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

Inheritance diagram for FunctionDerivative< dim >:

Public Types
enum	DifferenceFormula { Euler , UpwindEuler , FourthOrder }

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

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

virtual std::size_t	memory_consumption () const override

void	set_formula (const DifferenceFormula formula=Euler)

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	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 > > &gradients, const unsigned int component=0) const override

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

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

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 void	vector_gradients (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

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)

Static Public Member Functions
static DifferenceFormula	get_formula_of_order (const unsigned int ord)

Public Attributes
const unsigned int	n_components

Static Public Attributes
static const unsigned int	dimension = dim

Private Attributes
const Function< dim > &	f

double	h

AutoDerivativeFunction< dim >::DifferenceFormula	formula

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

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

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 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)

static ::ExceptionBase &	ExcInUse (int arg1, std::string arg2, std::string arg3)

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

using	map_value_type = decltype(counter_map)::value_type

using	map_iterator = decltype(counter_map)::iterator

static std::mutex	mutex

void	check_no_subscribers () const noexcept

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.

Definition at line 44 of file function_derivative.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.

Member Enumeration Documentation

◆ DifferenceFormula

template<int dim>

enum AutoDerivativeFunction::DifferenceFormula

inherited

Names of difference formulas.

Enumerator

Euler

The symmetric Euler formula of second order:

\[ u'(t) \approx \frac{u(t+h) - u(t-h)}{2h}. \]

UpwindEuler

The upwind Euler formula of first order:

\[ u'(t) \approx \frac{u(t) - u(t-h)}{h}. \]

FourthOrder

The fourth order scheme

\[ u'(t) \approx \frac{u(t-2h) - 8u(t-h) + 8u(t+h) - u(t+2h)}{12h}. \]

Definition at line 88 of file auto_derivative_function.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() [1/2]

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, RangeNumberType >.

Definition at line 92 of file function_derivative.cc.

◆ vector_value() [1/2]

template<int dim>

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

overridevirtual

Definition at line 123 of file function_derivative.cc.

◆ value_list() [1/2]

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

Definition at line 165 of file function_derivative.cc.

◆ memory_consumption()

template<int dim>

std::size_t FunctionDerivative< dim >::memory_consumption

overridevirtual

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.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 231 of file function_derivative.cc.

◆ set_formula() [2/2]

template<int dim>

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

inherited

Choose the difference formula. See the enum DifferenceFormula for available choices.

Definition at line 43 of file auto_derivative_function.cc.

◆ gradient()

template<int dim>

Tensor< 1, dim > AutoDerivativeFunction< dim >::gradient	(	const Point< dim > &	p,
		const unsigned int	component = `0`
	)		const

overridevirtualinherited

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

Compute numerical difference quotients using the preset DifferenceFormula.

Reimplemented from Function< dim, RangeNumberType >.

Definition at line 75 of file auto_derivative_function.cc.

◆ vector_gradient() [1/2]

template<int dim>

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

overridevirtualinherited

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

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 127 of file auto_derivative_function.cc.

◆ vector_gradient() [2/2]

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, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ gradient_list() [1/2]

template<int dim>

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

overridevirtualinherited

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.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 204 of file auto_derivative_function.cc.

◆ gradient_list() [2/2]

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, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ vector_gradient_list() [1/2]

template<int dim>

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

overridevirtualinherited

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.

Compute numerical difference quotients using the preset DifferenceFormula.

Definition at line 268 of file auto_derivative_function.cc.

◆ vector_gradient_list() [2/2]

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, DoFHandlerType, VectorType >, and Functions::ConstantFunction< dim, double >.

◆ get_formula_of_order()

template<int dim>

AutoDerivativeFunction< dim >::DifferenceFormula AutoDerivativeFunction< dim >::get_formula_of_order ( const unsigned int ord )

staticinherited

Return a DifferenceFormula of the order ord at minimum.

Definition at line 336 of file auto_derivative_function.cc.

◆ vector_value() [2/2]

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, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ value_list() [2/2]

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, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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, double >, and Functions::FEFieldFunction< dim, DoFHandlerType, VectorType >.

◆ 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.

◆ 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.

◆ 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.

◆ 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, DoFHandlerType, VectorType >.

◆ 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, DoFHandlerType, VectorType >.

◆ 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, DoFHandlerType, VectorType >.

◆ 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::LevelSet::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 >, and Functions::LevelSet::Sphere< dim >.

◆ 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.

◆ 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

◆ f

template<int dim>

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

private

Function for differentiation.

Definition at line 112 of file function_derivative.h.

◆ h

template<int dim>

double FunctionDerivative< dim >::h

private

Step size of the difference formula.

Definition at line 117 of file function_derivative.h.

◆ formula

template<int dim>

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

private

Difference formula.

Definition at line 122 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 127 of file function_derivative.h.

◆ ht

template<int dim>

std::vector<Tensor<1, dim> > AutoDerivativeFunction< dim >::ht

privateinherited

Includes the unit vectors scaled by h.

Definition at line 228 of file auto_derivative_function.h.

◆ dimension

template<int dim, typename RangeNumberType = double>

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

staticinherited

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

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 files:

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

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Private Attributes

Subscriptor functionality

Detailed Description

Member Typedef Documentation

◆ time_type

Member Enumeration Documentation

◆ DifferenceFormula

Constructor & Destructor Documentation

◆ FunctionDerivative() [1/2]

◆ FunctionDerivative() [2/2]

Member Function Documentation

◆ set_formula() [1/2]

◆ set_h()

◆ value()

◆ vector_value() [1/2]

◆ value_list() [1/2]

◆ memory_consumption()

◆ set_formula() [2/2]

◆ gradient()

◆ vector_gradient() [1/2]

◆ vector_gradient() [2/2]

◆ gradient_list() [1/2]

◆ gradient_list() [2/2]

◆ vector_gradient_list() [1/2]

◆ vector_gradient_list() [2/2]

◆ get_formula_of_order()

◆ vector_value() [2/2]

◆ value_list() [2/2]

◆ vector_value_list()

◆ vector_values()

◆ vector_gradients()

◆ laplacian()

◆ vector_laplacian()

◆ laplacian_list()

◆ vector_laplacian_list()

◆ hessian()

◆ vector_hessian()

◆ hessian_list()

◆ vector_hessian_list()

◆ get_time()

◆ set_time()

◆ advance_time()

Member Data Documentation

◆ f

◆ h

◆ formula

◆ incr

◆ ht

◆ dimension

◆ n_components

◆ time