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

Modified polynomial base functions. More...

#include <PolyModifiedBasis.hpp>

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

Public Member Functions
double	eval (LT level, IT index, double p) override
	Evaluate the basis function with given level and index.
double	eval (LT level, IT index, double p, double offset, double width)
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
	PolyModifiedBasis (size_t degree)
	Constructor.
	~PolyModifiedBasis () override
	Destructor.
Public Member Functions inherited from sgpp::base::Basis< LT, IT >
virtual	~Basis ()
	Destructor.

Protected Attributes
SPolyBase	polyBasis
	poly basis

Detailed Description

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

Modified polynomial base functions.

Special polynomial functions to cover values unequal 0 at the border. Implemented as seen in AWR 2 paper by Prof. Bungartz (http://www5.in.tum.de/wiki/index.php/Algorithmen_des_Wissenschaftlichen_Rechnens_II_-_Winter_08)

Constructor & Destructor Documentation

PolyModifiedBasis()

template<class LT , class IT >

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

inlineexplicit

Constructor.

Parameters

degree

the polynom's max. degree

~PolyModifiedBasis()

template<class LT , class IT >

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

inlineoverride

Destructor.

Member Function Documentation

eval() [1/2]

template<class LT , class IT >

double sgpp::base::PolyModifiedBasis< 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 h, and level.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalModPolyNaive::eval(), sgpp::base::OperationEvalModPolyNaive::eval(), sgpp::base::PolyModifiedBasis< LT, IT >::eval(), sgpp::base::PolyModifiedBasis< LT, IT >::evalHierToTop(), and sgpp::pde::OperationLaplaceModPoly::mult().

eval() [2/2]

template<class LT , class IT >

double sgpp::base::PolyModifiedBasis< LT, IT >::eval ( LT  level, IT  index, double  p, double  offset, double  width  )

inline

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

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity().

evalDx()

template<class LT , class IT >

double sgpp::base::PolyModifiedBasis< 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::PolyBasis< LT, IT >::evalDx(), level, and sgpp::base::PolyModifiedBasis< LT, IT >::polyBasis.

Referenced by sgpp::pde::OperationLaplaceModPoly::mult().

evalHierToTop()

template<class LT , class IT >

double sgpp::base::PolyModifiedBasis< 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::PolyModifiedBasis< LT, IT >::eval(), and level.

Referenced by sgpp::base::DehierarchisationModPoly::rec(), and sgpp::base::HierarchisationModPoly::rec().

getDegree()

template<class LT , class IT >

size_t sgpp::base::PolyModifiedBasis< 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::PolyBasis< LT, IT >::getDegree(), and sgpp::base::PolyModifiedBasis< LT, IT >::polyBasis.

getIntegral()

template<class LT , class IT >

double sgpp::base::PolyModifiedBasis< 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::PolyBasis< LT, IT >::getIntegral(), level, and sgpp::base::PolyModifiedBasis< LT, IT >::polyBasis.

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

Member Data Documentation

polyBasis

template<class LT , class IT >

SPolyBase sgpp::base::PolyModifiedBasis< LT, IT >::polyBasis

protected

poly basis

Referenced by sgpp::base::PolyModifiedBasis< LT, IT >::evalDx(), sgpp::base::PolyModifiedBasis< LT, IT >::getDegree(), and sgpp::base::PolyModifiedBasis< 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/PolyModifiedBasis.hpp