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 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 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 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 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)
def sum(self, o, *ops):
shape, = set(o.shape for o in ops)
indices = gem.indices(len(shape))
return gem.ComponentTensor(
gem.Sum(*[gem.Indexed(op, indices) for op in ops]), indices)
def compile_expression_dual_evaluation(expression,
to_element,
*,
domain=None,
interface=None,
parameters=None,
coffee=False):
"""Compile a UFL expression to be evaluated against a compile-time known reference element's dual basis.
Useful for interpolating UFL expressions into e.g. N1curl spaces.
:arg expression: UFL expression
:arg to_element: A FInAT element for the target space
:arg domain: optional UFL domain the expression is defined on (required when expression contains no domain).
:arg interface: backend module for the kernel interface
:arg parameters: parameters object
:arg coffee: compile coffee kernel instead of loopy kernel
"""
import coffee.base as ast
import loopy as lp
# Just convert FInAT element to FIAT for now.
# Dual evaluation in FInAT will bring a thorough revision.
to_element = to_element.fiat_equivalent
if any(len(dual.deriv_dict) != 0 for dual in to_element.dual_basis()):
raise NotImplementedError(
"Can only interpolate onto dual basis functionals without derivative evaluation, sorry!"
)
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Determine whether in complex mode
complex_mode = is_complex(parameters["scalar_type"])
# Find out which mapping to apply
try:
mapping, = set(to_element.mapping())
except ValueError:
raise NotImplementedError(
"Don't know how to interpolate onto zany spaces, sorry")
expression = apply_mapping(expression, mapping, domain)
# Apply UFL preprocessing
expression = ufl_utils.preprocess_expression(expression,
complex_mode=complex_mode)
# Initialise kernel builder
if interface is None:
if coffee:
import tsfc.kernel_interface.firedrake as firedrake_interface_coffee
interface = firedrake_interface_coffee.ExpressionKernelBuilder
else:
# Delayed import, loopy is a runtime dependency
import tsfc.kernel_interface.firedrake_loopy as firedrake_interface_loopy
interface = firedrake_interface_loopy.ExpressionKernelBuilder
builder = interface(parameters["scalar_type"])
arguments = extract_arguments(expression)
argument_multiindices = tuple(
builder.create_element(arg.ufl_element()).get_indices()
for arg in arguments)
# Replace coordinates (if any) unless otherwise specified by kwarg
if domain is None:
domain = expression.ufl_domain()
assert domain is not None
# Collect required coefficients
first_coefficient_fake_coords = False
coefficients = extract_coefficients(expression)
if has_type(expression, GeometricQuantity) or any(
fem.needs_coordinate_mapping(c.ufl_element())
for c in coefficients):
# Create a fake coordinate coefficient for a domain.
coords_coefficient = ufl.Coefficient(
ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
builder.domain_coordinate[domain] = coords_coefficient
builder.set_cell_sizes(domain)
coefficients = [coords_coefficient] + coefficients
first_coefficient_fake_coords = True
builder.set_coefficients(coefficients)
# Split mixed coefficients
expression = ufl_utils.split_coefficients(expression,
builder.coefficient_split)
# Translate to GEM
kernel_cfg = dict(
interface=builder,
ufl_cell=domain.ufl_cell(),
# FIXME: change if we ever implement
# interpolation on facets.
integral_type="cell",
argument_multiindices=argument_multiindices,
index_cache={},
scalar_type=parameters["scalar_type"])
if all(
isinstance(dual, PointEvaluation)
for dual in to_element.dual_basis()):
# This is an optimisation for point-evaluation nodes which
# should go away once FInAT offers the interface properly
qpoints = []
# Everything is just a point evaluation.
for dual in to_element.dual_basis():
ptdict = dual.get_point_dict()
qpoint, = ptdict.keys()
(qweight, component), = ptdict[qpoint]
assert allclose(qweight, 1.0)
assert component == ()
qpoints.append(qpoint)
point_set = PointSet(qpoints)
config = kernel_cfg.copy()
config.update(point_set=point_set)
# Allow interpolation onto QuadratureElements to refer to the quadrature
# rule they represent
if isinstance(to_element, FIAT.QuadratureElement):
assert allclose(asarray(qpoints), asarray(to_element._points))
quad_rule = QuadratureRule(point_set, to_element._weights)
config["quadrature_rule"] = quad_rule
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but nothing
# new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
shape_indices = tuple(gem.Index() for _ in expr.shape)
basis_indices = point_set.indices
ir = gem.Indexed(expr, shape_indices)
else:
# This is general code but is more unrolled than necssary.
dual_expressions = [] # one for each functional
broadcast_shape = len(expression.ufl_shape) - len(
to_element.value_shape())
shape_indices = tuple(gem.Index()
for _ in expression.ufl_shape[:broadcast_shape])
expr_cache = {} # Sharing of evaluation of the expression at points
for dual in to_element.dual_basis():
pts = tuple(sorted(dual.get_point_dict().keys()))
try:
expr, point_set = expr_cache[pts]
except KeyError:
point_set = PointSet(pts)
config = kernel_cfg.copy()
config.update(point_set=point_set)
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but
# nothing new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
expr = gem.partial_indexed(expr, shape_indices)
expr_cache[pts] = expr, point_set
weights = collections.defaultdict(list)
for p in pts:
for (w, cmp) in dual.get_point_dict()[p]:
weights[cmp].append(w)
qexprs = gem.Zero()
for cmp in sorted(weights):
qweights = gem.Literal(weights[cmp])
qexpr = gem.Indexed(expr, cmp)
qexpr = gem.index_sum(
gem.Indexed(qweights, point_set.indices) * qexpr,
point_set.indices)
qexprs = gem.Sum(qexprs, qexpr)
assert qexprs.shape == ()
assert set(qexprs.free_indices) == set(
chain(shape_indices, *argument_multiindices))
dual_expressions.append(qexprs)
basis_indices = (gem.Index(), )
ir = gem.Indexed(gem.ListTensor(dual_expressions), basis_indices)
# Build kernel body
return_indices = basis_indices + shape_indices + tuple(
chain(*argument_multiindices))
return_shape = tuple(i.extent for i in return_indices)
return_var = gem.Variable('A', return_shape)
if coffee:
return_arg = ast.Decl(parameters["scalar_type"],
ast.Symbol('A', rank=return_shape))
else:
return_arg = lp.GlobalArg("A",
dtype=parameters["scalar_type"],
shape=return_shape)
return_expr = gem.Indexed(return_var, return_indices)
# TODO: one should apply some GEM optimisations as in assembly,
# but we don't for now.
ir, = impero_utils.preprocess_gem([ir])
impero_c = impero_utils.compile_gem([(return_expr, ir)], return_indices)
index_names = dict(
(idx, "p%d" % i) for (i, idx) in enumerate(basis_indices))
# Handle kernel interface requirements
builder.register_requirements([ir])
# Build kernel tuple
return builder.construct_kernel(return_arg, impero_c, index_names,
first_coefficient_fake_coords)
