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

Hierarchical Not-a-knot B-spline basis. More...

#include <NakBsplineBoundaryCombigridBasis.hpp>

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

Public Member Functions
double	eval (LT l, IT i, double x) override
size_t	getDegree () const override
double	getIntegral (LT level, IT index) override
	returns the integal of the current basis function More...
	NakBsplineBoundaryCombigridBasis ()
	Default constructor. More...
	NakBsplineBoundaryCombigridBasis (size_t degree)
	Constructor. More...
	~NakBsplineBoundaryCombigridBasis () override
	Destructor. More...
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor. More...

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

Detailed Description

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

Hierarchical Not-a-knot B-spline basis.

This basis is designed to represent Bspline boundary interpolants from the combigrid module. Therefore it has the following unusual choice of basis functions: linear and quadratic terms on level 0 constant term on level 1

This means that this basis of level 0 cannot represent constant functions! It is therefore not suitabe for any application that cannot guarantee the existence of level 1 in every dimension

A combigrid interpolant which shall be interpolated with this class needs level (1,...,1) otherwise the boundary points cannot match

Constructor & Destructor Documentation

NakBsplineBoundaryCombigridBasis() [1/2]

template<class LT, class IT>

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

inline

Default constructor.

NakBsplineBoundaryCombigridBasis() [2/2]

template<class LT, class IT>

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

inlineexplicit

Constructor.

Parameters

degree

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

~NakBsplineBoundaryCombigridBasis()

template<class LT, class IT>

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

inlineoverride

Destructor.

Member Function Documentation

eval()

template<class LT, class IT>

double sgpp::base::NakBsplineBoundaryCombigridBasis< 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 basis function

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

Referenced by sgpp::combigrid::LTwoScalarProductHashMapNakBsplineBoundaryCombigrid::calculateScalarProduct(), python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), and sgpp::base::OperationEvalNakBsplineBoundaryCombigridNaive::eval().

getDegree()

template<class LT, class IT>

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

inlineoverridevirtual

Returns

B-spline degree

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

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

getIntegral()

template<class LT, class IT>

double sgpp::base::NakBsplineBoundaryCombigridBasis< 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

bsplineBasis

template<class LT, class IT>

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

protected

B-spline basis for B-spline evaluation.

Referenced by sgpp::base::NakBsplineBoundaryCombigridBasis< unsigned int, unsigned int >::eval(), and sgpp::base::NakBsplineBoundaryCombigridBasis< unsigned int, unsigned int >::getDegree().

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

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