npstat::GaussLegendreQuadrature Class Reference

#include <GaussLegendreQuadrature.hh>

Inheritance diagram for npstat::GaussLegendreQuadrature:

Public Types
enum	{ interval_quadrature = 1 }

Public Member Functions
	GaussLegendreQuadrature (unsigned npoints)
unsigned	npoints () const
void	getAbscissae (long double *abscissae, unsigned len) const
void	getAllAbscissae (long double *abscissae, unsigned len) const
void	getWeights (long double *weights, unsigned len) const
void	getAllWeights (long double *weights, unsigned len) const
template<typename FcnResult , typename FcnArg >
long double	integrate (const Functor1< FcnResult, FcnArg > &fcn, long double a, long double b) const
template<typename FcnResult , typename FcnArg >
long double	integrate (const Functor1< FcnResult, FcnArg > &fcn, long double a, long double b, unsigned nsplit) const
Public Member Functions inherited from npstat::AbsIntervalQuadrature1D
template<class Functor >
std::vector< std::pair< double, double > >	weightedIntegrationPoints (const Functor &weight, const long double left, const long double right) const
template<class Functor >
std::vector< std::pair< long double, long double > >	weightedIntegrationPointsLD (const Functor &weight, const long double left, const long double right) const

Static Public Member Functions
static bool	isAllowed (unsigned npoints)
static std::vector< unsigned >	allowedNPonts ()
static unsigned	minimalExactRule (unsigned polyDegree)

Detailed Description

Gauss-Legendre quadrature. Internally, operations are performed in long double precision.

Constructor & Destructor Documentation

GaussLegendreQuadrature()

npstat::GaussLegendreQuadrature::GaussLegendreQuadrature ( unsigned  npoints )

explicit

At the moment, the following numbers of points are supported: 2, 4, 6, 8, 10, 12, 16, 32, 64, 100, 128, 256, 512, 1024.

If an unsupported number of points is given in the constructor, std::invalid_argument exception will be thrown.

Member Function Documentation

allowedNPonts()

static std::vector<unsigned> npstat::GaussLegendreQuadrature::allowedNPonts ( )

static

The complete set of allowed rules, in the increasing order

getAbscissae()

void npstat::GaussLegendreQuadrature::getAbscissae	(	long double *	abscissae,
		unsigned	len
	)		const

The abscissae are returned for positive points only, so the buffer length should be at least npoints/2.

getAllAbscissae()

void npstat::GaussLegendreQuadrature::getAllAbscissae ( long double *  abscissae, unsigned  len  ) const

virtual

Return abscissae for all points

Implements npstat::AbsIntervalQuadrature1D.

getAllWeights()

void npstat::GaussLegendreQuadrature::getAllWeights ( long double *  weights, unsigned  len  ) const

virtual

Return weights for all points

Implements npstat::AbsIntervalQuadrature1D.

getWeights()

void npstat::GaussLegendreQuadrature::getWeights	(	long double *	weights,
		unsigned	len
	)		const

The weights are returned for positive points only, so the buffer length should be at least npoints/2.

integrate() [1/2]

template<typename FcnResult , typename FcnArg >

long double npstat::GaussLegendreQuadrature::integrate	(	const Functor1< FcnResult, FcnArg > &	fcn,
		long double	a,
		long double	b
	)		const

Perform the quadrature on the [a, b] interval

integrate() [2/2]

template<typename FcnResult , typename FcnArg >

long double npstat::GaussLegendreQuadrature::integrate	(	const Functor1< FcnResult, FcnArg > &	fcn,
		long double	a,
		long double	b,
		unsigned	nsplit
	)		const

This method splits the interval [a, b] into "nsplit" subintervals of equal length, applies Gauss-Legendre quadrature to each subinterval, and sums the results.

isAllowed()

static bool npstat::GaussLegendreQuadrature::isAllowed ( unsigned  npoints )

static

Check if the rule with the given number of points is supported

minimalExactRule()

static unsigned npstat::GaussLegendreQuadrature::minimalExactRule ( unsigned  polyDegree )

static

Minimum number of points, among the supported rules, which integrates a polynomial with the given degree exactly. Returns 0 if the degree is out of range.

npoints()

unsigned npstat::GaussLegendreQuadrature::npoints ( ) const

inlinevirtual

Return the number of quadrature points

Implements npstat::AbsIntervalQuadrature1D.

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

• nm/GaussLegendreQuadrature.hh