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

Inheritance diagram for FunctionDerivative< dim >:

Public Member Functions
	FunctionDerivative (const Function< dim > &f, const Point< dim > &direction, const double h=1.e-6)

	FunctionDerivative (const Function< dim > &f, const std::vector< Point< dim >> &direction, const double h=1.e-6)

void	set_formula (typename AutoDerivativeFunction< dim >::DifferenceFormula formula=AutoDerivativeFunction< dim >::Euler)

void	set_h (const double h)

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

virtual void	vector_value (const Point< dim > &p, Vector< double > &value) const override

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

std::size_t	memory_consumption () const

Public Member Functions inherited from AutoDerivativeFunction< dim >
	AutoDerivativeFunction (const double h, const unsigned int n_components=1, const double initial_time=0.0)

virtual	~AutoDerivativeFunction () override=default

void	set_formula (const DifferenceFormula formula=Euler)

void	set_h (const double h)

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

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

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

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

Public Member Functions inherited from Function< dim >
	Function (const unsigned int n_components=1, const time_type initial_time=0.0)

	Function (const Function &f)=default

virtual	~Function () override=0

Function &	operator= (const Function &f)

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 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

std::size_t	memory_consumption () const

Public Member Functions inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
	FunctionTime (const numbers::NumberTraits< double >::real_type initial_time=numbers::NumberTraits< double >::real_type(0.0))

virtual	~FunctionTime ()=default

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 Member Functions inherited from Subscriptor
	Subscriptor ()

	Subscriptor (const Subscriptor &)

	Subscriptor (Subscriptor &&) noexcept

virtual	~Subscriptor ()

Subscriptor &	operator= (const Subscriptor &)

Subscriptor &	operator= (Subscriptor &&) noexcept

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)

Private Attributes
const Function< dim > &	f

double	h

AutoDerivativeFunction< dim >::DifferenceFormula	formula

std::vector< Tensor< 1, dim > >	incr

Additional Inherited Members
Public Types inherited from AutoDerivativeFunction< dim >
enum	DifferenceFormula { Euler, UpwindEuler, FourthOrder }

Public Types inherited from Function< dim >
using	time_type = typename FunctionTime< typename numbers::NumberTraits< double >::real_type >::time_type

Public Types inherited from FunctionTime< numbers::NumberTraits< double >::real_type >
using	time_type = numbers::NumberTraits< double >::real_type

Static Public Member Functions inherited from AutoDerivativeFunction< dim >
static DifferenceFormula	get_formula_of_order (const unsigned int ord)

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

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

Public Attributes inherited from Function< dim >
const unsigned int	n_components

Static Public Attributes inherited from Function< dim >
static const unsigned int	dimension

Detailed Description

template<int dim>
class FunctionDerivative< dim >

Derivative of a function object. The value access functions of this class return the directional derivative of a function with respect to a direction provided on construction. If b is the vector, the derivative b . grad f is computed. This derivative is evaluated directly, not by computing the gradient of f and its scalar product with b.

The derivative is computed numerically, using one of the provided difference formulas (see set_formula for available schemes). Experimenting with h and the difference scheme may be necessary to obtain sufficient results.

Author: Guido Kanschat, 2000

Definition at line 45 of file function_derivative.h.

Constructor & Destructor Documentation

◆ FunctionDerivative() [1/2]

template<int dim>

FunctionDerivative< dim >::FunctionDerivative	(	const Function< dim > &	f,
		const Point< dim > &	direction,
		const double	h = `1.e-6`
	)

Constructor. Provided are the functions to compute derivatives of, the direction vector of the differentiation and the step size h of the difference formula.

Definition at line 26 of file function_derivative.cc.

◆ FunctionDerivative() [2/2]

template<int dim>

FunctionDerivative< dim >::FunctionDerivative	(	const Function< dim > &	f,
		const std::vector< Point< dim >> &	direction,
		const double	h = `1.e-6`
	)

Constructor. Provided are the functions to compute derivatives of and the direction vector of the differentiation in each quadrature point and the difference step size.

This is the constructor for a variable velocity field. Most probably, a new object of FunctionDerivative has to be constructed for each set of quadrature points.

The number of quadrature point must still be the same, when values are accessed.

Definition at line 40 of file function_derivative.cc.

Member Function Documentation

◆ set_formula()

template<int dim>

void FunctionDerivative< dim >::set_formula ( typename AutoDerivativeFunction< dim >::DifferenceFormula formula = AutoDerivativeFunction<dim>::Euler )

Choose the difference formula. This is set to the default in the constructor.

Formulas implemented right now are first order backward Euler (UpwindEuler), second order symmetric Euler (Euler) and a symmetric fourth order formula (FourthOrder).

Definition at line 57 of file function_derivative.cc.

◆ set_h()

template<int dim>

void FunctionDerivative< dim >::set_h ( const double h )

Change the base step size of the difference formula

Definition at line 81 of file function_derivative.cc.

◆ value()

template<int dim>

double FunctionDerivative< dim >::value	(	const Point< dim > &	p,
		const unsigned int	component = `0`
	)		const

overridevirtual

Return the value of the function at the given point. Unless there is only one component (i.e. the function is scalar), you should state the component you want to have evaluated; it defaults to zero, i.e. the first component.

Reimplemented from Function< dim >.

Definition at line 92 of file function_derivative.cc.

◆ vector_value()

template<int dim>

void FunctionDerivative< dim >::vector_value	(	const Point< dim > &	p,
		Vector< double > &	values
	)		const

overridevirtual

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 from Function< dim >.

Definition at line 123 of file function_derivative.cc.

◆ value_list()

template<int dim>

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

overridevirtual

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 from Function< dim >.

Definition at line 165 of file function_derivative.cc.

◆ memory_consumption()

template<int dim>

std::size_t FunctionDerivative< dim >::memory_consumption

Return an estimate for the memory consumption, in bytes, of this object. This is not exact (but will usually be close) because calculating the memory usage of trees (e.g., std::map) is difficult.

Definition at line 231 of file function_derivative.cc.

Member Data Documentation

◆ f

template<int dim>

const Function<dim>& FunctionDerivative< dim >::f

private

Function for differentiation.

Definition at line 113 of file function_derivative.h.

◆ h

template<int dim>

double FunctionDerivative< dim >::h

private

Step size of the difference formula.

Definition at line 118 of file function_derivative.h.

◆ formula

template<int dim>

AutoDerivativeFunction<dim>::DifferenceFormula FunctionDerivative< dim >::formula

private

Difference formula.

Definition at line 123 of file function_derivative.h.

◆ incr

template<int dim>

std::vector<Tensor<1, dim> > FunctionDerivative< dim >::incr

private

Helper object. Contains the increment vector for the formula.

Definition at line 128 of file function_derivative.h.

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

include/deal.II/base/function_derivative.h
source/base/function_derivative.cc

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim> class FunctionDerivative< dim >

Constructor & Destructor Documentation

◆ FunctionDerivative() [1/2]

◆ FunctionDerivative() [2/2]

Member Function Documentation

◆ set_formula()

◆ set_h()

◆ value()

◆ vector_value()

◆ value_list()

◆ memory_consumption()

Member Data Documentation

◆ f

◆ h

◆ formula

◆ incr

template<int dim>
class FunctionDerivative< dim >