npstat::GaussLegendreQuadratureQ Class Reference

#include <GaussLegendreQuadratureQ.hh>

Public Types
enum	{ interval_quadrature = 1 }

Public Member Functions
	GaussLegendreQuadratureQ (unsigned npoints)
unsigned	npoints () const
void	getAbscissae (lapack_double *abscissae, unsigned len) const
void	getAllAbscissae (lapack_double *abscissae, unsigned len) const
void	getWeights (lapack_double *weights, unsigned len) const
void	getAllWeights (lapack_double *weights, unsigned len) const
template<typename FcnResult , typename FcnArg >
lapack_double	integrate (const Functor1< FcnResult, FcnArg > &fcn, lapack_double a, lapack_double b) const
template<typename FcnResult , typename FcnArg >
lapack_double	integrate (const Functor1< FcnResult, FcnArg > &fcn, lapack_double a, lapack_double b, unsigned nsplit) const
template<class Functor >
std::vector< std::pair< lapack_double, lapack_double > >	weightedIntegrationPoints (const Functor &weight, lapack_double a, lapack_double b) 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 lapack_double precision.

Constructor & Destructor Documentation

GaussLegendreQuadratureQ()

npstat::GaussLegendreQuadratureQ::GaussLegendreQuadratureQ ( 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::GaussLegendreQuadratureQ::allowedNPonts ( )

static

The complete set of allowed rules, in the increasing order

getAbscissae()

void npstat::GaussLegendreQuadratureQ::getAbscissae	(	lapack_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::GaussLegendreQuadratureQ::getAllAbscissae	(	lapack_double *	abscissae,
		unsigned	len
	)		const

Return abscissae for all points

getAllWeights()

void npstat::GaussLegendreQuadratureQ::getAllWeights	(	lapack_double *	weights,
		unsigned	len
	)		const

Return weights for all points

getWeights()

void npstat::GaussLegendreQuadratureQ::getWeights	(	lapack_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 >

lapack_double npstat::GaussLegendreQuadratureQ::integrate	(	const Functor1< FcnResult, FcnArg > &	fcn,
		lapack_double	a,
		lapack_double	b
	)		const

Perform the quadrature on [a, b] interval

integrate() [2/2]

template<typename FcnResult , typename FcnArg >

lapack_double npstat::GaussLegendreQuadratureQ::integrate	(	const Functor1< FcnResult, FcnArg > &	fcn,
		lapack_double	a,
		lapack_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::GaussLegendreQuadratureQ::isAllowed ( unsigned  npoints )

static

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

minimalExactRule()

static unsigned npstat::GaussLegendreQuadratureQ::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::GaussLegendreQuadratureQ::npoints ( ) const

inline

Return the number of quadrature points

weightedIntegrationPoints()

template<class Functor >

std::vector<std::pair<lapack_double,lapack_double> > npstat::GaussLegendreQuadratureQ::weightedIntegrationPoints	(	const Functor &	weight,
		lapack_double	a,
		lapack_double	b
	)		const

Weighted integration points on the given interval, suitable for constructing orthogonal polynomials w.r.t. the given weight function (in particular, by ContOrthoPoly1D class). Naturally, rule with "npoints" points must be able to calculate polynomial normalization integrals exactly.

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

• nm/GaussLegendreQuadratureQ.hh