def minimum(f):
fmin = op2.Global(1, [1000], dtype=float)
op2.par_loop(op2.Kernel("""
static void minify(double *a, double *b) {
a[0] = a[0] > fabs(b[0]) ? fabs(b[0]) : a[0];
}
""", "minify"), f.dof_dset.set, fmin(op2.MIN), f.dat(op2.READ))
return fmin.data[0]
def max(f):
fmax = op2.Global(1, np.finfo(float).min, dtype=float)
op2.par_loop(op2.Kernel("""
static void maxify(double *a, double *b) {
a[0] = a[0] < fabs(b[0]) ? fabs(b[0]) : a[0];
}
""", "maxify"), f.dof_dset.set, fmax(op2.MAX), f.dat(op2.READ))
return fmax.data[0]
def min(f):
fmin = op2.Global(1, np.finfo(float).max, dtype=float)
op2.par_loop(op2.Kernel("""
void minify(double *a, double *b) {
a[0] = a[0] > fabs(b[0]) ? fabs(b[0]) : a[0];
}
""", "minify"), f.dof_dset.set, fmin(op2.MIN), f.dat(op2.READ))
return fmin.data[0]
def get_latlon_mesh(mesh):
"""Build 2D projected mesh of spherical mesh"""
crds_orig = mesh.coordinates
mesh_dg_fs = VectorFunctionSpace(mesh, "DG", 1)
crds_dg = Function(mesh_dg_fs)
crds_latlon = Function(mesh_dg_fs)
par_loop(
"""
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
dg[i][j] = cg[i][j];
}
}
""", dx, {
'dg': (crds_dg, WRITE),
'cg': (crds_orig, READ)
})
# lat-lon 'x' = atan2(y, x)
crds_latlon.dat.data[:, 0] = arctan2(crds_dg.dat.data[:, 1],
crds_dg.dat.data[:, 0])
# lat-lon 'y' = asin(z/sqrt(x^2 + y^2 + z^2))
crds_latlon.dat.data[:, 1] = (arcsin(
crds_dg.dat.data[:, 2] /
np_sqrt(crds_dg.dat.data[:, 0]**2 + crds_dg.dat.data[:, 1]**2 +
crds_dg.dat.data[:, 2]**2)))
crds_latlon.dat.data[:, 2] = 0.0
kernel = op2.Kernel(
"""
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
void splat_coords(double **coords) {
double diff0 = (coords[0][0] - coords[1][0]);
double diff1 = (coords[0][0] - coords[2][0]);
double diff2 = (coords[1][0] - coords[2][0]);
if (fabs(diff0) > PI || fabs(diff1) > PI || fabs(diff2) > PI) {
const int sign0 = coords[0][0] < 0 ? -1 : 1;
const int sign1 = coords[1][0] < 0 ? -1 : 1;
const int sign2 = coords[2][0] < 0 ? -1 : 1;
if (sign0 < 0) {
coords[0][0] += TWO_PI;
}
if (sign1 < 0) {
coords[1][0] += TWO_PI;
}
if (sign2 < 0) {
coords[2][0] += TWO_PI;
}
}
}
""", "splat_coords")
op2.par_loop(kernel, crds_latlon.cell_set,
crds_latlon.dat(op2.RW, crds_latlon.cell_node_map()))
return Mesh(crds_latlon)
def generate_loopy_kernel(slate_expr, tsfc_parameters=None):
cpu_time = time.time()
if len(slate_expr.ufl_domains()) > 1:
raise NotImplementedError("Multiple domains not implemented.")
Citations().register("Gibson2018")
# Create a loopy builder for the Slate expression,
# e.g. contains the loopy kernels coming from TSFC
gem_expr, var2terminal = slate_to_gem(slate_expr)
scalar_type = tsfc_parameters["scalar_type"]
slate_loopy, output_arg = gem_to_loopy(gem_expr, var2terminal, scalar_type)
builder = LocalLoopyKernelBuilder(expression=slate_expr,
tsfc_parameters=tsfc_parameters)
loopy_merged = merge_loopy(slate_loopy, output_arg, builder, var2terminal)
loopy_merged = loopy.register_function_id_to_in_knl_callable_mapper(
loopy_merged, inv_fn_lookup)
loopy_merged = loopy.register_function_id_to_in_knl_callable_mapper(
loopy_merged, solve_fn_lookup)
# WORKAROUND: Generate code directly from the loopy kernel here,
# then attach code as a c-string to the op2kernel
code = loopy.generate_code_v2(loopy_merged).device_code()
code = code.replace(f'void {loopy_merged.name}',
f'static void {loopy_merged.name}')
loopykernel = op2.Kernel(code,
loopy_merged.name,
include_dirs=BLASLAPACK_INCLUDE.split(),
ldargs=BLASLAPACK_LIB.split())
kinfo = KernelInfo(
kernel=loopykernel,
integral_type=
"cell", # slate can only do things as contributions to the cell integrals
oriented=builder.bag.needs_cell_orientations,
subdomain_id="otherwise",
domain_number=0,
coefficient_map=tuple(range(len(slate_expr.coefficients()))),
needs_cell_facets=builder.bag.needs_cell_facets,
pass_layer_arg=builder.bag.needs_mesh_layers,
needs_cell_sizes=builder.bag.needs_cell_sizes)
# Cache the resulting kernel
# Slate kernels are never split, so indicate that with None in the index slot.
idx = tuple([None] * slate_expr.rank)
logger.info(GREEN % "compile_slate_expression finished in %g seconds.",
time.time() - cpu_time)
return (SplitKernel(idx, kinfo), )
def min(f_in):
fmin = op2.Global(1, [np.finfo(float).max], dtype=float)
if len(f_in.ufl_shape) > 0:
mesh = f_in.function_space().mesh()
V = FunctionSpace(mesh, "DG", 1)
f = Function(V).project(sqrt(inner(f_in, f_in)))
else:
f = f_in
op2.par_loop(
op2.Kernel(
"""void minify(double *a, double *b)
{
a[0] = a[0] > fabs(b[0]) ? fabs(b[0]) : a[0];
}""", "minify"), f.dof_dset.set, fmin(op2.MIN), f.dat(op2.READ))
return fmin.data[0]
def generate_loopy_kernel(slate_expr, tsfc_parameters=None):
cpu_time = time.time()
if len(slate_expr.ufl_domains()) > 1:
raise NotImplementedError("Multiple domains not implemented.")
Citations().register("Gibson2018")
# Create a loopy builder for the Slate expression,
# e.g. contains the loopy kernels coming from TSFC
gem_expr, var2terminal = slate_to_gem(slate_expr)
scalar_type = tsfc_parameters["scalar_type"]
slate_loopy, output_arg = gem_to_loopy(gem_expr, var2terminal, scalar_type)
builder = LocalLoopyKernelBuilder(expression=slate_expr,
tsfc_parameters=tsfc_parameters)
name = "slate_wrapper"
loopy_merged = merge_loopy(slate_loopy, output_arg, builder, var2terminal,
name)
loopy_merged = loopy.register_callable(loopy_merged, INVCallable.name,
INVCallable())
loopy_merged = loopy.register_callable(loopy_merged, SolveCallable.name,
SolveCallable())
loopykernel = op2.Kernel(loopy_merged,
name,
include_dirs=BLASLAPACK_INCLUDE.split(),
ldargs=BLASLAPACK_LIB.split())
kinfo = KernelInfo(
kernel=loopykernel,
integral_type=
"cell", # slate can only do things as contributions to the cell integrals
oriented=builder.bag.needs_cell_orientations,
subdomain_id="otherwise",
domain_number=0,
coefficient_map=tuple(range(len(slate_expr.coefficients()))),
needs_cell_facets=builder.bag.needs_cell_facets,
pass_layer_arg=builder.bag.needs_mesh_layers,
needs_cell_sizes=builder.bag.needs_cell_sizes)
# Cache the resulting kernel
# Slate kernels are never split, so indicate that with None in the index slot.
idx = tuple([None] * slate_expr.rank)
logger.info(GREEN % "compile_slate_expression finished in %g seconds.",
time.time() - cpu_time)
return (SplitKernel(idx, 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(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
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), )
def get_latlon_mesh(mesh):
coords_orig = mesh.coordinates
coords_fs = coords_orig.function_space()
if coords_fs.extruded:
cell = mesh._base_mesh.ufl_cell().cellname()
DG1_hori_elt = FiniteElement("DG", cell, 1, variant="equispaced")
DG1_vert_elt = FiniteElement("DG", interval, 1, variant="equispaced")
DG1_elt = TensorProductElement(DG1_hori_elt, DG1_vert_elt)
else:
cell = mesh.ufl_cell().cellname()
DG1_elt = FiniteElement("DG", cell, 1, variant="equispaced")
vec_DG1 = VectorFunctionSpace(mesh, DG1_elt)
coords_dg = Function(vec_DG1).interpolate(coords_orig)
coords_latlon = Function(vec_DG1)
shapes = {"nDOFs": vec_DG1.finat_element.space_dimension(), 'dim': 3}
radius = np.min(
np.sqrt(coords_dg.dat.data[:, 0]**2 + coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2))
# lat-lon 'x' = atan2(y, x)
coords_latlon.dat.data[:, 0] = np.arctan2(coords_dg.dat.data[:, 1],
coords_dg.dat.data[:, 0])
# lat-lon 'y' = asin(z/sqrt(x^2 + y^2 + z^2))
coords_latlon.dat.data[:, 1] = np.arcsin(
coords_dg.dat.data[:, 2] /
np.sqrt(coords_dg.dat.data[:, 0]**2 + coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2))
# our vertical coordinate is radius - the minimum radius
coords_latlon.dat.data[:,
2] = np.sqrt(coords_dg.dat.data[:, 0]**2 +
coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2) - radius
# We need to ensure that all points in a cell are on the same side of the branch cut in longitude coords
# This kernel amends the longitude coords so that all longitudes in one cell are close together
kernel = op2.Kernel(
"""
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
void splat_coords(double *coords) {{
double max_diff = 0.0;
double diff = 0.0;
for (int i=0; i<{nDOFs}; i++) {{
for (int j=0; j<{nDOFs}; j++) {{
diff = coords[i*{dim}] - coords[j*{dim}];
if (fabs(diff) > max_diff) {{
max_diff = diff;
}}
}}
}}
if (max_diff > PI) {{
for (int i=0; i<{nDOFs}; i++) {{
if (coords[i*{dim}] < 0) {{
coords[i*{dim}] += TWO_PI;
}}
}}
}}
}}
""".format(**shapes), "splat_coords")
op2.par_loop(kernel, coords_latlon.cell_set,
coords_latlon.dat(op2.RW, coords_latlon.cell_node_map()))
return Mesh(coords_latlon)
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.
Returns: A `tuple` containing a `SplitKernel(idx, kinfo)`
"""
if not isinstance(slate_expr, TensorBase):
raise ValueError("Expecting a `TensorBase` expression, not %s" %
type(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")
# If the expression has already been symbolically compiled, then
# simply reuse the produced kernel.
if slate_expr._metakernel_cache is not None:
return slate_expr._metakernel_cache
# Initialize coefficients, shape and statements list
expr_coeffs = slate_expr.coefficients()
# We treat scalars as 1x1 MatrixBase objects, so we give
# the right shape to do so and everything just falls out.
# This bit here ensures the return result has the right
# shape
if slate_expr.rank == 0:
shape = (1, )
else:
shape = slate_expr.shape
statements = []
# Create a builder for the Slate expression
builder = KernelBuilder(expression=slate_expr,
tsfc_parameters=tsfc_parameters)
# Initialize coordinate, cell orientations and facet/layer
# symbols
coordsym = ast.Symbol("coords")
coords = None
cell_orientations = ast.Symbol("cell_orientations")
cellfacetsym = ast.Symbol("cell_facets")
mesh_layer_sym = ast.Symbol("layer")
inc = []
# We keep track of temporaries that have been declared
declared_temps = {}
for cxt_kernel in builder.context_kernels:
exp = cxt_kernel.tensor
t = builder.temps[exp]
if exp not in declared_temps:
# Declare and initialize the temporary
statements.append(ast.Decl(eigen_matrixbase_type(exp.shape), t))
statements.append(ast.FlatBlock("%s.setZero();\n" % t))
declared_temps[exp] = t
it_type = cxt_kernel.original_integral_type
if it_type not in supported_integral_types:
raise NotImplementedError("Type %s not supported." % it_type)
# Explicit checking of coordinates
coordinates = exp.ufl_domain().coordinates
if coords is not None:
assert coordinates == coords
else:
coords = coordinates
if it_type == "cell":
# Nothing difficult about cellwise integrals. Just need
# to get coefficient info, include_dirs and append
# function calls to the appropriate subkernels.
# If tensor is mixed, there will be more than one SplitKernel
incl = []
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)
statements.append(
ast.FunCall(kinfo.kernel.name, tensor, coordsym, *clist))
elif it_type in [
"interior_facet", "exterior_facet", "interior_facet_vert",
"exterior_facet_vert"
]:
# These integral types will require accessing local facet
# information and looping over facet indices.
builder.require_cell_facets()
loop_stmt, incl = facet_integral_loop(cxt_kernel, builder,
coordsym, cellfacetsym,
cell_orientations)
statements.append(loop_stmt)
elif it_type == "interior_facet_horiz":
# The infamous interior horizontal facet
# will have two SplitKernels: one top,
# one bottom. The mesh layer will determine
# which kernels we call.
builder.require_mesh_layers()
top_sks = [
k for k in cxt_kernel.tsfc_kernels
if k.kinfo.integral_type == "exterior_facet_top"
]
bottom_sks = [
k for k in cxt_kernel.tsfc_kernels
if k.kinfo.integral_type == "exterior_facet_bottom"
]
assert len(top_sks) == len(bottom_sks), (
"Number of top and bottom kernels should be equal")
# Top and bottom kernels need to be sorted by kinfo.indices
# if the space is mixed to ensure indices match.
top_sks = sorted(top_sks, key=lambda x: x.indices)
bottom_sks = sorted(bottom_sks, key=lambda x: x.indices)
stmt, incl = extruded_int_horiz_facet(exp, builder, top_sks,
bottom_sks, coordsym,
mesh_layer_sym,
cell_orientations)
statements.append(stmt)
elif it_type in ["exterior_facet_bottom", "exterior_facet_top"]:
# These kernels will only be called if we are on
# the top or bottom layers of the extruded mesh.
builder.require_mesh_layers()
stmt, incl = extruded_top_bottom_facet(cxt_kernel, builder,
coordsym, mesh_layer_sym,
cell_orientations)
statements.append(stmt)
else:
raise ValueError("Kernel type not recognized: %s" % it_type)
# Don't duplicate include lines
inc_dir = list(set(incl) - set(inc))
inc.extend(inc_dir)
# Now we handle any terms that require auxiliary temporaries,
# such as inverses, transposes and actions of a tensor on a
# coefficient
if builder.aux_exprs:
# The declared temps will be updated within this method
aux_statements = auxiliary_temporaries(builder, declared_temps)
statements.extend(aux_statements)
# Now we create the result statement by declaring its eigen type and
# using Eigen::Map to move between Eigen and C data structs.
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)
# Generate the complete c++ string performing the linear algebra operations
# on Eigen matrices/vectors
cpp_string = ast.FlatBlock(
metaphrase_slate_to_cpp(slate_expr, declared_temps))
statements.append(ast.Incr(result_sym, cpp_string))
# Finalize AST for macro kernel construction
builder._finalize_kernels_and_update()
# Generate arguments for the macro kernel
args = [result, ast.Decl("%s **" % SCALAR_TYPE, coordsym)]
# Orientation information
if builder.oriented:
args.append(ast.Decl("int **", cell_orientations))
# Coefficient information
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), cellfacetsym))
# 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", mesh_layer_sym))
# NOTE: In the future we may want to have more than one "macro_kernel"
macro_kernel_name = "compile_slate"
stmt = ast.Block(statements)
macro_kernel = builder.construct_macro_kernel(name=macro_kernel_name,
args=args,
statements=stmt)
# Tell the builder to construct the final ast
kernel_ast = builder.construct_ast([macro_kernel])
# Now we wrap up the kernel ast as a PyOP2 kernel.
# Include the Eigen header files
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, (
"No support for multiple domains yet!")
# 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)
idx = tuple([0] * slate_expr.rank)
kernels = (SplitKernel(idx, kinfo), )
# Store the resulting kernel for reuse
slate_expr._metakernel_cache = kernels
return kernels
def eigen_kernel(kernel, *args, **kwargs):
"""
Helper function to easily pass Eigen kernels to Firedrake via PyOP2.
"""
return op2.Kernel(kernel(*args, **kwargs), kernel.__name__, cpp=True, include_dirs=include_dir)