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

#include <BsplineModifiedClenshawCurtisBasis.hpp>

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

Public Member Functions
	BsplineModifiedClenshawCurtisBasis ()
	Default constructor. More...

	BsplineModifiedClenshawCurtisBasis (size_t degree)
	Constructor. More...

double	clenshawCurtisPoint (LT l, IT i) const

double	clenshawCurtisPointNegativeIndex (LT l, IT ni) const

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

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

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

size_t	getDegree () const

double	getIntegral (LT l, IT i) override

	~BsplineModifiedClenshawCurtisBasis () override
	Destructor. More...

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

Protected Member Functions
double	clenshawCurtisPoint (LT l, IT i, IT hInv) const

double	clenshawCurtisPointNegativeIndex (LT l, IT ni, IT hInv) const

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

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

double	modifiedBSpline (LT l, IT hInv, double x, size_t p)

double	modifiedBSplineDx (LT l, IT hInv, double x, size_t p)

double	modifiedBSplineDxDx (LT l, IT hInv, double x, size_t p)

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

Protected Attributes
ClenshawCurtisTable &	clenshawCurtisTable
	reference to the Clenshaw-Curtis cache table More...

DataVector	coordinates

size_t	degree
	degree of the B-spline More...

bool	integrationInitialized = false

DataVector	weights

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

omp_nest_lock_t	xiLock

Detailed Description

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

B-spline basis on Clenshaw-Curtis grids.

Constructor & Destructor Documentation

◆ BsplineModifiedClenshawCurtisBasis() [1/2]

template<class LT, class IT>

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

inline

Default constructor.

◆ BsplineModifiedClenshawCurtisBasis() [2/2]

template<class LT, class IT>

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

inlineexplicit

Constructor.

Parameters

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

◆ ~BsplineModifiedClenshawCurtisBasis()

template<class LT, class IT>

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

inlineoverride

Destructor.

Member Function Documentation

◆ clenshawCurtisPoint() [1/2]

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< 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

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::clenshawCurtisPoint(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::constructKnots(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::constructKnotsNegativeIndex(), sgpp::pde::OperationLaplaceModBsplineClenshawCurtis::mult(), sgpp::pde::OperationMatrixLTwoDotModBsplineClenshawCurtis::mult(), and sgpp::pde::OperationMatrixLTwoDotExplicitModBsplineClenshawCurtis::OperationMatrixLTwoDotExplicitModBsplineClenshawCurtis().

◆ clenshawCurtisPoint() [2/2]

template<class LT, class IT>

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

inlineprotected

Parameters

l	level of the grid point
i	index of the grid point
hInv	2^l

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

◆ clenshawCurtisPointNegativeIndex() [1/2]

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::clenshawCurtisPointNegativeIndex	(	LT	l,
		IT	ni
	)		const

inline

Parameters

l	level of the grid point
ni	neagtive index -i of the grid point

Returns: (-ni)-th Clenshaw-Curtis grid point with level l

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::clenshawCurtisPointNegativeIndex(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::constructKnots(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::constructKnotsNegativeIndex().

◆ clenshawCurtisPointNegativeIndex() [2/2]

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::clenshawCurtisPointNegativeIndex	(	LT	l,
		IT	ni,
		IT	hInv
	)		const

inlineprotected

Parameters

l	level of the grid point
ni	negative index -i of the grid point
hInv	2^l

Returns: (-ni)-th Clenshaw-Curtis grid point with level l

◆ constructKnots()

template<class LT, class IT>

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

inlineprotected

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
hInv	2^l

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSpline(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDx(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDxDx().

◆ constructKnotsNegativeIndex()

template<class LT, class IT>

void sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::constructKnotsNegativeIndex	(	LT	l,
		IT	ni,
		IT	hInv
	)

inlineprotected

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

Parameters

l	level of basis function
ni	negative index -i of basis function
hInv	2^l

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSpline(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDx(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDxDx().

◆ eval()

template<class LT, class IT>

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

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

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalModBsplineClenshawCurtisNaive::eval(), sgpp::base::OperationEvalGradientModBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianModBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeModBsplineClenshawCurtisNaive::evalPartialDerivative(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), sgpp::base::OperationMultipleEvalModBsplineClenshawCurtisNaive::mult(), sgpp::pde::OperationMatrixLTwoDotModBsplineClenshawCurtis::mult(), sgpp::pde::OperationLaplaceModBsplineClenshawCurtis::mult(), sgpp::base::OperationMultipleEvalModBsplineClenshawCurtisNaive::multTranspose(), and sgpp::pde::OperationMatrixLTwoDotExplicitModBsplineClenshawCurtis::OperationMatrixLTwoDotExplicitModBsplineClenshawCurtis().

◆ evalDx()

template<class LT, class IT>

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

inline

Parameters

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

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

Referenced by sgpp::base::OperationEvalGradientModBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianModBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeModBsplineClenshawCurtisNaive::evalPartialDerivative(), and sgpp::pde::OperationLaplaceModBsplineClenshawCurtis::mult().

◆ evalDxDx()

template<class LT, class IT>

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

Referenced by sgpp::base::OperationEvalHessianModBsplineClenshawCurtisNaive::evalHessian().

◆ getDegree()

template<class LT, class IT>

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

inlinevirtual

Returns: B-spline degree

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

◆ getIntegral()

template<class LT, class IT>

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

inlineoverridevirtual

Parameters

l	level of basis function
i	index of basis function

Returns: value of the integral

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

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

◆ modifiedBSpline()

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::modifiedBSpline	(	LT	l,
		IT	hInv,
		double	x,
		size_t	p
	)

inlineprotected

Parameters

l	level of basis function
hInv	2^l
x	evaluation point
p	B-spline degree

Returns: value of modified Clenshaw-Curtis B-spline (e.g. index == 1)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::eval().

◆ modifiedBSplineDx()

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::modifiedBSplineDx	(	LT	l,
		IT	hInv,
		double	x,
		size_t	p
	)

inlineprotected

Parameters

l	level of basis function
hInv	2^l
x	evaluation point
p	B-spline degree

Returns: value of derivative of modified Clenshaw-Curtis B-spline (e.g. index == 1)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx().

◆ modifiedBSplineDxDx()

template<class LT, class IT>

double sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::modifiedBSplineDxDx	(	LT	l,
		IT	hInv,
		double	x,
		size_t	p
	)

inlineprotected

Parameters

l	level of basis function
hInv	2^l
x	evaluation point
p	B-spline degree

Returns: value of 2nd derivative of modified Clenshaw-Curtis B-spline (e.g. index == 1)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx().

◆ nonUniformBSpline()

template<class LT, class IT>

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

inlineprotected

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 \(\{\xi_k, ... \xi_{k+p+1}\}\)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSpline(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSpline(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDx(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDxDx().

◆ nonUniformBSplineDx()

template<class LT, class IT>

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

inlineprotected

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 \(\{\xi_k, ... \xi_{k+p+1}\}\)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDx().

◆ nonUniformBSplineDxDx()

template<class LT, class IT>

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

inlineprotected

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 \(\{\xi_k, ... \xi_{k+p+1}\}\)

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::modifiedBSplineDxDx().

Member Data Documentation

◆ clenshawCurtisTable

template<class LT, class IT>

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

protected

reference to the Clenshaw-Curtis cache table

◆ coordinates

template<class LT, class IT>

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

protected

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ degree

template<class LT, class IT>

size_t sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::degree

protected

degree of the B-spline

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getDegree(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ integrationInitialized

template<class LT, class IT>

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

protected

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ weights

template<class LT, class IT>

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

protected

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ xi

template<class LT, class IT>

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

protected

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

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ xiLock

template<class LT, class IT>

omp_nest_lock_t sgpp::base::BsplineModifiedClenshawCurtisBasis< LT, IT >::xiLock

protected

Referenced by sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::BsplineModifiedClenshawCurtisBasis(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), and sgpp::base::BsplineModifiedClenshawCurtisBasis< unsigned int, unsigned int >::~BsplineModifiedClenshawCurtisBasis().

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

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

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ BsplineModifiedClenshawCurtisBasis() [1/2]

◆ BsplineModifiedClenshawCurtisBasis() [2/2]

◆ ~BsplineModifiedClenshawCurtisBasis()

Member Function Documentation

◆ clenshawCurtisPoint() [1/2]

◆ clenshawCurtisPoint() [2/2]

◆ clenshawCurtisPointNegativeIndex() [1/2]

◆ clenshawCurtisPointNegativeIndex() [2/2]

◆ constructKnots()

◆ constructKnotsNegativeIndex()

◆ eval()

◆ evalDx()

◆ evalDxDx()

◆ getDegree()

◆ getIntegral()

◆ modifiedBSpline()

◆ modifiedBSplineDx()

◆ modifiedBSplineDxDx()

◆ nonUniformBSpline()

◆ nonUniformBSplineDx()

◆ nonUniformBSplineDxDx()

Member Data Documentation

◆ clenshawCurtisTable

◆ coordinates

◆ degree

◆ integrationInitialized

◆ weights

◆ xi

◆ xiLock

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