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)

• GenericFunction
• Hierarchical

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(const FunctionSpace& V)

Create function on given function space

Arguments

V (FunctionSpace)

The function space.

Example

Function u(V);

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(const FunctionSpace& V, std::string filename)

Create function from vector of dofs stored to file

Arguments

V (FunctionSpace)

The function space.

filename_vector (std::string)

The name of the file containing the vector.

filename_dofdata (std::string)

The name of the file containing the dofmap data.

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 non_matching_eval(Array<double>& values, const Array<double>& x, const ufc::cell& ufc_cell) const

Evaluate function for given data (non-matching meshes) This method is deprecated as of dolfin 1.6.0. Please use eval(values, x) instead.

Arguments

values (Array <double>)

The values at the point.

x (Array <double>)

The coordinates of the point.

cell (ufc::cell)

The cell.

void restrict(double* w, const FiniteElement& element, const Cell& dolfin_cell, const double* vertex_coordinates, 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