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

Fundamental spline basis. More...

#include <FundamentalSplineBasis.hpp>

Inheritance diagram for sgpp::base::FundamentalSplineBasis< 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)
	FundamentalSplineBasis ()
	Default constructor.
	FundamentalSplineBasis (size_t degree)
	Constructor.
size_t	getDegree () const override
double	getIntegral (LT l, IT i) override
	~FundamentalSplineBasis () override
	Destructor.
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor.

Protected Attributes
BsplineBasis< LT, IT >	bsplineBasis
	B-spline basis.
std::vector< double >	coefficients
	B-spline coefficients.
DataVector	coordinates
	coordinates and weights for calculating integrals
bool	integrationInitialized = false
DataVector	weights

Detailed Description

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

Fundamental spline basis.

Constructor & Destructor Documentation

FundamentalSplineBasis() [1/2]

template<class LT , class IT >

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

inline

Default constructor.

FundamentalSplineBasis() [2/2]

template<class LT , class IT >

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

inlineexplicit

Constructor.

Parameters

degree

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

References sgpp::base::FundamentalSplineBasis< LT, IT >::bsplineBasis, and sgpp::base::FundamentalSplineBasis< LT, IT >::coefficients.

~FundamentalSplineBasis()

template<class LT , class IT >

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

inlineoverride

Destructor.

Member Function Documentation

eval()

template<class LT , class IT >

double sgpp::base::FundamentalSplineBasis< 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 spline basis function

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

References sgpp::base::FundamentalSplineBasis< LT, IT >::bsplineBasis, and sgpp::base::FundamentalSplineBasis< LT, IT >::coefficients.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalFundamentalSplineNaive::eval(), sgpp::base::OperationEvalFundamentalSplineNaive::eval(), sgpp::base::OperationEvalGradientFundamentalSplineNaive::evalGradient(), sgpp::base::OperationEvalGradientFundamentalSplineNaive::evalGradient(), sgpp::base::OperationEvalHessianFundamentalSplineNaive::evalHessian(), sgpp::base::OperationEvalHessianFundamentalSplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeFundamentalSplineNaive::evalPartialDerivative(), sgpp::base::OperationEvalPartialDerivativeFundamentalSplineNaive::evalPartialDerivative(), sgpp::base::FundamentalSplineBasis< LT, IT >::getIntegral(), sgpp::base::DehierarchisationFundamentalSpline::operator()(), sgpp::base::DehierarchisationFundamentalSplineBoundary::operator()(), sgpp::base::HierarchisationFundamentalSpline::operator()(), sgpp::base::HierarchisationFundamentalSplineBoundary::operator()(), sgpp::base::DehierarchisationFundamentalSpline::operator()(), sgpp::base::DehierarchisationFundamentalSplineBoundary::operator()(), sgpp::base::HierarchisationFundamentalSpline::operator()(), and sgpp::base::HierarchisationFundamentalSplineBoundary::operator()().

evalDx()

template<class LT , class IT >

double sgpp::base::FundamentalSplineBasis< 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 spline basis function

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

References sgpp::base::FundamentalSplineBasis< LT, IT >::bsplineBasis, and sgpp::base::FundamentalSplineBasis< LT, IT >::coefficients.

Referenced by sgpp::base::OperationEvalGradientFundamentalSplineNaive::evalGradient(), sgpp::base::OperationEvalGradientFundamentalSplineNaive::evalGradient(), sgpp::base::OperationEvalHessianFundamentalSplineNaive::evalHessian(), sgpp::base::OperationEvalHessianFundamentalSplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeFundamentalSplineNaive::evalPartialDerivative(), and sgpp::base::OperationEvalPartialDerivativeFundamentalSplineNaive::evalPartialDerivative().

evalDxDx()

template<class LT , class IT >

double sgpp::base::FundamentalSplineBasis< 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 spline basis function

References sgpp::base::FundamentalSplineBasis< LT, IT >::bsplineBasis, and sgpp::base::FundamentalSplineBasis< LT, IT >::coefficients.

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

getDegree()

template<class LT , class IT >

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

inlineoverridevirtual

Returns

fundamental spline degree

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

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

getIntegral()

template<class LT , class IT >

double sgpp::base::FundamentalSplineBasis< 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 >.

References sgpp::base::FundamentalSplineBasis< LT, IT >::bsplineBasis, sgpp::base::FundamentalSplineBasis< LT, IT >::coefficients, sgpp::base::FundamentalSplineBasis< LT, IT >::coordinates, sgpp::base::FundamentalSplineBasis< LT, IT >::eval(), sgpp::base::GaussLegendreQuadRule1D::getLevelPointsAndWeightsNormalized(), h, sgpp::base::FundamentalSplineBasis< LT, IT >::integrationInitialized, and sgpp::base::FundamentalSplineBasis< LT, IT >::weights.

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

Member Data Documentation

bsplineBasis

template<class LT , class IT >

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

protected

B-spline basis.

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

coefficients

template<class LT , class IT >

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

protected

B-spline coefficients.

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

coordinates

template<class LT , class IT >

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

protected

coordinates and weights for calculating integrals

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

integrationInitialized

template<class LT , class IT >

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

protected

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

weights

template<class LT , class IT >

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

protected

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

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

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