e, c))
def Integrals(expressions, quadrature_multiindex, argument_multiindices,
parameters):
# Concatenate
expressions = concatenate(expressions)
# Unroll
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
expressions = unroll_indexsum(expressions, predicate=predicate)
# Refactorise
def classify(quadrature_indices, expression):
if not quadrature_indices.intersection(expression.free_indices):
return OTHER
elif isinstance(expression, gem.Indexed) and isinstance(
expression.children[0], gem.Literal):
return ATOMIC
else:
return COMPOUND
classifier = partial(classify, set(quadrature_multiindex))
result = []
for expr, monomial_sum in zip(expressions,
collect_monomials(expressions, classifier)):
# Select quadrature indices that are present
quadrature_indices = set(index for index in quadrature_multiindex
if index in expr.free_indices)
products = []
for sum_indices, factors, rest in monomial_sum:
# Collapse quadrature literals for each monomial
if factors or quadrature_indices:
replacement = einsum(remove_componenttensors(factors),
quadrature_indices)
else:
replacement = gem.Literal(1)
# Rebuild expression
products.append(
gem.IndexSum(gem.Product(replacement, rest), sum_indices))
result.append(reduce(gem.Sum, products, gem.Zero()))
return result
def select_hcurl_transformer(element):
# Assume: something x interval
assert len(element.factors) == 2
assert element.factors[1].cell.get_shape() == LINE
# Globally consistent edge orientations of the reference
# quadrilateral: rightward horizontally, upward vertically.
# Tangential vectors interpret these as the positive direction.
dim = element.cell.get_spatial_dimension()
ks = tuple(fe.formdegree for fe in element.factors)
if element.mapping == "affine":
if ks == (1, 0):
# Can only be 2D. Make the scalar value the
# rightward-pointing tangential on the x-aligned edges.
return lambda v: [v, gem.Zero()]
elif ks == (0, 1):
# Can be any spatial dimension. Make the scalar value the
# upward-pointing tangential.
return lambda v: [gem.Zero()] * (dim - 1) + [v]
else:
assert False
elif element.mapping == "covariant piola":
# Second factor must be continuous interval. Just padding.
return lambda v: [
gem.Indexed(v, (0, )),
gem.Indexed(v, (1, )),
gem.Zero()
]
elif element.mapping == "contravariant piola":
# Second factor must be continuous interval. Rotate the
# 2-vector tangential component on the "base" cell 90 degrees
# clockwise into a 3-vector and pad.
return lambda v: [
gem.Product(gem.Literal(-1), gem.Indexed(v, (1, ))),
gem.Indexed(v, (0, )),
gem.Zero()
]
else:
assert False, "Unexpected original mapping!"
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 dg_injection_kernel(Vf, Vc, ncell):
from firedrake import Tensor, AssembledVector, TestFunction, TrialFunction
from firedrake.slate.slac import compile_expression
macro_builder = MacroKernelBuilder(ScalarType_c, ncell)
f = ufl.Coefficient(Vf)
macro_builder.set_coefficients([f])
macro_builder.set_coordinates(Vf.mesh())
Vfe = create_element(Vf.ufl_element())
macro_quadrature_rule = make_quadrature(
Vfe.cell, estimate_total_polynomial_degree(ufl.inner(f, f)))
index_cache = {}
parameters = default_parameters()
integration_dim, entity_ids = lower_integral_type(Vfe.cell, "cell")
macro_cfg = dict(interface=macro_builder,
ufl_cell=Vf.ufl_cell(),
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
index_cache=index_cache,
quadrature_rule=macro_quadrature_rule)
fexpr, = fem.compile_ufl(f, **macro_cfg)
X = ufl.SpatialCoordinate(Vf.mesh())
C_a, = fem.compile_ufl(X, **macro_cfg)
detJ = ufl_utils.preprocess_expression(
abs(ufl.JacobianDeterminant(f.ufl_domain())))
macro_detJ, = fem.compile_ufl(detJ, **macro_cfg)
Vce = create_element(Vc.ufl_element())
coarse_builder = firedrake_interface.KernelBuilder("cell", "otherwise", 0,
ScalarType_c)
coarse_builder.set_coordinates(Vc.mesh())
argument_multiindices = (Vce.get_indices(), )
argument_multiindex, = argument_multiindices
return_variable, = coarse_builder.set_arguments((ufl.TestFunction(Vc), ),
argument_multiindices)
integration_dim, entity_ids = lower_integral_type(Vce.cell, "cell")
# Midpoint quadrature for jacobian on coarse cell.
quadrature_rule = make_quadrature(Vce.cell, 0)
coarse_cfg = dict(interface=coarse_builder,
ufl_cell=Vc.ufl_cell(),
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
index_cache=index_cache,
quadrature_rule=quadrature_rule)
X = ufl.SpatialCoordinate(Vc.mesh())
K = ufl_utils.preprocess_expression(ufl.JacobianInverse(Vc.mesh()))
C_0, = fem.compile_ufl(X, **coarse_cfg)
K, = fem.compile_ufl(K, **coarse_cfg)
i = gem.Index()
j = gem.Index()
C_0 = gem.Indexed(C_0, (j, ))
C_0 = gem.index_sum(C_0, quadrature_rule.point_set.indices)
C_a = gem.Indexed(C_a, (j, ))
X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), C_a))
K_ij = gem.Indexed(K, (i, j))
K_ij = gem.index_sum(K_ij, quadrature_rule.point_set.indices)
X_a = gem.index_sum(gem.Product(K_ij, X_a), (j, ))
C_0, = quadrature_rule.point_set.points
C_0 = gem.Indexed(gem.Literal(C_0), (i, ))
# fine quad points in coarse reference space.
X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), X_a))
X_a = gem.ComponentTensor(X_a, (i, ))
# Coarse basis function evaluated at fine quadrature points
phi_c = fem.fiat_to_ufl(
Vce.point_evaluation(0, X_a, (Vce.cell.get_dimension(), 0)), 0)
tensor_indices = tuple(gem.Index(extent=d) for d in f.ufl_shape)
phi_c = gem.Indexed(phi_c, argument_multiindex + tensor_indices)
fexpr = gem.Indexed(fexpr, tensor_indices)
quadrature_weight = macro_quadrature_rule.weight_expression
expr = gem.Product(gem.IndexSum(gem.Product(phi_c, fexpr), tensor_indices),
gem.Product(macro_detJ, quadrature_weight))
quadrature_indices = macro_builder.indices + macro_quadrature_rule.point_set.indices
reps = spectral.Integrals([expr], quadrature_indices,
argument_multiindices, parameters)
assignments = spectral.flatten([(return_variable, reps)], index_cache)
return_variables, expressions = zip(*assignments)
expressions = impero_utils.preprocess_gem(expressions,
**spectral.finalise_options)
assignments = list(zip(return_variables, expressions))
impero_c = impero_utils.compile_gem(assignments,
quadrature_indices +
argument_multiindex,
remove_zeros=True)
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)
index_names.extend(zip(macro_builder.indices, ["entity"]))
body = generate_coffee(impero_c, index_names, parameters["precision"],
ScalarType_c)
retarg = ast.Decl(ScalarType_c,
ast.Symbol("R", rank=(Vce.space_dimension(), )))
local_tensor = coarse_builder.local_tensor
local_tensor.init = ast.ArrayInit(
numpy.zeros(Vce.space_dimension(), dtype=ScalarType_c))
body.children.insert(0, local_tensor)
args = [retarg] + macro_builder.kernel_args + [
macro_builder.coordinates_arg, coarse_builder.coordinates_arg
]
# Now we have the kernel that computes <f, phi_c>dx_c
# So now we need to hit it with the inverse mass matrix on dx_c
u = TrialFunction(Vc)
v = TestFunction(Vc)
expr = Tensor(ufl.inner(u, v) * ufl.dx).inv * AssembledVector(
ufl.Coefficient(Vc))
Ainv, = compile_expression(expr)
Ainv = Ainv.kinfo.kernel
A = ast.Symbol(local_tensor.sym.symbol)
R = ast.Symbol("R")
body.children.append(
ast.FunCall(Ainv.name, R, coarse_builder.coordinates_arg.sym, A))
from coffee.base import Node
assert isinstance(Ainv._code, Node)
return op2.Kernel(ast.Node([
Ainv._code,
ast.FunDecl("void",
"pyop2_kernel_injection_dg",
args,
body,
pred=["static", "inline"])
]),
name="pyop2_kernel_injection_dg",
cpp=True,
include_dirs=Ainv._include_dirs,
headers=Ainv._headers)
