def extruded_int_horiz_facet(exp, builder, top_sks, bottom_sks,
coordsym, mesh_layer_sym,
cell_orientations):
"""Generates a code statement for evaluating interior horizontal
facet integrals.
:arg exp: A :class:`TensorBase` expression.
:arg builder: A :class:`KernelBuilder` containing the expression context.
:arg top_sks: An iterable of index ordered TSFC kernels for the top
kernels.
:arg bottom_sks: An iterable of index ordered TSFC kernels for the bottom
kernels.
:arg coordsym: An `ast.Symbol` object representing coordinate arguments
for the kernel.
:arg mesh_layer_sym: An `ast.Symbol` representing the mesh layer.
:arg cell_orientations: An `ast.Symbol` representing cell orientation
information.
Returns: A COFFEE code statement and updated include_dirs
"""
t = builder.temps[exp]
nlayers = exp.ufl_domain().topological.layers - 1
incl = []
top_calls = []
bottom_calls = []
for top, btm in zip(top_sks, bottom_sks):
assert top.indices == btm.indices, (
"Top and bottom kernels must have the same indices"
)
index = top.indices
# Generate an iterable of coefficients to pass to the subkernel
# if any are required
c_set = top.kinfo.coefficient_map + btm.kinfo.coefficient_map
coefficient_map = tuple(OrderedDict.fromkeys(c_set))
clist = [c for ci in coefficient_map
for c in builder.coefficient(exp.coefficients()[ci])]
# TODO: Is this safe?
if top.kinfo.oriented and btm.kinfo.oriented:
clist.append(cell_orientations)
dirs = top.kinfo.kernel._include_dirs + btm.kinfo.kernel._include_dirs
incl.extend(tuple(OrderedDict.fromkeys(dirs)))
tensor = eigen_tensor(exp, t, index)
top_calls.append(ast.FunCall(top.kinfo.kernel.name,
tensor, coordsym, *clist))
bottom_calls.append(ast.FunCall(btm.kinfo.kernel.name,
tensor, coordsym, *clist))
else_stmt = ast.Block(top_calls + bottom_calls, open_scope=True)
inter_stmt = ast.If(ast.Eq(mesh_layer_sym, nlayers - 1),
(ast.Block(bottom_calls, open_scope=True),
else_stmt))
stmt = ast.If(ast.Eq(mesh_layer_sym, 0),
(ast.Block(top_calls, open_scope=True),
inter_stmt))
return stmt, incl
def extruded_top_bottom_facet(cxt_kernel, builder, coordsym, mesh_layer_sym,
cell_orientations):
"""Generates a code statement for evaluating exterior top/bottom
facet integrals.
:arg cxt_kernel: A :namedtuple:`ContextKernel` containing all relevant
integral types and TSFC kernels associated with the
form nested in the expression.
:arg builder: A :class:`KernelBuilder` containing the expression context.
:arg coordsym: An `ast.Symbol` object representing coordinate arguments
for the kernel.
:arg mesh_layer_sym: An `ast.Symbol` representing the mesh layer.
:arg cell_orientations: An `ast.Symbol` representing cell orientation
information.
Returns: A COFFEE code statement and updated include_dirs
"""
exp = cxt_kernel.tensor
t = builder.temps[exp]
nlayers = exp.ufl_domain().topological.layers - 1
incl = []
body = []
for splitkernel in cxt_kernel.tsfc_kernels:
index = splitkernel.indices
kinfo = splitkernel.kinfo
# Generate an iterable of coefficients to pass to the subkernel
# if any are required
clist = [
c for ci in kinfo.coefficient_map
for c in builder.coefficient(exp.coefficients()[ci])
]
if kinfo.oriented:
clist.insert(0, cell_orientations)
incl.extend(kinfo.kernel._include_dirs)
tensor = eigen_tensor(exp, t, index)
body.append(ast.FunCall(kinfo.kernel.name, tensor, coordsym, *clist))
if cxt_kernel.original_integral_type == "exterior_facet_bottom":
layer = 0
else:
layer = nlayers - 1
stmt = ast.If(ast.Eq(mesh_layer_sym, layer),
[ast.Block(body, open_scope=True)])
return stmt, incl
def tensor_assembly_calls(builder):
"""Generates a block of statements for assembling the local
finite element tensors.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information and assembly calls.
"""
assembly_calls = builder.assembly_calls
statements = [ast.FlatBlock("/* Assemble local tensors */\n")]
# Cell integrals are straightforward. Just splat them out.
statements.extend(assembly_calls["cell"])
if builder.needs_cell_facets:
# The for-loop will have the general structure:
#
# FOR (facet=0; facet<num_facets; facet++):
# IF (facet is interior):
# *interior calls
# ELSE IF (facet is exterior):
# *exterior calls
#
# If only interior (exterior) facets are present,
# then only a single IF-statement checking for interior
# (exterior) facets will be present within the loop. The
# cell facets are labelled `1` for interior, and `0` for
# exterior.
statements.append(ast.FlatBlock("/* Loop over cell facets */\n"))
int_calls = list(
chain(*[
assembly_calls[it_type]
for it_type in ("interior_facet", "interior_facet_vert")
]))
ext_calls = list(
chain(*[
assembly_calls[it_type]
for it_type in ("exterior_facet", "exterior_facet_vert")
]))
# Generate logical statements for handling exterior/interior facet
# integrals on subdomains.
# Currently only facet integrals are supported.
for sd_type in ("subdomains_exterior_facet",
"subdomains_interior_facet"):
stmts = []
for sd, sd_calls in groupby(assembly_calls[sd_type],
lambda x: x[0]):
_, calls = zip(*sd_calls)
if_sd = ast.Eq(
ast.Symbol(builder.cell_facet_sym,
rank=(builder.it_sym, 1)), sd)
stmts.append(
ast.If(if_sd, (ast.Block(calls, open_scope=True), )))
if sd_type == "subdomains_exterior_facet":
ext_calls.extend(stmts)
if sd_type == "subdomains_interior_facet":
int_calls.extend(stmts)
# Compute the number of facets to loop over
domain = builder.expression.ufl_domain()
if domain.cell_set._extruded:
num_facets = domain.ufl_cell()._cells[0].num_facets()
else:
num_facets = domain.ufl_cell().num_facets()
if_ext = ast.Eq(
ast.Symbol(builder.cell_facet_sym, rank=(builder.it_sym, 0)), 0)
if_int = ast.Eq(
ast.Symbol(builder.cell_facet_sym, rank=(builder.it_sym, 0)), 1)
body = []
if ext_calls:
body.append(
ast.If(if_ext, (ast.Block(ext_calls, open_scope=True), )))
if int_calls:
body.append(
ast.If(if_int, (ast.Block(int_calls, open_scope=True), )))
statements.append(
ast.For(ast.Decl("unsigned int", builder.it_sym, init=0),
ast.Less(builder.it_sym, num_facets),
ast.Incr(builder.it_sym, 1), body))
if builder.needs_mesh_layers:
# In the presence of interior horizontal facet calls, an
# IF-ELIF-ELSE block is generated using the mesh levels
# as conditions for which calls are needed:
#
# IF (layer == bottom_layer):
# *bottom calls
# ELSE IF (layer == top_layer):
# *top calls
# ELSE:
# *top calls
# *bottom calls
#
# Any extruded top or bottom calls for extruded facets are
# included within the appropriate mesh-level IF-blocks. If
# no interior horizontal facet calls are present, then
# standard IF-blocks are generated for exterior top/bottom
# facet calls when appropriate:
#
# IF (layer == bottom_layer):
# *bottom calls
#
# IF (layer == top_layer):
# *top calls
#
# The mesh level is an integer provided as a macro kernel
# argument.
# FIXME: No variable layers assumption
statements.append(ast.FlatBlock("/* Mesh levels: */\n"))
num_layers = ast.Symbol(builder.mesh_layer_count_sym, rank=(0, ))
layer = builder.mesh_layer_sym
types = [
"interior_facet_horiz_top", "interior_facet_horiz_bottom",
"exterior_facet_top", "exterior_facet_bottom"
]
decide = [
ast.Less(layer, num_layers),
ast.Greater(layer, 0),
ast.Eq(layer, num_layers),
ast.Eq(layer, 0)
]
for (integral_type, which) in zip(types, decide):
statements.append(
ast.If(which, (ast.Block(assembly_calls[integral_type],
open_scope=True), )))
return statements
def tensor_assembly_calls(builder):
"""Generates a block of statements for assembling the local
finite element tensors.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information and
assembly calls.
"""
statements = [ast.FlatBlock("/* Assemble local tensors */\n")]
# Cell integrals are straightforward. Just splat them out.
statements.extend(builder.assembly_calls["cell"])
if builder.needs_cell_facets:
# The for-loop will have the general structure:
#
# FOR (facet=0; facet<num_facets; facet++):
# IF (facet is interior):
# *interior calls
# ELSE IF (facet is exterior):
# *exterior calls
#
# If only interior (exterior) facets are present,
# then only a single IF-statement checking for interior
# (exterior) facets will be present within the loop. The
# cell facets are labelled `1` for interior, and `0` for
# exterior.
statements.append(ast.FlatBlock("/* Loop over cell facets */\n"))
int_calls = list(
chain(*[
builder.assembly_calls[it_type]
for it_type in ("interior_facet", "interior_facet_vert")
]))
ext_calls = list(
chain(*[
builder.assembly_calls[it_type]
for it_type in ("exterior_facet", "exterior_facet_vert")
]))
# Compute the number of facets to loop over
domain = builder.expression.ufl_domain()
if domain.cell_set._extruded:
num_facets = domain.ufl_cell()._cells[0].num_facets()
else:
num_facets = domain.ufl_cell().num_facets()
if_ext = ast.Eq(
ast.Symbol(builder.cell_facet_sym, rank=(builder.it_sym, )), 0)
if_int = ast.Eq(
ast.Symbol(builder.cell_facet_sym, rank=(builder.it_sym, )), 1)
body = []
if ext_calls:
body.append(
ast.If(if_ext, (ast.Block(ext_calls, open_scope=True), )))
if int_calls:
body.append(
ast.If(if_int, (ast.Block(int_calls, open_scope=True), )))
statements.append(
ast.For(ast.Decl("unsigned int", builder.it_sym, init=0),
ast.Less(builder.it_sym, num_facets),
ast.Incr(builder.it_sym, 1), body))
if builder.needs_mesh_layers:
# In the presence of interior horizontal facet calls, an
# IF-ELIF-ELSE block is generated using the mesh levels
# as conditions for which calls are needed:
#
# IF (layer == bottom_layer):
# *bottom calls
# ELSE IF (layer == top_layer):
# *top calls
# ELSE:
# *top calls
# *bottom calls
#
# Any extruded top or bottom calls for extruded facets are
# included within the appropriate mesh-level IF-blocks. If
# no interior horizontal facet calls are present, then
# standard IF-blocks are generated for exterior top/bottom
# facet calls when appropriate:
#
# IF (layer == bottom_layer):
# *bottom calls
#
# IF (layer == top_layer):
# *top calls
#
# The mesh level is an integer provided as a macro kernel
# argument.
# FIXME: No variable layers assumption
statements.append(ast.FlatBlock("/* Mesh levels: */\n"))
num_layers = builder.expression.ufl_domain().topological.layers - 1
int_top = builder.assembly_calls["interior_facet_horiz_top"]
int_btm = builder.assembly_calls["interior_facet_horiz_bottom"]
ext_top = builder.assembly_calls["exterior_facet_top"]
ext_btm = builder.assembly_calls["exterior_facet_bottom"]
bottom = ast.Block(int_top + ext_btm, open_scope=True)
top = ast.Block(int_btm + ext_top, open_scope=True)
rest = ast.Block(int_btm + int_top, open_scope=True)
statements.append(
ast.If(ast.Eq(builder.mesh_layer_sym, 0),
(bottom,
ast.If(ast.Eq(builder.mesh_layer_sym, num_layers - 1),
(top, rest)))))
return statements
def compile_expression(slate_expr, tsfc_parameters=None):
"""Takes a SLATE expression `slate_expr` and returns the appropriate
:class:`firedrake.op2.Kernel` object representing the SLATE expression.
:arg slate_expr: a :class:'TensorBase' expression.
:arg tsfc_parameters: an optional `dict` of form compiler parameters to
be passed onto TSFC during the compilation of ufl forms.
"""
if not isinstance(slate_expr, TensorBase):
raise ValueError(
"Expecting a `slate.TensorBase` expression, not a %r" % slate_expr)
# TODO: Get PyOP2 to write into mixed dats
if any(len(a.function_space()) > 1 for a in slate_expr.arguments()):
raise NotImplementedError("Compiling mixed slate expressions")
# Initialize shape and statements list
shape = slate_expr.shape
statements = []
# Create a builder for the SLATE expression
builder = KernelBuilder(expression=slate_expr,
tsfc_parameters=tsfc_parameters)
# Initialize coordinate and facet symbols
coordsym = ast.Symbol("coords")
coords = None
cellfacetsym = ast.Symbol("cell_facets")
inc = []
# Now we construct the list of statements to provide to the builder
context_temps = builder.temps.copy()
for exp, t in context_temps.items():
statements.append(ast.Decl(eigen_matrixbase_type(exp.shape), t))
statements.append(ast.FlatBlock("%s.setZero();\n" % t))
for splitkernel in builder.kernel_exprs[exp]:
clist = []
index = splitkernel.indices
kinfo = splitkernel.kinfo
integral_type = kinfo.integral_type
if integral_type not in [
"cell", "interior_facet", "exterior_facet"
]:
raise NotImplementedError(
"Integral type %s not currently supported." %
integral_type)
coordinates = exp.ufl_domain().coordinates
if coords is not None:
assert coordinates == coords
else:
coords = coordinates
for cindex in kinfo.coefficient_map:
c = exp.coefficients()[cindex]
# Handles both mixed and non-mixed coefficient cases
clist.extend(builder.extract_coefficient(c))
inc.extend(kinfo.kernel._include_dirs)
tensor = eigen_tensor(exp, t, index)
if integral_type in ["interior_facet", "exterior_facet"]:
builder.require_cell_facets()
itsym = ast.Symbol("i0")
clist.append(ast.FlatBlock("&%s" % itsym))
loop_body = []
nfacet = exp.ufl_domain().ufl_cell().num_facets()
if integral_type == "exterior_facet":
checker = 1
else:
checker = 0
loop_body.append(
ast.If(
ast.Eq(ast.Symbol(cellfacetsym, rank=(itsym, )),
checker), [
ast.Block([
ast.FunCall(kinfo.kernel.name, tensor,
coordsym, *clist)
],
open_scope=True)
]))
loop = ast.For(ast.Decl("unsigned int", itsym, init=0),
ast.Less(itsym, nfacet), ast.Incr(itsym, 1),
loop_body)
statements.append(loop)
else:
statements.append(
ast.FunCall(kinfo.kernel.name, tensor, coordsym, *clist))
# Now we handle any terms that require auxiliary data (if any)
if bool(builder.aux_exprs):
aux_temps, aux_statements = auxiliary_information(builder)
context_temps.update(aux_temps)
statements.extend(aux_statements)
result_sym = ast.Symbol("T%d" % len(builder.temps))
result_data_sym = ast.Symbol("A%d" % len(builder.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)
cpp_string = ast.FlatBlock(
metaphrase_slate_to_cpp(slate_expr, context_temps))
statements.append(ast.Assign(result_sym, cpp_string))
# Generate arguments for the macro kernel
args = [result, ast.Decl("%s **" % SCALAR_TYPE, coordsym)]
for c in slate_expr.coefficients():
if isinstance(c, Constant):
ctype = "%s *" % SCALAR_TYPE
else:
ctype = "%s **" % SCALAR_TYPE
args.extend([
ast.Decl(ctype, sym_c) for sym_c in builder.extract_coefficient(c)
])
if builder.needs_cell_facets:
args.append(ast.Decl("char *", cellfacetsym))
macro_kernel_name = "compile_slate"
kernel_ast, oriented = builder.construct_ast(
name=macro_kernel_name, args=args, statements=ast.Block(statements))
inc.extend(["%s/include/eigen3/" % d for d in PETSC_DIR])
op2kernel = op2.Kernel(
kernel_ast,
macro_kernel_name,
cpp=True,
include_dirs=inc,
headers=['#include <Eigen/Dense>', '#define restrict __restrict'])
assert len(slate_expr.ufl_domains()) == 1
kinfo = KernelInfo(kernel=op2kernel,
integral_type="cell",
oriented=oriented,
subdomain_id="otherwise",
domain_number=0,
coefficient_map=range(len(slate_expr.coefficients())),
needs_cell_facets=builder.needs_cell_facets)
idx = tuple([0] * slate_expr.rank)
return (SplitKernel(idx, kinfo), )
_to_sum = lambda o: ast.Sum(_ast(o[0]), _to_sum(o[1:])) if len(
o) > 1 else _ast(o[0])
_to_prod = lambda o: ast.Prod(_ast(o[0]), _to_sum(o[1:])) if len(
o) > 1 else _ast(o[0])
_to_aug_assign = lambda op, o: op(_ast(o[0]), _ast(o[1]))
_ast_map = {
MathFunction:
(lambda e: ast.FunCall(e._name, *[_ast(o) for o in e.ufl_operands])),
ufl.algebra.Sum: (lambda e: ast.Par(_to_sum(e.ufl_operands))),
ufl.algebra.Product: (lambda e: ast.Par(_to_prod(e.ufl_operands))),
ufl.algebra.Division:
(lambda e: ast.Par(ast.Div(*[_ast(o) for o in e.ufl_operands]))),
ufl.algebra.Abs: (lambda e: ast.FunCall("abs", _ast(e.ufl_operands[0]))),
Assign: (lambda e: _to_aug_assign(e._ast, e.ufl_operands)),
AugmentedAssignment: (lambda e: _to_aug_assign(e._ast, e.ufl_operands)),
ufl.constantvalue.ScalarValue: (lambda e: ast.Symbol(e._value)),
ufl.constantvalue.Zero: (lambda e: ast.Symbol(0)),
ufl.classes.Conditional:
(lambda e: ast.Ternary(*[_ast(o) for o in e.ufl_operands])),
ufl.classes.EQ: (lambda e: ast.Eq(*[_ast(o) for o in e.ufl_operands])),
ufl.classes.NE: (lambda e: ast.NEq(*[_ast(o) for o in e.ufl_operands])),
ufl.classes.LT: (lambda e: ast.Less(*[_ast(o) for o in e.ufl_operands])),
ufl.classes.LE: (lambda e: ast.LessEq(*[_ast(o) for o in e.ufl_operands])),
ufl.classes.GT: (lambda e: ast.Greater(*[_ast(o)
for o in e.ufl_operands])),
ufl.classes.GE:
(lambda e: ast.GreaterEq(*[_ast(o) for o in e.ufl_operands]))
}
def facet_integral_loop(cxt_kernel, builder, coordsym, cellfacetsym,
cell_orientations):
"""Generates a code statement for evaluating exterior/interior facet
integrals.
:arg cxt_kernel: A :namedtuple:`ContextKernel` containing all relevant
integral types and TSFC kernels associated with the
form nested in the expression.
:arg builder: A :class:`KernelBuilder` containing the expression context.
:arg coordsym: An `ast.Symbol` object representing coordinate arguments
for the kernel.
:arg cellfacetsym: An `ast.Symbol` representing the cell facets.
:arg cell_orientations: An `ast.Symbol` representing cell orientation
information.
Returns: A COFFEE code statement and updated include_dirs
"""
exp = cxt_kernel.tensor
t = builder.temps[exp]
it_type = cxt_kernel.original_integral_type
itsym = ast.Symbol("i0")
chker = {
"interior_facet": 1,
"interior_facet_vert": 1,
"exterior_facet": 0,
"exterior_facet_vert": 0
}
# Compute the correct number of facets for a particular facet measure
if it_type in ["interior_facet", "exterior_facet"]:
# Non-extruded case
nfacet = exp.ufl_domain().ufl_cell().num_facets()
elif it_type in ["interior_facet_vert", "exterior_facet_vert"]:
# Extrusion case
base_cell = exp.ufl_domain().ufl_cell()._cells[0]
nfacet = base_cell.num_facets()
else:
raise ValueError("Integral type %s not supported." % it_type)
incl = []
funcalls = []
checker = chker[it_type]
for splitkernel in cxt_kernel.tsfc_kernels:
index = splitkernel.indices
kinfo = splitkernel.kinfo
# Generate an iterable of coefficients to pass to the subkernel
# if any are required
clist = [
c for ci in kinfo.coefficient_map
for c in builder.coefficient(exp.coefficients()[ci])
]
incl.extend(kinfo.kernel._include_dirs)
tensor = eigen_tensor(exp, t, index)
if kinfo.oriented:
clist.insert(0, cell_orientations)
clist.append(ast.FlatBlock("&%s" % itsym))
funcalls.append(
ast.FunCall(kinfo.kernel.name, tensor, coordsym, *clist))
loop_body = ast.If(
ast.Eq(ast.Symbol(cellfacetsym, rank=(itsym, )), checker),
[ast.Block(funcalls, open_scope=True)])
loop_stmt = ast.For(ast.Decl("unsigned int", itsym, init=0),
ast.Less(itsym, nfacet), ast.Incr(itsym, 1), loop_body)
return loop_stmt, incl
