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

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.
double	evalBasis (LT level, IT index, double p)
	Evaluate a basis function.
double	evalDx (LT level, IT index, double x) override
	Evaluate the basis functions derivative with given level and index.
double	evalHierToTop (LT level, IT index, DataVector &coeffs, double pos)
	Evaluates all the hierarchical ancestors of the node defined by level and index.
size_t	getDegree () const override
	Returns the polynomial degree of the basis.
double	getIntegral (LT level, IT index) override
	returns the integal of the current basis function
	PolyClenshawCurtisBasis (size_t degree)
	Constructor.
	~PolyClenshawCurtisBasis () override
	Destructor.
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor.

Protected Attributes
ClenshawCurtisTable &	clenshawCurtisTable
	reference to the Clenshaw-Curtis cache table
size_t	degree
	the polynom's max degree
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

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::degree, and sgpp::base::PolyClenshawCurtisBasis< LT, IT >::idxtable.

~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 >.

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalBasis(), sgpp::base::ClenshawCurtisTable::getPoint(), and level.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalPolyClenshawCurtisNaive::eval(), sgpp::base::OperationEvalPolyClenshawCurtisNaive::eval(), sgpp::base::PolyClenshawCurtisBoundaryBasis< LT, IT >::eval(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalDx(), sgpp::base::PolyModifiedClenshawCurtisBasis< LT, IT >::evalDx(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalHierToTop(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::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.

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::degree, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::HashGridPoint::getIndex(), sgpp::base::HashGridPoint::getLevel(), sgpp::base::ClenshawCurtisTable::getPoint(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::idxtable, level, and sgpp::base::HashGridPoint::setAsHierarchicalGridPoint().

Referenced by sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval().

evalDx()

template<class LT , class IT >

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

inlineoverridevirtual

Evaluate the basis functions derivative 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 functions derivative.

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

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::degree, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::HashGridPoint::getIndex(), sgpp::base::HashGridPoint::getLevel(), sgpp::base::ClenshawCurtisTable::getPoint(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::idxtable, level, and sgpp::base::HashGridPoint::setAsHierarchicalGridPoint().

Referenced by sgpp::base::PolyClenshawCurtisBoundaryBasis< LT, IT >::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

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval(), and level.

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 >.

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::degree.

Referenced by sgpp::base::PolyClenshawCurtisBoundaryBasis< LT, IT >::getDegree(), and sgpp::base::PolyModifiedClenshawCurtisBasis< LT, IT >::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 >.

References sgpp::base::PolyClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::degree, sgpp::base::PolyClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::QuadRule1D::getLevelPointsAndWeights(), sgpp::base::ClenshawCurtisTable::getPoint(), h, and level.

Referenced by sgpp::base::OperationQuadraturePolyClenshawCurtis::doQuadrature(), sgpp::base::PolyClenshawCurtisBoundaryBasis< LT, IT >::getIntegral(), and sgpp::base::PolyModifiedClenshawCurtisBasis< LT, IT >::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< LT, IT >::eval(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalDx(), and sgpp::base::PolyClenshawCurtisBasis< LT, IT >::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< LT, IT >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalDx(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::getDegree(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::getIntegral(), and sgpp::base::PolyClenshawCurtisBasis< LT, IT >::PolyClenshawCurtisBasis().

idxtable

template<class LT , class IT >

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

protected

Referenced by sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalBasis(), sgpp::base::PolyClenshawCurtisBasis< LT, IT >::evalDx(), and sgpp::base::PolyClenshawCurtisBasis< LT, IT >::PolyClenshawCurtisBasis().

---

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

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