Reference documentation for deal.II version Git b304a00 2017-03-22 15:49:17 -0600
Public Member Functions | Static Public Member Functions | List of all members
Polynomials::Legendre Class Reference

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

Inheritance diagram for Polynomials::Legendre:
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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 doublex) const
 
void value (const doublex, std::vector< double > &values) const
 
void value (const doublex, const unsigned int n_derivatives, double *values) const
 
unsigned int degree () const
 
void scale (const doublefactor)
 
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 &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (Subscriptor &&)
 
void subscribe (const char *identifier=0) const
 
void unsubscribe (const char *identifier=0) 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, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *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 doublefactor)
 
static void shift (std::vector< double > &coefficients, const number2 shift)
 
static void multiply (std::vector< double > &coefficients, const doublefactor)
 
- 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 389 of file polynomial.h.

Constructor & Destructor Documentation

Polynomials::Legendre::Legendre ( const unsigned int  p)

Constructor for polynomial of degree p.

Definition at line 845 of file polynomial.cc.

Member Function Documentation

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 873 of file polynomial.cc.


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