ScalarFunctionFromFunctionObject< dim, RangeNumberType > Class Template Reference

#include <deal.II/base/function.h>

Inheritance diagram for ScalarFunctionFromFunctionObject< dim, RangeNumberType >:

Public Types
using	time_type = typename FunctionTime< typename numbers::NumberTraits< RangeNumberType >::real_type >::time_type

Public Member Functions
	ScalarFunctionFromFunctionObject (const std::function< RangeNumberType(const Point< dim > &)> &function_object)
virtual RangeNumberType	value (const Point< dim > &p, const unsigned int component=0) const override
virtual void	vector_value (const Point< dim > &p, Vector< RangeNumberType > &values) const
virtual void	value_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
virtual void	vector_value_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const
virtual void	vector_values (const std::vector< Point< dim > > &points, std::vector< std::vector< RangeNumberType > > &values) const
virtual Tensor< 1, dim, RangeNumberType >	gradient (const Point< dim > &p, const unsigned int component=0) const
virtual void	vector_gradient (const Point< dim > &p, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients) const
virtual void	gradient_list (const std::vector< Point< dim > > &points, std::vector< Tensor< 1, dim, RangeNumberType > > &gradients, const unsigned int component=0) const
virtual void	vector_gradients (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const
virtual void	vector_gradient_list (const std::vector< Point< dim > > &points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &gradients) const
virtual RangeNumberType	laplacian (const Point< dim > &p, const unsigned int component=0) const
virtual void	vector_laplacian (const Point< dim > &p, Vector< RangeNumberType > &values) const
virtual void	laplacian_list (const std::vector< Point< dim > > &points, std::vector< RangeNumberType > &values, const unsigned int component=0) const
virtual void	vector_laplacian_list (const std::vector< Point< dim > > &points, std::vector< Vector< RangeNumberType > > &values) const
virtual SymmetricTensor< 2, dim, RangeNumberType >	hessian (const Point< dim > &p, const unsigned int component=0) const
virtual void	vector_hessian (const Point< dim > &p, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &values) const
virtual void	hessian_list (const std::vector< Point< dim > > &points, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &values, const unsigned int component=0) const
virtual void	vector_hessian_list (const std::vector< Point< dim > > &points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType > > > &values) const
virtual std::size_t	memory_consumption () const
Number	get_time () const
virtual void	set_time (const Number new_time)
virtual void	advance_time (const Number delta_t)

Public Attributes
const unsigned int	n_components

Static Public Attributes
static constexpr unsigned int	dimension = dim

Private Attributes
const std::function< RangeNumberType(const Point< dim > &)>	function_object
Number	time

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
std::atomic< unsigned int >	counter
std::map< std::string, unsigned int >	counter_map
std::vector< std::atomic< bool > * >	validity_pointers
const std::type_info *	object_info
void	subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
void	unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const
unsigned int	n_subscriptions () const
template<typename StreamType >
void	list_subscribers (StreamType &stream) const
void	list_subscribers () const
template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
using	map_value_type = decltype(counter_map)::value_type
using	map_iterator = decltype(counter_map)::iterator
static std::mutex	mutex
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)
static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)
void	check_no_subscribers () const noexcept

Detailed Description

template<int dim, typename RangeNumberType = double>
class ScalarFunctionFromFunctionObject< dim, RangeNumberType >

This class provides a way to convert a scalar function of the kind

RangeNumberType foo (const Point<dim> &);

into an object of type Function<dim>. Since the argument returns a scalar, the result is clearly a Function object for which function.n_components == 1. The class works by storing a pointer to the given function and every time function.value(p,component) is called, calls foo(p) and returns the corresponding value. It also makes sure that component is in fact zero, as needs be for scalar functions.

The class provides an easy way to turn a simple global function into something that has the required Function<dim> interface for operations like VectorTools::interpolate_boundary_values() etc., and thereby allows for simpler experimenting without having to write all the boiler plate code of declaring a class that is derived from Function and implementing the Function::value() function. An example of this is given in the results section of step-53.

The class gains additional expressive power because the argument it takes does not have to be a pointer to an actual function. Rather, it is a function object, i.e., it can also be the result of a lambda function or some other object that can be called with a single argument. For example, if you need a Function object that returns the norm of a point, you could write it like so:

template <int dim, typename RangeNumberType>
class Norm : public Function<dim, RangeNumberType>
{
public:
  virtual RangeNumberType
  value(const Point<dim> & p,
        const unsigned int component) const
  {
    Assert (component == 0, ExcMessage ("This object is scalar!"));
    return p.norm();
  }
};
 
Norm<2> my_norm_object;

and then pass the my_norm_object around, or you could write it like so:

ScalarFunctionFromFunctionObject<dim, RangeNumberType> my_norm_object(
  &Point<dim>::norm);

Similarly, to generate an object that computes the distance to a point q, we could do this:

template <int dim, typename RangeNumberType>
class DistanceTo : public Function<dim, RangeNumberType>
{
public:
  DistanceTo (const Point<dim> &q) : q(q) {}
 
  virtual RangeNumberType
  value (const Point<dim> & p,
         const unsigned int component) const
  {
    Assert(component == 0, ExcMessage("This object is scalar!"));
    return q.distance(p);
  }
private:
  const Point<dim> q;
};
 
Point<2> q (2, 3);
DistanceTo<2> my_distance_object;

or we could write it like so:

ScalarFunctionFromFunctionObject<dim, RangeNumberType> my_distance_object(
  [&q](const Point<dim> &p){return q.distance(p);});

The savings in work to write this are apparent.

Finally, these lambda functions can be used as a way to map points in different ways. As an example, let us assume that we have computed the solution to a one-dimensional problem and that that solution resides in the following variables:

DoFHandler<1>  dof_handler_1d;
Vector<double> solution_1d;

We will denote this solution function described by this DoFHandler and vector object by \(u_h(x)\) where \(x\) is a vector with just one component, and consequently is not shown in boldface. Then assume that we want this \(u_h(x)\) to be used as a boundary condition for a 2d problem at the line \(y=0\). Let's say that this line corresponds to boundary indicator 123. If we say that the 2d problem is associated with

DoFHandler<2> dof_handler_2d;

then in order to evaluate the boundary conditions for this 2d problem, we would want to call VectorTools::interpolate_boundary_values() via

AffineConstraints<double> boundary_values_2d;
VectorTools::interpolate_boundary_values (dof_handler_2d,
                                          123,
                                          ???,
                                          boundary_values_2d);

The question here is what to use as the Function object that can be passed as third argument. It needs to be a Function<2> object, i.e., it receives a 2d input point and is supposed to return the value at that point. What we want it to do is to just take the \(x\) component of the input point and evaluate the 1d solution at that point, knowing that at the boundary with indicator 123, the \(y\) component of the input point must be zero. This all can be achieved via the following function object:

Functions::FEFieldFunction<1>
  solution_1d_as_function_object (dof_handler_1d, solution_1d);
auto boundary_evaluator
  = [&] (const Point<2> &p)
    {
       // First extract the x component of the input point:
       const Point<1> point_on_axis (p[0]);
 
       // Then evaluate the 1d solution at that point:
       return solution_1d_as_function_object.value(point_on_axis);
    }
 
AffineConstraints<double> boundary_values_2d;
VectorTools::interpolate_boundary_values (dof_handler_2d,
                                          123,
                                          ScalarFunctionFromFunctionObject<2>(boundary_evaluator),
                                          boundary_values_2d);

Definition at line 824 of file function.h.

Member Typedef Documentation

time_type

template<int dim, typename RangeNumberType = double>

using Function< dim, RangeNumberType >::time_type = typename FunctionTime< typename numbers::NumberTraits<RangeNumberType>::real_type>::time_type

inherited

The scalar-valued real type used for representing time.

Definition at line 169 of file function.h.

Constructor & Destructor Documentation

ScalarFunctionFromFunctionObject()

template<int dim, typename RangeNumberType = double>

ScalarFunctionFromFunctionObject< dim, RangeNumberType >::ScalarFunctionFromFunctionObject ( const std::function< RangeNumberType(const Point< dim > &)> &  function_object )

explicit

Given a function object that takes a Point and returns a RangeNumberType value, convert this into an object that matches the Function<dim, RangeNumberType> interface.

Member Function Documentation

value()

template<int dim, typename RangeNumberType = double>

virtual RangeNumberType ScalarFunctionFromFunctionObject< dim, RangeNumberType >::value ( const Point< dim > &  p, const unsigned int  component = 0  ) const

overridevirtual

Return the value of the function at the given point. Returns the value the function given to the constructor produces for this point.

Reimplemented from Function< dim, RangeNumberType >.

vector_value()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_value ( const Point< dim > &  p, Vector< RangeNumberType > &  values  ) const

virtualinherited

Return all components of a vector-valued function at a given point.

values shall have the right size beforehand, i.e. n_components.

The default implementation will call value() for each component.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, VectorFunctionFromScalarFunctionObject< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, Functions::IncrementalFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

value_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::value_list ( const std::vector< Point< dim > > &  points, std::vector< RangeNumberType > &  values, const unsigned int  component = 0  ) const

virtualinherited

Set values to the point values of the specified component of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array.

By default, this function repeatedly calls value() for each point separately, to fill the output array.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

vector_value_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_value_list ( const std::vector< Point< dim > > &  points, std::vector< Vector< RangeNumberType > > &  values  ) const

virtualinherited

Set values to the point values of the function at the points. It is assumed that values already has the right size, i.e. the same size as the points array, and that all elements be vectors with the same number of components as this function has.

By default, this function repeatedly calls vector_value() for each point separately, to fill the output array.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, VectorFunctionFromTensorFunction< dim, RangeNumberType >, ComponentSelectFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

vector_values()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_values ( const std::vector< Point< dim > > &  points, std::vector< std::vector< RangeNumberType > > &  values  ) const

virtualinherited

For each component of the function, fill a vector of values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

gradient()

template<int dim, typename RangeNumberType = double>

virtual Tensor< 1, dim, RangeNumberType > Function< dim, RangeNumberType >::gradient ( const Point< dim > &  p, const unsigned int  component = 0  ) const

virtualinherited

Return the gradient of the specified component of the function at the given point.

Reimplemented in Functions::SignedDistance::Plane< dim >, Functions::SignedDistance::Ellipsoid< dim >, Functions::CosineGradFunction< dim >, AutoDerivativeFunction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, FunctionFromFunctionObjects< dim, RangeNumberType >, Functions::Bessel1< dim >, Functions::CSpline< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::CutOffFunctionTensorProduct< dim >, Functions::CutOffFunctionC1< dim >, Functions::CutOffFunctionCinfty< dim >, Functions::Monomial< dim, Number >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::Polynomial< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::CoordinateRestriction< dim >, Functions::SignedDistance::Sphere< dim >, and NonMatching::internal::DiscreteQuadratureGeneratorImplementation::RefSpaceFEFieldFunction< dim, VectorType >.

vector_gradient()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_gradient ( const Point< dim > &  p, std::vector< Tensor< 1, dim, RangeNumberType > > &  gradients  ) const

virtualinherited

Return the gradient of all components of the function at the given point.

Reimplemented in Functions::ConstantFunction< dim, RangeNumberType >, and Functions::FEFieldFunction< dim, VectorType, spacedim >.

gradient_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::gradient_list ( const std::vector< Point< dim > > &  points, std::vector< Tensor< 1, dim, RangeNumberType > > &  gradients, const unsigned int  component = 0  ) const

virtualinherited

Set gradients to the gradients of the specified component of the function at the points. It is assumed that gradients already has the right size, i.e. the same size as the points array.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.

vector_gradients()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_gradients ( const std::vector< Point< dim > > &  points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &  gradients  ) const

virtualinherited

For each component of the function, fill a vector of gradient values, one for each point.

The default implementation of this function in Function calls value_list() for each component. In order to improve performance, this can be reimplemented in derived classes to speed up performance.

vector_gradient_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_gradient_list ( const std::vector< Point< dim > > &  points, std::vector< std::vector< Tensor< 1, dim, RangeNumberType > > > &  gradients  ) const

virtualinherited

Set gradients to the gradients of the function at the points, for all components. It is assumed that gradients already has the right size, i.e. the same size as the points array.

The outer loop over gradients is over the points in the list, the inner loop over the different components of the function.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >, and Functions::ConstantFunction< dim, RangeNumberType >.

laplacian()

template<int dim, typename RangeNumberType = double>

virtual RangeNumberType Function< dim, RangeNumberType >::laplacian ( const Point< dim > &  p, const unsigned int  component = 0  ) const

virtualinherited

Compute the Laplacian of a given component at point p.

Reimplemented in Functions::CosineGradFunction< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::SquareFunction< dim >, Functions::Q1WedgeFunction< dim >, Functions::PillowFunction< dim >, Functions::CosineFunction< dim >, Functions::ExpFunction< dim >, Functions::SlitSingularityFunction< dim >, Functions::JumpFunction< dim >, Functions::FourierCosineFunction< dim >, Functions::FourierSineFunction< dim >, Functions::FourierSineSum< dim >, Functions::FourierCosineSum< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::FEFieldFunction< dim, VectorType, spacedim >, Functions::ConstantFunction< dim, RangeNumberType >, and Functions::ConstantFunction< dim, double >.

vector_laplacian()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_laplacian ( const Point< dim > &  p, Vector< RangeNumberType > &  values  ) const

virtualinherited

Compute the Laplacian of all components at point p and store them in values.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

laplacian_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::laplacian_list ( const std::vector< Point< dim > > &  points, std::vector< RangeNumberType > &  values, const unsigned int  component = 0  ) const

virtualinherited

Compute the Laplacian of one component at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

vector_laplacian_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_laplacian_list ( const std::vector< Point< dim > > &  points, std::vector< Vector< RangeNumberType > > &  values  ) const

virtualinherited

Compute the Laplacians of all components at a set of points.

Reimplemented in Functions::FEFieldFunction< dim, VectorType, spacedim >.

hessian()

template<int dim, typename RangeNumberType = double>

virtual SymmetricTensor< 2, dim, RangeNumberType > Function< dim, RangeNumberType >::hessian ( const Point< dim > &  p, const unsigned int  component = 0  ) const

virtualinherited

Compute the Hessian of a given component at point p, that is the gradient of the gradient of the function.

Reimplemented in Functions::SignedDistance::Plane< dim >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::CSpline< dim >, Functions::CosineFunction< dim >, Functions::Spherical< dim >, Functions::SymbolicFunction< dim, RangeNumberType >, Functions::CoordinateRestriction< dim >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::SignedDistance::Sphere< dim >, and NonMatching::internal::DiscreteQuadratureGeneratorImplementation::RefSpaceFEFieldFunction< dim, VectorType >.

vector_hessian()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_hessian ( const Point< dim > &  p, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &  values  ) const

virtualinherited

Compute the Hessian of all components at point p and store them in values.

hessian_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::hessian_list ( const std::vector< Point< dim > > &  points, std::vector< SymmetricTensor< 2, dim, RangeNumberType > > &  values, const unsigned int  component = 0  ) const

virtualinherited

Compute the Hessian of one component at a set of points.

vector_hessian_list()

template<int dim, typename RangeNumberType = double>

virtual void Function< dim, RangeNumberType >::vector_hessian_list ( const std::vector< Point< dim > > &  points, std::vector< std::vector< SymmetricTensor< 2, dim, RangeNumberType > > > &  values  ) const

virtualinherited

Compute the Hessians of all components at a set of points.

memory_consumption()

template<int dim, typename RangeNumberType = double>

virtual std::size_t Function< dim, RangeNumberType >::memory_consumption ( ) const

virtualinherited

Return an estimate for the memory consumption, in bytes, of this object.

This function is virtual and can be overloaded by derived classes.

Reimplemented in Functions::FlowFunction< dim >, Functions::FlowFunction< 2 >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, ComponentSelectFunction< dim, RangeNumberType >, Functions::CSpline< dim >, FunctionDerivative< dim >, Functions::JumpFunction< dim >, Functions::InterpolatedTensorProductGridData< dim >, Functions::InterpolatedUniformGridData< dim >, Functions::Polynomial< dim >, and Functions::Spherical< dim >.

get_time()

template<typename Number = double>

Number FunctionTime< Number >::get_time ( ) const

inherited

Return the value of the time variable.

set_time()

template<typename Number = double>

virtual void FunctionTime< Number >::set_time ( const Number  new_time )

virtualinherited

Set the time to new_time, overwriting the old value.

advance_time()

template<typename Number = double>

virtual void FunctionTime< Number >::advance_time ( const Number  delta_t )

virtualinherited

Advance the time by the given time step delta_t.

Member Data Documentation

function_object

template<int dim, typename RangeNumberType = double>

const std::function<RangeNumberType(const Point<dim> &)> ScalarFunctionFromFunctionObject< dim, RangeNumberType >::function_object

private

The function object which we call when this class's value() or value_list() functions are called.

Definition at line 847 of file function.h.

dimension

template<int dim, typename RangeNumberType = double>

constexpr unsigned int Function< dim, RangeNumberType >::dimension = dim

staticconstexprinherited

Export the value of the template parameter as a static member constant. Sometimes useful for some expression template programming.

Definition at line 159 of file function.h.

n_components

template<int dim, typename RangeNumberType = double>

const unsigned int Function< dim, RangeNumberType >::n_components

inherited

Number of vector components.

Definition at line 164 of file function.h.

time

template<typename Number = double>

Number FunctionTime< Number >::time

privateinherited

Store the present time.

Definition at line 113 of file function_time.h.

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The documentation for this class was generated from the following file:

• include/deal.II/base/function.h