Inheritance diagram for npstat::DensityOrthoPoly1D:

Public Member Functions
	DensityOrthoPoly1D (const AbsDistribution1D &distro, unsigned maxDegree, unsigned nIntegPoints, OrthoPolyMethod m=OPOLY_STIELTJES)

	DensityOrthoPoly1D (const DensityOrthoPoly1D &)

DensityOrthoPoly1D &	operator= (const DensityOrthoPoly1D &)

virtual DensityOrthoPoly1D *	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 (unsigned deg) const

virtual std::pair< long double, long double >	recurrenceCoeffs (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

◆ DensityOrthoPoly1D()

npstat::DensityOrthoPoly1D::DensityOrthoPoly1D	(	const AbsDistribution1D &	distro,
		unsigned	maxDegree,
		unsigned	nIntegPoints,
		OrthoPolyMethod	m = `OPOLY_STIELTJES`
	)

"nIntegPoints" parameter is the number of integration points for the Fejer 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.

The support of the weight for the integration purpose will be set to [distro.quantile(0.0), distro.quantile(1.0)]. If this interval is very wide, the results may be meaningless (monomials like x^n can exceed the floating point dynamic range, etc).