def to_reference_coordinates(ufl_coordinate_element):
# Set up UFL form
cell = ufl_coordinate_element.cell()
domain = ufl.Mesh(ufl_coordinate_element)
K = ufl.JacobianInverse(domain)
x = ufl.SpatialCoordinate(domain)
x0_element = ufl.VectorElement("Real", cell, 0)
x0 = ufl.Coefficient(ufl.FunctionSpace(domain, x0_element))
expr = ufl.dot(K, x - x0)
# Translation to GEM
C = ufl.Coefficient(ufl.FunctionSpace(domain, ufl_coordinate_element))
expr = ufl_utils.preprocess_expression(expr)
expr = ufl_utils.simplify_abs(expr)
builder = firedrake_interface.KernelBuilderBase()
builder.domain_coordinate[domain] = C
builder._coefficient(C, "C")
builder._coefficient(x0, "x0")
dim = cell.topological_dimension()
point = gem.Variable('X', (dim,))
context = tsfc.fem.GemPointContext(
interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
)
translator = tsfc.fem.Translator(context)
ir = map_expr_dag(translator, expr)
# Unroll result
ir = [gem.Indexed(ir, alpha) for alpha in numpy.ndindex(ir.shape)]
# Unroll IndexSums
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
ir = gem.optimise.unroll_indexsum(ir, predicate=predicate)
# Translate to COFFEE
ir = impero_utils.preprocess_gem(ir)
return_variable = gem.Variable('dX', (dim,))
assignments = [(gem.Indexed(return_variable, (i,)), e)
for i, e in enumerate(ir)]
impero_c = impero_utils.compile_gem(assignments, ())
body = tsfc.coffee.generate(impero_c, {}, parameters["precision"])
body.open_scope = False
return body
def __init__(self, mesh, element, name):
self._ufl_function_space = ufl.FunctionSpace(mesh.ufl_mesh(), element)
self.name = name
self.comm = mesh.comm
self._mesh = mesh
self.dof_dset = op2.GlobalDataSet(self.make_dat())
self.node_set = self.dof_dset.set
def __init__(self, mesh):
"""
Create function that evaluates to the facet area/length on each facet.
*Arguments*
mesh
a :py:class:`Mesh <dolfin.cpp.Mesh>`.
*Example of usage*
.. code-block:: python
mesh = UnitSquare(4,4)
fa = FacetArea(mesh)
"""
# Handle MultiMesh
if isinstance(mesh, cpp.MultiMesh):
mesh = mesh.part(0)
# Initialize C++ part
cpp.FacetArea.__init__(self, mesh)
# Initialize UFL part
# NB! This is defined as a piecewise constant function for each cell, not for each facet!
ufl_element = ufl.FiniteElement("Discontinuous Lagrange", mesh.ufl_cell(), 0)
ufl_function_space = ufl.FunctionSpace(mesh.ufl_domain(), ufl_element)
ufl.Coefficient.__init__(self, ufl_function_space, count=self.id())
def __init__(self,
cell=None,
element=None,
domain=None,
name=None,
label=None):
# Some messy cell/domain handling for compatibility, will be
# straightened out later
if domain is None:
ufl_domain = None
else:
if isinstance(domain, ufl.domain.AbstractDomain):
ufl_domain = domain
else:
# Probably getting a Mesh here, from existing dolfin
# tests. Will be the same later anyway.
ufl_domain = domain.ufl_domain()
if cell is None:
cell = ufl_domain.ufl_cell()
# Initialise base class
ufl_function_space = ufl.FunctionSpace(ufl_domain, element)
ufl.Coefficient.__init__(self, ufl_function_space, count=self.id())
name = name or "f_" + str(ufl.Coefficient.count(self))
label = label or "User defined expression"
self._cpp_object.rename(name, label)
def test_custom_quadrature(compile_args):
ve = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(ve)
e = ufl.FiniteElement("P", mesh.ufl_cell(), 2)
V = ufl.FunctionSpace(mesh, e)
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
points = [[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [0.5, 0.5], [0.0, 0.5], [0.5, 0.0]]
weights = [1 / 12] * 6
a = u * v * ufl.dx(metadata={"quadrature_rule": "custom",
"quadrature_points": points, "quadrature_weights": weights})
forms = [a]
compiled_forms, module = ffcx.codegeneration.jit.compile_forms(forms, cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
form = compiled_forms[0][0]
default_integral = form.create_cell_integral(-1)
A = np.zeros((6, 6), dtype=np.float64)
w = np.array([], dtype=np.float64)
c = np.array([], dtype=np.float64)
coords = np.array([0.0, 0.0, 1.0, 0.0, 0.0, 1.0], dtype=np.float64)
default_integral.tabulate_tensor(
ffi.cast("double *", A.ctypes.data),
ffi.cast("double *", w.ctypes.data),
ffi.cast("double *", c.ctypes.data),
ffi.cast("double *", coords.ctypes.data), ffi.NULL, ffi.NULL, 0)
# Check that A is diagonal
assert np.count_nonzero(A - np.diag(np.diagonal(A))) == 0
def __init__(self, value, cell=None, name=None):
"""
Create constant-valued function with given value.
*Arguments*
value
The value may be either a single scalar value, or a
tuple/list of values for vector-valued functions, or
nested lists or a numpy array for tensor-valued
functions.
cell
Optional argument. A :py:class:`Cell
<ufl.Cell>` which defines the geometrical
dimensions the Constant is defined for.
name
Optional argument. A str which overrules the default
name of the Constant.
The data type Constant represents a constant value that is
unknown at compile-time. Its values can thus be changed
without requiring re-generation and re-compilation of C++
code.
*Examples of usage*
.. code-block:: python
p = Constant(pi/4) # scalar
C = Constant((0.0, -1.0, 0.0)) # constant vector
"""
# TODO: Either take mesh instead of cell, or drop cell and let
# grad(c) be undefined.
if cell is not None:
cell = ufl.as_cell(cell)
ufl_domain = None
array = numpy.array(value)
rank = len(array.shape)
floats = list(map(float, array.flat))
# Create UFL element and initialize constant
if rank == 0:
ufl_element = ufl.FiniteElement("Real", cell, 0)
cpp.Constant.__init__(self, floats[0])
elif rank == 1:
ufl_element = ufl.VectorElement("Real", cell, 0, dim=len(floats))
cpp.Constant.__init__(self, floats)
else:
ufl_element = ufl.TensorElement("Real", cell, 0, shape=array.shape)
cpp.Constant.__init__(self, list(array.shape), floats)
# Initialize base classes
ufl_function_space = ufl.FunctionSpace(ufl_domain, ufl_element)
ufl.Coefficient.__init__(self, ufl_function_space, count=self.id())
# Set name as given or automatic
name = name or "f_%d" % self.count()
self.rename(name, "a Constant")
def __init__(self, mesh, element, name=None, real_tensorproduct=False):
super(FunctionSpace, self).__init__()
if type(element) is ufl.MixedElement:
raise ValueError("Can't create FunctionSpace for MixedElement")
finat_element = create_element(element)
if isinstance(finat_element, finat.TensorFiniteElement):
# Retrieve scalar element
finat_element = finat_element.base_element
# Used for reconstruction of mixed/component spaces
self.real_tensorproduct = real_tensorproduct
sdata = get_shared_data(mesh,
finat_element,
real_tensorproduct=real_tensorproduct)
# 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_function_space = ufl.FunctionSpace(mesh.ufl_mesh(), element)
self._shared_data = sdata
self._mesh = mesh
self.rank = len(self.shape)
r"""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.value_size = int(numpy.prod(self.shape, dtype=int))
r"""The total number of degrees of freedom at each function
space node."""
self.name = name
r"""The (optional) descriptive name for this space."""
self.node_set = sdata.node_set
r"""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)
r"""A :class:`pyop2.DataSet` representing the function space
degrees of freedom."""
self.comm = self.node_set.comm
self.finat_element = finat_element
self.extruded = sdata.extruded
self.offset = sdata.offset
self.cell_boundary_masks = sdata.cell_boundary_masks
self.interior_facet_boundary_masks = sdata.interior_facet_boundary_masks
def set_coordinates(self, domain):
"""Prepare the coordinate field.
:arg domain: :class:`ufl.Domain`
"""
# Create a fake coordinate coefficient for a domain.
f = ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
self.domain_coordinate[domain] = f
self.coordinates_arg = self._coefficient(f, "macro_coords")
def test_matvec(compile_args):
"""Test evaluation of linear rank-0 form.
Evaluates expression c * A_ij * f_j where c is a Constant,
A_ij is a user specified constant matrix and f_j is j-th component
of user specified vector-valued finite element function (in P1 space).
"""
e = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(e)
V = ufl.FunctionSpace(mesh, e)
f = ufl.Coefficient(V)
a_mat = np.array([[1.0, 2.0], [1.0, 1.0]])
a = ufl.as_matrix(a_mat)
expr = ufl.Constant(mesh) * ufl.dot(a, f)
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
obj, module = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
kernel = obj[0][0]
c_type, np_type = float_to_type("double")
A = np.zeros((3, 2), dtype=np_type)
f_mat = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
# Coefficient storage XYXYXY
w = np.array(f_mat.T.flatten(), dtype=np_type)
c = np.array([0.5], dtype=np_type)
# Coords storage XYXYXY
coords = np.array([0.0, 0.0, 1.0, 0.0, 0.0, 1.0], dtype=np.float64)
kernel.tabulate_expression(
ffi.cast('{type} *'.format(type=c_type), A.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), w.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), c.ctypes.data),
ffi.cast('double *', coords.ctypes.data))
# Check the computation against correct NumPy value
assert np.allclose(A, 0.5 * np.dot(a_mat, f_mat).T)
# Prepare NumPy array of points attached to the expression
length = kernel.num_points * kernel.topological_dimension
points_kernel = np.frombuffer(
ffi.buffer(kernel.points, length * ffi.sizeof("double")), np.double)
points_kernel = points_kernel.reshape(points.shape)
assert np.allclose(points, points_kernel)
# Check the value shape attached to the expression
value_shape = np.frombuffer(
ffi.buffer(kernel.value_shape,
kernel.num_components * ffi.sizeof("int")), np.intc)
assert np.allclose(expr.ufl_shape, value_shape)
def test_ufl_only_spatialcoordinate():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("P", ufl.triangle, 2))
x, y = ufl.SpatialCoordinate(mesh)
expr = x * y - y**2 + x
W = V
to_element = create_element(W.ufl_element())
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
assert first_coeff_fake_coords is True
def test_ufl_only_simple():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("P", ufl.triangle, 2))
v = ufl.Coefficient(V)
expr = ufl.inner(v, v)
W = V
to_element = create_element(W.ufl_element())
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
assert first_coeff_fake_coords is False
def test_rank1(compile_args):
"""Tests evaluation of rank-1 form.
Builds a linear operator which takes vector-valued functions in P1 space
and evaluates expression [u_y, u_x] + grad(u_x) at specified points.
"""
e = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(e)
V = ufl.FunctionSpace(mesh, e)
u = ufl.TrialFunction(V)
expr = ufl.as_vector([u[1], u[0]]) + ufl.grad(u[0])
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
obj, module = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
kernel = obj[0][0]
c_type, np_type = float_to_type("double")
# 2 components for vector components of expression
# 3 points of evaluation
# 6 degrees of freedom for rank1 form
A = np.zeros((3, 2, 6), dtype=np_type)
# Coefficient storage XYXYXY
w = np.array([0.0], dtype=np_type)
c = np.array([0.0], dtype=np_type)
# Coords storage XYXYXY
coords = np.array(points.flatten(), dtype=np.float64)
kernel.tabulate_expression(
ffi.cast('{type} *'.format(type=c_type), A.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), w.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), c.ctypes.data),
ffi.cast('double *', coords.ctypes.data))
f = np.array([[1.0, 2.0, 3.0], [-4.0, -5.0, 6.0]])
# Apply the operator on some test input data
u_ffcx = np.einsum("ijk,k", A, f.T.flatten())
# Compute the correct values using NumPy
# Gradf0 is gradient of f[0], each component of the gradient is constant
gradf0 = np.array(
[[f[0, 1] - f[0, 0], f[0, 1] - f[0, 0], f[0, 1] - f[0, 0]],
[f[0, 2] - f[0, 0], f[0, 2] - f[0, 0], f[0, 2] - f[0, 0]]])
u_correct = np.array([f[1], f[0]]) + gradf0
assert np.allclose(u_ffcx, u_correct.T)
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")
sdata = get_shared_data(mesh, 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) in {ufl.TensorElement, ufl.VectorElement}:
# The number of "free" dofs is given by reference_value_shape,
# not value_shape due to symmetry specifications
rvs = element.reference_value_shape()
# This requires that the sub element is not itself a
# tensor element (which is checked by the top level
# constructor of function spaces)
sub = element.sub_elements()[0].value_shape()
self.shape = rvs[:len(rvs) - len(sub)]
else:
self.shape = ()
self._ufl_function_space = ufl.FunctionSpace(mesh.ufl_mesh(), element)
self._shared_data = sdata
self._mesh = mesh
self.rank = len(self.shape)
r"""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.value_size = int(numpy.prod(self.shape, dtype=int))
r"""The total number of degrees of freedom at each function
space node."""
self.name = name
r"""The (optional) descriptive name for this space."""
self.node_set = sdata.node_set
r"""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)
r"""A :class:`pyop2.DataSet` representing the function space
degrees of freedom."""
self.comm = self.node_set.comm
# Need to create finat element again as sdata does not
# want to carry finat_element.
self.finat_element = create_element(element)
# Used for reconstruction of mixed/component spaces.
# sdata carries real_tensorproduct.
self.real_tensorproduct = sdata.real_tensorproduct
self.extruded = sdata.extruded
self.offset = sdata.offset
self.cell_boundary_masks = sdata.cell_boundary_masks
self.interior_facet_boundary_masks = sdata.interior_facet_boundary_masks
def set_coordinates(self, domain):
"""Prepare the coordinate field.
:arg domain: :class:`ufl.Domain`
"""
# Create a fake coordinate coefficient for a domain.
f = ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
self.domain_coordinate[domain] = f
self.coordinates_args, expression = prepare_coordinates(
f, "coordinate_dofs", interior_facet=self.interior_facet)
self.coefficient_map[f] = expression
def __init__(self, spaces, name=None):
super(MixedFunctionSpace, self).__init__()
self._spaces = tuple(IndexedFunctionSpace(i, s, self)
for i, s in enumerate(spaces))
mesh, = set(s.mesh() for s in spaces)
self._ufl_function_space = ufl.FunctionSpace(mesh.ufl_mesh(),
ufl.MixedElement(*[s.ufl_element() for s in spaces]))
self.name = name or "_".join(str(s.name) for s in spaces)
self._subspaces = {}
self._mesh = mesh
self.comm = self.node_set.comm
def test_ufl_only_shape_mismatch():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("RT", ufl.triangle, 1))
v = ufl.Coefficient(V)
expr = ufl.inner(v, v)
assert expr.ufl_shape == ()
W = V
to_element = create_element(W.ufl_element())
assert to_element.value_shape == (2, )
with pytest.raises(ValueError):
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
def __init__(self, mesh):
"Create function that evaluates to the mesh coordinates at each vertex."
# Initialize C++ part
cpp.MeshCoordinates.__init__(self, mesh)
# Initialize UFL part
ufl_element = mesh.ufl_domain().ufl_coordinate_element()
if ufl_element.family() != "Lagrange" or ufl_element.degree() != 1:
cpp.dolfin_error("specialfunctions.py",
"initialize MeshCoordinates",
"dolfin::MeshCoordinates only supports affine meshes")
ufl_function_space = ufl.FunctionSpace(mesh.ufl_domain(), ufl_element)
ufl.Coefficient.__init__(self, ufl_function_space, count=self.id())
def test_estimated_degree():
cell = ufl.tetrahedron
mesh = ufl.Mesh(ufl.VectorElement('P', cell, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement('P', cell, 1))
f = ufl.Coefficient(V)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = u * v * ufl.tanh(ufl.sqrt(ufl.sinh(f) / ufl.sin(f**f))) * ufl.dx
handler = MockHandler()
logger.addHandler(handler)
with pytest.raises(RuntimeError):
compile_form(a)
logger.removeHandler(handler)
def __init__(self, value):
self.dat, rank, shape = _globalify(value)
cell = None
domain = None
if rank == 0:
e = ufl.FiniteElement("Real", cell, 0)
elif rank == 1:
e = ufl.VectorElement("Real", cell, 0, shape[0])
elif rank == 2:
e = ufl.TensorElement("Real", cell, 0, shape=shape)
fs = ufl.FunctionSpace(domain, e)
super(Constant, self).__init__(fs)
self._repr = 'Constant(%r, %r)' % (self.ufl_element(), self.count())
def __init__(self, value, domain=None):
# Init also called in mesh constructor, but constant can be built without mesh
utils._init()
self.dat, rank, shape = _globalify(value)
cell = None
if domain is not None:
domain = ufl.as_domain(domain)
cell = domain.ufl_cell()
if rank == 0:
e = ufl.FiniteElement("Real", cell, 0)
elif rank == 1:
e = ufl.VectorElement("Real", cell, 0, shape[0])
elif rank == 2:
e = ufl.TensorElement("Real", cell, 0, shape=shape)
fs = ufl.FunctionSpace(domain, e)
super(Constant, self).__init__(fs)
self._repr = 'Constant(%r, %r)' % (self.ufl_element(), self.count())
def __init__(self, value, cell, name=None, symmetry=None):
cell = ufl.as_cell(cell)
ufl_domain = None
array = numpy.array(value)
rank = len(array.shape)
floats = list(map(float, array.flat))
assert rank == 2
ufl_element = ufl.TensorElement("Real",
cell,
0,
shape=array.shape,
symmetry=symmetry)
cpp.Constant.__init__(self, list(array.shape), floats)
ufl_function_space = ufl.FunctionSpace(ufl_domain, ufl_element)
ufl.Coefficient.__init__(self, ufl_function_space, count=self.id())
name = name or "f_%d" % self.count()
self.rename(name, "a Constant")
def V(request, mesh):
return ufl.FunctionSpace(mesh, request.param("CG", mesh.ufl_cell(), 2))
def compile_expression_dual_evaluation(expression,
to_element,
*,
domain=None,
interface=None,
parameters=None,
coffee=False):
"""Compile a UFL expression to be evaluated against a compile-time known reference element's dual basis.
Useful for interpolating UFL expressions into e.g. N1curl spaces.
:arg expression: UFL expression
:arg to_element: A FInAT element for the target space
:arg domain: optional UFL domain the expression is defined on (required when expression contains no domain).
:arg interface: backend module for the kernel interface
:arg parameters: parameters object
:arg coffee: compile coffee kernel instead of loopy kernel
"""
import coffee.base as ast
import loopy as lp
# Just convert FInAT element to FIAT for now.
# Dual evaluation in FInAT will bring a thorough revision.
to_element = to_element.fiat_equivalent
if any(len(dual.deriv_dict) != 0 for dual in to_element.dual_basis()):
raise NotImplementedError(
"Can only interpolate onto dual basis functionals without derivative evaluation, sorry!"
)
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Determine whether in complex mode
complex_mode = is_complex(parameters["scalar_type"])
# Find out which mapping to apply
try:
mapping, = set(to_element.mapping())
except ValueError:
raise NotImplementedError(
"Don't know how to interpolate onto zany spaces, sorry")
expression = apply_mapping(expression, mapping, domain)
# Apply UFL preprocessing
expression = ufl_utils.preprocess_expression(expression,
complex_mode=complex_mode)
# Initialise kernel builder
if interface is None:
if coffee:
import tsfc.kernel_interface.firedrake as firedrake_interface_coffee
interface = firedrake_interface_coffee.ExpressionKernelBuilder
else:
# Delayed import, loopy is a runtime dependency
import tsfc.kernel_interface.firedrake_loopy as firedrake_interface_loopy
interface = firedrake_interface_loopy.ExpressionKernelBuilder
builder = interface(parameters["scalar_type"])
arguments = extract_arguments(expression)
argument_multiindices = tuple(
builder.create_element(arg.ufl_element()).get_indices()
for arg in arguments)
# Replace coordinates (if any) unless otherwise specified by kwarg
if domain is None:
domain = expression.ufl_domain()
assert domain is not None
# Collect required coefficients
first_coefficient_fake_coords = False
coefficients = extract_coefficients(expression)
if has_type(expression, GeometricQuantity) or any(
fem.needs_coordinate_mapping(c.ufl_element())
for c in coefficients):
# Create a fake coordinate coefficient for a domain.
coords_coefficient = ufl.Coefficient(
ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
builder.domain_coordinate[domain] = coords_coefficient
builder.set_cell_sizes(domain)
coefficients = [coords_coefficient] + coefficients
first_coefficient_fake_coords = True
builder.set_coefficients(coefficients)
# Split mixed coefficients
expression = ufl_utils.split_coefficients(expression,
builder.coefficient_split)
# Translate to GEM
kernel_cfg = dict(
interface=builder,
ufl_cell=domain.ufl_cell(),
# FIXME: change if we ever implement
# interpolation on facets.
integral_type="cell",
argument_multiindices=argument_multiindices,
index_cache={},
scalar_type=parameters["scalar_type"])
if all(
isinstance(dual, PointEvaluation)
for dual in to_element.dual_basis()):
# This is an optimisation for point-evaluation nodes which
# should go away once FInAT offers the interface properly
qpoints = []
# Everything is just a point evaluation.
for dual in to_element.dual_basis():
ptdict = dual.get_point_dict()
qpoint, = ptdict.keys()
(qweight, component), = ptdict[qpoint]
assert allclose(qweight, 1.0)
assert component == ()
qpoints.append(qpoint)
point_set = PointSet(qpoints)
config = kernel_cfg.copy()
config.update(point_set=point_set)
# Allow interpolation onto QuadratureElements to refer to the quadrature
# rule they represent
if isinstance(to_element, FIAT.QuadratureElement):
assert allclose(asarray(qpoints), asarray(to_element._points))
quad_rule = QuadratureRule(point_set, to_element._weights)
config["quadrature_rule"] = quad_rule
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but nothing
# new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
shape_indices = tuple(gem.Index() for _ in expr.shape)
basis_indices = point_set.indices
ir = gem.Indexed(expr, shape_indices)
else:
# This is general code but is more unrolled than necssary.
dual_expressions = [] # one for each functional
broadcast_shape = len(expression.ufl_shape) - len(
to_element.value_shape())
shape_indices = tuple(gem.Index()
for _ in expression.ufl_shape[:broadcast_shape])
expr_cache = {} # Sharing of evaluation of the expression at points
for dual in to_element.dual_basis():
pts = tuple(sorted(dual.get_point_dict().keys()))
try:
expr, point_set = expr_cache[pts]
except KeyError:
point_set = PointSet(pts)
config = kernel_cfg.copy()
config.update(point_set=point_set)
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but
# nothing new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
expr = gem.partial_indexed(expr, shape_indices)
expr_cache[pts] = expr, point_set
weights = collections.defaultdict(list)
for p in pts:
for (w, cmp) in dual.get_point_dict()[p]:
weights[cmp].append(w)
qexprs = gem.Zero()
for cmp in sorted(weights):
qweights = gem.Literal(weights[cmp])
qexpr = gem.Indexed(expr, cmp)
qexpr = gem.index_sum(
gem.Indexed(qweights, point_set.indices) * qexpr,
point_set.indices)
qexprs = gem.Sum(qexprs, qexpr)
assert qexprs.shape == ()
assert set(qexprs.free_indices) == set(
chain(shape_indices, *argument_multiindices))
dual_expressions.append(qexprs)
basis_indices = (gem.Index(), )
ir = gem.Indexed(gem.ListTensor(dual_expressions), basis_indices)
# Build kernel body
return_indices = basis_indices + shape_indices + tuple(
chain(*argument_multiindices))
return_shape = tuple(i.extent for i in return_indices)
return_var = gem.Variable('A', return_shape)
if coffee:
return_arg = ast.Decl(parameters["scalar_type"],
ast.Symbol('A', rank=return_shape))
else:
return_arg = lp.GlobalArg("A",
dtype=parameters["scalar_type"],
shape=return_shape)
return_expr = gem.Indexed(return_var, return_indices)
# TODO: one should apply some GEM optimisations as in assembly,
# but we don't for now.
ir, = impero_utils.preprocess_gem([ir])
impero_c = impero_utils.compile_gem([(return_expr, ir)], return_indices)
index_names = dict(
(idx, "p%d" % i) for (i, idx) in enumerate(basis_indices))
# Handle kernel interface requirements
builder.register_requirements([ir])
# Build kernel tuple
return builder.construct_kernel(return_arg, impero_c, index_names,
first_coefficient_fake_coords)
def ufl_function_space(self):
from firedrake.ufl_expr import reconstruct_element
return ufl.FunctionSpace(
self._mesh,
reconstruct_element(self._topological.ufl_element(),
cell=self._mesh.ufl_cell()))
def coordinate_coefficient(domain):
"""Create a fake coordinate coefficient for a domain."""
return ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
def holzapfel_ogden(mesh, q, p, nf=0):
# Based on https://gist.github.com/meg-simula/3ab3fd63264c8cf1912b
#
# Original credit note:
# "Original implementation by Gabriel Balaban,
# modified by Marie E. Rognes"
from ufl import (Constant, VectorConstant, Identity, Coefficient,
TestFunction, conditional, det, diff, dot, exp,
grad, inner, tr, variable)
# Define some random parameters
a = Constant(mesh)
b = Constant(mesh)
a_s = Constant(mesh)
b_s = Constant(mesh)
a_f = Constant(mesh)
b_f = Constant(mesh)
a_fs = Constant(mesh)
b_fs = Constant(mesh)
# For more fun, make these general vector fields rather than
# constants:
e_s = VectorConstant(mesh)
e_f = VectorConstant(mesh)
# Define the isochoric energy contribution
def isochoric(C):
I_1 = tr(C)
I4_f = dot(e_f, C*e_f)
I4_s = dot(e_s, C*e_s)
I8_fs = dot(e_s, C*e_f)
def heaviside(x):
return conditional(x < 1, 0, 1)
def scaled_exp(a, b, x):
return a/(2*b)*(exp(b*x) - 1)
E_1 = scaled_exp(a, b, I_1 - 3)
E_f = heaviside(I4_f)*scaled_exp(a_f, b_f, (I4_f - 1)**2)
E_s = heaviside(I4_s)*scaled_exp(a_s, b_s, (I4_s - 1)**2)
E_3 = scaled_exp(a_fs, b_fs, I8_fs**2)
E = E_1 + E_f + E_s + E_3
return E
# Define mesh and function space
V = ufl.FunctionSpace(mesh, ufl.VectorElement("CG", mesh.ufl_cell(), q))
u = Coefficient(V)
v = TestFunction(V)
# Misc elasticity related tensors and other quantities
I = Identity(mesh.ufl_cell().topological_dimension())
F = grad(u) + I
F = variable(F)
J = det(F)
Cbar = J**(-2/3)*F.T*F
# Define energy
Psi = isochoric(Cbar)
# Find first Piola-Kirchhoff tensor
P = diff(Psi, F)
# Define the variational formulation
it = inner(P, grad(v))
P = ufl.FunctionSpace(mesh, ufl.VectorElement('P', mesh.ufl_cell(), p))
f = [ufl.Coefficient(P) for _ in range(nf)]
return ufl.derivative(reduce(ufl.inner,
list(map(ufl.div, f)) + [it])*ufl.dx, u)