def test_triangle_variant_spectral_fail_l2():
ufl_element = ufl.FiniteElement('DP L2',
ufl.triangle,
2,
variant='spectral')
with pytest.raises(ValueError):
create_element(ufl_element)
def test_cache_hit_vector(ufl_vector_element):
A = f.create_element(ufl_vector_element)
B = f.create_element(ufl_vector_element)
assert A is B
assert all(a == A.elements()[0] for a in A.elements())
def test_cache_miss_vector(ufl_vector_element):
A = f.create_element(ufl_vector_element)
B = f.create_element(ufl_vector_element, vector_is_mixed=False)
assert A is not B
assert A.elements()[0] is not B
def test_tensor_prod_simple(ufl_A, ufl_B):
tensor_ufl = ufl.TensorProductElement(ufl_A, ufl_B)
tensor = f.create_element(tensor_ufl)
A = f.create_element(ufl_A)
B = f.create_element(ufl_B)
assert isinstance(tensor, f.supported_elements[tensor_ufl.family()])
assert tensor.A is A
assert tensor.B is B
def test_tensor_prod_simple(ufl_A, ufl_B):
tensor_ufl = ufl.TensorProductElement(ufl_A, ufl_B)
tensor = create_element(tensor_ufl)
A = create_element(ufl_A)
B = create_element(ufl_B)
assert isinstance(tensor, supported_elements[tensor_ufl.family()])
assert tensor.A is A
assert tensor.B is B
def test_tensor_prod_simple(ufl_A, ufl_B):
tensor_ufl = ufl.TensorProductElement(ufl_A, ufl_B)
tensor = create_element(tensor_ufl)
A = create_element(ufl_A)
B = create_element(ufl_B)
assert isinstance(tensor, FIAT.TensorProductElement)
assert tensor.A is A
assert tensor.B is B
def test_tensor_prod_simple(ufl_A, ufl_B):
tensor_ufl = ufl.TensorProductElement(ufl_A, ufl_B)
tensor = create_element(tensor_ufl)
A = create_element(ufl_A)
B = create_element(ufl_B)
assert isinstance(tensor, FIAT.TensorProductElement)
assert tensor.A is A
assert tensor.B is B
def test_triangle_vector(mixed, ufl_element, ufl_vector_element):
scalar = f.create_element(ufl_element)
vector = f.create_element(ufl_vector_element, vector_is_mixed=mixed)
if not mixed:
assert isinstance(scalar, f.supported_elements[ufl_element.family()])
assert isinstance(vector, f.supported_elements[ufl_element.family()])
else:
assert isinstance(vector, f.MixedElement)
assert isinstance(vector.elements()[0], f.supported_elements[ufl_element.family()])
assert len(vector.elements()) == ufl_vector_element.num_sub_elements()
def test_quadrilateral_variant_spectral_rtcf():
element = create_element(
ufl.FiniteElement('RTCF', ufl.quadrilateral, 2, variant='spectral'))
assert isinstance(element.element.A.A, FIAT.GaussLobattoLegendre)
assert isinstance(element.element.A.B, FIAT.GaussLegendre)
assert isinstance(element.element.B.A, FIAT.GaussLegendre)
assert isinstance(element.element.B.B, FIAT.GaussLobattoLegendre)
def compile_python_kernel(expression, to_pts, to_element, fs, coords):
"""Produce a :class:`PyOP2.Kernel` wrapping the eval method on the
function provided."""
coords_space = coords.function_space()
coords_element = create_element(coords_space.ufl_element(), vector_is_mixed=False)
X_remap = list(coords_element.tabulate(0, to_pts).values())[0]
# The par_loop will just pass us arguments, since it doesn't
# know about keyword args at all so unpack into a dict that we
# can pass to the user's eval method.
def kernel(output, x, *args):
kwargs = {}
for (slot, _), arg in zip(expression._user_args, args):
kwargs[slot] = arg
X = numpy.dot(X_remap.T, x)
for i in range(len(output)):
# Pass a slice for the scalar case but just the
# current vector in the VFS case. This ensures the
# eval method has a Dolfin compatible API.
expression.eval(output[i:i+1, ...] if numpy.ndim(output) == 1 else output[i, ...],
X[i:i+1, ...] if numpy.ndim(X) == 1 else X[i, ...], **kwargs)
coefficients = [coords]
for _, arg in expression._user_args:
coefficients.append(GlobalWrapper(arg))
return kernel, False, False, tuple(coefficients)
def _calculate_values(function, points, dimension, cell_mask=None):
"""Calculate function values at given reference points
:arg function: function to be sampled
:arg points: points to be sampled in reference space
:arg cell_mask: Masks for cell node list
"""
import numpy.ma as ma
function_space = function.function_space()
keys = {1: (0,),
2: (0, 0)}
fiat_element = create_element(function_space.ufl_element(), vector_is_mixed=False)
elem = fiat_element.tabulate(0, points)[keys[dimension]]
cell_node_list = function_space.cell_node_list
if cell_mask is not None:
cell_mask = np.tile(cell_mask.reshape(-1, 1), cell_node_list.shape[1])
cell_node_list = ma.compress_rows(ma.masked_array(cell_node_list,
mask=cell_mask))
data = function.dat.data_ro[cell_node_list]
if function.ufl_shape == ():
vec_length = 1
else:
vec_length = function.ufl_shape[0]
if vec_length == 1:
data = np.reshape(data, data.shape+(1, ))
return np.einsum("ijk,jl->ilk", data, elem)
def _calculate_values(function, points, dimension, cell_mask=None):
"""Calculate function values at given reference points
:arg function: function to be sampled
:arg points: points to be sampled in reference space
:arg cell_mask: Masks for cell node list
"""
import numpy.ma as ma
function_space = function.function_space()
keys = {1: (0,),
2: (0, 0)}
fiat_element = create_element(function_space.ufl_element(), vector_is_mixed=False)
elem = fiat_element.tabulate(0, points)[keys[dimension]]
cell_node_list = function_space.cell_node_list
if cell_mask is not None:
cell_mask = np.tile(cell_mask.reshape(-1, 1), cell_node_list.shape[1])
cell_node_list = ma.compress_rows(ma.masked_array(cell_node_list,
mask=cell_mask))
data = function.dat.data_ro[cell_node_list]
if function.ufl_shape == ():
vec_length = 1
else:
vec_length = function.ufl_shape[0]
if vec_length == 1:
data = np.reshape(data, data.shape+(1, ))
return np.einsum("ijk,jl->ilk", data, elem)
def get_transfer_kernel(coarse, fine, typ=None):
ch, level = get_level(coarse.mesh())
mesh = ch[0]
assert hasattr(mesh, "_shared_data_cache")
key = entity_dofs_key(coarse.finat_element.entity_dofs()) + (typ, coarse.dim)
cache = mesh._shared_data_cache["hierarchy_transfer_kernel"]
try:
return cache[key]
except KeyError:
if not (coarse.ufl_element() == fine.ufl_element()):
raise ValueError("Can't transfer between different spaces")
ch, level = get_level(coarse.mesh())
fh, fine_level = get_level(fine.mesh())
refinements_per_level = ch.refinements_per_level
assert ch is fh
assert refinements_per_level*level + 1 == refinements_per_level*fine_level
dim = coarse.dim
element = create_element(coarse.ufl_element(), vector_is_mixed=False)
omap = fine.cell_node_map().values
c2f, vperm = ch._cells_vperm[int(level*refinements_per_level)]
indices, _ = get_unique_indices(element,
omap[c2f[0, :], ...].reshape(-1),
vperm[0, :],
offset=None)
if typ == "prolong":
kernel = get_prolongation_kernel(element, indices, dim)
elif typ == "inject":
kernel = get_injection_kernel(element, indices, dim)
elif typ == "restrict":
discontinuous = element.entity_dofs() == element.entity_closure_dofs()
kernel = get_restriction_kernel(element, indices, dim, no_weights=discontinuous)
else:
raise ValueError("Unknown transfer type '%s'" % typ)
return cache.setdefault(key, kernel)
def convert_finiteelement(element):
cell = as_fiat_cell(element.cell())
if element.family() not in supported_elements:
return fiat_compat(element)
lmbda = supported_elements.get(element.family())
if lmbda is None:
if element.cell().cellname() != "quadrilateral":
raise ValueError("%s is supported, but handled incorrectly" %
element.family())
# Handle quadrilateral short names like RTCF and RTCE.
element = element.reconstruct(cell=quad_tpc)
return finat.QuadrilateralElement(create_element(element))
kind = element.variant()
if kind is None:
kind = 'equispaced' # default variant
if element.family() == "Lagrange":
if kind == 'equispaced':
lmbda = finat.Lagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLobattoLegendre
else:
raise ValueError("Variant %r not supported on %s" %
(kind, element.cell()))
elif element.family() == "Discontinuous Lagrange":
kind = element.variant() or 'equispaced'
if kind == 'equispaced':
lmbda = finat.DiscontinuousLagrange
elif kind == 'spectral' and element.cell().cellname() == 'interval':
lmbda = finat.GaussLegendre
else:
raise ValueError("Variant %r not supported on %s" %
(kind, element.cell()))
return lmbda(cell, element.degree())
def fix_coarse_boundaries(cV, fV):
# With lots of help from Lawrence Mitchell
c2fmap = coarse_to_fine_node_map(cV, fV)
cmesh = cV.mesh()
ch, level = get_level(cmesh)
refinements_per_level = ch.refinements_per_level
element = create_element(cV.ufl_element(), vector_is_mixed=False)
omap = fV.cell_node_map().values
c2f, vperm = ch._cells_vperm[int(level * refinements_per_level)]
indices, _ = get_unique_indices(element,
omap[c2f[0, :], ...].reshape(-1),
vperm[0, :],
offset=None)
weights = restriction_weights(element)[indices]
sums = (weights > 0).sum(axis=1)
indices_to_fix = where(sums <= cmesh.topological_dimension())[0]
nodelist = unique(c2fmap.values[:, indices_to_fix])
class FixedDirichletBC(DirichletBC):
def __init__(self, V, g, nodelist):
self.nodelist = nodelist
DirichletBC.__init__(self, V, g, "on_boundary")
@utils.cached_property
def nodes(self):
return self.nodelist
bc = FixedDirichletBC(fV, (0, 0), nodelist)
return bc
def compile_python_kernel(expression, to_pts, to_element, fs, coords):
"""Produce a :class:`PyOP2.Kernel` wrapping the eval method on the
function provided."""
coords_space = coords.function_space()
coords_element = create_element(coords_space.ufl_element(), vector_is_mixed=False)
X_remap = list(coords_element.tabulate(0, to_pts).values())[0]
# The par_loop will just pass us arguments, since it doesn't
# know about keyword args at all so unpack into a dict that we
# can pass to the user's eval method.
def kernel(output, x, *args):
kwargs = {}
for (slot, _), arg in zip(expression._user_args, args):
kwargs[slot] = arg
X = numpy.dot(X_remap.T, x)
for i in range(len(output)):
# Pass a slice for the scalar case but just the
# current vector in the VFS case. This ensures the
# eval method has a Dolfin compatible API.
expression.eval(output[i:i+1, ...] if numpy.ndim(output) == 1 else output[i, ...],
X[i:i+1, ...] if numpy.ndim(X) == 1 else X[i, ...], **kwargs)
coefficients = [coords]
for _, arg in expression._user_args:
coefficients.append(GlobalWrapper(arg))
return kernel, False, False, tuple(coefficients)
def _interpolator(V, dat, expr, subset):
to_element = create_element(V.ufl_element(), vector_is_mixed=False)
to_pts = []
if V.ufl_element().mapping() != "identity":
raise NotImplementedError("Can only interpolate onto elements "
"with affine mapping. Try projecting instead")
for dual in to_element.dual_basis():
if not isinstance(dual, FIAT.functional.PointEvaluation):
raise NotImplementedError("Can only interpolate onto point "
"evaluation operators. Try projecting instead")
to_pts.append(list(iterkeys(dual.pt_dict))[0])
if len(expr.ufl_shape) != len(V.ufl_element().value_shape()):
raise RuntimeError('Rank mismatch: Expression rank %d, FunctionSpace rank %d'
% (len(expr.ufl_shape), len(V.ufl_element().value_shape())))
if expr.ufl_shape != V.ufl_element().value_shape():
raise RuntimeError('Shape mismatch: Expression shape %r, FunctionSpace shape %r'
% (expr.ufl_shape, V.ufl_element().value_shape()))
mesh = V.ufl_domain()
coords = mesh.coordinates
if not isinstance(expr, (firedrake.Expression, SubExpression)):
if expr.ufl_domain() and expr.ufl_domain() != V.mesh():
raise NotImplementedError("Interpolation onto another mesh not supported.")
if expr.ufl_shape != V.shape:
raise ValueError("UFL expression has incorrect shape for interpolation.")
ast, oriented, coefficients = compile_ufl_kernel(expr, to_pts, coords)
kernel = op2.Kernel(ast, ast.name)
indexed = True
elif hasattr(expr, "eval"):
kernel, oriented, coefficients = compile_python_kernel(expr, to_pts, to_element, V, coords)
indexed = False
elif expr.code is not None:
kernel, oriented, coefficients = compile_c_kernel(expr, to_pts, to_element, V, coords)
indexed = True
else:
raise RuntimeError("Attempting to evaluate an Expression which has no value.")
cell_set = coords.cell_set
if subset is not None:
assert subset.superset == cell_set
cell_set = subset
args = [kernel, cell_set]
if indexed:
args.append(dat(op2.WRITE, V.cell_node_map()[op2.i[0]]))
else:
args.append(dat(op2.WRITE, V.cell_node_map()))
if oriented:
co = mesh.cell_orientations()
args.append(co.dat(op2.READ, co.cell_node_map()))
for coefficient in coefficients:
args.append(coefficient.dat(op2.READ, coefficient.cell_node_map()))
return partial(op2.par_loop, *args)
def prolongation_transfer_kernel_action(Vf, expr):
from tsfc import compile_expression_dual_evaluation
from tsfc.fiatinterface import create_element
coords = Vf.ufl_domain().coordinates
to_element = create_element(Vf.ufl_element(), vector_is_mixed=False)
ast, oriented, needs_cell_sizes, coefficients, _ = compile_expression_dual_evaluation(
expr, to_element, coords, coffee=False)
return op2.Kernel(ast, ast.name)
def firedrake_local_to_cart(element):
r"""Gets the list of nodes for an element (provided they exist.)
:arg element: a ufl element.
:returns: a list of arrays of floats where each array is a node.
"""
fiat_element = create_element(element, vector_is_mixed=False)
# TODO: Surely there is an easier way that I've forgotten?
return [np.array(list(phi.get_point_dict().keys())[0])
for phi in fiat_element.dual_basis()]
def prolongation_transfer_kernel_aij(Pk, P1):
# Works for Pk, Pm; I just retain the notation
# P1 to remind you that P1 is of lower degree
# than Pk
from tsfc import compile_expression_dual_evaluation
from tsfc.fiatinterface import create_element
from firedrake import TestFunction
expr = TestFunction(P1)
coords = Pk.ufl_domain().coordinates
to_element = create_element(Pk.ufl_element(), vector_is_mixed=False)
ast, oriented, needs_cell_sizes, coefficients, _ = compile_expression_dual_evaluation(expr, to_element, coords, coffee=False)
kernel = op2.Kernel(ast, ast.name)
return kernel
def _bezier_calculate_points(function):
"""Calculate points values for a function used for bezier plotting
:arg function: 1D Function with 1 < deg < 4
"""
deg = function.function_space().ufl_element().degree()
M = np.empty([deg + 1, deg + 1], dtype=float)
fiat_element = create_element(function.function_space().ufl_element(), vector_is_mixed=False)
basis = fiat_element.dual_basis()
for i in range(deg + 1):
for j in range(deg + 1):
M[i, j] = _bernstein(list(basis[j].get_point_dict().keys())[0][0],
i, deg)
M_inv = np.linalg.inv(M)
cell_node_list = function.function_space().cell_node_list
return np.dot(function.dat.data_ro[cell_node_list], M_inv)
def _bezier_calculate_points(function):
"""Calculate points values for a function used for bezier plotting
:arg function: 1D Function with 1 < deg < 4
"""
deg = function.function_space().ufl_element().degree()
M = np.empty([deg + 1, deg + 1], dtype=float)
fiat_element = create_element(function.function_space().ufl_element(), vector_is_mixed=False)
basis = fiat_element.dual_basis()
for i in range(deg + 1):
for j in range(deg + 1):
M[i, j] = _bernstein(basis[j].get_point_dict().keys()[0][0],
i, deg)
M_inv = np.linalg.inv(M)
cell_node_list = function.function_space().cell_node_list
return np.dot(function.dat.data_ro[cell_node_list], M_inv)
def __init__(self, mesh, element, name=None):
super(FunctionSpace, self).__init__()
if type(element) is ufl.MixedElement:
raise ValueError("Can't create FunctionSpace for MixedElement")
fiat_element = create_element(element, vector_is_mixed=False)
sdata = get_shared_data(mesh, fiat_element)
# The function space shape is the number of dofs per node,
# hence it is not always the value_shape. Vector and Tensor
# element modifiers *must* live on the outside!
if type(element) is ufl.TensorElement:
# UFL enforces value_shape of the subelement to be empty
# on a TensorElement.
self.shape = element.value_shape()
elif type(element) is ufl.VectorElement:
# First dimension of the value_shape is the VectorElement
# shape.
self.shape = element.value_shape()[:1]
else:
self.shape = ()
self._ufl_element = element
self._shared_data = sdata
self._mesh = mesh
self.rank = len(self.shape)
"""The rank of this :class:`FunctionSpace`. Spaces where the
element is scalar-valued (or intrinsically vector-valued) have
rank zero. Spaces built on :class:`~ufl.classes.VectorElement` or
:class:`~ufl.classes.TensorElement` instances have rank equivalent to
the number of components of their
:meth:`~ufl.classes.FiniteElementBase.value_shape`."""
self.dim = numpy.prod(self.shape, dtype=int)
"""The total number of degrees of freedom at each function
space node."""
self.name = name
"""The (optional) descriptive name for this space."""
self.node_set = sdata.node_set
"""A :class:`pyop2.Set` representing the function space nodes."""
self.dof_dset = op2.DataSet(self.node_set, self.shape or 1,
name="%s_nodes_dset" % self.name)
"""A :class:`pyop2.DataSet` representing the function space
degrees of freedom."""
self.comm = self.node_set.comm
self.fiat_element = fiat_element
self.extruded = sdata.extruded
self.offset = sdata.offset
self.bt_masks = sdata.bt_masks
def __init__(self, mesh, element, name=None):
super(FunctionSpace, self).__init__()
if type(element) is ufl.MixedElement:
raise ValueError("Can't create FunctionSpace for MixedElement")
fiat_element = create_element(element, vector_is_mixed=False)
sdata = get_shared_data(mesh, fiat_element)
# The function space shape is the number of dofs per node,
# hence it is not always the value_shape. Vector and Tensor
# element modifiers *must* live on the outside!
if type(element) is ufl.TensorElement:
# UFL enforces value_shape of the subelement to be empty
# on a TensorElement.
self.shape = element.value_shape()
elif type(element) is ufl.VectorElement:
# First dimension of the value_shape is the VectorElement
# shape.
self.shape = element.value_shape()[:1]
else:
self.shape = ()
self._ufl_element = element
self._shared_data = sdata
self._mesh = mesh
self.rank = len(self.shape)
"""The rank of this :class:`FunctionSpace`. Spaces where the
element is scalar-valued (or intrinsically vector-valued) have
rank zero. Spaces built on :class:`~ufl.classes.VectorElement` or
:class:`~ufl.classes.TensorElement` instances have rank equivalent to
the number of components of their
:meth:`~ufl.classes.FiniteElementBase.value_shape`."""
self.dim = numpy.prod(self.shape, dtype=int)
"""The total number of degrees of freedom at each function
space node."""
self.name = name
"""The (optional) descriptive name for this space."""
self.node_set = sdata.node_set
"""A :class:`pyop2.Set` representing the function space nodes."""
self.dof_dset = op2.DataSet(self.node_set, self.shape or 1,
name="%s_nodes_dset" % self.name)
"""A :class:`pyop2.DataSet` representing the function space
degrees of freedom."""
self.comm = self.node_set.comm
self.fiat_element = fiat_element
self.extruded = sdata.extruded
self.offset = sdata.offset
self.bt_masks = sdata.bt_masks
def prepare_arguments(arguments, indices, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg indices: Argument indices
:arg interior_facet: interior facet integral?
:returns: (funarg, prepare, expressions)
funarg - :class:`coffee.Decl` function argument
prepare - list of COFFEE nodes to be prepended to the
kernel body
expressions - GEM expressions referring to the argument
tensor
"""
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A"), pointers=[()])
varexp = gem.Variable("A", (None,))
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
space_dimensions = tuple(element.space_dimension() for element in elements)
for i, sd in zip(indices, space_dimensions):
i.set_extent(sd)
if arguments and interior_facet:
shape = tuple(2 * element.space_dimension() for element in elements)
strides = cumulative_strides(shape)
expressions = []
for restrictions in product((0, 1), repeat=len(arguments)):
offset = sum(r * sd * stride
for r, sd, stride in zip(restrictions, space_dimensions, strides))
expressions.append(gem.FlexiblyIndexed(
varexp,
((offset,
tuple((i, s) for i, s in zip(indices, shape))),)
))
else:
shape = space_dimensions
expressions = [gem.FlexiblyIndexed(varexp, ((0, tuple(zip(indices, space_dimensions))),))]
zero = coffee.FlatBlock(
str.format("memset({name}, 0, {size} * sizeof(*{name}));\n",
name=funarg.sym.gencode(), size=numpy.product(shape, dtype=int))
)
return funarg, [zero], expressions
def prepare_coordinates(coefficient, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
coordinates.
:arg coefficient: UFL Coefficient
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: (funarg, expression)
funarg - :class:`coffee.Decl` function argument
expression - GEM expression referring to the Coefficient
values
"""
if not interior_facet:
funargs = [coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("",)],
qualifiers=["const"])]
else:
funargs = [coffee.Decl(SCALAR_TYPE, coffee.Symbol(name+"_0"),
pointers=[("",)],
qualifiers=["const"]),
coffee.Decl(SCALAR_TYPE, coffee.Symbol(name+"_1"),
pointers=[("",)],
qualifiers=["const"])]
fiat_element = create_element(coefficient.ufl_element())
shape = (fiat_element.space_dimension(),)
gdim = coefficient.ufl_element().cell().geometric_dimension()
assert len(shape) == 1 and shape[0] % gdim == 0
num_nodes = shape[0] // gdim
# Translate coords from XYZXYZXYZXYZ into XXXXYYYYZZZZ
# NOTE: See dolfin/mesh/Cell.h:get_coordinate_dofs for ordering scheme
indices = list(map(int, numpy.arange(num_nodes * gdim).reshape(num_nodes, gdim).transpose().flat))
if not interior_facet:
variable = gem.Variable(name, shape)
expression = gem.ListTensor([gem.Indexed(variable, (i,)) for i in indices])
else:
variable0 = gem.Variable(name+"_0", shape)
variable1 = gem.Variable(name+"_1", shape)
expression = gem.ListTensor([[gem.Indexed(variable0, (i,)) for i in indices],
[gem.Indexed(variable1, (i,)) for i in indices]])
return funargs, expression
def prepare_coefficients(coefficients, coefficient_numbers, name, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients. Mixed element Coefficients are rearranged here for
interior facet integrals.
:arg coefficient: iterable of UFL Coefficients
:arg coefficient_numbers: iterable of coefficient indices in the original form
:arg name: unique name to refer to the Coefficient in the kernel
:arg interior_facet: interior facet integral?
:returns: (funarg, expressions)
funarg - :class:`coffee.Decl` function argument
expressions- GEM expressions referring to the Coefficient
values
"""
assert len(coefficients) == len(coefficient_numbers)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("const",), ()],
qualifiers=["const"])
varexp = gem.Variable(name, (None, None))
expressions = []
for coefficient_number, coefficient in zip(coefficient_numbers, coefficients):
if coefficient.ufl_element().family() == 'Real':
shape = coefficient.ufl_shape
else:
fiat_element = create_element(coefficient.ufl_element())
shape = (fiat_element.space_dimension(),)
if interior_facet:
shape = (2,) + shape
alpha = tuple(gem.Index() for s in shape)
expressions.append(gem.ComponentTensor(
gem.FlexiblyIndexed(
varexp, ((coefficient_number, ()),
(0, tuple(zip(alpha, shape))))
),
alpha
))
return funarg, expressions
def tabulate(ufl_element, order, points, entity, epsilon):
"""Ask FIAT to tabulate ``points`` up to order ``order``, then
rearranges the result into a series of ``(c, D, table)`` tuples,
where:
c: component index (for vector-valued and tensor-valued elements)
D: derivative tuple (e.g. (1, 2) means d/dx d^2/dy^2)
table: tabulation matrix for the given component and derivative.
shape: len(points) x space_dimension
:arg ufl_element: element to tabulate
:arg order: FIAT gives all derivatives up to this order
:arg points: points to tabulate the element on
:arg entity: particular entity to tabulate on
"""
element = create_element(ufl_element)
phi = element.space_dimension()
C = ufl_element.reference_value_size()
q = len(points)
for D, fiat_table in iteritems(element.tabulate(order, points, entity)):
if isinstance(fiat_table, Exception):
# In the case an exception is found in the fiat table, do not
# perform any rounding
gem_fail = gem.Failure((q, phi), fiat_table)
for c in range(C):
yield c, D, gem_fail
else:
reordered_table = fiat_table.reshape(phi, C, q).transpose(1, 2, 0) # (C, q, phi)
for c, table in enumerate(reordered_table):
# Copied from FFC (ffc/quadrature/quadratureutils.py)
table[abs(table) < epsilon] = 0
table[abs(table - 1.0) < epsilon] = 1.0
table[abs(table + 1.0) < epsilon] = -1.0
table[abs(table - 0.5) < epsilon] = 0.5
table[abs(table + 0.5) < epsilon] = -0.5
if spanning_degree(ufl_element) <= sum(D) and ufl_element.family() != "HDiv Trace":
assert compat.allclose(table, table.mean(axis=0, keepdims=True), equal_nan=True)
table = table[0]
yield c, D, gem.Literal(table)
def compile_element(ufl_element, cdim):
"""Generates C code for point evaluations.
:arg ufl_element: UFL element of the function space
:arg cdim: ``cdim`` of the function space
:returns: C code as string
"""
from tsfc.constants import PRECISION
from firedrake.pointquery_utils import set_float_formatting, format
from tsfc.fiatinterface import create_element
from FIAT.reference_element import TensorProductCell as two_product_cell
import sympy as sp
import numpy as np
# Set code generation parameters
set_float_formatting(PRECISION)
def calculate_basisvalues(ufl_cell, fiat_element):
f_component = format["component"]
f_decl = format["declaration"]
f_float_decl = format["float declaration"]
f_tensor = format["tabulate tensor"]
f_new_line = format["new line"]
tdim = ufl_cell.topological_dimension()
gdim = ufl_cell.geometric_dimension()
code = []
# Symbolic tabulation
tabs = fiat_element.tabulate(0, np.array([[sp.Symbol("reference_coords.X[%d]" % i)
for i in xrange(tdim)]]))
tabs = tabs[(0,) * tdim]
tabs = tabs.reshape(tabs.shape[:-1])
# Generate code for intermediate values
s_code, (theta,) = ssa_arrays([tabs])
for name, value in s_code:
code += [f_decl(f_float_decl, name, c_print(value))]
# Prepare Jacobian, Jacobian inverse and determinant
s_detJ = sp.Symbol('detJ')
s_J = np.array([[sp.Symbol("J[{i}*{tdim} + {j}]".format(i=i, j=j, tdim=tdim))
for j in range(tdim)]
for i in range(gdim)])
s_Jinv = np.array([[sp.Symbol("K[{i}*{gdim} + {j}]".format(i=i, j=j, gdim=gdim))
for j in range(gdim)]
for i in range(tdim)])
# Apply transformations
phi = []
for i, val in enumerate(theta):
mapping = fiat_element.mapping()[i]
if mapping == "affine":
phi.append(val)
elif mapping == "contravariant piola":
phi.append(s_J.dot(val) / s_detJ)
elif mapping == "covariant piola":
phi.append(s_Jinv.transpose().dot(val))
else:
raise ValueError("Unknown mapping: %s" % mapping)
phi = np.asarray(phi, dtype=object)
# Dump tables of basis values
code += ["", "\t// Values of basis functions"]
code += [f_decl("double", f_component("phi", phi.shape),
f_new_line + f_tensor(phi))]
shape = phi.shape
if len(shape) <= 1:
vdim = 1
elif len(shape) == 2:
vdim = shape[1]
return "\n".join(code), vdim
# Create FIAT element
element = create_element(ufl_element, vector_is_mixed=False)
cell = ufl_element.cell()
calculate_basisvalues, vdim = calculate_basisvalues(cell, element)
extruded = isinstance(element.get_reference_element(), two_product_cell)
code = {
"cdim": cdim,
"vdim": vdim,
"geometric_dimension": cell.geometric_dimension(),
"ndofs": element.space_dimension(),
"calculate_basisvalues": calculate_basisvalues,
"extruded_arg": ", int nlayers" if extruded else "",
"nlayers": ", f->n_layers" if extruded else "",
}
evaluate_template_c = """static inline void evaluate_kernel(double *result, double *phi_, double **F)
{
const int ndofs = %(ndofs)d;
const int cdim = %(cdim)d;
const int vdim = %(vdim)d;
double (*phi)[vdim] = (double (*)[vdim]) phi_;
// F: ndofs x cdim
// phi: ndofs x vdim
// result = F' * phi: cdim x vdim
//
// Usually cdim == 1 or vdim == 1.
for (int q = 0; q < cdim * vdim; q++) {
result[q] = 0.0;
}
for (int i = 0; i < ndofs; i++) {
for (int c = 0; c < cdim; c++) {
for (int v = 0; v < vdim; v++) {
result[c*vdim + v] += F[i][c] * phi[i][v];
}
}
}
}
static inline void wrap_evaluate(double *result, double *phi, double *data, int *map%(extruded_arg)s, int cell);
int evaluate(struct Function *f, double *x, double *result)
{
struct ReferenceCoords reference_coords;
int cell = locate_cell(f, x, %(geometric_dimension)d, &to_reference_coords, &reference_coords);
if (cell == -1) {
return -1;
}
if (!result) {
return 0;
}
double *J = reference_coords.J;
double *K = reference_coords.K;
double detJ = reference_coords.detJ;
%(calculate_basisvalues)s
wrap_evaluate(result, (double *)phi, f->f, f->f_map%(nlayers)s, cell);
return 0;
}
"""
return evaluate_template_c % code
def convert_vectorelement(element):
scalar_element = create_element(element.sub_elements()[0])
return finat.TensorFiniteElement(scalar_element,
(element.num_sub_elements(), ))
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 _interpolator(V, tensor, expr, subset, arguments, access):
try:
to_element = create_element(V.ufl_element(), vector_is_mixed=False)
except KeyError:
# FInAT only elements
raise NotImplementedError("Don't know how to create FIAT element for %s" % V.ufl_element())
if access is op2.READ:
raise ValueError("Can't have READ access for output function")
if len(expr.ufl_shape) != len(V.ufl_element().value_shape()):
raise RuntimeError('Rank mismatch: Expression rank %d, FunctionSpace rank %d'
% (len(expr.ufl_shape), len(V.ufl_element().value_shape())))
if expr.ufl_shape != V.ufl_element().value_shape():
raise RuntimeError('Shape mismatch: Expression shape %r, FunctionSpace shape %r'
% (expr.ufl_shape, V.ufl_element().value_shape()))
mesh = V.ufl_domain()
coords = mesh.coordinates
if not isinstance(expr, firedrake.Expression):
if expr.ufl_domain() and expr.ufl_domain() != V.mesh():
raise NotImplementedError("Interpolation onto another mesh not supported.")
ast, oriented, needs_cell_sizes, coefficients, _ = compile_expression_dual_evaluation(expr, to_element, coords, coffee=False)
kernel = op2.Kernel(ast, ast.name)
elif hasattr(expr, "eval"):
to_pts = []
for dual in to_element.dual_basis():
if not isinstance(dual, FIAT.functional.PointEvaluation):
raise NotImplementedError("Can only interpolate Python kernels with Lagrange elements")
pts, = dual.pt_dict.keys()
to_pts.append(pts)
kernel, oriented, needs_cell_sizes, coefficients = compile_python_kernel(expr, to_pts, to_element, V, coords)
else:
raise RuntimeError("Attempting to evaluate an Expression which has no value.")
cell_set = coords.cell_set
if subset is not None:
assert subset.superset == cell_set
cell_set = subset
parloop_args = [kernel, cell_set]
if tensor in set((c.dat for c in coefficients)):
output = tensor
tensor = op2.Dat(tensor.dataset)
if access is not op2.WRITE:
copyin = (partial(output.copy, tensor), )
else:
copyin = ()
copyout = (partial(tensor.copy, output), )
else:
copyin = ()
copyout = ()
if isinstance(tensor, op2.Global):
parloop_args.append(tensor(access))
elif isinstance(tensor, op2.Dat):
parloop_args.append(tensor(access, V.cell_node_map()))
else:
assert access == op2.WRITE # Other access descriptors not done for Matrices.
parloop_args.append(tensor(op2.WRITE, (V.cell_node_map(),
arguments[0].function_space().cell_node_map())))
if oriented:
co = mesh.cell_orientations()
parloop_args.append(co.dat(op2.READ, co.cell_node_map()))
if needs_cell_sizes:
cs = mesh.cell_sizes
parloop_args.append(cs.dat(op2.READ, cs.cell_node_map()))
for coefficient in coefficients:
m_ = coefficient.cell_node_map()
parloop_args.append(coefficient.dat(op2.READ, m_))
for o in coefficients:
domain = o.ufl_domain()
if domain is not None and domain.topology != mesh.topology:
raise NotImplementedError("Interpolation onto another mesh not supported.")
parloop = op2.ParLoop(*parloop_args).compute
if isinstance(tensor, op2.Mat):
return parloop, tensor.assemble
else:
return copyin + (parloop, ) + copyout
def fiat_compat(element):
from tsfc.fiatinterface import create_element
from finat.fiat_elements import FiatElement
assert element.cell().is_simplex()
return FiatElement(create_element(element))
def compile_coordinate_element(ufl_coordinate_element):
"""Generates C code for changing to reference coordinates.
:arg ufl_coordinate_element: UFL element of the coordinates
:returns: C code as string
"""
from tsfc.constants import PRECISION
from tsfc.fiatinterface import create_element
from firedrake.pointeval_utils import ssa_arrays, c_print
from FIAT.reference_element import TensorProductCell as two_product_cell
import sympy as sp
import numpy as np
# Set code generation parameters
set_float_formatting(PRECISION)
def dX_norm_square(topological_dimension):
return " + ".join("dX[{0}]*dX[{0}]".format(i)
for i in xrange(topological_dimension))
def X_isub_dX(topological_dimension):
return "\n".join("\tX[{0}] -= dX[{0}];".format(i)
for i in xrange(topological_dimension))
def is_affine(ufl_element):
return ufl_element.cell().is_simplex() and ufl_element.degree() <= 1 and ufl_element.family() in ["Discontinuous Lagrange", "Lagrange"]
def inside_check(ufl_cell, fiat_cell):
dim = ufl_cell.topological_dimension()
point = tuple(sp.Symbol("X[%d]" % i) for i in xrange(dim))
return " && ".join("(%s)" % arg for arg in fiat_cell.contains_point(point, epsilon=1e-14).args)
def init_X(fiat_element):
f_float = format["floating point"]
f_assign = format["assign"]
fiat_cell = fiat_element.get_reference_element()
vertices = np.array(fiat_cell.get_vertices())
X = np.average(vertices, axis=0)
return "\n".join(f_assign("X[%d]" % i, f_float(v)) for i, v in enumerate(X))
def to_reference_coordinates(ufl_cell, fiat_element):
f_decl = format["declaration"]
f_float_decl = format["float declaration"]
# Get the element cell name and geometric dimension.
cell = ufl_cell
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
code = []
# Symbolic tabulation
tabs = fiat_element.tabulate(1, np.array([[sp.Symbol("X[%d]" % i) for i in xrange(tdim)]]))
tabs = sorted((d, value.reshape(value.shape[:-1])) for d, value in tabs.iteritems())
# Generate code for intermediate values
s_code, d_phis = ssa_arrays(map(lambda (k, v): v, tabs), prefix="t")
phi = d_phis.pop(0)
for name, value in s_code:
code += [f_decl(f_float_decl, name, c_print(value))]
# Cell coordinate data
C = np.array([[sp.Symbol("C[%d][%d]" % (i, j)) for j in range(gdim)]
for i in range(fiat_element.space_dimension())])
# Generate physical coordinates
x = phi.dot(C)
for i, e in enumerate(x):
code += ["\tx[%d] = %s;" % (i, e)]
# Generate Jacobian
grad_phi = np.vstack(reversed(d_phis))
J = np.transpose(grad_phi.dot(C))
for i, row in enumerate(J):
for j, e in enumerate(row):
code += ["\tJ[%d * %d + %d] = %s;" % (i, tdim, j, e)]
# Get code snippets for Jacobian, inverse of Jacobian and mapping of
# coordinates from physical element to the FIAT reference element.
code += ["compute_jacobian_inverse_%s(K, detJ, J);" % cellname[cell]]
# FIXME: use cell orientations!
# if needs_orientation:
# code_ += [format["orientation"]["ufc"](tdim, gdim)]
x = np.array([sp.Symbol("x[%d]" % i) for i in xrange(gdim)])
x0 = np.array([sp.Symbol("x0[%d]" % i) for i in xrange(gdim)])
K = np.array([[sp.Symbol("K[%d]" % (i*gdim + j)) for j in range(gdim)]
for i in range(tdim)])
dX = K.dot(x - x0)
for i, e in enumerate(dX):
code += ["\tdX[%d] = %s;" % (i, e)]
return "\n".join(code)
# Create FIAT element
element = create_element(ufl_coordinate_element, vector_is_mixed=False)
cell = ufl_coordinate_element.cell()
# calculate_basisvalues, vdim = calculate_basisvalues(cell, element)
extruded = isinstance(element.get_reference_element(), two_product_cell)
code = {
"geometric_dimension": cell.geometric_dimension(),
"topological_dimension": cell.topological_dimension(),
"inside_predicate": inside_check(cell, element.get_reference_element()),
"to_reference_coords": to_reference_coordinates(cell, element),
"init_X": init_X(element),
"max_iteration_count": 1 if is_affine(ufl_coordinate_element) else 16,
"convergence_epsilon": 1e-12,
"dX_norm_square": dX_norm_square(cell.topological_dimension()),
"X_isub_dX": X_isub_dX(cell.topological_dimension()),
"extruded_arg": ", int nlayers" if extruded else "",
"nlayers": ", f->n_layers" if extruded else "",
}
evaluate_template_c = """#include <math.h>
#include <firedrake_geometry.h>
struct ReferenceCoords {
double X[%(geometric_dimension)d];
double J[%(geometric_dimension)d * %(topological_dimension)d];
double K[%(topological_dimension)d * %(geometric_dimension)d];
double detJ;
};
static inline void to_reference_coords_kernel(void *result_, double *x0, int *return_value, double **C)
{
struct ReferenceCoords *result = (struct ReferenceCoords *) result_;
const int space_dim = %(geometric_dimension)d;
/*
* Mapping coordinates from physical to reference space
*/
double *X = result->X;
%(init_X)s
double x[space_dim];
double *J = result->J;
double *K = result->K;
double detJ;
double dX[%(topological_dimension)d];
int converged = 0;
for (int it = 0; !converged && it < %(max_iteration_count)d; it++) {
%(to_reference_coords)s
if (%(dX_norm_square)s < %(convergence_epsilon)g * %(convergence_epsilon)g) {
converged = 1;
}
%(X_isub_dX)s
}
result->detJ = detJ;
// Are we inside the reference element?
*return_value = %(inside_predicate)s;
}
static inline void wrap_to_reference_coords(void *result_, double *x, int *return_value,
double *coords, int *coords_map%(extruded_arg)s, int cell);
int to_reference_coords(void *result_, struct Function *f, int cell, double *x)
{
int return_value;
wrap_to_reference_coords(result_, x, &return_value, f->coords, f->coords_map%(nlayers)s, cell);
return return_value;
}
"""
return evaluate_template_c % code
def _interpolator(V, dat, expr, subset, access):
to_element = create_element(V.ufl_element(), vector_is_mixed=False)
to_pts = []
if access is op2.READ:
raise ValueError("Can't have READ access for output function")
if V.ufl_element().mapping() != "identity":
raise NotImplementedError("Can only interpolate onto elements "
"with affine mapping. Try projecting instead")
for dual in to_element.dual_basis():
if not isinstance(dual, FIAT.functional.PointEvaluation):
raise NotImplementedError("Can only interpolate onto point "
"evaluation operators. Try projecting instead")
pts, = dual.pt_dict.keys()
to_pts.append(pts)
if len(expr.ufl_shape) != len(V.ufl_element().value_shape()):
raise RuntimeError('Rank mismatch: Expression rank %d, FunctionSpace rank %d'
% (len(expr.ufl_shape), len(V.ufl_element().value_shape())))
if expr.ufl_shape != V.ufl_element().value_shape():
raise RuntimeError('Shape mismatch: Expression shape %r, FunctionSpace shape %r'
% (expr.ufl_shape, V.ufl_element().value_shape()))
mesh = V.ufl_domain()
coords = mesh.coordinates
if not isinstance(expr, firedrake.Expression):
if expr.ufl_domain() and expr.ufl_domain() != V.mesh():
raise NotImplementedError("Interpolation onto another mesh not supported.")
if expr.ufl_shape != V.shape:
raise ValueError("UFL expression has incorrect shape for interpolation.")
ast, oriented, needs_cell_sizes, coefficients, _ = compile_ufl_kernel(expr, to_pts, coords, coffee=False)
kernel = op2.Kernel(ast, ast.name)
elif hasattr(expr, "eval"):
kernel, oriented, needs_cell_sizes, coefficients = compile_python_kernel(expr, to_pts, to_element, V, coords)
else:
raise RuntimeError("Attempting to evaluate an Expression which has no value.")
cell_set = coords.cell_set
if subset is not None:
assert subset.superset == cell_set
cell_set = subset
args = [kernel, cell_set]
if dat in set((c.dat for c in coefficients)):
output = dat
dat = op2.Dat(dat.dataset)
if access is not op2.WRITE:
copyin = (partial(output.copy, dat), )
else:
copyin = ()
copyout = (partial(dat.copy, output), )
else:
copyin = ()
copyout = ()
args.append(dat(access, V.cell_node_map()))
if oriented:
co = mesh.cell_orientations()
args.append(co.dat(op2.READ, co.cell_node_map()))
if needs_cell_sizes:
cs = mesh.cell_sizes
args.append(cs.dat(op2.READ, cs.cell_node_map()))
for coefficient in coefficients:
m_ = coefficient.cell_node_map()
args.append(coefficient.dat(op2.READ, m_))
for o in coefficients:
domain = o.ufl_domain()
if domain is not None and domain.topology != mesh.topology:
raise NotImplementedError("Interpolation onto another mesh not supported.")
return copyin + (op2.ParLoop(*args).compute, ) + copyout
def test_triangle_basic(ufl_element):
element = create_element(ufl_element)
assert isinstance(element, supported_elements[ufl_element.family()])
def test_interval_variant(family, variant, expected_cls):
ufl_element = ufl.FiniteElement(family, ufl.interval, 3, variant=variant)
assert isinstance(create_element(ufl_element), expected_cls)
def compile_element(ufl_element, cdim):
"""Generates C code for point evaluations.
:arg ufl_element: UFL element of the function space
:arg cdim: ``cdim`` of the function space
:returns: C code as string
"""
from tsfc import default_parameters
from firedrake.pointquery_utils import set_float_formatting, format
from tsfc.fiatinterface import create_element
from FIAT.reference_element import TensorProductCell as two_product_cell
import sympy as sp
import numpy as np
# Set code generation parameters
set_float_formatting(default_parameters()["precision"])
def calculate_basisvalues(ufl_cell, fiat_element):
f_component = format["component"]
f_decl = format["declaration"]
f_float_decl = format["float declaration"]
f_tensor = format["tabulate tensor"]
f_new_line = format["new line"]
tdim = ufl_cell.topological_dimension()
gdim = ufl_cell.geometric_dimension()
code = []
# Symbolic tabulation
tabs = fiat_element.tabulate(
0,
np.array([[
sp.Symbol("reference_coords.X[%d]" % i) for i in range(tdim)
]]))
tabs = tabs[(0, ) * tdim]
tabs = tabs.reshape(tabs.shape[:-1])
# Generate code for intermediate values
s_code, (theta, ) = ssa_arrays([tabs])
for name, value in s_code:
code += [f_decl(f_float_decl, name, c_print(value))]
# Prepare Jacobian, Jacobian inverse and determinant
s_detJ = sp.Symbol('detJ')
s_J = np.array([[
sp.Symbol("J[{i}*{tdim} + {j}]".format(i=i, j=j, tdim=tdim))
for j in range(tdim)
] for i in range(gdim)])
s_Jinv = np.array([[
sp.Symbol("K[{i}*{gdim} + {j}]".format(i=i, j=j, gdim=gdim))
for j in range(gdim)
] for i in range(tdim)])
# Apply transformations
phi = []
for i, val in enumerate(theta):
mapping = fiat_element.mapping()[i]
if mapping == "affine":
phi.append(val)
elif mapping == "contravariant piola":
phi.append(s_J.dot(val) / s_detJ)
elif mapping == "covariant piola":
phi.append(s_Jinv.transpose().dot(val))
else:
raise ValueError("Unknown mapping: %s" % mapping)
phi = np.asarray(phi, dtype=object)
# Dump tables of basis values
code += ["", "\t// Values of basis functions"]
code += [
f_decl("double", f_component("phi", phi.shape),
f_new_line + f_tensor(phi))
]
shape = phi.shape
if len(shape) <= 1:
vdim = 1
elif len(shape) == 2:
vdim = shape[1]
return "\n".join(code), vdim
# Create FIAT element
element = create_element(ufl_element, vector_is_mixed=False)
cell = ufl_element.cell()
calculate_basisvalues, vdim = calculate_basisvalues(cell, element)
extruded = isinstance(element.get_reference_element(), two_product_cell)
code = {
"cdim": cdim,
"vdim": vdim,
"geometric_dimension": cell.geometric_dimension(),
"ndofs": element.space_dimension(),
"calculate_basisvalues": calculate_basisvalues,
"extruded_arg": ", %s nlayers" % as_cstr(IntType) if extruded else "",
"nlayers": ", f->n_layers" if extruded else "",
"IntType": as_cstr(IntType),
}
evaluate_template_c = """static inline void evaluate_kernel(double *result, double *phi_, double **F)
{
const int ndofs = %(ndofs)d;
const int cdim = %(cdim)d;
const int vdim = %(vdim)d;
double (*phi)[vdim] = (double (*)[vdim]) phi_;
// F: ndofs x cdim
// phi: ndofs x vdim
// result = F' * phi: cdim x vdim
//
// Usually cdim == 1 or vdim == 1.
for (int q = 0; q < cdim * vdim; q++) {
result[q] = 0.0;
}
for (int i = 0; i < ndofs; i++) {
for (int c = 0; c < cdim; c++) {
for (int v = 0; v < vdim; v++) {
result[c*vdim + v] += F[i][c] * phi[i][v];
}
}
}
}
static inline void wrap_evaluate(double *result, double *phi, double *data, %(IntType)s *map%(extruded_arg)s, %(IntType)s cell);
int evaluate(struct Function *f, double *x, double *result)
{
struct ReferenceCoords reference_coords;
int cell = locate_cell(f, x, %(geometric_dimension)d, &to_reference_coords, &reference_coords);
if (cell == -1) {
return -1;
}
if (!result) {
return 0;
}
double *J = reference_coords.J;
double *K = reference_coords.K;
double detJ = reference_coords.detJ;
%(calculate_basisvalues)s
wrap_evaluate(result, (double *)phi, f->f, f->f_map%(nlayers)s, cell);
return 0;
}
"""
return evaluate_template_c % code
def test_triangle_basic(ufl_element):
element = f.create_element(ufl_element)
assert isinstance(element, f.supported_elements[ufl_element.family()])
def test_quadrilateral_variant_spectral_rtcf():
element = create_element(ufl.FiniteElement('RTCF', ufl.quadrilateral, 2, variant='spectral'))
assert isinstance(element.element._elements[0].A, FIAT.GaussLobattoLegendre)
assert isinstance(element.element._elements[0].B, FIAT.GaussLegendre)
assert isinstance(element.element._elements[1].A, FIAT.GaussLegendre)
assert isinstance(element.element._elements[1].B, FIAT.GaussLobattoLegendre)
def test_quadrilateral_variant_spectral_dq():
element = create_element(ufl.FiniteElement('DQ', ufl.quadrilateral, 1, variant='spectral'))
assert isinstance(element.element.A, FIAT.GaussLegendre)
assert isinstance(element.element.B, FIAT.GaussLegendre)
def test_triangle_variant_spectral_fail():
ufl_element = ufl.FiniteElement('DP', ufl.triangle, 2, variant='spectral')
with pytest.raises(ValueError):
create_element(ufl_element)
def test_cache_hit(ufl_element):
A = create_element(ufl_element)
B = create_element(ufl_element)
assert A is B
def _interpolator(V, dat, expr, subset, access):
to_element = create_element(V.ufl_element(), vector_is_mixed=False)
to_pts = []
if access is op2.READ:
raise ValueError("Can't have READ access for output function")
if V.ufl_element().mapping() != "identity":
raise NotImplementedError("Can only interpolate onto elements "
"with affine mapping. Try projecting instead")
for dual in to_element.dual_basis():
if not isinstance(dual, FIAT.functional.PointEvaluation):
raise NotImplementedError("Can only interpolate onto point "
"evaluation operators. Try projecting instead")
pts, = dual.pt_dict.keys()
to_pts.append(pts)
if len(expr.ufl_shape) != len(V.ufl_element().value_shape()):
raise RuntimeError('Rank mismatch: Expression rank %d, FunctionSpace rank %d'
% (len(expr.ufl_shape), len(V.ufl_element().value_shape())))
if expr.ufl_shape != V.ufl_element().value_shape():
raise RuntimeError('Shape mismatch: Expression shape %r, FunctionSpace shape %r'
% (expr.ufl_shape, V.ufl_element().value_shape()))
mesh = V.ufl_domain()
coords = mesh.coordinates
if not isinstance(expr, firedrake.Expression):
if expr.ufl_domain() and expr.ufl_domain() != V.mesh():
raise NotImplementedError("Interpolation onto another mesh not supported.")
if expr.ufl_shape != V.shape:
raise ValueError("UFL expression has incorrect shape for interpolation.")
ast, oriented, needs_cell_sizes, coefficients, _ = compile_ufl_kernel(expr, to_pts, coords, coffee=False)
kernel = op2.Kernel(ast, ast.name)
elif hasattr(expr, "eval"):
kernel, oriented, needs_cell_sizes, coefficients = compile_python_kernel(expr, to_pts, to_element, V, coords)
else:
raise RuntimeError("Attempting to evaluate an Expression which has no value.")
cell_set = coords.cell_set
if subset is not None:
assert subset.superset == cell_set
cell_set = subset
args = [kernel, cell_set]
if dat in set((c.dat for c in coefficients)):
output = dat
dat = op2.Dat(dat.dataset)
if access is not op2.WRITE:
copyin = (partial(output.copy, dat), )
else:
copyin = ()
copyout = (partial(dat.copy, output), )
else:
copyin = ()
copyout = ()
args.append(dat(access, V.cell_node_map()))
if oriented:
co = mesh.cell_orientations()
args.append(co.dat(op2.READ, co.cell_node_map()))
if needs_cell_sizes:
cs = mesh.cell_sizes
args.append(cs.dat(op2.READ, cs.cell_node_map()))
for coefficient in coefficients:
m_ = coefficient.cell_node_map()
args.append(coefficient.dat(op2.READ, m_))
for o in coefficients:
domain = o.ufl_domain()
if domain is not None and domain.topology != mesh.topology:
raise NotImplementedError("Interpolation onto another mesh not supported.")
return copyin + (partial(op2.par_loop, *args), ) + copyout
def prepare_arguments(arguments, indices, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Arguments. Vector Arguments are rearranged here for interior
facet integrals.
:arg arguments: UFL Arguments
:arg indices: Argument indices
:arg interior_facet: interior facet integral?
:returns: (funarg, prepare, expression, finalise)
funarg - :class:`coffee.Decl` function argument
prepare - list of COFFEE nodes to be prepended to the
kernel body
expressions - GEM expressions referring to the argument
tensor
finalise - list of COFFEE nodes to be appended to the
kernel body
"""
assert isinstance(interior_facet, bool)
if len(arguments) == 0:
# No arguments
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=(1,)))
expression = gem.Indexed(gem.Variable("A", (1,)), (0,))
return funarg, [], [expression], []
elements = tuple(create_element(arg.ufl_element()) for arg in arguments)
if not interior_facet:
# Not an interior facet integral
shape = tuple(element.space_dimension() for element in elements)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=shape))
expression = gem.Indexed(gem.Variable("A", shape), indices)
return funarg, [], [expression], []
if not any(isinstance(element, MixedElement) for element in elements):
# Interior facet integral, but no vector (mixed) arguments
shape = tuple(2 * element.space_dimension() for element in elements)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=shape))
varexp = gem.Variable("A", shape)
expressions = []
for restrictions in product((0, 1), repeat=len(arguments)):
expressions.append(gem.FlexiblyIndexed(
varexp,
tuple((r * e.space_dimension(), ((i, e.space_dimension()),))
for e, i, r in zip(elements, indices, restrictions))
))
return funarg, [], expressions, []
# Interior facet integral + vector (mixed) argument(s)
shape = tuple(element.space_dimension() for element in elements)
funarg_shape = tuple(s * 2 for s in shape)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol("A", rank=funarg_shape))
prepare = []
expressions = []
references = []
for restrictions in product((0, 1), repeat=len(arguments)):
name = "A" + "".join(map(str, restrictions))
prepare.append(coffee.Decl(SCALAR_TYPE,
coffee.Symbol(name, rank=shape),
init=coffee.ArrayInit(numpy.zeros(1))))
expressions.append(gem.Indexed(gem.Variable(name, shape), indices))
for multiindex in numpy.ndindex(shape):
references.append(coffee.Symbol(name, multiindex))
restriction_shape = []
for e in elements:
if isinstance(e, MixedElement):
restriction_shape += [len(e.elements()),
e.elements()[0].space_dimension()]
else:
restriction_shape += [1, e.space_dimension()]
restriction_shape = tuple(restriction_shape)
references = numpy.array(references)
if len(arguments) == 1:
references = references.reshape((2,) + restriction_shape)
references = references.transpose(1, 0, 2)
elif len(arguments) == 2:
references = references.reshape((2, 2) + restriction_shape)
references = references.transpose(2, 0, 3, 4, 1, 5)
references = references.reshape(funarg_shape)
finalise = []
for multiindex in numpy.ndindex(funarg_shape):
finalise.append(coffee.Assign(coffee.Symbol("A", rank=multiindex),
references[multiindex]))
return funarg, prepare, expressions, finalise
def test_cache_hit(ufl_element):
A = f.create_element(ufl_element)
B = f.create_element(ufl_element)
assert A is B
def test_quadrilateral_variant_spectral_dq():
element = create_element(
ufl.FiniteElement('DQ', ufl.quadrilateral, 1, variant='spectral'))
assert isinstance(element.element.A, FIAT.GaussLegendre)
assert isinstance(element.element.B, FIAT.GaussLegendre)
def fiat_compat(element):
from tsfc.fiatinterface import create_element
return FiatElementWrapper(create_element(element),
degree=spanning_degree(element))
def fiat_compat(element):
from tsfc.fiatinterface import create_element
from finat.fiat_elements import FiatElement
assert element.cell().is_simplex()
return FiatElement(create_element(element))
def convert_tensorproductelement(element):
cell = element.cell()
if type(cell) is not ufl.TensorProductCell:
raise ValueError("TensorProductElement not on TensorProductCell?")
return finat.TensorProductElement(
[create_element(elem) for elem in element.sub_elements()])
def prepare_coefficient(coefficient, name, mode=None, interior_facet=False):
"""Bridges the kernel interface and the GEM abstraction for
Coefficients. Mixed element Coefficients are rearranged here for
interior facet integrals.
:arg coefficient: UFL Coefficient
:arg name: unique name to refer to the Coefficient in the kernel
:arg mode: 'manual_loop' or 'list_tensor'; two ways to deal with
interior facet integrals on mixed elements
:arg interior_facet: interior facet integral?
:returns: (funarg, prepare, expression)
funarg - :class:`coffee.Decl` function argument
prepare - list of COFFEE nodes to be prepended to the
kernel body
expression - GEM expression referring to the Coefficient
values
"""
if mode is None:
mode = 'manual_loop'
assert mode in ['manual_loop', 'list_tensor']
assert isinstance(interior_facet, bool)
if coefficient.ufl_element().family() == 'Real':
# Constant
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("restrict",)],
qualifiers=["const"])
expression = gem.reshape(gem.Variable(name, (None,)),
coefficient.ufl_shape)
return funarg, [], expression
fiat_element = create_element(coefficient.ufl_element())
size = fiat_element.space_dimension()
if not interior_facet:
# Simple case
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("const", "restrict"), ("restrict",)],
qualifiers=["const"])
expression = gem.reshape(gem.Variable(name, (size, 1)), (size,), ())
return funarg, [], expression
if not isinstance(fiat_element, MixedElement):
# Interior facet integral
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("const", "restrict"), ("restrict",)],
qualifiers=["const"])
expression = gem.reshape(
gem.Variable(name, (2 * size, 1)), (2, size), ()
)
return funarg, [], expression
# Interior facet integral + mixed / vector element
# Here we need to reorder the coefficient values.
#
# Incoming ordering: E1+ E1- E2+ E2- E3+ E3-
# Required ordering: E1+ E2+ E3+ E1- E2- E3-
#
# Each of E[n]{+,-} is a vector of basis function coefficients for
# subelement E[n].
#
# There are two code generation method to reorder the values.
# We have not done extensive research yet as to which way yield
# faster code.
if mode == 'manual_loop':
# In this case we generate loops outside the GEM abstraction
# to reorder the values. A whole E[n]{+,-} block is copied by
# a single loop.
name_ = name + "_"
shape = (2, size)
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name_),
pointers=[("const", "restrict"), ("restrict",)],
qualifiers=["const"])
prepare = [coffee.Decl(SCALAR_TYPE, coffee.Symbol(name, rank=shape))]
expression = gem.Variable(name, shape)
offset = 0
i = coffee.Symbol("i")
for element in fiat_element.elements():
space_dim = element.space_dimension()
loop_body = coffee.Assign(coffee.Symbol(name, rank=(0, "i"),
offset=((1, 0), (1, offset))),
coffee.Symbol(name_, rank=("i", 0),
offset=((1, 2 * offset), (1, 0))))
prepare.append(coffee_for(i, space_dim, loop_body))
loop_body = coffee.Assign(coffee.Symbol(name, rank=(1, "i"),
offset=((1, 0), (1, offset))),
coffee.Symbol(name_, rank=("i", 0),
offset=((1, 2 * offset + space_dim), (1, 0))))
prepare.append(coffee_for(i, space_dim, loop_body))
offset += space_dim
return funarg, prepare, expression
elif mode == 'list_tensor':
# In this case we generate a gem.ListTensor to do the
# reordering. Every single element in a E[n]{+,-} block is
# referenced separately.
funarg = coffee.Decl(SCALAR_TYPE, coffee.Symbol(name),
pointers=[("const", "restrict"), ("restrict",)],
qualifiers=["const"])
variable = gem.Variable(name, (2 * size, 1))
facet_0 = []
facet_1 = []
offset = 0
for element in fiat_element.elements():
space_dim = element.space_dimension()
for i in range(offset, offset + space_dim):
facet_0.append(gem.Indexed(variable, (i, 0)))
offset += space_dim
for i in range(offset, offset + space_dim):
facet_1.append(gem.Indexed(variable, (i, 0)))
offset += space_dim
expression = gem.ListTensor(numpy.array([facet_0, facet_1]))
return funarg, [], expression
def convert_tensorelement(element):
scalar_element = create_element(element.sub_elements()[0])
return finat.TensorFiniteElement(scalar_element,
element.reference_value_shape())
def test_interval_variant(family, variant, expected_cls):
ufl_element = ufl.FiniteElement(family, ufl.interval, 3, variant=variant)
assert isinstance(create_element(ufl_element), expected_cls)
def compile_coordinate_element(ufl_coordinate_element):
"""Generates C code for changing to reference coordinates.
:arg ufl_coordinate_element: UFL element of the coordinates
:returns: C code as string
"""
from tsfc import default_parameters
from tsfc.fiatinterface import create_element
from firedrake.pointeval_utils import ssa_arrays, c_print
from FIAT.reference_element import TensorProductCell as two_product_cell
import sympy as sp
import numpy as np
# Set code generation parameters
set_float_formatting(default_parameters()["precision"])
def dX_norm_square(topological_dimension):
return " + ".join("dX[{0}]*dX[{0}]".format(i)
for i in range(topological_dimension))
def X_isub_dX(topological_dimension):
return "\n".join("\tX[{0}] -= dX[{0}];".format(i)
for i in range(topological_dimension))
def is_affine(ufl_element):
return ufl_element.cell().is_simplex(
) and ufl_element.degree() <= 1 and ufl_element.family() in [
"Discontinuous Lagrange", "Lagrange"
]
def inside_check(ufl_cell, fiat_cell):
dim = ufl_cell.topological_dimension()
point = tuple(sp.Symbol("X[%d]" % i) for i in range(dim))
return " && ".join(
"(%s)" % arg
for arg in fiat_cell.contains_point(point, epsilon=1e-14).args)
def init_X(fiat_element):
f_float = format["floating point"]
f_assign = format["assign"]
fiat_cell = fiat_element.get_reference_element()
vertices = np.array(fiat_cell.get_vertices())
X = np.average(vertices, axis=0)
return "\n".join(
f_assign("X[%d]" % i, f_float(v)) for i, v in enumerate(X))
def to_reference_coordinates(ufl_cell, fiat_element):
f_decl = format["declaration"]
f_float_decl = format["float declaration"]
# Get the element cell name and geometric dimension.
cell = ufl_cell
gdim = cell.geometric_dimension()
tdim = cell.topological_dimension()
code = []
# Symbolic tabulation
tabs = fiat_element.tabulate(
1, np.array([[sp.Symbol("X[%d]" % i) for i in range(tdim)]]))
tabs = sorted((d, value.reshape(value.shape[:-1]))
for d, value in tabs.iteritems())
# Generate code for intermediate values
s_code, d_phis = ssa_arrays([v for k, v in tabs], prefix="t")
phi = d_phis.pop(0)
for name, value in s_code:
code += [f_decl(f_float_decl, name, c_print(value))]
# Cell coordinate data
C = np.array([[sp.Symbol("C[%d][%d]" % (i, j)) for j in range(gdim)]
for i in range(fiat_element.space_dimension())])
# Generate physical coordinates
x = phi.dot(C)
for i, e in enumerate(x):
code += ["\tx[%d] = %s;" % (i, e)]
# Generate Jacobian
grad_phi = np.vstack(reversed(d_phis))
J = np.transpose(grad_phi.dot(C))
for i, row in enumerate(J):
for j, e in enumerate(row):
code += ["\tJ[%d * %d + %d] = %s;" % (i, tdim, j, e)]
# Get code snippets for Jacobian, inverse of Jacobian and mapping of
# coordinates from physical element to the FIAT reference element.
code += ["compute_jacobian_inverse_%s(K, detJ, J);" % cellname[cell]]
# FIXME: use cell orientations!
# if needs_orientation:
# code_ += [format["orientation"]["ufc"](tdim, gdim)]
x = np.array([sp.Symbol("x[%d]" % i) for i in range(gdim)])
x0 = np.array([sp.Symbol("x0[%d]" % i) for i in range(gdim)])
K = np.array(
[[sp.Symbol("K[%d]" % (i * gdim + j)) for j in range(gdim)]
for i in range(tdim)])
dX = K.dot(x - x0)
for i, e in enumerate(dX):
code += ["\tdX[%d] = %s;" % (i, e)]
return "\n".join(code)
# Create FIAT element
element = create_element(ufl_coordinate_element, vector_is_mixed=False)
cell = ufl_coordinate_element.cell()
# calculate_basisvalues, vdim = calculate_basisvalues(cell, element)
extruded = isinstance(element.get_reference_element(), two_product_cell)
code = {
"geometric_dimension": cell.geometric_dimension(),
"topological_dimension": cell.topological_dimension(),
"inside_predicate": inside_check(cell,
element.get_reference_element()),
"to_reference_coords": to_reference_coordinates(cell, element),
"init_X": init_X(element),
"max_iteration_count": 1 if is_affine(ufl_coordinate_element) else 16,
"convergence_epsilon": 1e-12,
"dX_norm_square": dX_norm_square(cell.topological_dimension()),
"X_isub_dX": X_isub_dX(cell.topological_dimension()),
"extruded_arg": ", int nlayers" if extruded else "",
"nlayers": ", f->n_layers" if extruded else "",
}
evaluate_template_c = """#include <math.h>
#include <firedrake_geometry.h>
struct ReferenceCoords {
double X[%(geometric_dimension)d];
double J[%(geometric_dimension)d * %(topological_dimension)d];
double K[%(topological_dimension)d * %(geometric_dimension)d];
double detJ;
};
static inline void to_reference_coords_kernel(void *result_, double *x0, int *return_value, double **C)
{
struct ReferenceCoords *result = (struct ReferenceCoords *) result_;
const int space_dim = %(geometric_dimension)d;
/*
* Mapping coordinates from physical to reference space
*/
double *X = result->X;
%(init_X)s
double x[space_dim];
double *J = result->J;
double *K = result->K;
double detJ;
double dX[%(topological_dimension)d];
int converged = 0;
for (int it = 0; !converged && it < %(max_iteration_count)d; it++) {
%(to_reference_coords)s
if (%(dX_norm_square)s < %(convergence_epsilon)g * %(convergence_epsilon)g) {
converged = 1;
}
%(X_isub_dX)s
}
result->detJ = detJ;
// Are we inside the reference element?
*return_value = %(inside_predicate)s;
}
static inline void wrap_to_reference_coords(void *result_, double *x, int *return_value,
double *coords, int *coords_map%(extruded_arg)s, int cell);
int to_reference_coords(void *result_, struct Function *f, int cell, double *x)
{
int return_value;
wrap_to_reference_coords(result_, x, &return_value, f->coords, f->coords_map%(nlayers)s, cell);
return return_value;
}
"""
return evaluate_template_c % code