Polynomial basis functions. More...

#include <PolyClenshawCurtisBasis.hpp>

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

Public Member Functions
double	eval (LT level, IT index, double p) override
	Evaluate the basis function with given level and index. More...

double	evalBasis (LT level, IT index, double p)
	Evaluate a basis function. More...

double	evalDx (LT level, IT index, double x)

double	evalHierToTop (LT level, IT index, DataVector &coeffs, double pos)
	Evaluates all the hierarchical ancestors of the node defined by level and index. More...

size_t	getDegree () const override
	Returns the polynomial degree of the basis. More...

double	getIntegral (LT level, IT index) override
	returns the integal of the current basis function More...

	PolyClenshawCurtisBasis (size_t degree)
	Constructor. More...

	~PolyClenshawCurtisBasis () override
	Destructor. More...

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

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

size_t	degree
	the polynom's max degree More...

std::vector< int >	idxtable

Detailed Description

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

Polynomial basis functions.

Version: $HEAD$

Constructor & Destructor Documentation

◆ PolyClenshawCurtisBasis()

template<class LT, class IT>

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

inlineexplicit

Constructor.

Parameters

degree the polynom's max. degree

◆ ~PolyClenshawCurtisBasis()

template<class LT, class IT>

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

inlineoverride

Destructor.

Member Function Documentation

◆ eval()

template<class LT, class IT>

double sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval	(	LT	level,
		IT	index,
		double	x
	)

inlineoverridevirtual

Evaluate the basis function with given level and index.

Parameters

level	level of the basis function
index	index of the basis function
x	evaluation point

Returns: value of the basis function.

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

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalPolyClenshawCurtisNaive::eval(), sgpp::base::PolyClenshawCurtisBoundaryBasis< unsigned int, unsigned int >::eval(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::PolyModifiedClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalHierToTop(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), sgpp::base::OperationMultipleEvalPolyClenshawCurtisNaive::mult(), sgpp::pde::OperationLaplacePolyClenshawCurtis::mult(), and sgpp::base::OperationMultipleEvalPolyClenshawCurtisNaive::multTranspose().

◆ evalBasis()

template<class LT, class IT>

double sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalBasis	(	LT	level,
		IT	index,
		double	p
	)

inline

Evaluate a basis function.

Has a dependence on the absolute position of grid point and support.

We compute the roots in units of h = grid spacing at level l = 2 ** -l.

Due to limited polynomial degree, we compute the roots of the Lagrange polynomial bottom up.

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

◆ evalDx()

template<class LT, class IT>

double sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalDx	(	LT	level,
		IT	index,
		double	x
	)

inline

Referenced by sgpp::base::PolyClenshawCurtisBoundaryBasis< unsigned int, unsigned int >::evalDx(), and sgpp::pde::OperationLaplacePolyClenshawCurtis::mult().

◆ evalHierToTop()

template<class LT, class IT>

double sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalHierToTop	(	LT	level,
		IT	index,
		DataVector &	coeffs,
		double	pos
	)

inline

Evaluates all the hierarchical ancestors of the node defined by level and index.

NOTE: It does not evaluate the current node itself.

Parameters

level
index
coeffs
pos

Returns

Referenced by sgpp::base::DehierarchisationPolyClenshawCurtis::rec(), and sgpp::base::HierarchisationPolyClenshawCurtis::rec().

◆ getDegree()

template<class LT, class IT>

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

inlineoverridevirtual

Returns the polynomial degree of the basis.

Returns: polynomial degree of the basis

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

Referenced by sgpp::base::PolyClenshawCurtisBoundaryBasis< unsigned int, unsigned int >::getDegree(), and sgpp::base::PolyModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getDegree().

◆ getIntegral()

template<class LT, class IT>

double sgpp::base::PolyClenshawCurtisBasis< 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 >.

Referenced by sgpp::base::OperationQuadraturePolyClenshawCurtis::doQuadrature(), sgpp::base::PolyModifiedClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), and sgpp::base::PolyClenshawCurtisBoundaryBasis< unsigned int, unsigned int >::getIntegral().

Member Data Documentation

◆ clenshawCurtisTable

template<class LT, class IT>

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

protected

reference to the Clenshaw-Curtis cache table

Referenced by sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), and sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ degree

template<class LT, class IT>

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

protected

the polynom's max degree

Referenced by sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::getDegree(), and sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().

◆ idxtable

template<class LT, class IT>

std::vector<int> sgpp::base::PolyClenshawCurtisBasis< LT, IT >::idxtable

protected

Referenced by sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), and sgpp::base::PolyClenshawCurtisBasis< unsigned int, unsigned int >::PolyClenshawCurtisBasis().

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

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

Public Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

◆ PolyClenshawCurtisBasis()

◆ ~PolyClenshawCurtisBasis()

Member Function Documentation

◆ eval()

◆ evalBasis()

◆ evalDx()

◆ evalHierToTop()

◆ getDegree()

◆ getIntegral()

Member Data Documentation

◆ clenshawCurtisTable

◆ degree

◆ idxtable

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