Reference documentation for deal.II version 9.4.0
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Public Types | Public Member Functions | Public Attributes | Static Public Attributes | Private Attributes | List of all members
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, 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)
 

Public Attributes

const unsigned int n_components
 

Static Public Attributes

static constexpr unsigned int dimension
 

Private Attributes

const std::function< RangeNumberType(const Point< dim > &)> function_object
 
numbers::NumberTraits< double >::real_type 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 intcounter
 
std::map< std::string, unsigned intcounter_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 ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)
 
static ::ExceptionBaseExcNoSubscriber (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> &);
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;
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:1473
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:

DoFHandler<1> dof_handler_1d;
Vector<double> solution_1d;
Definition: vector.h:109

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 824 of file function.h.

Member Typedef Documentation

◆ time_type

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

◆ 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

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

◆ 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 Functions::ConstantFunction< dim, RangeNumberType >, Functions::ConstantFunction< dim, double >, and ComponentSelectFunction< dim, RangeNumberType >.

◆ 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.

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

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.


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