Inheritance diagram for npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >:

Public Member Functions
	ClassicalOrthoPoly1DFromWeight (const Functor1D &fcn, const unsigned maxDegree, const unsigned nIntegPoints, const long double i_xmin, const long double i_xmax, const OrthoPolyMethod m=OPOLY_STIELTJES, const bool useFejerQuadrature=true)

virtual ClassicalOrthoPoly1DFromWeight *	clone () const

virtual long double	weight (const long double x) const

virtual double	xmin () const

virtual double	xmax () const

virtual unsigned	maxDegree () const

virtual std::pair< long double, long double >	monicRecurrenceCoeffs (const unsigned deg) const

virtual std::pair< long double, long double >	recurrenceCoeffs (const unsigned deg) const

Public Member Functions inherited from npstat::AbsClassicalOrthoPoly1D
Matrix< long double >	jacobiMatrix (unsigned n) const

long double	poly (unsigned deg, long double x) const

long double	monic (unsigned deg, long double x) const

std::pair< long double, long double >	twopoly (unsigned deg1, unsigned deg2, long double x) const

void	allpoly (long double x, long double *values, unsigned maxdeg) const

void	allmonic (long double x, long double *values, unsigned maxdeg) const

double	series (const double *coeffs, unsigned maxdeg, double x) const

double	integrateSeries (const double *coeffs, unsigned maxdeg) const

template<class Functor , class Quadrature >
void	calculateCoeffs (const Functor &fcn, const Quadrature &quad, double *coeffs, unsigned maxdeg) const

template<class Numeric >
void	sampleCoeffs (const Numeric coords, unsigned long lenCoords, double coeffs, unsigned maxdeg) const

template<class Numeric >
void	sampleCoeffVars (const Numeric coords, unsigned long lenCoords, const double coeffs, unsigned maxdeg, double *variances) const

template<class Numeric >
Matrix< double >	sampleCoeffCovariance (const Numeric coords, unsigned long lenCoords, const double coeffs, unsigned maxdeg) const

template<class Numeric >
void	sampleCoeffs (const Numeric coords, unsigned long lenCoords, Numeric location, Numeric scale, double coeffs, unsigned maxdeg) const

template<class Numeric >
void	sampleCoeffVars (const Numeric coords, unsigned long lenCoords, Numeric location, Numeric scale, const double coeffs, unsigned maxdeg, double *variances) const

template<class Numeric >
Matrix< double >	sampleCoeffCovariance (const Numeric coords, unsigned long lenCoords, Numeric location, Numeric scale, const double coeffs, unsigned maxdeg) const

template<class Pair >
void	weightedSampleCoeffs (const Pair points, unsigned long numPoints, double coeffs, unsigned maxdeg) const

template<class Pair >
void	weightedSampleCoeffVars (const Pair points, unsigned long nPoints, const double coeffs, unsigned maxdeg, double *variances) const

template<class Pair >
Matrix< double >	weightedSampleCoeffCovariance (const Pair points, unsigned long nPoints, const double coeffs, unsigned maxdeg) const

template<class Pair >
void	weightedSampleCoeffs (const Pair points, unsigned long numPoints, typename Pair::first_type location, typename Pair::first_type scale, double coeffs, unsigned maxdeg) const

template<class Pair >
void	weightedSampleCoeffVars (const Pair points, unsigned long nPoints, typename Pair::first_type location, typename Pair::first_type scale, const double coeffs, unsigned maxdeg, double *variances) const

template<class Pair >
Matrix< double >	weightedSampleCoeffCovariance (const Pair points, unsigned long nPoints, typename Pair::first_type location, typename Pair::first_type scale, const double coeffs, unsigned maxdeg) const

template<class Quadrature >
double	empiricalKroneckerDelta (const Quadrature &quad, unsigned deg1, unsigned deg2) const

Matrix< double >	empiricalKroneckerMatrix (const AbsIntervalQuadrature1D &quad, unsigned maxdeg) const

template<class Quadrature >
double	jointAverage (const Quadrature &q, unsigned deg1, unsigned deg2, unsigned deg3, unsigned deg4) const

template<class Quadrature >
double	jointAverage (const Quadrature &q, const unsigned *degrees, unsigned nDegrees, bool checkedForZeros=false) const

template<class Quadrature >
double	directQuadrature (const Quadrature &q, unsigned deg1, unsigned deg2, unsigned deg3, unsigned deg4) const

template<class Quadrature >
double	directQuadrature (const Quadrature &q, const unsigned *degrees, unsigned nDegrees, bool checkedForZeros=false) const

double	integratePoly (unsigned degree, unsigned power) const

double	jointIntegral (const unsigned *degrees, unsigned nDegrees) const

template<typename Numeric , typename Real >
void	sampleAverages (const Numeric coords, unsigned long lenCoords, Real averages, unsigned maxdeg) const

template<class Pair , typename Real >
void	weightedPointsAverages (const Pair points, unsigned long numPoints, Real averages, unsigned maxdeg) const

template<class Functor , typename Real >
void	extWeightAverages (const Functor &extWeight, const AbsIntervalQuadrature1D &quad, Real *averages, unsigned maxdeg) const

template<class Numeric >
Matrix< double >	sampleProductAverages (const Numeric *coords, unsigned long lenCoords, unsigned maxdeg) const

template<class Functor >
Matrix< double >	extWeightProductAverages (const Functor &extWeight, const AbsIntervalQuadrature1D &quad, unsigned maxdeg) const

template<class Numeric >
double	jointSampleAverage (const Numeric coords, unsigned long lenCoords, const unsigned degrees, unsigned lenDegrees) const

template<class Numeric >
std::pair< double, double >	twoJointSampleAverages (const Numeric coords, unsigned long lenCoords, const unsigned degrees1, unsigned lenDegrees1, const unsigned *degrees2, unsigned lenDegrees2) const

CPP11_auto_ptr< StorablePolySeries1D >	makeStorablePolySeries (unsigned maxPolyDeg, const double *coeffs=0, unsigned maxdeg=0, double shift=0.0) const

long double	location () const

long double	scale () const

Additional Inherited Members
Public Types inherited from npstat::AbsClassicalOrthoPoly1D
typedef OrthoPoly1DDeg	degree_functor

typedef OrthoPoly1DWeight	weight_functor

Static Protected Member Functions inherited from npstat::AbsClassicalOrthoPoly1D
static int	kdelta (const unsigned i, const unsigned j)

Constructor & Destructor Documentation

◆ ClassicalOrthoPoly1DFromWeight()

template<class Functor1D >

npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >::ClassicalOrthoPoly1DFromWeight	(	const Functor1D &	fcn,
		const unsigned	maxDegree,
		const unsigned	nIntegPoints,
		const long double	i_xmin,
		const long double	i_xmax,
		const OrthoPolyMethod	m = `OPOLY_STIELTJES`,
		const bool	useFejerQuadrature = `true`
	)

inline

"nIntegPoints" parameter is the number of integration points for the Fejer or rectangular rule quadrature. Note that Fejer quadrature with n points can integrate exactly polynomials of degree n-1 and that this quadrature will be used for calculating various inner products in which the density is used as the weight. Therefore, "nIntegPoints" should be at least 2*maxDegree + 1 + C, where "C" is the polynomial degree that can be used to approximate the density reasonably well.

Rectangular rule quadrature can be used for densities whose multiple derivatives become very close to 0 near the support boundaries. In particular, rectangular quadrature is expected to be useful for KDE densities estimated with symmetric beta kernels without boundary correction and with support on an appropriately extended interval.

Member Function Documentation

◆ clone()

template<class Functor1D >

virtual ClassicalOrthoPoly1DFromWeight* npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >::clone ( ) const

inlinevirtual

Virtual copy constructor

Implements npstat::AbsClassicalOrthoPoly1D.

◆ maxDegree()

template<class Functor1D >

virtual unsigned npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >::maxDegree ( ) const

inlinevirtual

Maximum polynomial degree supported

Reimplemented from npstat::AbsClassicalOrthoPoly1D.

◆ weight()

template<class Functor1D >

virtual long double npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >::weight ( const long double x ) const

inlinevirtual

The weight function should be normalized

Implements npstat::AbsClassicalOrthoPoly1D.

◆ xmin()

template<class Functor1D >

virtual double npstat::ClassicalOrthoPoly1DFromWeight< Functor1D >::xmin ( ) const

inlinevirtual

Support of the polynomial

Implements npstat::AbsClassicalOrthoPoly1D.

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

nm/ClassicalOrthoPoly1DFromWeight.hh

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ ClassicalOrthoPoly1DFromWeight()

Member Function Documentation

◆ clone()

◆ maxDegree()

◆ weight()

◆ xmin()