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

Inheritance diagram for Polynomials::LagrangeEquidistant:

Public Member Functions
	LagrangeEquidistant (const unsigned int n, const unsigned int support_point)

Public Member Functions inherited from Polynomials::Polynomial< double >
	Polynomial (const std::vector< double > &coefficients)

	Polynomial (const unsigned int n)

	Polynomial (const std::vector< Point< 1 > > &lagrange_support_points, const unsigned int evaluation_point)

	Polynomial ()

double	value (const double x) const

void	value (const double x, std::vector< double > &values) const

void	value (const double x, const unsigned int n_derivatives, double *values) const

unsigned int	degree () const

void	scale (const double factor)

void	shift (const number2 offset)

Polynomial< double >	derivative () const

Polynomial< double >	primitive () const

Polynomial< double > &	operator*= (const double s)

Polynomial< double > &	operator*= (const Polynomial< double > &p)

Polynomial< double > &	operator+= (const Polynomial< double > &p)

Polynomial< double > &	operator-= (const Polynomial< double > &p)

bool	operator== (const Polynomial< double > &p) const

void	print (std::ostream &out) const

void	serialize (Archive &ar, const unsigned int version)

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 (const char *identifier=nullptr) const

void	unsubscribe (const char *identifier=nullptr) const

unsigned int	n_subscriptions () const

void	list_subscribers () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)

Static Public Member Functions
static std::vector< Polynomial< double > >	generate_complete_basis (const unsigned int degree)

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)

Static Private Member Functions
static void	compute_coefficients (const unsigned int n, const unsigned int support_point, std::vector< double > &a)

Additional Inherited Members
Protected Member Functions inherited from Polynomials::Polynomial< double >
void	transform_into_standard_form ()

Static Protected Member Functions inherited from Polynomials::Polynomial< double >
static void	scale (std::vector< double > &coefficients, const double factor)

static void	shift (std::vector< double > &coefficients, const number2 shift)

static void	multiply (std::vector< double > &coefficients, const double factor)

Protected Attributes inherited from Polynomials::Polynomial< double >
std::vector< double >	coefficients

bool	in_lagrange_product_form

std::vector< double >	lagrange_support_points

double	lagrange_weight

Detailed Description

Lagrange polynomials with equidistant interpolation points in [0,1]. The polynomial of degree n has got n+1 interpolation points. The interpolation points are sorted in ascending order. This order gives an index to each interpolation point. A Lagrangian polynomial equals to 1 at its ‘support point’, and 0 at all other interpolation points. For example, if the degree is 3, and the support point is 1, then the polynomial represented by this object is cubic and its value is 1 at the point x=1/3, and zero at the point x=0, x=2/3, and x=1. All the polynomials have polynomial degree equal to degree, but together they span the entire space of polynomials of degree less than or equal degree.

The Lagrange polynomials are implemented up to degree 10.

Author: Ralf Hartmann, 2000

Definition at line 325 of file polynomial.h.

Constructor & Destructor Documentation

◆ LagrangeEquidistant()

Polynomials::LagrangeEquidistant::LagrangeEquidistant	(	const unsigned int	n,
		const unsigned int	support_point
	)

Constructor. Takes the degree n of the Lagrangian polynomial and the index support_point of the support point. Fills the coefficients of the base class Polynomial.

Definition at line 723 of file polynomial.cc.

Member Function Documentation

◆ generate_complete_basis()

std::vector< Polynomial< double > > Polynomials::LagrangeEquidistant::generate_complete_basis ( const unsigned int degree )

static

Return a vector of polynomial objects of degree degree, which then spans the full space of polynomials up to the given degree. The polynomials are generated by calling the constructor of this class with the same degree but support point running from zero to degree. This function may be used to initialize the TensorProductPolynomials and PolynomialSpace classes.

Definition at line 807 of file polynomial.cc.

◆ compute_coefficients()

void Polynomials::LagrangeEquidistant::compute_coefficients	(	const unsigned int	n,
		const unsigned int	support_point,
		std::vector< double > &	a
	)

staticprivate

Compute the coefficients of the base class Polynomial. This function is static to allow to be called in the constructor.

Definition at line 748 of file polynomial.cc.

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

deal.II/base/polynomial.h
source/base/polynomial.cc

Public Member Functions

Static Public Member Functions