Polynomials::Legendre Class Reference

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

Inheritance diagram for Polynomials::Legendre:

Public Member Functions
	Legendre (const unsigned int p)
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 (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 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)

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

Legendre polynomials of arbitrary degree. Constructing a Legendre polynomial of degree p, the roots will be computed by the Gauss formula of the respective number of points and a representation of the polynomial by its roots.

Note

The polynomials defined by this class differ in two aspects by what is usually referred to as Legendre polynomials: (i) This classes defines them on the reference interval \([0,1]\), rather than the commonly used interval \([-1,1]\). (ii) The polynomials have been scaled in such a way that they are orthonormal, not just orthogonal; consequently, the polynomials do not necessarily have boundary values equal to one.

Author

Guido Kanschat, 2000

Definition at line 397 of file polynomial.h.

Constructor & Destructor Documentation

Legendre()

Polynomials::Legendre::Legendre

(

const unsigned int

p

)

Constructor for polynomial of degree p.

Definition at line 839 of file polynomial.cc.

Member Function Documentation

generate_complete_basis()

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

static

Return a vector of Legendre polynomial objects of degrees zero through degree, which then spans the full space of polynomials up to the given degree. This function may be used to initialize the TensorProductPolynomials and PolynomialSpace classes.

Definition at line 866 of file polynomial.cc.

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

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