sgpp::base::FundamentalNakSplineBasis< LT, IT > Class Template Reference

Fundamental not-a-knot spline basis. More...

#include <FundamentalNakSplineBasis.hpp>

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

Public Member Functions
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)
	FundamentalNakSplineBasis ()
	Default constructor.
	FundamentalNakSplineBasis (size_t degree)
	Constructor.
int	getCoefficients (LT l, IT i, std::vector< double > &coefficients)
size_t	getDegree () const override
double	getIntegral (LT level, IT index) override
	returns the integal of the current basis function
	~FundamentalNakSplineBasis () override
	Destructor.
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor.

Protected Attributes
std::vector< double >	coefficients
	B-spline coefficients.
FundamentalSplineBasis< LT, IT >	fundamentalSplineBasis
	fundamental spline basis
NakBsplineBasis< LT, IT >	nakBsplineBasis
	not-a-knot B-spline basis
NakBsplineBasisDeriv1< LT, IT >	nakBsplineBasisDeriv1
	1st derivative of not-a-knot B-spline basis
NakBsplineBasisDeriv2< LT, IT >	nakBsplineBasisDeriv2
	2nd derivative of not-a-knot B-spline basis

Detailed Description

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

Fundamental not-a-knot spline basis.

Constructor & Destructor Documentation

FundamentalNakSplineBasis() [1/2]

template<class LT , class IT >

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

inline

Default constructor.

FundamentalNakSplineBasis() [2/2]

template<class LT , class IT >

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

inlineexplicit

Constructor.

Parameters

degree

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

~FundamentalNakSplineBasis()

template<class LT , class IT >

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

inlineoverride

Destructor.

Member Function Documentation

eval()

template<class LT , class IT >

double sgpp::base::FundamentalNakSplineBasis< 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 fundamental not-a-knot spline basis function

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

References sgpp::base::FundamentalNakSplineBasis< LT, IT >::coefficients, sgpp::base::FundamentalNakSplineBasis< LT, IT >::fundamentalSplineBasis, sgpp::base::FundamentalNakSplineBasis< LT, IT >::getCoefficients(), and sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasis.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalFundamentalNakSplineNaive::eval(), sgpp::base::OperationEvalFundamentalNakSplineNaive::eval(), sgpp::base::OperationEvalGradientFundamentalNakSplineNaive::evalGradient(), sgpp::base::OperationEvalGradientFundamentalNakSplineNaive::evalGradient(), sgpp::base::OperationEvalHessianFundamentalNakSplineNaive::evalHessian(), sgpp::base::OperationEvalHessianFundamentalNakSplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeFundamentalNakSplineNaive::evalPartialDerivative(), sgpp::base::OperationEvalPartialDerivativeFundamentalNakSplineNaive::evalPartialDerivative(), sgpp::base::DehierarchisationFundamentalNakSplineBoundary::operator()(), sgpp::base::HierarchisationFundamentalNakSplineBoundary::operator()(), sgpp::base::DehierarchisationFundamentalNakSplineBoundary::operator()(), and sgpp::base::HierarchisationFundamentalNakSplineBoundary::operator()().

evalDx()

template<class LT , class IT >

double sgpp::base::FundamentalNakSplineBasis< 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 fundamental not-a-knot spline basis function

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

References sgpp::base::FundamentalNakSplineBasis< LT, IT >::coefficients, sgpp::base::FundamentalNakSplineBasis< LT, IT >::fundamentalSplineBasis, sgpp::base::FundamentalNakSplineBasis< LT, IT >::getCoefficients(), and sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasisDeriv1.

Referenced by sgpp::base::OperationEvalGradientFundamentalNakSplineNaive::evalGradient(), sgpp::base::OperationEvalGradientFundamentalNakSplineNaive::evalGradient(), sgpp::base::OperationEvalHessianFundamentalNakSplineNaive::evalHessian(), sgpp::base::OperationEvalHessianFundamentalNakSplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeFundamentalNakSplineNaive::evalPartialDerivative(), and sgpp::base::OperationEvalPartialDerivativeFundamentalNakSplineNaive::evalPartialDerivative().

evalDxDx()

template<class LT , class IT >

double sgpp::base::FundamentalNakSplineBasis< 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 fundamental not-a-knot spline basis function

References sgpp::base::FundamentalNakSplineBasis< LT, IT >::coefficients, sgpp::base::FundamentalNakSplineBasis< LT, IT >::fundamentalSplineBasis, sgpp::base::FundamentalNakSplineBasis< LT, IT >::getCoefficients(), and sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasisDeriv2.

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

getCoefficients()

template<class LT , class IT >

int sgpp::base::FundamentalNakSplineBasis< LT, IT >::getCoefficients ( LT  l, IT  i, std::vector< double > &  coefficients  )

inline

References sgpp::base::FundamentalNakSplineBasis< LT, IT >::coefficients, and sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasis.

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

getDegree()

template<class LT , class IT >

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

inlineoverridevirtual

Returns

fundamental not-a-knot spline degree

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

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

getIntegral()

template<class LT , class IT >

double sgpp::base::FundamentalNakSplineBasis< 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 >.

Member Data Documentation

coefficients

template<class LT , class IT >

std::vector<double> sgpp::base::FundamentalNakSplineBasis< LT, IT >::coefficients

protected

B-spline coefficients.

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

fundamentalSplineBasis

template<class LT , class IT >

FundamentalSplineBasis<LT, IT> sgpp::base::FundamentalNakSplineBasis< LT, IT >::fundamentalSplineBasis

protected

fundamental spline basis

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

nakBsplineBasis

template<class LT , class IT >

NakBsplineBasis<LT, IT> sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasis

protected

not-a-knot B-spline basis

Referenced by sgpp::base::FundamentalNakSplineBasis< LT, IT >::eval(), sgpp::base::FundamentalNakSplineBasis< LT, IT >::getCoefficients(), and sgpp::base::FundamentalNakSplineBasis< LT, IT >::getDegree().

nakBsplineBasisDeriv1

template<class LT , class IT >

NakBsplineBasisDeriv1<LT, IT> sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasisDeriv1

protected

1st derivative of not-a-knot B-spline basis

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

nakBsplineBasisDeriv2

template<class LT , class IT >

NakBsplineBasisDeriv2<LT, IT> sgpp::base::FundamentalNakSplineBasis< LT, IT >::nakBsplineBasisDeriv2

protected

2nd derivative of not-a-knot B-spline basis

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

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

• base/src/sgpp/base/operation/hash/common/basis/FundamentalNakSplineBasis.hpp