Function

class dolfin.cpp.function.Function(*args)

Bases: dolfin.cpp.function.GenericFunction, dolfin.cpp.function.HierarchicalFunction

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 \(u_h\).

Overloaded versions

• Function(V)

  Create function on given function space

  Arguments

  V (FunctionSpace)

  The function space.

  Example

  Note

  No example code available for this function.

• Function(V)

  Create function on given function space (shared data)

  Arguments

  V (FunctionSpace)

  The function space.

• Function(V, 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(V, filename)

  Create function from vector of dofs stored to file

  Arguments

  V (FunctionSpace)

  The function space.

  filename_vector (str)

  The name of the file containing the vector.

  filename_dofdata (str)

  The name of the file containing the dofmap data.

• Function(V, filename)

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

  Arguments

  V (FunctionSpace)

  The function space.

  filename_dofdata (str)

  The name of the file containing the dofmap data.

• Function(v)

  Copy constructor

  Arguments

  v (Function)

  The object to be copied.

• Function(v, i)

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

  Arguments

  v (Function)

  The function to be copied.

  i (int)

  Index of subfunction.

child()

Return the child Function in the hierarchy

compute_vertex_values()

Overloaded versions

• compute_vertex_values(vertex_values, mesh)

  Compute values at all mesh vertices

  Arguments

  vertex_values (numpy.array(float))

  The values at all vertices.

  mesh (Mesh)

  The mesh.

• compute_vertex_values(vertex_values)

  Compute values at all mesh vertices

  Arguments

  vertex_values (numpy.array(float))

  The values at all vertices.

copy(deepcopy=False)

Return a copy of itself

Arguments

deepcopy (bool)

If false (default) the dof vector is shared.

Returns

_Function_

The Function

eval()

Overloaded versions

• eval(values, x)

  Evaluate function at given coordinates

  Arguments

  values (numpy.array(float))

  The values.

  x (numpy.array(float))

  The coordinates.

• eval(values, x, dolfin_cell, ufc_cell)

  Evaluate function at given coordinates in given cell

  Arguments

  values (numpy.array(float))

  The values.

  x (numpy.array(float))

  The coordinates.

  dolfin_cell (Cell)

  The cell.

  ufc_cell (ufc::cell)

  The ufc::cell.

• eval(values, x, cell)

  Evaluate at given point in given cell

  Arguments

  values (numpy.array(float))

  The values at the point.

  x (numpy.array(float))

  The coordinates of the point.

  cell (ufc::cell)

  The cell which contains the given point.

extrapolate()

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

Arguments

v (Function)

The function to be extrapolated.

function_space()

Return the FunctionSpace

geometric_dimension()

Return geometric dimension

Returns

int

The geometric dimension.

get_allow_extrapolation()

Check if extrapolation is permitted when evaluating the Function

Returns

bool

True if extrapolation is permitted, otherwise false

interpolate()

Interpolate function (on possibly non-matching meshes)

Arguments

v (GenericFunction)

The function to be interpolated.

leaf_node()

Return the finest Function in hierarchy

non_matching_eval()

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 (numpy.array(float))

The values at the point.

x (numpy.array(float))

The coordinates of the point.

cell (ufc::cell)

The cell.

parent()

Return the parent Function in the hierarchy

root_node()

Return the coarsest Function in hierarchy

set_allow_extrapolation()

Allow extrapolation when evaluating the Function

Arguments

allow_extrapolation (bool)

Whether or not permit extrapolation.

sub()

Extract subfunction

Arguments

i (int)

Index of subfunction.

Returns

Function

The subfunction.

thisown None

The membership flag

vector()

Overloaded versions

• vector()

  Return vector of expansion coefficients (non-const version)

  Returns

  GenericVector

  The vector of expansion coefficients.

• vector()

  Return vector of expansion coefficients (const version)

  Returns

  GenericVector

  The vector of expansion coefficients (const).