#include <ClassicalOrthoPolys1D.hh>

Inheritance diagram for npstat::JacobiOrthoPoly1D:

Public Member Functions
	JacobiOrthoPoly1D (double alpha, double beta)

virtual JacobiOrthoPoly1D *	clone () const

double	alpha () const

double	beta () const

long double	weight (long double x) const

double	xmin () const

double	xmax () const

void	derivativeCoeffs (const double coeffs, unsigned maxdeg, double derivCoeffs) const

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

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

Public Member Functions inherited from npstat::AbsClassicalOrthoPoly1D
virtual unsigned	maxDegree () const

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)

Detailed Description

The weight function for Jacobi polynomials is proportional to (1 - x)^alpha (1 + x)^beta

Member Function Documentation

◆ clone()

virtual JacobiOrthoPoly1D* npstat::JacobiOrthoPoly1D::clone ( ) const

inlinevirtual

Virtual copy constructor

Implements npstat::AbsClassicalOrthoPoly1D.

◆ derivativeCoeffs()

void npstat::JacobiOrthoPoly1D::derivativeCoeffs	(	const double *	coeffs,
		unsigned	maxdeg,
		double *	derivCoeffs
	)		const

The following function generates coefficients for derivatives of the Jacobi polynomial series. The derivative series should be evaluated using a JacobiOrthoPoly1D(alpha_+1, beta_+1) object and with maxdeg argument decreased by 1. The array "coeffs" should have at least maxdeg+1 elements, while the "derivativeCoeffs" buffer should have at least maxdeg elements.