Class Function

python/dolfinx/fem/function.py:335–626

A finite element function. A finite element function is represented by a function space (domain, element and dofmap) and a vector holding the degrees-of-freedom.

class Function(ufl.Coefficient, Generic[Scalar]):
    """A finite element function.

    A finite element function is represented by a function space
    (domain, element and dofmap) and a vector holding the
    degrees-of-freedom.

    """

    _cpp_object: (
        _cpp.fem.Function_complex64
        | _cpp.fem.Function_complex128
        | _cpp.fem.Function_float32
        | _cpp.fem.Function_float64
    )

    _x: la.Vector[Scalar]

    def __init__(
        self,
        V: FunctionSpace,
        x: la.Vector[Scalar] | None = None,
        name: str | None = None,
        dtype: npt.DTypeLike | None = None,
    ):
        """Initialize a finite element Function.

        Args:
            V: The function space that the Function is defined on.
            x: Function degree-of-freedom vector. Typically required
                only when reading a saved Function from file.
            name: Function name.
            dtype: Scalar type. Is not set, the DOLFINx default scalar
                type is used.
        """
        if x is not None:
            if dtype is None:
                dtype = x.array.dtype
            else:
                assert x.array.dtype == dtype, "Incompatible Vector and dtype."
        else:
            if dtype is None:
                dtype = default_scalar_type

        assert np.issubdtype(V.element.dtype, np.dtype(dtype).type(0).real.dtype), (
            "Incompatible FunctionSpace dtype and requested dtype."
        )

        # Create cpp Function
        def functiontype(dtype):
            if np.issubdtype(dtype, np.float32):
                return _cpp.fem.Function_float32
            elif np.issubdtype(dtype, np.float64):
                return _cpp.fem.Function_float64
            elif np.issubdtype(dtype, np.complex64):
                return _cpp.fem.Function_complex64
            elif np.issubdtype(dtype, np.complex128):
                return _cpp.fem.Function_complex128