#include <quadrature.h>

Inheritance diagram for MathTL::QuadratureRule< DIM >:

Public Types
typedef QuadratureRule< DIM-1 >	SubQuadratureRule
Public Member Functions
	QuadratureRule ()
	QuadratureRule (const QuadratureRule< DIM > &Q)
	QuadratureRule (const SubQuadratureRule &Q, const QuadratureRule< 1 > &Q1)
virtual	~QuadratureRule ()
unsigned int	get_N () const
void	get_points (Array1D< Point< DIM > > &points) const
void	get_weights (Array1D< double > &weights) const
double	integrate (const Function< DIM, double > &f) const
double	integrate (const Function< DIM, double > &f, const Point< DIM > &a, const Point< DIM > &b) const
template<>
	QuadratureRule (const QuadratureRule< 0 > &Q, const QuadratureRule< 1 > &Q1)
Protected Attributes
Array1D< Point< DIM > >	points_
Array1D< double >	weights_

Detailed Description

template<unsigned int DIM>
class MathTL::QuadratureRule< DIM >

A base class for N-point quadrature rules in DIM space dimensions on a box spanned by a,b R^{DIM} Q(f) = {k=1}^N w_k f(x_k) with nodes x_k and weights w_k. Internally, we store the nodes and weights for quadrature on [0,1]^{DIM} and scale the nodes appropriately when quadrature has to be performed

(this class is _not_ intended to be used in practice, please use derived special versions below instead!)

Member Typedef Documentation

template<unsigned int DIM>

typedef QuadratureRule<DIM-1> MathTL::QuadratureRule< DIM >::SubQuadratureRule

typedef for lower-dimensional quadrature rule

Constructor & Destructor Documentation

template<unsigned int DIM>

MathTL::QuadratureRule< DIM >::QuadratureRule ( )

default constructor: yields empty quadrature rule

template<unsigned int DIM>

MathTL::QuadratureRule< DIM >::QuadratureRule ( const QuadratureRule< DIM > & Q )

copy constructor: copy points and weights

template<unsigned int DIM>

MathTL::QuadratureRule< DIM >::QuadratureRule	(	const SubQuadratureRule< DIM > &	Q,
		const QuadratureRule< 1 > &	Q1
	)

construct quadrature rule as a tensor product from a lower dimensional one and a one-dimensional one

template<unsigned int DIM>

MathTL::QuadratureRule< DIM >::~QuadratureRule ( ) [virtual]

virtual destructor

Member Function Documentation

template<unsigned int DIM>

unsigned int MathTL::QuadratureRule< DIM >::get_N ( ) const [inline]

return number of quadrature points

template<unsigned int DIM>

void MathTL::QuadratureRule< DIM >::get_points ( Array1D< Point< DIM > > & points ) const [inline]

return all quadrature points

template<unsigned int DIM>

void MathTL::QuadratureRule< DIM >::get_weights ( Array1D< double > & weights ) const [inline]

return quadrature weights

template<unsigned int DIM>

double MathTL::QuadratureRule< DIM >::integrate ( const Function< DIM, double > & f ) const

evaluate quadrature rule on [0,1]^{DIM} (we assume that the function is real-valued)

template<unsigned int DIM>

double MathTL::QuadratureRule< DIM >::integrate	(	const Function< DIM, double > &	f,
		const Point< DIM > &	a,
		const Point< DIM > &	b
	)		const

Evaluate quadrature rule on [a,b] where a,b are points in R^d. We do so by rescaling the integral to one over [0,1]^{DIM} (we assume that the function is real-valued)