Function.h

Note

The documentation on this page was automatically extracted from the DOLFIN C++ code and may need to be edited or expanded.

class Function

Parent class(es)

This class represents a function \(u_h\) in a finite element function space \(V_h\), given by

\[u_h = \sum_{i=1}^{n} U_i \phi_i\]

where \(\{\phi_i\}_{i=1}^{n}\) is a basis for \(V_h\), and \(U\) is a vector of expansion coefficients for \(u_h\).

explicit Function(std::shared_ptr<const FunctionSpace> V)

Create function on given function space (shared data)

Arguments
V (FunctionSpace)
The function space.
Function(std::shared_ptr<const FunctionSpace> V, std::shared_ptr<GenericVector> x)

Create function on given function space with a given vector (shared data)

Warning: This constructor is intended for internal library use only

Arguments
V (FunctionSpace)
The function space.
x (GenericVector)
The vector.
Function(std::shared_ptr<const FunctionSpace> V, std::string filename)

Create function from vector of dofs stored to file (shared data)

Arguments
V (FunctionSpace)
The function space.
filename_dofdata (std::string)
The name of the file containing the dofmap data.
Function(const Function &v)

Copy constructor

Arguments
v (Function)
The object to be copied.
Function(const Function &v, std::size_t i)

Sub-function constructor with shallow copy of vector (used in Python interface)

Arguments
v (Function)
The function to be copied.
i (std::size_t)
Index of subfunction.
const Function &operator=(const Function &v)

Assignment from function

Arguments
v (Function)
Another function.
const Function &operator=(const Expression &v)

Assignment from expression using interpolation

Arguments
v (Expression)
The expression.
void operator=(const FunctionAXPY &axpy)

Assignment from linear combination of function

Arguments
v (FunctionAXPY)
A linear combination of other Functions
Function &operator[](std::size_t i) const

Extract subfunction

Arguments
i (std::size_t)
Index of subfunction.
Returns
Function
The subfunction.
FunctionAXPY operator+(const Function &other) const

Add operator with other function

Returns
FunctionAXPY
Return a linear combination of Functions
FunctionAXPY operator+(const FunctionAXPY &axpy) const

Add operator with other linear combination of functions

Returns
FunctionAXPY
Return a linear combination of Functions
FunctionAXPY operator-(const Function &other) const

Subtraction operator with other function

Returns
FunctionAXPY
Return a linear combination of Functions
FunctionAXPY operator-(const FunctionAXPY &axpy) const

Subtraction operator with other linear combination of functions

Returns
FunctionAXPY
Return a linear combination of Functions
FunctionAXPY operator*(double scalar) const

Scale operator

Returns
FunctionAXPY
Return a linear combination of Functions
FunctionAXPY operator/(double scalar) const

Scale operator

Returns
FunctionAXPY
Return a linear combination of Functions
std::shared_ptr<const FunctionSpace> function_space() const

Return shared pointer to function space

Returns
FunctionSpace
Return the shared pointer.
std::shared_ptr<GenericVector> vector()

Return vector of expansion coefficients (non-const version)

Returns
GenericVector
The vector of expansion coefficients.
std::shared_ptr<const GenericVector> vector() const

Return vector of expansion coefficients (const version)

Returns
GenericVector
The vector of expansion coefficients (const).
bool in(const FunctionSpace &V) const

Check if function is a member of the given function space

Arguments
V (FunctionSpace)
The function space.
Returns
bool
True if the function is in the function space.
std::size_t geometric_dimension() const

Return geometric dimension

Returns
std::size_t
The geometric dimension.
void eval(Array<double> &values, const Array<double> &x) const

Evaluate function at given coordinates

Arguments
values (Array <double>)
The values.
x (Array <double>)
The coordinates.
void eval(Array<double> &values, const Array<double> &x, const Cell &dolfin_cell, const ufc::cell &ufc_cell) const

Evaluate function at given coordinates in given cell

Arguments
values (Array <double>)
The values.
x (Array <double>)
The coordinates.
dolfin_cell (Cell)
The cell.
ufc_cell (ufc::cell)
The ufc::cell.
void interpolate(const GenericFunction &v)

Interpolate function (on possibly non-matching meshes)

Arguments
v (GenericFunction)
The function to be interpolated.
void extrapolate(const Function &v)

Extrapolate function (from a possibly lower-degree function space)

Arguments
v (Function)
The function to be extrapolated.
std::size_t value_rank() const

Return value rank

Returns
std::size_t
The value rank.
std::size_t value_dimension(std::size_t i) const

Return value dimension for given axis

Arguments
i (std::size_t)
The index of the axis.
Returns
std::size_t
The value dimension.
void eval(Array<double> &values, const Array<double> &x, const ufc::cell &cell) const

Evaluate at given point in given cell

Arguments
values (Array <double>)
The values at the point.
x (Array <double>)
The coordinates of the point.
cell (ufc::cell)
The cell which contains the given point.
void restrict(double *w, const FiniteElement &element, const Cell &dolfin_cell, const double *coordinate_dofs, const ufc::cell &ufc_cell) const

Restrict function to local cell (compute expansion coefficients w)

Arguments
w (list of doubles)
Expansion coefficients.
element (FiniteElement)
The element.
dolfin_cell (Cell)
The cell.
ufc_cell (ufc::cell).
The ufc::cell.
void compute_vertex_values(std::vector<double> &vertex_values, const Mesh &mesh) const

Compute values at all mesh vertices

Arguments
vertex_values (Array <double>)
The values at all vertices.
mesh (Mesh)
The mesh.
void compute_vertex_values(std::vector<double> &vertex_values)

Compute values at all mesh vertices

Arguments
vertex_values (Array <double>)
The values at all vertices.
void set_allow_extrapolation(bool allow_extrapolation)

Allow extrapolation when evaluating the Function

Arguments
allow_extrapolation (bool)
Whether or not permit extrapolation.
bool get_allow_extrapolation() const

Check if extrapolation is permitted when evaluating the Function

Returns
bool
True if extrapolation is permitted, otherwise false