Reference documentation for deal.II version GIT ca9e7e8105 2023-03-24 14:15:03+00:00
ScalarFunctionFromFunctionObject< dim, RangeNumberType > Class Template Reference

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

Inheritance diagram for ScalarFunctionFromFunctionObject< dim, RangeNumberType >:
[legend]

## Public Types

using time_type = typename FunctionTime< typename numbers::NumberTraits< double >::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< 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, doublegradient (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, doublehessian (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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (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> &);
Definition: point.h:110

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;
virtual RangeNumberType value(const Point< dim > &p, const unsigned int component=0) const override
numbers::NumberTraits< Number >::real_type norm() const
#define Assert(cond, exc)
Definition: exceptions.h:1586
static ::ExceptionBase & ExcMessage(std::string arg1)

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

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:

[&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:

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;
123,
???,
boundary_values_2d);
void interpolate_boundary_values(const Mapping< dim, spacedim > &mapping, const DoFHandler< dim, spacedim > &dof, const std::map< types::boundary_id, const Function< spacedim, number > * > &function_map, std::map< types::global_dof_index, number > &boundary_values, const ComponentMask &component_mask=ComponentMask())

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:

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;
123,
boundary_values_2d);

Definition at line 803 of file function.h.

## ◆ time_type

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

The scalar-valued real type used for representing time.

Definition at line 169 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 230 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 235 of file subscriptor.h.

## ◆ 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.

## ◆ 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< 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, double >.

## ◆ value_list()

 virtual void Function< dim, double >::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, double >.

## ◆ vector_value_list()

 virtual void Function< dim, double >::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, double >.

## ◆ vector_values()

 virtual void Function< dim, double >::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.

 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.

 virtual void Function< dim, double >::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, double >.

 virtual void Function< dim, double >::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::ConstantFunction< dim, double >.

 virtual void Function< dim, double >::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.

 virtual void Function< dim, double >::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::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.

## ◆ vector_laplacian()

 virtual void Function< dim, double >::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.

## ◆ laplacian_list()

 virtual void Function< dim, double >::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.

## ◆ vector_laplacian_list()

 virtual void Function< dim, double >::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.

## ◆ 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.

## ◆ vector_hessian()

 virtual void Function< dim, double >::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()

 virtual void Function< dim, double >::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()

 virtual void Function< dim, double >::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()

 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.

## ◆ 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 Number new_time )
virtualinherited

Set the time to new_time, overwriting the old value.

 virtual void FunctionTime< numbers::NumberTraits< double >::real_type >::advance_time ( const Number 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 136 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 156 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 204 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 53 of file subscriptor.cc.

## ◆ function_object

template<int dim, typename RangeNumberType = double>
 const std::function &)> 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 826 of file function.h.

## ◆ dimension

 constexpr 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 159 of file function.h.

## ◆ n_components

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

Number of vector components.

Definition at line 164 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 113 of file function_time.h.

## ◆ counter

 std::atomic 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 219 of file subscriptor.h.

## ◆ counter_map

 std::map Subscriptor::counter_map
mutableprivateinherited

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

Definition at line 225 of file subscriptor.h.

## ◆ validity_pointers

 std::vector *> 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 241 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 249 of file subscriptor.h.

## ◆ mutex

 std::mutex Subscriptor::mutex
staticprivateinherited

A mutex used to ensure data consistency when printing out the list of subscribers.

Definition at line 271 of file subscriptor.h.

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