npstat::ScalableClassicalOrthoPoly1D Class Reference

Public Types
typedef ScalableOrthoPoly1DDeg	degree_functor
typedef ScalableOrthoPoly1DWeight	weight_functor

Public Member Functions
	ScalableClassicalOrthoPoly1D (const AbsClassicalOrthoPoly1D &poly, long double location, long double scale)
	ScalableClassicalOrthoPoly1D (const AbsClassicalOrthoPoly1D &poly, double location, double scale)
	ScalableClassicalOrthoPoly1D (const ScalableClassicalOrthoPoly1D &)
ScalableClassicalOrthoPoly1D &	operator= (const ScalableClassicalOrthoPoly1D &)
ScalableClassicalOrthoPoly1D *	clone () const
long double	location () const
long double	scale () const
Matrix< long double >	jacobiMatrix (const unsigned n) const
void	setLocation (const long double v)
void	setScale (const long double v)
long double	weight (const long double x) const
double	xmin () const
double	xmax () const
unsigned	maxDegree () const
long double	poly (const unsigned deg, const long double x) const
long double	monic (const unsigned deg, const long double x) const
std::pair< long double, long double >	twopoly (const unsigned deg1, const unsigned deg2, const long double x) const
void	allpoly (const long double x, long double *values, const unsigned maxdeg) const
void	allmonic (const long double x, long double *values, const unsigned maxdeg) const
double	series (const double *coeffs, const unsigned maxdeg, const double x) const
double	integrateSeries (const double *coeffs, const 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, const unsigned long lenCoords, double *coeffs, const unsigned maxdeg) const
template<class Numeric >
void	sampleCoeffVars (const Numeric *coords, const unsigned long lenCoords, const double *coeffs, const unsigned maxdeg, double *variances) const
template<class Numeric >
npstat::Matrix< double >	sampleCoeffCovariance (const Numeric *coords, const unsigned long lenCoords, const double *coeffs, const unsigned maxdeg) const
template<class Pair >
void	weightedSampleCoeffs (const Pair *points, const unsigned long numPoints, double *coeffs, const unsigned maxdeg) const
template<class Pair >
void	weightedSampleCoeffVars (const Pair *points, const unsigned long nPoints, const double *coeffs, const unsigned maxdeg, double *variances) const
template<class Pair >
npstat::Matrix< double >	weightedSampleCoeffCovariance (const Pair *points, const unsigned long nPoints, const double *coeffs, const unsigned maxdeg) const
template<class 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 Functor >
Matrix< double >	extWeightProductAverages (const Functor &extWeight, const AbsIntervalQuadrature1D &quad, unsigned maxdeg) const

Member Function Documentation

allpoly()

void npstat::ScalableClassicalOrthoPoly1D::allpoly ( const long double  x, long double *  values, const unsigned  maxdeg  ) const

inline

Values of all orthonormal polynomials up to some degree. Faster than calling "poly" multiple times. The size of the "values" array should be at least maxdeg + 1.

calculateCoeffs()

template<class Functor , class Quadrature >

void npstat::ScalableClassicalOrthoPoly1D::calculateCoeffs	(	const Functor &	fcn,
		const Quadrature &	quad,
		double *	coeffs,
		unsigned	maxdeg
	)		const

Build the coefficients of the orthogonal polynomial series for the given function. The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).

extWeightAverages()

template<class Functor , typename Real >

void npstat::ScalableClassicalOrthoPoly1D::extWeightAverages	(	const Functor &	extWeight,
		const AbsIntervalQuadrature1D &	quad,
		Real *	averages,
		unsigned	maxdeg
	)		const

Averages of the polynomial values weighted by an external weight function. The length of array "averages" should be at least maxdeg + 1.

extWeightProductAverages()

template<class Functor >

Matrix<double> npstat::ScalableClassicalOrthoPoly1D::extWeightProductAverages	(	const Functor &	extWeight,
		const AbsIntervalQuadrature1D &	quad,
		unsigned	maxdeg
	)		const

Pairwise products of the polynomial values weighted by an external weight function. The returned matrix will be symmetric and will have the dimensions (maxdeg + 1) x (maxdeg + 1).

sampleAverages()

template<class Numeric , typename Real >

void npstat::ScalableClassicalOrthoPoly1D::sampleAverages	(	const Numeric *	coords,
		unsigned long	lenCoords,
		Real *	averages,
		unsigned	maxdeg
	)		const

Unweighted averages of the polynomial values for the given sample. The length of array "averages" should be at least maxdeg + 1.

sampleCoeffs()

template<class Numeric >

void npstat::ScalableClassicalOrthoPoly1D::sampleCoeffs ( const Numeric *  coords, const unsigned long  lenCoords, double *  coeffs, const unsigned  maxdeg  ) const

inline

Build the coefficients of the orthogonal polynomial series for the given sample of points (empirical density function). The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).

twopoly()

std::pair<long double,long double> npstat::ScalableClassicalOrthoPoly1D::twopoly ( const unsigned  deg1, const unsigned  deg2, const long double  x  ) const

inline

Values of two orthonormal polynomials. Faster than calling "poly" two times.

weightedPointsAverages()

template<class Pair , typename Real >

void npstat::ScalableClassicalOrthoPoly1D::weightedPointsAverages	(	const Pair *	points,
		unsigned long	numPoints,
		Real *	averages,
		unsigned	maxdeg
	)		const

Averages of the polynomial values for the given sample of weighted points (not weighting by the polynomial weight function). The first element of the pair will be treated as the coordinate and the second element will be treated as weight. Weights must not be negative. The length of array "averages" should be at least maxdeg + 1.

weightedSampleCoeffs()

template<class Pair >

void npstat::ScalableClassicalOrthoPoly1D::weightedSampleCoeffs ( const Pair *  points, const unsigned long  numPoints, double *  coeffs, const unsigned  maxdeg  ) const

inline

Build the coefficients of the orthogonal polynomial series for the given sample of weighted points (empirical density function). The first element of the pair will be treated as the coordinate and the second element will be treated as weight. Weights must not be negative. The length of the array "coeffs" should be at least maxdeg + 1. Note that the coefficients are returned in the order of increasing degree (same order is used by the "series" function).

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

• nm/ScalableClassicalOrthoPoly1D.hh