SG++-Doxygen-Documentation
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B-spline basis on Clenshaw-Curtis grids. More...
#include <BsplineClenshawCurtisBasis.hpp>
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... | |
ClenshawCurtisTable & | clenshawCurtisTable |
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... | |
B-spline basis on Clenshaw-Curtis grids.
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inline |
Default constructor.
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inlineexplicit |
Constructor.
degree | B-spline degree, must be odd (if it's even, degree - 1 is used) |
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inlineoverride |
Destructor.
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inline |
l | level of the grid point |
i | index of the grid point |
Referenced by sgpp::pde::OperationLaplaceBsplineClenshawCurtis::mult(), sgpp::pde::OperationMatrixLTwoDotBsplineClenshawCurtis::mult(), and sgpp::pde::OperationMatrixLTwoDotExplicitBsplineClenshawCurtis::OperationMatrixLTwoDotExplicitBsplineClenshawCurtis().
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Construct the (p+2) Clenshaw-Curtis knots of a B-spline basis function and save them in xi.
l | level of basis function |
i | index of basis function |
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), and sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().
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inlineoverridevirtual |
l | level of basis function |
i | index of basis function |
x | evaluation point |
Implements sgpp::base::Basis< LT, IT >.
Referenced by python.uq.analysis.asgc.ASGCAnalysis.ASGCAnalysis::estimateDensity(), sgpp::base::OperationEvalBsplineClenshawCurtisNaive::eval(), sgpp::base::OperationEvalGradientBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeBsplineClenshawCurtisNaive::evalPartialDerivative(), sgpp::base::OperationMultipleEvalBsplineClenshawCurtisNaive::mult(), sgpp::pde::OperationMatrixLTwoDotBsplineClenshawCurtis::mult(), sgpp::pde::OperationLaplaceBsplineClenshawCurtis::mult(), sgpp::base::OperationMultipleEvalBsplineClenshawCurtisNaive::multTranspose(), and sgpp::pde::OperationMatrixLTwoDotExplicitBsplineClenshawCurtis::OperationMatrixLTwoDotExplicitBsplineClenshawCurtis().
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inline |
l | level of basis function |
i | index of basis function |
x | evaluation point |
Referenced by sgpp::base::OperationEvalGradientBsplineClenshawCurtisNaive::evalGradient(), sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian(), sgpp::base::OperationEvalPartialDerivativeBsplineClenshawCurtisNaive::evalPartialDerivative(), and sgpp::pde::OperationLaplaceBsplineClenshawCurtis::mult().
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inline |
l | level of basis function |
i | index of basis function |
x | evaluation point |
Referenced by sgpp::base::OperationEvalHessianBsplineClenshawCurtisNaive::evalHessian().
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inlineoverridevirtual |
Implements sgpp::base::Basis< LT, IT >.
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l | level of basis function |
i | index of basis function |
Implements sgpp::base::Basis< LT, IT >.
Referenced by sgpp::base::OperationQuadratureBsplineClenshawCurtis::doQuadrature().
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inline |
x | evaluation point |
p | B-spline degree |
k | index of B-spline in the knot sequence |
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSpline(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDx(), and sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDxDx().
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x | evaluation point |
p | B-spline degree |
k | index of B-spline in the knot sequence |
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDx().
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inline |
x | evaluation point |
p | B-spline degree |
k | index of B-spline in the knot sequence |
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx().
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protected |
B-spline basis for B-spline evaluation.
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::constructKnots(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::eval(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDx(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::evalDxDx(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::getDegree(), and sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral().
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reference to the Clenshaw-Curtis cache table
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::clenshawCurtisPoint(), and sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::constructKnots().
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temporary helper vector of fixed size p+2 containing B-spline knots
Referenced by sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::constructKnots(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::getIntegral(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSpline(), sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDx(), and sgpp::base::BsplineClenshawCurtisBasis< unsigned int, unsigned int >::nonUniformBSplineDxDx().