Not-a-knot B-spline basis. More...

#include <NakBsplineModifiedBasis.hpp>

Inheritance diagram for sgpp::base::NakBsplineModifiedBasis< LT, IT >:

Public Member Functions
double	basisMean (LT l, IT i, size_t start, size_t stop, double offset, double hik, std::shared_ptr< sgpp::base::DataVector > quadCoordinates, std::shared_ptr< sgpp::base::DataVector > quadWeights, std::shared_ptr< sgpp::base::Distribution > pdf)

double	eval (LT l, IT i, double x) override

double	evalDx (LT l, IT i, double x) override

size_t	getDegree () const override

double	getIntegral (LT level, IT index) override
	returns the integal of the current basis function

double	getMean (LT l, IT i, std::shared_ptr< sgpp::base::Distribution > pdf, std::shared_ptr< sgpp::base::DataVector > quadCoordinates, std::shared_ptr< sgpp::base::DataVector > quadWeights)
	Calculates the mean int b_i(x) rho(x) dx of a basis function b_i w.r.t.

	NakBsplineModifiedBasis ()
	Default constructor.

	NakBsplineModifiedBasis (size_t degree)
	Constructor.

	~NakBsplineModifiedBasis () override
	Destructor.

Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor.

Protected Attributes
NakBsplineBasis< LT, IT >	nakBsplineBasis
	B-spline basis for B-spline evaluation.

NakBsplineModifiedBasisDeriv1< LT, IT >	nakBsplineModifiedBasisDeriv1
	NakBsplineMOdifiedBAsisDeriv1 for derivative evaluations.

Detailed Description

template<class LT, class IT>
class sgpp::base::NakBsplineModifiedBasis< LT, IT >

Not-a-knot B-spline basis.

Constructor & Destructor Documentation

◆ NakBsplineModifiedBasis() [1/2]

template<class LT , class IT >

sgpp::base::NakBsplineModifiedBasis< LT, IT >::NakBsplineModifiedBasis ( )

inline

Default constructor.

◆ NakBsplineModifiedBasis() [2/2]

template<class LT , class IT >

sgpp::base::NakBsplineModifiedBasis< LT, IT >::NakBsplineModifiedBasis ( size_t degree )

inlineexplicit

Constructor.

Parameters

degree B-spline degree, must be odd (if it's even, degree - 1 is used)

References sgpp::base::NakBsplineModifiedBasis< LT, IT >::getDegree().

◆ ~NakBsplineModifiedBasis()

template<class LT , class IT >

sgpp::base::NakBsplineModifiedBasis< LT, IT >::~NakBsplineModifiedBasis ( )

inlineoverride

Destructor.

Member Function Documentation

◆ basisMean()

template<class LT , class IT >

double sgpp::base::NakBsplineModifiedBasis< LT, IT >::basisMean	(	LT	l,
		IT	i,
		size_t	start,
		size_t	stop,
		double	offset,
		double	hik,
		std::shared_ptr< sgpp::base::DataVector >	quadCoordinates,
		std::shared_ptr< sgpp::base::DataVector >	quadWeights,
		std::shared_ptr< sgpp::base::Distribution >	pdf
	)

inline

References sgpp::base::NakBsplineModifiedBasis< LT, IT >::eval().

Referenced by sgpp::base::NakBsplineModifiedBasis< LT, IT >::getMean().

◆ eval()

template<class LT , class IT >

double sgpp::base::NakBsplineModifiedBasis< LT, IT >::eval	(	LT	l,
		IT	i,
		double	x
	)

inlineoverridevirtual

Parameters

l	level of basis function
i	index of basis function
x	evaluation point

Returns: value of basis function

Implements sgpp::base::Basis< LT, IT >.

References sgpp::base::NakBsplineModifiedBasis< LT, IT >::getDegree(), and sgpp::base::NakBsplineModifiedBasis< LT, IT >::nakBsplineBasis.

Referenced by sgpp::base::NakBsplineModifiedBasis< LT, IT >::basisMean(), python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalModNakBsplineNaive::eval(), sgpp::base::OperationEvalNakBsplineModifiedNaive::eval(), sgpp::base::OperationEvalModNakBsplineNaive::eval(), sgpp::base::OperationEvalNakBsplineModifiedNaive::eval(), sgpp::base::OperationEvalGradientModNakBsplineNaive::evalGradient(), sgpp::base::OperationEvalGradientNakBsplineModifiedNaive::evalGradient(), sgpp::base::OperationEvalGradientModNakBsplineNaive::evalGradient(), sgpp::base::OperationEvalGradientNakBsplineModifiedNaive::evalGradient(), sgpp::base::OperationEvalHessianModNakBsplineNaive::evalHessian(), sgpp::base::OperationEvalHessianModNakBsplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeModNakBsplineNaive::evalPartialDerivative(), sgpp::base::OperationEvalPartialDerivativeModNakBsplineNaive::evalPartialDerivative(), sgpp::base::OperationMultipleEvalNakBsplineModifiedNaive::mult(), and sgpp::base::OperationMultipleEvalNakBsplineModifiedNaive::multTranspose().

◆ evalDx()

template<class LT , class IT >

double sgpp::base::NakBsplineModifiedBasis< LT, IT >::evalDx	(	LT	l,
		IT	i,
		double	x
	)

inlineoverridevirtual

Parameters

l	level of basis function
i	index of basis function
x	evaluation point

Returns: value of derivative of wavelet basis function

Implements sgpp::base::Basis< LT, IT >.

References sgpp::base::NakBsplineModifiedBasis< LT, IT >::nakBsplineModifiedBasisDeriv1.

Referenced by sgpp::base::OperationEvalGradientNakBsplineModifiedNaive::evalGradient(), and sgpp::base::OperationEvalGradientNakBsplineModifiedNaive::evalGradient().

◆ getDegree()

template<class LT , class IT >

size_t sgpp::base::NakBsplineModifiedBasis< LT, IT >::getDegree ( ) const

inlineoverridevirtual

Returns: B-spline degree

Implements sgpp::base::Basis< LT, IT >.

References sgpp::base::NakBsplineModifiedBasis< LT, IT >::nakBsplineBasis.

Referenced by sgpp::base::NakBsplineModifiedBasis< LT, IT >::eval(), sgpp::base::NakBsplineModifiedBasis< LT, IT >::getMean(), and sgpp::base::NakBsplineModifiedBasis< LT, IT >::NakBsplineModifiedBasis().

◆ getIntegral()

template<class LT , class IT >

double sgpp::base::NakBsplineModifiedBasis< LT, IT >::getIntegral	(	LT	level,
		IT	index
	)

inlineoverridevirtual

returns the integal of the current basis function

Parameters

level	level of the basis function
index	index of the basis function

Returns

Implements sgpp::base::Basis< LT, IT >.

Referenced by sgpp::base::OperationQuadratureNakBsplineModified::doQuadrature().

◆ getMean()

template<class LT , class IT >

double sgpp::base::NakBsplineModifiedBasis< LT, IT >::getMean	(	LT	l,
		IT	i,
		std::shared_ptr< sgpp::base::Distribution >	pdf,
		std::shared_ptr< sgpp::base::DataVector >	quadCoordinates,
		std::shared_ptr< sgpp::base::DataVector >	quadWeights
	)

inline

Calculates the mean int b_i(x) rho(x) dx of a basis function b_i w.r.t.

the probability density function rho

Parameters

l	level of basis function
i	index of basis function
pdf	probability density function
quadCoordinates	coordinates of the quadrature rule to be used
quadWeights	weights of the quadrature rule to be used