SG++
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
 
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...
 
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
Parameters
llevel of the grid point
iindex of the grid point
Returns
i-th Clenshaw-Curtis grid point with level l
template<class LT, class IT>
void sgpp::base::BsplineClenshawCurtisBasis< LT, IT >::constructKnots ( LT  l,
IT  i 
)
inline

Construct the (p+2) Clenshaw-Curtis knots of a B-spline basis function and save them in xi.

Parameters
llevel of basis function
iindex of basis function

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

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

Referenced by sgpp::base::OperationEvalGradientBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), and sgpp::base::OperationEvalPartialDerivativeBsplineClenshawCurtisNaive::evalPartialDerivative().

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
inline
Returns
B-spline degree
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


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