Function¶

class dolfin.functions.function.Function(*args, **kwargs)¶

Bases: ufl.coefficient.Coefficient, dolfin.cpp.function.Function

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 \(u_h\).

Arguments

There is a maximum of three arguments. The first argument must be a Function or a FunctionSpace.

If instantiated from another Function, the (optional) second argument must be an integer denoting the number of sub functions to extract.

In addition can a name argument be passed overruling the default name

Examples

Create a Function:

from a FunctionSpace V
```
f = Function(V)
```
from cpp.Function f

Warning: this constructor is intended for internal libray use only. No copying is done - f is only wrapped as Function.
```
g = Function(f)
```
from a FunctionSpace V and a GenericVector v

Warning: this constructor is intended for internal libray use only.
```
g = Function(V, v)
```
from a FunctionSpace and a filename containg a GenericVector
```
g = Function(V, 'MyVectorValues.xml')
```

Initialize Function.

assign(rhs)¶

Assign either a Function or linear combination of Functions.

Arguments

rhs (_Function_): A Function or a linear combination of Functions. If a linear combination is passed all Functions need to be in the same FunctionSpaces.

split(deepcopy=False)¶

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.

Arguments

deepcopy: Copy sub function vector instead of sharing

str(verbose=False)¶: Return an informative str representation of itself

sub(i, deepcopy=False)¶

Return a sub function.

The sub functions are numbered from i = 0..N-1, where N is the total number of sub spaces.

Arguments

i: The number of the sub function

ufl_evaluate(x, component, derivatives)¶: Function used by ufl to evaluate the Function