SG++-Doxygen-Documentation
sgpp::base::BsplineClenshawCurtisBasis< LT, IT > Class Template Reference

B-spline basis on Clenshaw-Curtis grids. More...

#include <BsplineClenshawCurtisBasis.hpp>

Inheritance diagram for sgpp::base::BsplineClenshawCurtisBasis< LT, IT >:
sgpp::base::Basis< LT, IT >

Public Member Functions

 BsplineClenshawCurtisBasis ()
 Default constructor. More...
 
 BsplineClenshawCurtisBasis (size_t degree)
 Constructor. More...
 
double clenshawCurtisPoint (LT l, IT i) const
 
void constructKnots (LT l, IT i)
 Construct the (p+2) Clenshaw-Curtis knots of a B-spline basis function and save them in xi. More...
 
double eval (LT l, IT i, double x) override
 
double evalDx (LT l, IT i, double x)
 
double evalDxDx (LT l, IT i, double x)
 
size_t getDegree () const override
 
double getIntegral (LT l, IT i) override
 
double nonUniformBSpline (double x, size_t p, size_t k) const
 
double nonUniformBSplineDx (double x, size_t p, size_t k) const
 
double nonUniformBSplineDxDx (double x, size_t p, size_t k) const
 
 ~BsplineClenshawCurtisBasis () 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...
 
ClenshawCurtisTableclenshawCurtisTable
 reference to the Clenshaw-Curtis cache table More...
 
DataVector coordinates
 
bool integrationInitialized = false
 
DataVector weights
 
std::vector< double > xi
 temporary helper vector of fixed size p+2 containing B-spline knots More...
 

Detailed Description

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

B-spline basis on Clenshaw-Curtis grids.

Constructor & Destructor Documentation

template<class LT, class IT>
sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::BsplineClenshawCurtisBasis ( )
inline

Default constructor.

template<class LT, class IT>
sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::BsplineClenshawCurtisBasis ( size_t  degree)
inlineexplicit

Constructor.

Parameters
degreeB-spline degree, must be odd (if it's even, degree - 1 is used)
template<class LT, class IT>
sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::~BsplineClenshawCurtisBasis ( )
inlineoverride

Destructor.

Member Function Documentation

template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::clenshawCurtisPoint ( LT  l,
IT  i 
) const
inline
template<class LT, class IT>
void sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots ( LT  l,
IT  i 
)
inline
template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDx ( LT  l,
IT  i,
double  x 
)
inline
template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::evalDxDx ( LT  l,
IT  i,
double  x 
)
inline
Parameters
llevel of basis function
iindex of basis function
xevaluation point
Returns
value of 2nd derivative of Clenshaw-Curtis B-spline basis function

Referenced by sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian().

template<class LT, class IT>
size_t sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getDegree ( ) const
inlineoverridevirtual
Returns
B-spline degree

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

template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::getIntegral ( LT  l,
IT  i 
)
inlineoverridevirtual
Parameters
llevel of basis function
iindex of basis function
Returns
integral of the basis function

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

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

template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSpline ( double  x,
size_t  p,
size_t  k 
) const
inline
template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDx ( double  x,
size_t  p,
size_t  k 
) const
inline
Parameters
xevaluation point
pB-spline degree
kindex of B-spline in the knot sequence
Returns
value of derivative of non-uniform B-spline with knots \(\{\xi_k, ... \xi_{k+p+1}\}\)

Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDx().

template<class LT, class IT>
double sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::nonUniformBSplineDxDx ( double  x,
size_t  p,
size_t  k 
) const
inline
Parameters
xevaluation point
pB-spline degree
kindex of B-spline in the knot sequence
Returns
value of 2nd derivative of non-uniform B-spline with knots \(\{\xi_k, ... \xi_{k+p+1}\}\)

Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx().

Member Data Documentation

template<class LT, class IT>
bool sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::integrationInitialized = false
protected

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