Source code for dolfinx.fem.function

# Copyright (C) 2009-2019 Chris N. Richardson, Garth N. Wells and Michal Habera
# This file is part of DOLFINx (
# 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[] = 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(), # Set name if name is None: = "f_{}".format(self.count()) else: = 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 @name.setter def name(self, name): = name @property def id(self) -> int: """Return object id index.""" return def __str__(self): """Return a pretty print representation of it self.""" return
[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(, mesh.ufl_cell(),, 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 @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(, mesh.ufl_cell(),, 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(, mesh.ufl_cell(),, shape, symmetry) return FunctionSpace(mesh, ufl_element)