# Copyright (C) 2009-2019 Chris N. Richardson, Garth N. Wells and Michal Habera
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Collection of functions and function spaces"""
import typing
from functools import singledispatch
import cffi
import numpy as np
import ufl
import ufl.algorithms
import ufl.algorithms.analysis
from dolfinx import common, cpp, jit
from dolfinx.fem import dofmap
[docs]class Constant(ufl.Constant):
def __init__(self, domain, c: typing.Union[np.ndarray, typing.Sequence, float]):
"""A constant with respect to a domain.
Parameters
----------
domain : DOLFINx or UFL mesh
c
Value of the constant.
"""
c_np = np.asarray(c)
super().__init__(domain, c_np.shape)
self._cpp_object = cpp.fem.Constant(c_np.shape, c_np.flatten())
@property
def value(self):
"""Returns value of the constant."""
return self._cpp_object.value()
@value.setter
def value(self, v):
np.copyto(self._cpp_object.value(), np.asarray(v))
[docs]class Expression:
def __init__(self,
ufl_expression: ufl.core.expr.Expr,
x: np.ndarray,
form_compiler_parameters: dict = {}, jit_parameters: dict = {}):
"""Create DOLFINx Expression.
Represents a mathematical expression evaluated at a pre-defined set of
points on the reference cell. This class closely follows the concept of a
UFC Expression.
This functionality can be used to evaluate a gradient of a Function at
the quadrature points in all cells. This evaluated gradient can then be
used as input to a non-FEniCS function that calculates a material
constitutive model.
Parameters
----------
ufl_expression
Pure UFL expression
x
Array of points of shape (num_points, tdim) on the reference
element.
form_compiler_parameters
Parameters used in FFCx compilation of this Expression. Run `ffcx
--help` in the commandline to see all available options.
jit_parameters
Parameters controlling JIT compilation of C code.
Note
----
This wrapper is responsible for the FFCx compilation of the UFL Expr
and attaching the correct data to the underlying C++ Expression.
"""
assert x.ndim < 3
num_points = x.shape[0] if x.ndim == 2 else 1
x = np.reshape(x, (num_points, -1))
mesh = ufl_expression.ufl_domain().ufl_cargo()
# Compile UFL expression with JIT
self._ufc_expression, module, self._code = jit.ffcx_jit(mesh.mpi_comm(), (ufl_expression, x),
form_compiler_parameters=form_compiler_parameters,
jit_parameters=jit_parameters)
self._ufl_expression = ufl_expression
# Setup data (evaluation points, coefficients, constants, mesh, value_size).
# Tabulation function.
ffi = cffi.FFI()
fn = ffi.cast("uintptr_t", self.ufc_expression.tabulate_expression)
value_size = ufl.product(self.ufl_expression.ufl_shape)
ufl_coefficients = ufl.algorithms.extract_coefficients(ufl_expression)
coefficients = [ufl_coefficient._cpp_object for ufl_coefficient in ufl_coefficients]
ufl_constants = ufl.algorithms.analysis.extract_constants(ufl_expression)
constants = [ufl_constant._cpp_object for ufl_constant in ufl_constants]
self._cpp_object = cpp.fem.Expression(coefficients, constants, mesh, x, fn, value_size)
[docs] def eval(self, cells: np.ndarray, u: typing.Optional[np.ndarray] = None) -> np.ndarray:
"""Evaluate Expression in cells.
Parameters
----------
cells
local indices of cells to evaluate expression.
u: optional
array of shape (num_cells, num_points*value_size) to
store result of expression evaluation.
Returns
-------
u: np.ndarray
The i-th row of u contains the expression evaluated on cells[i].
Note
----
This function allocates u of the appropriate size if u is not passed.
"""
cells = np.asarray(cells, dtype=np.int32)
assert cells.ndim == 1
num_cells = cells.shape[0]
# Allocate memory for result if u was not provided
if u is None:
if common.has_petsc_complex:
u = np.empty((num_cells, self.num_points * self.value_size), dtype=np.complex128)
else:
u = np.empty((num_cells, self.num_points * self.value_size), dtype=np.float64)
self._cpp_object.eval(cells, u)
else:
assert u.ndim < 3
assert u.size == num_cells * self.num_points * self.value_size
assert u.shape[0] == num_cells
assert u.shape[1] == self.num_points * self.value_size
self._cpp_object.eval(cells, u)
return u
@property
def ufl_expression(self):
"""Return the original UFL Expression"""
return self._ufl_expression
@property
def x(self):
"""Return the evaluation points on the reference cell"""
return self._cpp_object.x
@property
def num_points(self):
"""Return the number of evaluation points on the reference cell."""
return self._cpp_object.num_points
@property
def value_size(self):
"""Return the value size of the expression"""
return self._cpp_object.value_size
@property
def ufc_expression(self):
"""Return the compiled ufc_expression object"""
return self._ufc_expression
@property
def code(self):
"""Return C code strings"""
return self._code
[docs]class Function(ufl.Coefficient):
"""A finite element function that is represented by a function
space (domain, element and dofmap) and a vector holding the
degrees-of-freedom
"""
def __init__(self,
V: "FunctionSpace",
x: typing.Optional[cpp.la.Vector] = None,
name: typing.Optional[str] = None):
"""Initialize finite element Function."""
# Create cpp Function
if x is not None:
self._cpp_object = cpp.fem.Function(V._cpp_object, x)
else:
self._cpp_object = cpp.fem.Function(V._cpp_object)
# Initialize the ufl.FunctionSpace
super().__init__(V.ufl_function_space(), count=self._cpp_object.id)
# Set name
if name is None:
self.name = "f_{}".format(self.count())
else:
self.name = name
# Store DOLFINx FunctionSpace object
self._V = V
@property
def function_space(self) -> "FunctionSpace":
"""Return the FunctionSpace"""
return self._V
[docs] def ufl_evaluate(self, x, component, derivatives):
"""Function used by ufl to evaluate the Expression"""
# FIXME: same as dolfinx.expression.Expression version. Find way
# to re-use.
assert derivatives == () # TODO: Handle derivatives
if component:
shape = self.ufl_shape
assert len(shape) == len(component)
value_size = ufl.product(shape)
index = ufl.utils.indexflattening.flatten_multiindex(
component, ufl.utils.indexflattening.shape_to_strides(shape))
values = np.zeros(value_size)
# FIXME: use a function with a return value
self(*x, values=values)
return values[index]
else:
# Scalar evaluation
return self(*x)
[docs] def eval(self, x: np.ndarray, cells: np.ndarray, u=None) -> np.ndarray:
"""Evaluate Function at points x, where x has shape (num_points, 3),
and cells has shape (num_points,) and cell[i] is the index of the
cell containing point x[i]. If the cell index is negative the
point is ignored."""
# Make sure input coordinates are a NumPy array
x = np.asarray(x, dtype=np.float64)
assert x.ndim < 3
num_points = x.shape[0] if x.ndim == 2 else 1
x = np.reshape(x, (num_points, -1))
if x.shape[1] != 3:
raise ValueError("Coordinate(s) for Function evaluation must have length 3.")
# Make sure cells are a NumPy array
cells = np.asarray(cells, dtype=np.int32)
assert cells.ndim < 2
num_points_c = cells.shape[0] if cells.ndim == 1 else 1
cells = np.reshape(cells, num_points_c)
# Allocate memory for return value if not provided
if u is None:
value_size = ufl.product(self.ufl_element().value_shape())
if common.has_petsc_complex:
u = np.empty((num_points, value_size), dtype=np.complex128)
else:
u = np.empty((num_points, value_size))
self._cpp_object.eval(x, cells, u)
if num_points == 1:
u = np.reshape(u, (-1, ))
return u
[docs] def interpolate(self, u) -> None:
"""Interpolate an expression"""
@singledispatch
def _interpolate(u):
try:
self._cpp_object.interpolate(u._cpp_object)
except AttributeError:
self._cpp_object.interpolate(u)
@_interpolate.register(int)
def _(u_ptr):
self._cpp_object.interpolate_ptr(u_ptr)
_interpolate(u)
[docs] def compute_point_values(self):
return self._cpp_object.compute_point_values()
[docs] def copy(self):
"""Return a copy of the Function. The FunctionSpace is shared and the
degree-of-freedom vector is copied.
"""
return Function(self.function_space,
self._cpp_object.vector.copy())
@property
def vector(self):
"""Return the vector holding Function degrees-of-freedom."""
return self._cpp_object.vector
@property
def x(self):
"""Return the vector holding Function degrees-of-freedom."""
return self._cpp_object.x
@property
def name(self) -> str:
"""Name of the Function."""
return self._cpp_object.name
@name.setter
def name(self, name):
self._cpp_object.name = name
@property
def id(self) -> int:
"""Return object id index."""
return self._cpp_object.id
def __str__(self):
"""Return a pretty print representation of it self."""
return self.name
[docs] def sub(self, i: int):
"""Return a sub function.
The sub functions are numbered from i = 0..N-1, where N is the
total number of sub spaces.
"""
return Function(self._V.sub(i), self.x, name="{}-{}".format(str(self), i))
[docs] def split(self):
"""Extract any sub functions.
A sub function can be extracted from a discrete function that
is in a mixed, vector, or tensor FunctionSpace. The sub
function resides in the subspace of the mixed space.
"""
num_sub_spaces = self.function_space.num_sub_spaces()
if num_sub_spaces == 1:
raise RuntimeError("No subfunctions to extract")
return tuple(self.sub(i) for i in range(num_sub_spaces))
[docs] def collapse(self):
u_collapsed = self._cpp_object.collapse()
V_collapsed = FunctionSpace(None, self.ufl_element(),
u_collapsed.function_space)
return Function(V_collapsed, u_collapsed.x)
class ElementMetaData(typing.NamedTuple):
"""Data for representing a finite element"""
family: str
degree: int
form_degree: typing.Optional[int] = None # noqa
[docs]class FunctionSpace(ufl.FunctionSpace):
"""A space on which Functions (fields) can be defined."""
def __init__(self,
mesh: cpp.mesh.Mesh,
element: typing.Union[ufl.FiniteElementBase, ElementMetaData],
cppV: typing.Optional[cpp.fem.FunctionSpace] = None,
form_compiler_parameters: dict = {},
jit_parameters: dict = {}):
"""Create a finite element function space."""
# Create function space from a UFL element and existing cpp
# FunctionSpace
if cppV is not None:
assert mesh is None
ufl_domain = cppV.mesh.ufl_domain()
super().__init__(ufl_domain, element)
self._cpp_object = cppV
return
# Initialise the ufl.FunctionSpace
if isinstance(element, ufl.FiniteElementBase):
super().__init__(mesh.ufl_domain(), element)
else:
e = ElementMetaData(*element)
ufl_element = ufl.FiniteElement(e.family, mesh.ufl_cell(), e.degree, form_degree=e.form_degree)
super().__init__(mesh.ufl_domain(), ufl_element)
# Compile dofmap and element and create DOLFIN objects
(self._ufc_element, self._ufc_dofmap), module, code = jit.ffcx_jit(
mesh.mpi_comm(), self.ufl_element(), form_compiler_parameters=form_compiler_parameters,
jit_parameters=jit_parameters)
ffi = cffi.FFI()
cpp_element = cpp.fem.FiniteElement(ffi.cast("uintptr_t", ffi.addressof(self._ufc_element)))
cpp_dofmap = cpp.fem.create_dofmap(mesh.mpi_comm(), ffi.cast(
"uintptr_t", ffi.addressof(self._ufc_dofmap)), mesh.topology, cpp_element)
# Initialize the cpp.FunctionSpace
self._cpp_object = cpp.fem.FunctionSpace(mesh, cpp_element, cpp_dofmap)
[docs] def clone(self) -> "FunctionSpace":
"""Return a new FunctionSpace :math:`W` which shares data with this
FunctionSpace :math:`V`, but with a different unique integer ID.
This function is helpful for defining mixed problems and using
blocked linear algebra. For example, a matrix block defined on
the spaces :math:`V \\times W` where, :math:`V` and :math:`W`
are defined on the same finite element and mesh can be
identified as an off-diagonal block whereas the :math:`V \\times
V` and :math:`V \\times V` matrices can be identified as
diagonal blocks. This is relevant for the handling of boundary
conditions.
"""
Vcpp = cpp.fem.FunctionSpace(self._cpp_object.mesh, self._cpp_object.element, self._cpp_object.dofmap)
return FunctionSpace(None, self.ufl_element(), Vcpp)
[docs] def dolfin_element(self):
"""Return the DOLFINx element."""
return self._cpp_object.element
[docs] def num_sub_spaces(self) -> int:
"""Return the number of sub spaces."""
return self.dolfin_element().num_sub_elements()
[docs] def sub(self, i: int) -> "FunctionSpace":
"""Return the i-th sub space."""
assert self.ufl_element().num_sub_elements() > i
sub_element = self.ufl_element().sub_elements()[i]
cppV_sub = self._cpp_object.sub([i])
return FunctionSpace(None, sub_element, cppV_sub)
[docs] def component(self):
"""Return the component relative to the parent space."""
return self._cpp_object.component()
[docs] def contains(self, V) -> bool:
"""Check whether a FunctionSpace is in this FunctionSpace, or is the
same as this FunctionSpace.
"""
return self._cpp_object.contains(V._cpp_object)
def __contains__(self, u):
"""Check whether a function is in the FunctionSpace."""
try:
return u._in(self._cpp_object)
except AttributeError:
try:
return u._cpp_object._in(self._cpp_object)
except Exception as e:
raise RuntimeError("Unable to check if object is in FunctionSpace ({})".format(e))
def __eq__(self, other):
"""Comparison for equality."""
return super().__eq__(other) and self._cpp_object == other._cpp_object
def __ne__(self, other):
"""Comparison for inequality."""
return super().__ne__(other) or self._cpp_object != other._cpp_object
[docs] def ufl_cell(self):
return self._cpp_object.mesh.ufl_cell()
[docs] def ufl_function_space(self) -> ufl.FunctionSpace:
"""Return the UFL function space"""
return self
@property
def id(self) -> int:
"""The unique identifier"""
return self._cpp_object.id
@property
def element(self):
return self._cpp_object.element
@property
def dofmap(self) -> "dofmap.DofMap":
"""Return the degree-of-freedom map associated with the function space."""
return dofmap.DofMap(self._cpp_object.dofmap)
@property
def mesh(self):
"""Return the mesh on which the function space is defined."""
return self._cpp_object.mesh
[docs] def collapse(self, collapsed_dofs: bool = False):
"""Collapse a subspace and return a new function space and a map from
new to old dofs.
*Arguments*
collapsed_dofs
Return the map from new to old dofs
*Returns*
FunctionSpace
The new function space.
dict
The map from new to old dofs (optional)
"""
cpp_space, dofs = self._cpp_object.collapse()
V = FunctionSpace(None, self.ufl_element(), cpp_space)
if collapsed_dofs:
return V, dofs
else:
return V
[docs] def tabulate_dof_coordinates(self):
return self._cpp_object.tabulate_dof_coordinates()
[docs]def VectorFunctionSpace(mesh: cpp.mesh.Mesh,
element: ElementMetaData,
dim=None,
restriction=None) -> "FunctionSpace":
"""Create vector finite element (composition of scalar elements) function space."""
e = ElementMetaData(*element)
ufl_element = ufl.VectorElement(e.family, mesh.ufl_cell(), e.degree, form_degree=e.form_degree, dim=dim)
return FunctionSpace(mesh, ufl_element)
[docs]def TensorFunctionSpace(mesh: cpp.mesh.Mesh,
element: ElementMetaData,
shape=None,
symmetry: bool = None,
restriction=None) -> "FunctionSpace":
"""Create tensor finite element (composition of scalar elements) function space."""
e = ElementMetaData(*element)
ufl_element = ufl.TensorElement(e.family, mesh.ufl_cell(), e.degree, shape, symmetry)
return FunctionSpace(mesh, ufl_element)