def create_pyop2_node(typ, exp1, exp2):
"""Create an expr node starting from two FFC symbols."""
if typ == 2:
return pyop2.Prod(exp1, exp2)
if typ == 3:
return pyop2.Sum(exp1, exp2)
if typ == 4:
return pyop2.Div(exp1, exp2)
def auxiliary_information(builder):
"""This function generates any auxiliary information regarding special handling of
expressions that do not have any integral forms or subkernels associated with it.
:arg builder: a :class:`SlateKernelBuilder` object that contains all the necessary
temporary and expression information.
Returns: a mapping of the form ``{aux_node: aux_temp}``, where `aux_node` is an
already assembled data-object provided as a `ufl.Coefficient` and `aux_temp`
is the corresponding temporary.
a list of auxiliary statements are returned that contain temporary declarations
and any code-blocks needed to evaluate the expression.
"""
aux_temps = {}
aux_statements = []
for i, exp in enumerate(builder.aux_exprs):
if isinstance(exp, Action):
acting_coefficient = exp._acting_coefficient
assert isinstance(acting_coefficient, Coefficient)
temp = ast.Symbol("C%d" % i)
V = acting_coefficient.function_space()
node_extent = V.fiat_element.space_dimension()
dof_extent = np.prod(V.ufl_element().value_shape())
aux_statements.append(
ast.Decl(
eigen_matrixbase_type(shape=(dof_extent * node_extent, )),
temp))
aux_statements.append(ast.FlatBlock("%s.setZero();\n" % temp))
# Now we unpack the coefficient and insert its entries into a 1D vector temporary
isym = ast.Symbol("i1")
jsym = ast.Symbol("j1")
tensor_index = ast.Sum(ast.Prod(dof_extent, isym), jsym)
# Inner-loop running over dof_extent
inner_loop = ast.For(
ast.Decl("unsigned int", jsym, init=0),
ast.Less(jsym, dof_extent), ast.Incr(jsym, 1),
ast.Assign(
ast.Symbol(temp, rank=(tensor_index, )),
ast.Symbol(builder.coefficient_map[acting_coefficient],
rank=(isym, jsym))))
# Outer-loop running over node_extent
loop = ast.For(ast.Decl("unsigned int", isym, init=0),
ast.Less(isym, node_extent), ast.Incr(isym, 1),
inner_loop)
aux_statements.append(loop)
aux_temps[acting_coefficient] = temp
else:
raise NotImplementedError(
"Auxiliary expression type %s not currently implemented." %
type(exp))
return aux_temps, aux_statements
def get_restriction_kernel(fiat_element, unique_indices, dim=1, no_weights=False):
weights = restriction_weights(fiat_element)[unique_indices].T
ncdof = weights.shape[0]
nfdof = weights.shape[1]
arglist = [ast.Decl("double", ast.Symbol("coarse", (ncdof*dim, ))),
ast.Decl("double *restrict *restrict ", ast.Symbol("fine", ()),
qualifiers=["const"])]
if not no_weights:
arglist.append(ast.Decl("double *restrict *restrict", ast.Symbol("count_weights", ()),
qualifiers=["const"]))
all_ones = np.allclose(weights, 1.0)
if all_ones:
w = []
else:
w_sym = ast.Symbol("weights", (ncdof, nfdof))
init = ast.ArrayInit(format_array_literal(weights))
w = [ast.Decl("double", w_sym, init,
qualifiers=["const"])]
i = ast.Symbol("i", ())
j = ast.Symbol("j", ())
k = ast.Symbol("k", ())
fine = ast.Symbol("fine", (j, k))
if no_weights:
if all_ones:
assign = fine
else:
assign = ast.Prod(fine, ast.Symbol("weights", (i, j)))
else:
if all_ones:
assign = ast.Prod(fine, ast.Symbol("count_weights", (j, 0)))
else:
assign = ast.Prod(fine,
ast.Prod(ast.Symbol("weights", (i, j)),
ast.Symbol("count_weights", (j, 0))))
assignment = ast.Incr(ast.Symbol("coarse", (ast.Sum(k, ast.Prod(i, ast.c_sym(dim))),)),
assign)
k_loop = ast.For(ast.Decl("int", k, ast.c_sym(0)),
ast.Less(k, ast.c_sym(dim)),
ast.Incr(k, ast.c_sym(1)),
ast.Block([assignment], open_scope=True))
j_loop = ast.For(ast.Decl("int", j, ast.c_sym(0)),
ast.Less(j, ast.c_sym(nfdof)),
ast.Incr(j, ast.c_sym(1)),
ast.Block([k_loop], open_scope=True))
i_loop = ast.For(ast.Decl("int", i, ast.c_sym(0)),
ast.Less(i, ast.c_sym(ncdof)),
ast.Incr(i, ast.c_sym(1)),
ast.Block([j_loop], open_scope=True))
k = ast.FunDecl("void", "restriction", arglist, ast.Block(w + [i_loop]),
pred=["static", "inline"])
return op2.Kernel(k, "restriction", opts=parameters["coffee"])
def get_injection_kernel(fiat_element, unique_indices, dim=1):
weights = injection_weights(fiat_element)[unique_indices].T
ncdof = weights.shape[0]
nfdof = weights.shape[1]
# What if we have multiple nodes in same location (DG)? Divide by
# rowsum.
weights = weights / np.sum(weights, axis=1).reshape(-1, 1)
all_same = np.allclose(weights, weights[0, 0])
arglist = [
ast.Decl("double", ast.Symbol("coarse", (ncdof * dim, ))),
ast.Decl("double *restrict *restrict ",
ast.Symbol("fine", ()),
qualifiers=["const"])
]
if all_same:
w_sym = ast.Symbol("weights", ())
w = [ast.Decl("double", w_sym, weights[0, 0], qualifiers=["const"])]
else:
init = ast.ArrayInit(format_array_literal(weights))
w_sym = ast.Symbol("weights", (ncdof, nfdof))
w = [ast.Decl("double", w_sym, init, qualifiers=["const"])]
i = ast.Symbol("i", ())
j = ast.Symbol("j", ())
k = ast.Symbol("k", ())
if all_same:
assign = ast.Prod(ast.Symbol("fine", (j, k)), w_sym)
else:
assign = ast.Prod(ast.Symbol("fine", (j, k)),
ast.Symbol("weights", (i, j)))
assignment = ast.Incr(
ast.Symbol("coarse", (ast.Sum(k, ast.Prod(i, ast.c_sym(dim))), )),
assign)
k_loop = ast.For(ast.Decl("int", k, ast.c_sym(0)),
ast.Less(k, ast.c_sym(dim)), ast.Incr(k, ast.c_sym(1)),
ast.Block([assignment], open_scope=True))
j_loop = ast.For(ast.Decl("int", j, ast.c_sym(0)),
ast.Less(j, ast.c_sym(nfdof)), ast.Incr(j, ast.c_sym(1)),
ast.Block([k_loop], open_scope=True))
i_loop = ast.For(ast.Decl("int", i, ast.c_sym(0)),
ast.Less(i, ast.c_sym(ncdof)), ast.Incr(i, ast.c_sym(1)),
ast.Block([j_loop], open_scope=True))
k = ast.FunDecl("void",
"injection",
arglist,
ast.Block(w + [i_loop]),
pred=["static", "inline"])
return op2.Kernel(k, "injection", opts=parameters["coffee"])
def get_prolongation_kernel(fiat_element, unique_indices, dim=1):
weights = get_restriction_weights(fiat_element)[unique_indices]
nfdof = weights.shape[0]
ncdof = weights.shape[1]
arglist = [
ast.Decl("double", ast.Symbol("fine", (nfdof * dim, ))),
ast.Decl("double",
ast.Symbol("*restrict *restrict coarse", ()),
qualifiers=["const"])
]
all_same = np.allclose(weights, weights[0, 0])
if all_same:
w_sym = ast.Symbol("weights", ())
w = [ast.Decl("double", w_sym, weights[0, 0], qualifiers=["const"])]
else:
w_sym = ast.Symbol("weights", (nfdof, ncdof))
init = ast.ArrayInit(format_array_literal(weights))
w = [ast.Decl("double", w_sym, init, qualifiers=["const"])]
i = ast.Symbol("i", ())
j = ast.Symbol("j", ())
k = ast.Symbol("k", ())
if all_same:
assign = ast.Prod(ast.Symbol("coarse", (j, k)), w_sym)
else:
assign = ast.Prod(ast.Symbol("coarse", (j, k)),
ast.Symbol("weights", (i, j)))
assignment = ast.Incr(
ast.Symbol("fine", (ast.Sum(k, ast.Prod(i, ast.c_sym(dim))), )),
assign)
k_loop = ast.For(ast.Decl("int", k, ast.c_sym(0)),
ast.Less(k, ast.c_sym(dim)), ast.Incr(k, ast.c_sym(1)),
ast.Block([assignment], open_scope=True))
j_loop = ast.For(ast.Decl("int", j, ast.c_sym(0)),
ast.Less(j, ast.c_sym(ncdof)), ast.Incr(j, ast.c_sym(1)),
ast.Block([k_loop], open_scope=True))
i_loop = ast.For(ast.Decl("int", i, ast.c_sym(0)),
ast.Less(i, ast.c_sym(nfdof)), ast.Incr(i, ast.c_sym(1)),
ast.Block([j_loop], open_scope=True))
k = ast.FunDecl("void",
"prolongation",
arglist,
ast.Block(w + [i_loop]),
pred=["static", "inline"])
return op2.Kernel(k, "prolongation", opts=parameters["coffee"])
def coefficient_temporaries(builder, declared_temps):
"""Generates coefficient temporary statements for assigning
coefficients to vector temporaries.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information.
:arg declared_temps: A `dict` keeping track of all declared
temporaries. This dictionary is updated as coefficients
are assigned temporaries.
'AssembledVector's require creating coefficient temporaries to
store data. The temporaries are created by inspecting the function
space of the coefficient to compute node and dof extents. The
coefficient is then assigned values by looping over both the node
extent and dof extent (double FOR-loop). A double FOR-loop is needed
for each function space (if the function space is mixed, then a loop
will be constructed for each component space). The general structure
of each coefficient loop will be:
FOR (i1=0; i1<node_extent; i1++):
FOR (j1=0; j1<dof_extent; j1++):
VT0[offset + (dof_extent * i1) + j1] = w_0_0[i1][j1]
VT1[offset + (dof_extent * i1) + j1] = w_1_0[i1][j1]
.
.
.
where wT0, wT1, ... are temporaries for coefficients sharing the
same node and dof extents. The offset is computed based on whether
the function space is mixed. The offset is always 0 for non-mixed
coefficients. If the coefficient is mixed, then the offset is
incremented by the total number of nodal unknowns associated with
the component spaces of the mixed space.
"""
statements = [ast.FlatBlock("/* Coefficient temporaries */\n")]
j = ast.Symbol("j1")
loops = [ast.FlatBlock("/* Loops for coefficient temps */\n")]
for dofs, cinfo_list in builder.coefficient_vecs.items():
# Collect all coefficients which share the same node/dof extent
assignments = []
for cinfo in cinfo_list:
fs_i = cinfo.space_index
offset = cinfo.offset_index
c_shape = cinfo.shape
vector = cinfo.vector
function = vector._function
t = cinfo.local_temp
if vector not in declared_temps:
# Declare and initialize coefficient temporary
c_type = eigen_matrixbase_type(shape=c_shape)
statements.append(ast.Decl(c_type, t))
declared_temps[vector] = t
# Assigning coefficient values into temporary
coeff_sym = ast.Symbol(builder.coefficient(function)[fs_i],
rank=(j, ))
index = ast.Sum(offset, j)
coeff_temp = ast.Symbol(t, rank=(index, ))
assignments.append(ast.Assign(coeff_temp, coeff_sym))
# loop over dofs
loop = ast.For(ast.Decl("unsigned int", j, init=0), ast.Less(j, dofs),
ast.Incr(j, 1), assignments)
loops.append(loop)
statements.extend(loops)
return statements
a.function = weakref.proxy(a.function)
vals.append((k, args))
if result._expression_cache is not None:
result._expression_cache[key] = vals
def assemble_expression(expr, subset=None):
"""Evaluates UFL expressions on :class:`.Function`\s pointwise and assigns
into a new :class:`.Function`."""
result = function.Function(ExpressionWalker().walk(expr)[2])
evaluate_expression(Assign(result, expr), subset)
return result
_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)),
def auxiliary_temporaries(builder, declared_temps):
"""This function generates auxiliary information regarding special
handling of expressions that require creating additional temporaries.
:arg builder: a :class:`KernelBuilder` object that contains all the
necessary temporary and expression information.
:arg declared_temps: a `dict` of temporaries that have already been
declared and assigned values. This will be
updated in this method and referenced later
in the compiler.
Returns: a list of auxiliary statements are returned that contain temporary
declarations and any code-blocks needed to evaluate the
expression.
"""
aux_statements = []
for exp in builder.aux_exprs:
if isinstance(exp, Inverse):
if builder._ref_counts[exp] > 1:
# Get the temporary for the particular expression
result = metaphrase_slate_to_cpp(exp, declared_temps)
# Now we use the generated result and assign the value to the
# corresponding temporary.
temp = ast.Symbol("auxT%d" % len(declared_temps))
shape = exp.shape
aux_statements.append(
ast.Decl(eigen_matrixbase_type(shape), temp))
aux_statements.append(ast.FlatBlock("%s.setZero();\n" % temp))
aux_statements.append(ast.Assign(temp, result))
# Update declared temps
declared_temps[exp] = temp
elif isinstance(exp, Action):
# Action computations are relatively inexpensive, so
# we don't waste memory space on creating temps for
# these expressions. However, we must create a temporary
# for the actee coefficient (if we haven't already).
actee, = exp.actee
if actee not in declared_temps:
# Declare a temporary for the coefficient
V = actee.function_space()
shape_array = [(Vi.finat_element.space_dimension(),
np.prod(Vi.shape)) for Vi in V.split()]
ctemp = ast.Symbol("auxT%d" % len(declared_temps))
shape = sum(n * d for (n, d) in shape_array)
typ = eigen_matrixbase_type(shape=(shape, ))
aux_statements.append(ast.Decl(typ, ctemp))
aux_statements.append(ast.FlatBlock("%s.setZero();\n" % ctemp))
# Now we populate the temporary with the coefficient
# information and insert in the right place.
offset = 0
for i, shp in enumerate(shape_array):
node_extent, dof_extent = shp
# Now we unpack the function and insert its entries into a
# 1D vector temporary
isym = ast.Symbol("i1")
jsym = ast.Symbol("j1")
tensor_index = ast.Sum(
offset, ast.Sum(ast.Prod(dof_extent, isym), jsym))
# Inner-loop running over dof_extent
coeff_sym = ast.Symbol(builder.coefficient(actee)[i],
rank=(isym, jsym))
coeff_temp = ast.Symbol(ctemp, rank=(tensor_index, ))
inner_loop = ast.For(
ast.Decl("unsigned int", jsym, init=0),
ast.Less(jsym, dof_extent), ast.Incr(jsym, 1),
ast.Assign(coeff_temp, coeff_sym))
# Outer-loop running over node_extent
loop = ast.For(ast.Decl("unsigned int", isym, init=0),
ast.Less(isym, node_extent),
ast.Incr(isym, 1), inner_loop)
aux_statements.append(loop)
offset += node_extent * dof_extent
# Update declared temporaries with the coefficient
declared_temps[actee] = ctemp
else:
raise NotImplementedError(
"Auxiliary expr type %s not currently implemented." %
type(exp))
return aux_statements
def _expression_sum(expr, parameters):
return coffee.Sum(*[expression(c, parameters)
for c in expr.children])
def compile_c_kernel(expression, to_pts, to_element, fs, coords):
"""Produce a :class:`PyOP2.Kernel` from the c expression provided."""
coords_space = coords.function_space()
coords_element = create_element(coords_space.ufl_element(),
vector_is_mixed=False)
names = {v[0] for v in expression._user_args}
X = list(coords_element.tabulate(0, to_pts).values())[0]
# Produce C array notation of X.
X_str = "{{" + "},\n{".join([",".join(map(str, x)) for x in X.T]) + "}}"
A = utils.unique_name("A", names)
X = utils.unique_name("X", names)
x_ = utils.unique_name("x_", names)
k = utils.unique_name("k", names)
d = utils.unique_name("d", names)
i_ = utils.unique_name("i", names)
# x is a reserved name.
x = "x"
if "x" in names:
raise ValueError(
"cannot use 'x' as a user-defined Expression variable")
ass_exp = [
ast.Assign(ast.Symbol(A, (k, ), ((len(expression.code), i), )),
ast.FlatBlock("%s" % code))
for i, code in enumerate(expression.code)
]
dim = coords_space.value_size
ndof = to_element.space_dimension()
xndof = coords_element.space_dimension()
nfdof = to_element.space_dimension() * numpy.prod(fs.value_size, dtype=int)
init_X = ast.Decl(typ="double",
sym=ast.Symbol(X, rank=(ndof, xndof)),
qualifiers=["const"],
init=X_str)
init_x = ast.Decl(typ="double",
sym=ast.Symbol(x, rank=(coords_space.value_size, )))
init_pi = ast.Decl(typ="double",
sym="pi",
qualifiers=["const"],
init="3.141592653589793")
init = ast.Block([init_X, init_x, init_pi])
incr_x = ast.Incr(
ast.Symbol(x, rank=(d, )),
ast.Prod(ast.Symbol(X, rank=(k, i_)),
ast.Symbol(x_, rank=(ast.Sum(ast.Prod(i_, dim), d), ))))
assign_x = ast.Assign(ast.Symbol(x, rank=(d, )), 0)
loop_x = ast.For(init=ast.Decl("unsigned int", i_, 0),
cond=ast.Less(i_, xndof),
incr=ast.Incr(i_, 1),
body=[incr_x])
block = ast.For(init=ast.Decl("unsigned int", d, 0),
cond=ast.Less(d, dim),
incr=ast.Incr(d, 1),
body=[assign_x, loop_x])
loop = ast.c_for(k, ndof, ast.Block([block] + ass_exp, open_scope=True))
user_args = []
user_init = []
for _, arg in expression._user_args:
if arg.shape == (1, ):
user_args.append(ast.Decl("double *", "%s_" % arg.name))
user_init.append(
ast.FlatBlock("const double %s = *%s_;" %
(arg.name, arg.name)))
else:
user_args.append(ast.Decl("double *", arg.name))
kernel_code = ast.FunDecl(
"void", "expression_kernel", [
ast.Decl("double", ast.Symbol(A, (nfdof, ))),
ast.Decl("double*", x_)
] + user_args, ast.Block(user_init + [init, loop], open_scope=False))
coefficients = [coords]
for _, arg in expression._user_args:
coefficients.append(GlobalWrapper(arg))
return op2.Kernel(kernel_code,
kernel_code.name), False, tuple(coefficients)
def coefficient_temporaries(builder, declared_temps):
"""Generates coefficient temporary statements for assigning
coefficients to vector temporaries.
:arg builder: The :class:`LocalKernelBuilder` containing
all relevant expression information.
:arg declared_temps: A `dict` keeping track of all declared
temporaries. This dictionary is updated
as coefficients are assigned temporaries.
Action computations require creating coefficient temporaries to
compute the matrix-vector product. The temporaries are created by
inspecting the function space of the coefficient to compute node
and dof extents. The coefficient is then assigned values by looping
over both the node extent and dof extent (double FOR-loop). A double
FOR-loop is needed for each function space (if the function space is
mixed, then a loop will be constructed for each component space).
The general structure of each coefficient loop will be:
FOR (i1=0; i1<node_extent; i1++):
FOR (j1=0; j1<dof_extent; j1++):
wT0[offset + (dof_extent * i1) + j1] = w_0_0[i1][j1]
wT1[offset + (dof_extent * i1) + j1] = w_1_0[i1][j1]
.
.
.
where wT0, wT1, ... are temporaries for coefficients sharing the
same node and dof extents. The offset is computed based on whether
the function space is mixed. The offset is always 0 for non-mixed
coefficients. If the coefficient is mixed, then the offset is
incremented by the total number of nodal unknowns associated with
the component spaces of the mixed space.
"""
statements = [ast.FlatBlock("/* Coefficient temporaries */\n")]
i_sym = ast.Symbol("i1")
j_sym = ast.Symbol("j1")
loops = [ast.FlatBlock("/* Loops for coefficient temps */\n")]
for (nodes, dofs), cinfo_list in builder.action_coefficients.items():
# Collect all coefficients which share the same node/dof extent
assignments = []
for cinfo in cinfo_list:
fs_i = cinfo.space_index
offset = cinfo.offset_index
c_shape = cinfo.shape
actee = cinfo.coefficient
if actee not in declared_temps:
# Declare and initialize coefficient temporary
c_type = eigen_matrixbase_type(shape=c_shape)
t = ast.Symbol("wT%d" % len(declared_temps))
statements.append(ast.Decl(c_type, t))
statements.append(ast.FlatBlock("%s.setZero();\n" % t))
declared_temps[actee] = t
# Assigning coefficient values into temporary
coeff_sym = ast.Symbol(builder.coefficient(actee)[fs_i],
rank=(i_sym, j_sym))
index = ast.Sum(offset, ast.Sum(ast.Prod(dofs, i_sym), j_sym))
coeff_temp = ast.Symbol(t, rank=(index, ))
assignments.append(ast.Assign(coeff_temp, coeff_sym))
# Inner-loop running over dof extent
inner_loop = ast.For(ast.Decl("unsigned int", j_sym, init=0),
ast.Less(j_sym, dofs), ast.Incr(j_sym, 1),
assignments)
# Outer-loop running over node extent
loop = ast.For(ast.Decl("unsigned int", i_sym, init=0),
ast.Less(i_sym, nodes), ast.Incr(i_sym, 1), inner_loop)
loops.append(loop)
statements.extend(loops)
return statements
