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

B-spline basis on Noboundary grids. More...

#include <BsplineBasis.hpp>

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

Public Member Functions
	BsplineBasis ()
	Default constructor. More...
	BsplineBasis (size_t degree)
	Constructor. More...
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 override
double	getIntegral (LT level, IT index) override
double	uniformBSpline (double x, size_t p) const
double	uniformBSplineDx (double x, size_t p) const
double	uniformBSplineDxDx (double x, size_t p) const
	~BsplineBasis () override
	Destructor. More...
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor. More...

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

Detailed Description

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

B-spline basis on Noboundary grids.

Constructor & Destructor Documentation

BsplineBasis() [1/2]

template<class LT, class IT>

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

inline

Default constructor.

BsplineBasis() [2/2]

template<class LT, class IT>

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

inlineexplicit

Constructor.

Parameters

degree

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

~BsplineBasis()

template<class LT, class IT>

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

inlineoverride

Destructor.

Member Function Documentation

eval()

template<class LT, class IT>

double sgpp::base::BsplineBasis< 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 B-spline basis function

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

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalBsplineNaive::eval(), sgpp::base::OperationEvalGradientBsplineNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeBsplineNaive::evalPartialDerivative(), sgpp::combigrid::expUniformNakBspline(), sgpp::base::OperationMultipleEvalBsplineNaive::mult(), sgpp::pde::OperationLaplaceBspline::mult(), sgpp::base::OperationMultipleEvalBsplineNaive::multTranspose(), and sgpp::pde::OperationLaplaceExplicitBspline::OperationLaplaceExplicitBspline().

evalDx()

template<class LT, class IT>

double sgpp::base::BsplineBasis< 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 B-spline basis function

Referenced by sgpp::base::OperationEvalGradientBsplineNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeBsplineNaive::evalPartialDerivative(), sgpp::pde::OperationLaplaceBspline::mult(), and sgpp::pde::OperationLaplaceExplicitBspline::OperationLaplaceExplicitBspline().

evalDxDx()

template<class LT, class IT>

double sgpp::base::BsplineBasis< 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 B-spline basis function

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

getDegree()

template<class LT, class IT>

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

inlineoverridevirtual

Returns

B-spline degree

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

getIntegral()

template<class LT, class IT>

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

inlineoverridevirtual

Parameters

level	level of basis function
index	index of basis function

Returns

value of the Integral

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

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

uniformBSpline()

template<class LT, class IT>

double sgpp::base::BsplineBasis< LT, IT >::uniformBSpline ( double  x, size_t  p  ) const

inline

Parameters

x	evaluation point
p	B-spline degree

Returns

value of uniform B-spline (with knots \(\{0, 1, ..., p+1\}\))

Referenced by sgpp::base::BsplineBasis< unsigned int, unsigned int >::eval(), sgpp::optimization::test_problems::TremblingParabolaObjective::splineTrembling(), sgpp::base::BsplineBasis< unsigned int, unsigned int >::uniformBSpline(), sgpp::base::BsplineBasis< unsigned int, unsigned int >::uniformBSplineDx(), and sgpp::base::BsplineBasis< unsigned int, unsigned int >::uniformBSplineDxDx().

uniformBSplineDx()

template<class LT, class IT>

double sgpp::base::BsplineBasis< LT, IT >::uniformBSplineDx ( double  x, size_t  p  ) const

inline

Parameters

x	evaluation point
p	B-spline degree

Returns

value of derivative of uniform B-spline (with knots \(\{0, 1, ..., p+1\}\))

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

uniformBSplineDxDx()

template<class LT, class IT>

double sgpp::base::BsplineBasis< LT, IT >::uniformBSplineDxDx ( double  x, size_t  p  ) const

inline

Parameters

x	evaluation point
p	B-spline degree

Returns

value of 2nd derivative of uniform B-spline (with knots \(\{0, 1, ..., p+1\}\))

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

Member Data Documentation

degree

template<class LT, class IT>

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

protected

degree of the B-spline

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

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

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