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

Inheritance diagram for ScalarFunctionFromFunctionObject< dim, RangeNumberType >:

[legend]

Public Types
using	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< double > &values) const

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

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

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

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

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

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

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

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

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

virtual void	vector_laplacian (const Point< dim > &p, Vector< double > &values) const

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

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

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

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

virtual void	hessian_list (const std::vector< Point< dim > > &points, std::vector< SymmetricTensor< 2, dim, double > > &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, double > > > &values) const

virtual std::size_t	memory_consumption () const

numbers::NumberTraits< double >::real_type	get_time () const

virtual void	set_time (const numbers::NumberTraits< double >::real_type new_time)

virtual void	advance_time (const numbers::NumberTraits< double >::real_type delta_t)

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Subscriptor functionality
Classes derived from Subscriptor provide a facility to subscribe to this object. This is mostly used by the SmartPointer class.
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

Static Public Member Functions
static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBase &	ExcNoSubscriber (std::string arg1, std::string arg2)

Public Attributes
const unsigned int	n_components

Static Public Attributes
static constexpr unsigned int	dimension

Private Types
using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

Private Member Functions
void	check_no_subscribers () const noexcept

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

numbers::NumberTraits< double >::real_type	time

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

Static Private Attributes
static std::mutex	mutex

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> &);

Point

Definition point.h:111

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);

ScalarFunctionFromFunctionObject

Definition function.h:803

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;

DoFHandler

Definition dof_handler.h:317

Vector

Definition vector.h:120

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 802 of file function.h.

Member Typedef Documentation

◆ time_type

using Function< dim, double >::time_type

inherited

The scalar-valued real type used for representing time.

Definition at line 168 of file function.h.

◆ map_value_type

using Subscriptor::map_value_type = decltype(counter_map)::value_type

privateinherited

The data type used in counter_map.

Definition at line 229 of file subscriptor.h.

◆ map_iterator

using Subscriptor::map_iterator = decltype(counter_map)::iterator

privateinherited

The iterator type used in counter_map.

Definition at line 234 of file subscriptor.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, double >.

◆ vector_value()

virtual void Function< dim, double >::vector_value	(	const Point< dim > &	p,
		Vector< double > &	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, double >.

◆ value_list()

virtual void Function< dim, double >::value_list	(	const std::vector< Point< dim > > &	points,
		std::vector< double > &	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, double >.

◆ vector_value_list()

virtual void Function< dim, double >::vector_value_list	(	const std::vector< Point< dim > > &	points,
		std::vector< Vector< double > > &	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, double >.

◆ vector_values()

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

virtual Tensor< 1, dim, double > Function< dim, double >::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 FunctionFromFunctionObjects< dim, RangeNumberType >, Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, Functions::Monomial< dim, Number >, Functions::SymbolicFunction< dim, RangeNumberType >, and VectorFunctionFromTensorFunction< dim, RangeNumberType >.

◆ vector_gradient()

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

virtualinherited

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

Reimplemented in Functions::ConstantFunction< dim, double >.

◆ gradient_list()

virtual void Function< dim, double >::gradient_list	(	const std::vector< Point< dim > > &	points,
		std::vector< Tensor< 1, dim, double > > &	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::ConstantFunction< dim, double >.

◆ vector_gradients()

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

virtual void Function< dim, double >::vector_gradient_list	(	const std::vector< Point< dim > > &	points,
		std::vector< std::vector< Tensor< 1, dim, double > > > &	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::ConstantFunction< dim, double >.

◆ laplacian()

virtual double Function< dim, double >::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::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, and Functions::SymbolicFunction< dim, RangeNumberType >.

◆ vector_laplacian()

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

virtualinherited

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

◆ laplacian_list()

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

virtualinherited

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

◆ vector_laplacian_list()

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

virtualinherited

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

◆ hessian()

virtual SymmetricTensor< 2, dim, double > Function< dim, double >::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::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, Functions::IdentityFunction< dim, RangeNumberType >, and Functions::SymbolicFunction< dim, RangeNumberType >.

◆ vector_hessian()

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

virtualinherited

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

◆ hessian_list()

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

virtualinherited

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

◆ vector_hessian_list()

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

virtualinherited

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

◆ memory_consumption()

virtual std::size_t Function< dim, double >::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 ComponentSelectFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, RangeNumberType >, and Functions::ConstantFunction< dim, double >.

◆ get_time()

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::get_time ( ) const

inherited

Return the value of the time variable.

◆ set_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::set_time ( const numbers::NumberTraits< double >::real_type new_time )

virtualinherited

Set the time to new_time, overwriting the old value.

◆ advance_time()

virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::advance_time ( const numbers::NumberTraits< double >::real_type delta_t )

virtualinherited

Advance the time by the given time step delta_t.

◆ subscribe()

void Subscriptor::subscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = "" ) const

inherited

Subscribes a user of the object by storing the pointer validity. The subscriber may be identified by text supplied as identifier.

Definition at line 135 of file subscriptor.cc.

◆ unsubscribe()

void Subscriptor::unsubscribe	(	std::atomic< bool > *const	validity,
		const std::string &	identifier = "" ) const

inherited

Unsubscribes a user from the object.

Note: The identifier and the validity pointer must be the same as the one supplied to subscribe().

Definition at line 155 of file subscriptor.cc.

◆ n_subscriptions()

unsigned int Subscriptor::n_subscriptions ( ) const

inlineinherited

Return the present number of subscriptions to this object. This allows to use this class for reference counted lifetime determination where the last one to unsubscribe also deletes the object.

Definition at line 300 of file subscriptor.h.

◆ list_subscribers() [1/2]

template<typename StreamType >

void Subscriptor::list_subscribers ( StreamType & stream ) const

inlineinherited

List the subscribers to the input stream.

Definition at line 317 of file subscriptor.h.

◆ list_subscribers() [2/2]

void Subscriptor::list_subscribers ( ) const

inherited

List the subscribers to deallog.

Definition at line 203 of file subscriptor.cc.

◆ serialize()

template<class Archive >

void Subscriptor::serialize	(	Archive &	ar,
		const unsigned int	version )

inlineinherited

Read or write the data of this object to or from a stream for the purpose of serialization using the BOOST serialization library.

This function does not actually serialize any of the member variables of this class. The reason is that what this class stores is only who subscribes to this object, but who does so at the time of storing the contents of this object does not necessarily have anything to do with who subscribes to the object when it is restored. Consequently, we do not want to overwrite the subscribers at the time of restoring, and then there is no reason to write the subscribers out in the first place.

Definition at line 309 of file subscriptor.h.

◆ check_no_subscribers()

void Subscriptor::check_no_subscribers ( ) const

privatenoexceptinherited

Check that there are no objects subscribing to this object. If this check passes then it is safe to destroy the current object. It this check fails then this function will either abort or print an error message to deallog (by using the AssertNothrow mechanism), but will not throw an exception.

Note: Since this function is just a consistency check it does nothing in release mode.; If this function is called when there is an uncaught exception then, rather than aborting, this function prints an error message to the standard error stream and returns.

Definition at line 52 of file subscriptor.cc.

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 825 of file function.h.

◆ dimension

unsigned int Function< dim, double >::dimension

staticconstexprinherited

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

Definition at line 158 of file function.h.

◆ n_components

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

inherited

Number of vector components.

Definition at line 163 of file function.h.

◆ time

numbers::NumberTraits< double >::real_type FunctionTime< numbers::NumberTraits< double >::real_type >::time

privateinherited

Store the present time.

Definition at line 112 of file function_time.h.

◆ counter

std::atomic<unsigned int> Subscriptor::counter

mutableprivateinherited

Store the number of objects which subscribed to this object. Initially, this number is zero, and upon destruction it shall be zero again (i.e. all objects which subscribed should have unsubscribed again).

The creator (and owner) of an object is counted in the map below if HE manages to supply identification.

We use the mutable keyword in order to allow subscription to constant objects also.

This counter may be read from and written to concurrently in multithreaded code: hence we use the std::atomic class template.

Definition at line 218 of file subscriptor.h.

◆ counter_map

std::map<std::string, unsigned int> Subscriptor::counter_map

mutableprivateinherited

In this map, we count subscriptions for each different identification string supplied to subscribe().

Definition at line 224 of file subscriptor.h.

◆ validity_pointers

std::vector<std::atomic<bool> *> Subscriptor::validity_pointers

mutableprivateinherited

In this vector, we store pointers to the validity bool in the SmartPointer objects that subscribe to this class.

Definition at line 240 of file subscriptor.h.

◆ object_info

const std::type_info* Subscriptor::object_info

mutableprivateinherited

Pointer to the typeinfo object of this object, from which we can later deduce the class name. Since this information on the derived class is neither available in the destructor, nor in the constructor, we obtain it in between and store it here.

Definition at line 248 of file subscriptor.h.

◆ mutex

std::mutex Subscriptor::mutex

staticprivateinherited

A mutex used to ensure data consistency when accessing the mutable members of this class. This lock is used in the subscribe() and unsubscribe() functions, as well as in list_subscribers().

Definition at line 271 of file subscriptor.h.

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

include/deal.II/base/function.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Private Types

Private Member Functions

Private Attributes

Static Private Attributes

Detailed Description

Member Typedef Documentation

◆ time_type

◆ map_value_type

◆ map_iterator

Constructor & Destructor Documentation

◆ ScalarFunctionFromFunctionObject()

Member Function Documentation

◆ value()

◆ vector_value()

◆ value_list()

◆ vector_value_list()

◆ vector_values()

◆ gradient()

◆ vector_gradient()

◆ gradient_list()

◆ vector_gradients()

◆ vector_gradient_list()

◆ laplacian()

◆ vector_laplacian()

◆ laplacian_list()

◆ vector_laplacian_list()

◆ hessian()

◆ vector_hessian()

◆ hessian_list()

◆ vector_hessian_list()

◆ memory_consumption()

◆ get_time()

◆ set_time()

◆ advance_time()

◆ subscribe()

◆ unsubscribe()

◆ n_subscriptions()

◆ list_subscribers() [1/2]

◆ list_subscribers() [2/2]

◆ serialize()

◆ check_no_subscribers()

Member Data Documentation

◆ function_object

◆ dimension

◆ n_components

◆ time

◆ counter

◆ counter_map

◆ validity_pointers

◆ object_info

◆ mutex