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

Inheritance diagram for Functions::Polynomial< dim >:

Public Member Functions
	Polynomial (const Table< 2, double > &exponents, const std::vector< double > &coefficients)

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

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

virtual Tensor< 1, dim >	gradient (const Point< dim > &p, const unsigned int component=0) 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 (const Point< dim > &p, Vector< double > &values) 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 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 Table< 2, double >	exponents

const std::vector< double >	coefficients

Additional Inherited Members
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 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 Functions::Polynomial< dim >

A class that represents a function object for a polynomial. A polynomial is composed by the summation of multiple monomials. If the polynomial has n monomials and the dimension is equal to dim, the polynomial can be written as \(\sum_{i=1}^{n} a_{i}(\prod_{d=1}^{dim} x_{d}^{\alpha_{i,d}})\), where \(a_{i}\) are the coefficients of the monomials and \(\alpha_{i,d}\) are their exponents. The class's constructor takes a Table<2,double> to describe the set of exponents and a Vector<double> to describe the set of coefficients.

Author: Ángel Rodríguez, 2015

Definition at line 1612 of file function_lib.h.

Constructor & Destructor Documentation

◆ Polynomial()

template<int dim>

Functions::Polynomial< dim >::Polynomial	(	const Table< 2, double > &	exponents,
		const std::vector< double > &	coefficients
	)

Constructor. The coefficients and the exponents of the polynomial are passed as arguments. The Table<2, double> exponents has a number of rows equal to the number of monomials of the polynomial and a number of columns equal to dim. The i-th row of the exponents table contains the \({\alpha_{i,d}}\) exponents of the i-th monomial \(a_{i}\prod_{d=1}^{dim} x_{d}^{\alpha_{i,d}}\). The i-th element of the coefficients vector contains the coefficient \(a_{i}\) for the i-th monomial.

Definition at line 2730 of file function_lib.cc.

Member Function Documentation

◆ value()

template<int dim>

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

overridevirtual

Function value at one point.

Reimplemented from Function< dim >.

Definition at line 2746 of file function_lib.cc.

◆ value_list()

template<int dim>

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

overridevirtual

Function values at multiple points.

Reimplemented from Function< dim >.

Definition at line 2773 of file function_lib.cc.

◆ gradient()

template<int dim>

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

overridevirtual

Function gradient at one point.

Reimplemented from Function< dim >.

Definition at line 2788 of file function_lib.cc.

Member Data Documentation

◆ exponents

template<int dim>

const Table<2, double> Functions::Polynomial< dim >::exponents

private

The set of exponents.

Definition at line 1653 of file function_lib.h.

◆ coefficients

template<int dim>

const std::vector<double> Functions::Polynomial< dim >::coefficients

private

The set of coefficients.

Definition at line 1658 of file function_lib.h.

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

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

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<int dim> class Functions::Polynomial< dim >

Constructor & Destructor Documentation

◆ Polynomial()

Member Function Documentation

◆ value()

◆ value_list()

◆ gradient()

Member Data Documentation

◆ exponents

◆ coefficients

template<int dim>
class Functions::Polynomial< dim >