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

Modified polynomial base functions. More...

#include <LinearModifiedClenshawCurtisBasis.hpp>

Inheritance diagram for sgpp::base::LinearModifiedClenshawCurtisBasis< 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
	LinearModifiedClenshawCurtisBasis ()
	Constructor.
	~LinearModifiedClenshawCurtisBasis () 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
SLinearClenshawCurtisBase	linearBasis
	poly basis

Detailed Description

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

LinearModifiedClenshawCurtisBasis()

template<class LT , class IT >

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

inline

Constructor.

~LinearModifiedClenshawCurtisBasis()

template<class LT , class IT >

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

inlineoverride

Destructor.

Member Function Documentation

eval() [1/2]

template<class LT , class IT >

double sgpp::base::LinearModifiedClenshawCurtisBasis< 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::LinearModifiedClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::ClenshawCurtisTable::getPoint(), and level.

Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalModLinearClenshawCurtisNaive::eval(), sgpp::base::OperationEvalModLinearClenshawCurtisNaive::eval(), sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::eval(), sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::evalHierToTop(), sgpp::base::OperationMultipleEvalModLinearClenshawCurtisNaive::mult(), and sgpp::base::OperationMultipleEvalModLinearClenshawCurtisNaive::multTranspose().

eval() [2/2]

template<class LT , class IT >

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

inline

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

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

evalDx()

template<class LT , class IT >

double sgpp::base::LinearModifiedClenshawCurtisBasis< 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 >.

evalHierToTop()

template<class LT , class IT >

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

Referenced by sgpp::base::DehierarchisationModLinearClenshawCurtis::rec(), and sgpp::base::HierarchisationModLinearClenshawCurtis::rec().

getDegree()

template<class LT , class IT >

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

inlineoverridevirtual

Returns the polynomial degree of the basis.

Returns

polynomial degree of the basis

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

getIntegral()

template<class LT , class IT >

double sgpp::base::LinearModifiedClenshawCurtisBasis< 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::LinearModifiedClenshawCurtisBasis< LT, IT >::clenshawCurtisTable, sgpp::base::LinearClenshawCurtisBasis< LT, IT >::getIntegral(), sgpp::base::ClenshawCurtisTable::getPoint(), level, and sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::linearBasis.

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

Member Data Documentation

clenshawCurtisTable

template<class LT , class IT >

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

protected

reference to the Clenshaw-Curtis cache table

Referenced by sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::eval(), and sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::getIntegral().

linearBasis

template<class LT , class IT >

SLinearClenshawCurtisBase sgpp::base::LinearModifiedClenshawCurtisBasis< LT, IT >::linearBasis

protected

poly basis

Referenced by sgpp::base::LinearModifiedClenshawCurtisBasis< 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/LinearModifiedClenshawCurtisBasis.hpp