def construct_ast(self, macro_kernels):
"""Constructs the final kernel AST.
:arg macro_kernels: A `list` of macro kernel functions, which
call subkernels and perform elemental
linear algebra.
Returns: The complete kernel AST as a COFFEE `ast.Node`
"""
assert isinstance(
macro_kernels,
list), ("Please wrap all macro kernel functions in a list")
assert self._is_finalized, (
"AST not finalized. Did you forget to call "
"builder._finalize_kernels_and_update()?")
kernel_ast = self.finalized_ast
kernel_ast.extend(macro_kernels)
return ast.Node(kernel_ast)
def construct_ast(self, name, args, statements):
"""Constructs the full kernel AST of a given SLATE expression. The :class:`Transformer`
is used to perform the conversion from standard C into the Eigen C++ template library
syntax.
:arg name: a string denoting the name of the macro kernel.
:arg args: a list of arguments for the macro_kernel.
:arg statements: a `coffee.base.Block` of instructions, which contains declarations
of temporaries, function calls to all subkernels and any auxilliary
information needed to evaulate the SLATE expression.
E.g. facet integral loops and action loops.
Returns: the full kernel AST to be converted into a PyOP2 kernel, as well as any
orientation information.
"""
# all kernel body statements must be wrapped up as a coffee.base.Block
assert isinstance(statements, ast.Block)
macro_kernel = ast.FunDecl("void",
name,
args,
statements,
pred=["static", "inline"])
kernel_list = []
transformer = Transformer()
oriented = False
# Assume self.kernel_exprs is populated at this point
for kernel_items in self.kernel_exprs.values():
for ks in kernel_items:
oriented = oriented or ks.kinfo.oriented
# TODO: Extend multiple domains support
assert ks.kinfo.subdomain_id == "otherwise"
kast = transformer.visit(ks.kinfo.kernel._ast)
kernel_list.append(kast)
kernel_list.append(macro_kernel)
return ast.Node(kernel_list), oriented
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 generate_kernel_ast(builder, statements, declared_temps):
"""Glues together the complete AST for the Slate expression
contained in the :class:`LocalKernelBuilder`.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information.
:arg statements: A list of COFFEE objects containing all
assembly calls and temporary declarations.
:arg declared_temps: A `dict` containing all previously
declared temporaries.
Return: A `KernelInfo` object describing the complete AST.
"""
slate_expr = builder.expression
if slate_expr.rank == 0:
# Scalars are treated as 1x1 MatrixBase objects
shape = (1, )
else:
shape = slate_expr.shape
# Now we create the result statement by declaring its eigen type and
# using Eigen::Map to move between Eigen and C data structs.
statements.append(ast.FlatBlock("/* Map eigen tensor into C struct */\n"))
result_sym = ast.Symbol("T%d" % len(declared_temps))
result_data_sym = ast.Symbol("A%d" % len(declared_temps))
result_type = "Eigen::Map<%s >" % eigen_matrixbase_type(shape)
result = ast.Decl(ScalarType_c,
ast.Symbol(result_data_sym),
pointers=[("restrict", )])
result_statement = ast.FlatBlock(
"%s %s((%s *)%s);\n" %
(result_type, result_sym, ScalarType_c, result_data_sym))
statements.append(result_statement)
# Generate the complete c++ string performing the linear algebra operations
# on Eigen matrices/vectors
statements.append(ast.FlatBlock("/* Linear algebra expression */\n"))
cpp_string = ast.FlatBlock(slate_to_cpp(slate_expr, declared_temps))
statements.append(ast.Incr(result_sym, cpp_string))
# Generate arguments for the macro kernel
args = [
result,
ast.Decl(ScalarType_c,
builder.coord_sym,
pointers=[("restrict", )],
qualifiers=["const"])
]
# Orientation information
if builder.oriented:
args.append(
ast.Decl("int",
builder.cell_orientations_sym,
pointers=[("restrict", )],
qualifiers=["const"]))
# Coefficient information
expr_coeffs = slate_expr.coefficients()
for c in expr_coeffs:
args.extend([
ast.Decl(ScalarType_c,
csym,
pointers=[("restrict", )],
qualifiers=["const"]) for csym in builder.coefficient(c)
])
# Facet information
if builder.needs_cell_facets:
f_sym = builder.cell_facet_sym
f_arg = ast.Symbol("arg_cell_facets")
f_dtype = as_cstr(cell_to_facets_dtype)
# cell_facets is locally a flattened 2-D array. We typecast here so we
# can access its entries using standard array notation.
cast = "%s (*%s)[2] = (%s (*)[2])%s;\n" % (f_dtype, f_sym, f_dtype,
f_arg)
statements.insert(0, ast.FlatBlock(cast))
args.append(
ast.Decl(f_dtype,
f_arg,
pointers=[("restrict", )],
qualifiers=["const"]))
# NOTE: We need to be careful about the ordering here. Mesh layers are
# added as the final argument to the kernel
# and the amount of layers before that.
if builder.needs_mesh_layers:
args.append(
ast.Decl("int",
builder.mesh_layer_count_sym,
pointers=[("restrict", )],
qualifiers=["const"]))
args.append(ast.Decl("int", builder.mesh_layer_sym))
# Cell size information
if builder.needs_cell_sizes:
args.append(
ast.Decl(ScalarType_c,
builder.cell_size_sym,
pointers=[("restrict", )],
qualifiers=["const"]))
# Macro kernel
macro_kernel_name = "pyop2_kernel_compile_slate"
stmts = ast.Block(statements)
macro_kernel = ast.FunDecl("void",
macro_kernel_name,
args,
stmts,
pred=["static", "inline"])
# Construct the final ast
kernel_ast = ast.Node(builder.templated_subkernels + [macro_kernel])
# Now we wrap up the kernel ast as a PyOP2 kernel and include the
# Eigen header files
include_dirs = list(builder.include_dirs)
include_dirs.append(EIGEN_INCLUDE_DIR)
op2kernel = op2.Kernel(
kernel_ast,
macro_kernel_name,
cpp=True,
include_dirs=include_dirs,
headers=['#include <Eigen/Dense>', '#define restrict __restrict'])
op2kernel.num_flops = builder.expression_flops + builder.terminal_flops
# Send back a "TSFC-like" SplitKernel object with an
# index and KernelInfo
kinfo = KernelInfo(kernel=op2kernel,
integral_type=builder.integral_type,
oriented=builder.oriented,
subdomain_id="otherwise",
domain_number=0,
coefficient_map=slate_expr.coeff_map,
needs_cell_facets=builder.needs_cell_facets,
pass_layer_arg=builder.needs_mesh_layers,
needs_cell_sizes=builder.needs_cell_sizes)
return kinfo
def generate_kernel_ast(builder, statements, declared_temps):
"""Glues together the complete AST for the Slate expression
contained in the :class:`LocalKernelBuilder`.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information.
:arg statements: A list of COFFEE objects containing all
assembly calls and temporary declarations.
:arg declared_temps: A `dict` containing all previously
declared temporaries.
Return: A `KernelInfo` object describing the complete AST.
"""
slate_expr = builder.expression
if slate_expr.rank == 0:
# Scalars are treated as 1x1 MatrixBase objects
shape = (1, )
else:
shape = slate_expr.shape
# Now we create the result statement by declaring its eigen type and
# using Eigen::Map to move between Eigen and C data structs.
statements.append(ast.FlatBlock("/* Map eigen tensor into C struct */\n"))
result_sym = ast.Symbol("T%d" % len(declared_temps))
result_data_sym = ast.Symbol("A%d" % len(declared_temps))
result_type = "Eigen::Map<%s >" % eigen_matrixbase_type(shape)
result = ast.Decl(SCALAR_TYPE, ast.Symbol(result_data_sym, shape))
result_statement = ast.FlatBlock(
"%s %s((%s *)%s);\n" %
(result_type, result_sym, SCALAR_TYPE, result_data_sym))
statements.append(result_statement)
# Generate the complete c++ string performing the linear algebra operations
# on Eigen matrices/vectors
statements.append(ast.FlatBlock("/* Linear algebra expression */\n"))
cpp_string = ast.FlatBlock(
metaphrase_slate_to_cpp(slate_expr, declared_temps))
statements.append(ast.Incr(result_sym, cpp_string))
# Generate arguments for the macro kernel
args = [result, ast.Decl("%s **" % SCALAR_TYPE, builder.coord_sym)]
# Orientation information
if builder.oriented:
args.append(ast.Decl("int **", builder.cell_orientations_sym))
# Coefficient information
expr_coeffs = slate_expr.coefficients()
for c in expr_coeffs:
if isinstance(c, Constant):
ctype = "%s *" % SCALAR_TYPE
else:
ctype = "%s **" % SCALAR_TYPE
args.extend([ast.Decl(ctype, csym) for csym in builder.coefficient(c)])
# Facet information
if builder.needs_cell_facets:
args.append(
ast.Decl("%s *" % as_cstr(cell_to_facets_dtype),
builder.cell_facet_sym))
# NOTE: We need to be careful about the ordering here. Mesh layers are
# added as the final argument to the kernel.
if builder.needs_mesh_layers:
args.append(ast.Decl("int", builder.mesh_layer_sym))
# Macro kernel
macro_kernel_name = "compile_slate"
stmts = ast.Block(statements)
macro_kernel = ast.FunDecl("void",
macro_kernel_name,
args,
stmts,
pred=["static", "inline"])
# Construct the final ast
kernel_ast = ast.Node(builder.templated_subkernels + [macro_kernel])
# Now we wrap up the kernel ast as a PyOP2 kernel and include the
# Eigen header files
include_dirs = builder.include_dirs
include_dirs.extend(["%s/include/eigen3/" % d for d in PETSC_DIR])
op2kernel = op2.Kernel(
kernel_ast,
macro_kernel_name,
cpp=True,
include_dirs=include_dirs,
headers=['#include <Eigen/Dense>', '#define restrict __restrict'])
# Send back a "TSFC-like" SplitKernel object with an
# index and KernelInfo
kinfo = KernelInfo(kernel=op2kernel,
integral_type=builder.integral_type,
oriented=builder.oriented,
subdomain_id="otherwise",
domain_number=0,
coefficient_map=tuple(range(len(expr_coeffs))),
needs_cell_facets=builder.needs_cell_facets,
pass_layer_arg=builder.needs_mesh_layers)
return kinfo
