B-spline basis on Clenshaw-Curtis grids. More...

#include <BsplineClenshawCurtisBasis.hpp>

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

Public Member Functions
	BsplineClenshawCurtisBasis ()
	Default constructor.

	BsplineClenshawCurtisBasis (size_t degree)
	Constructor.

double	clenshawCurtisPoint (LT l, IT i) const

void	constructKnots (LT l, IT i)
	Construct the (p+2) Clenshaw-Curtis knots of a B-spline basis function and save them in xi.

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

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

double	evalDxDx (LT l, IT i, double x)

size_t	getDegree () const override

double	getIntegral (LT l, IT i) override

double	nonUniformBSpline (double x, size_t p, size_t k) const

double	nonUniformBSplineDx (double x, size_t p, size_t k) const

double	nonUniformBSplineDxDx (double x, size_t p, size_t k) const

	~BsplineClenshawCurtisBasis () override
	Destructor.

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

Protected Attributes
BsplineBasis< LT, IT >	bsplineBasis
	B-spline basis for B-spline evaluation.

ClenshawCurtisTable &	clenshawCurtisTable
	reference to the Clenshaw-Curtis cache table

DataVector	coordinates

bool	integrationInitialized = false

DataVector	weights

std::vector< double >	xi
	temporary helper vector of fixed size p+2 containing B-spline knots

Detailed Description

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

B-spline basis on Clenshaw-Curtis grids.

Constructor & Destructor Documentation

◆ BsplineClenshawCurtisBasis() [1/2]

template<class LT , class IT >

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

inline

Default constructor.

◆ BsplineClenshawCurtisBasis() [2/2]

template<class LT , class IT >

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

inlineexplicit

Constructor.

Parameters

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

◆ ~BsplineClenshawCurtisBasis()

template<class LT , class IT >

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

inlineoverride

Destructor.

Member Function Documentation

◆ clenshawCurtisPoint()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisPoint	(	LT	l,
		IT	i
	)		const

inline

Parameters

l	level of the grid point
i	index of the grid point

Returns: i-th Clenshaw-Curtis grid point with level l

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, and sgpp::base::ClenshawCurtisTable::getPoint().

Referenced by sgpp::pde::OperationLaplaceBsplineClenshawCurtis::mult(), and sgpp::pde::OperationMatrixLTwoDotBsplineClenshawCurtis::mult().

◆ constructKnots()

template<class LT , class IT >

void sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots	(	LT	l,
		IT	i
	)

inline

Construct the (p+2) Clenshaw-Curtis knots of a B-spline basis function and save them in xi.

Parameters

l	level of basis function
i	index of basis function

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::ClenshawCurtisTable::getPoint(), h, and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi.

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDx(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDxDx(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral().

◆ eval()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< 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 Clenshaw-Curtis B-spline basis function

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

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline().

◆ evalDx()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< 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 Clenshaw-Curtis B-spline basis function

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

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDx().

Referenced by sgpp::base::OperationEvalGradientBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalGradientBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeBsplineClenshawCurtisNaive::evalPartialDerivative(), sgpp::base::OperationEvalPartialDerivativeBsplineClenshawCurtisNaive::evalPartialDerivative(), and sgpp::pde::OperationLaplaceBsplineClenshawCurtis::mult().

◆ evalDxDx()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDxDx	(	LT	l,
		IT	i,
		double	x
	)

inline

Parameters

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

Returns: value of 2nd derivative of Clenshaw-Curtis B-spline basis function

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDxDx().

Referenced by sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), and sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian().

◆ getDegree()

template<class LT , class IT >

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

inlineoverridevirtual

Returns: B-spline degree

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

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis.

◆ getIntegral()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral	(	LT	l,
		IT	i
	)

inlineoverridevirtual

Parameters

l	level of basis function
i	index of basis function

Returns: integral of the basis function

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

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::coordinates, sgpp::base::GaussLegendreQuadRule1D::getLevelPointsAndWeightsNormalized(), h, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::integrationInitialized, sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::weights, and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi.

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

◆ nonUniformBSpline()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline	(	double	x,
		size_t	p,
		size_t	k
	)		const

inline

Parameters

x	evaluation point
p	B-spline degree
k	index of B-spline in the knot sequence

Returns: value of non-uniform B-spline with knots \(\{\xi_k, ... \xi_{k+p+1}\}\)

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi.

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDx(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDxDx().

◆ nonUniformBSplineDx()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDx	(	double	x,
		size_t	p,
		size_t	k
	)		const

inline

Parameters

x	evaluation point
p	B-spline degree
k	index of B-spline in the knot sequence

Returns: value of derivative of non-uniform B-spline with knots \(\{\xi_k, ... \xi_{k+p+1}\}\)

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi.

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDx().

◆ nonUniformBSplineDxDx()

template<class LT , class IT >

double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDxDx	(	double	x,
		size_t	p,
		size_t	k
	)		const

inline

Parameters

x	evaluation point
p	B-spline degree
k	index of B-spline in the knot sequence

Returns: value of 2nd derivative of non-uniform B-spline with knots \(\{\xi_k, ... \xi_{k+p+1}\}\)

References sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi.

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDxDx().

Member Data Documentation

◆ bsplineBasis

template<class LT , class IT >

BsplineBasis<LT, IT> sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::bsplineBasis

protected

B-spline basis for B-spline evaluation.

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDx(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDxDx(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getDegree(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral().

◆ clenshawCurtisTable

template<class LT , class IT >

ClenshawCurtisTable& sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisTable

protected

reference to the Clenshaw-Curtis cache table

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisPoint(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots().

◆ coordinates

template<class LT , class IT >

DataVector sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::coordinates

protected

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral().

◆ integrationInitialized

template<class LT , class IT >

bool sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::integrationInitialized = false

protected

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral().

◆ weights

template<class LT , class IT >

DataVector sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::weights

protected

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral().

◆ xi

template<class LT , class IT >

std::vector<double> sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::xi

protected

temporary helper vector of fixed size p+2 containing B-spline knots

Referenced by sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline(), sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDx(), and sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDxDx().

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

base/src/sgpp/base/operation/hash/common/basis/BsplineClenshawCurtisBasis.hpp

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ BsplineClenshawCurtisBasis() [1/2]

◆ BsplineClenshawCurtisBasis() [2/2]

◆ ~BsplineClenshawCurtisBasis()

Member Function Documentation

◆ clenshawCurtisPoint()

◆ constructKnots()

◆ eval()

◆ evalDx()

◆ evalDxDx()

◆ getDegree()

◆ getIntegral()

◆ nonUniformBSpline()

◆ nonUniformBSplineDx()

◆ nonUniformBSplineDxDx()

Member Data Documentation

◆ bsplineBasis

◆ clenshawCurtisTable

◆ coordinates

◆ integrationInitialized

◆ weights

◆ xi