#include <sgpp/base/datatypes/DataMatrix.hpp>
#include <sgpp/base/datatypes/DataVector.hpp>
#include <sgpp/base/operation/hash/common/basis/BsplineBasis.hpp>
#include <sgpp/combigrid/GeneralFunction.hpp>
#include <sgpp/combigrid/common/GridConversion.hpp>
#include <sgpp/combigrid/definitions.hpp>
#include <sgpp/combigrid/operation/CombigridMultiOperation.hpp>
#include <sgpp/combigrid/operation/CombigridOperation.hpp>
#include <sgpp/combigrid/operation/Configurations.hpp>
#include <sgpp/combigrid/operation/multidim/AveragingLevelManager.hpp>
#include <sgpp/combigrid/operation/multidim/LevelManager.hpp>
#include <sgpp/combigrid/operation/multidim/fullgrid/AbstractFullGridEvaluationStrategy.hpp>
#include <sgpp/combigrid/storage/tree/CombigridTreeStorage.hpp>
#include <sgpp/optimization/function/scalar/InterpolantScalarFunction.hpp>
#include <sgpp/optimization/sle/solver/Auto.hpp>
#include <sgpp/optimization/sle/system/FullSLE.hpp>
#include <sgpp/optimization/sle/system/HierarchisationSLE.hpp>
#include <sgpp/optimization/tools/Printer.hpp>
#include <sgpp/quadrature/sampling/NaiveSampleGenerator.hpp>
#include <vector>

Functions
sgpp::combigrid::GridFunction	BSplineCoefficientGridFunction (sgpp::combigrid::MultiFunction func, sgpp::combigrid::CombiHierarchies::Collection grids, size_t degree)
	Creates the GridFunction that calculates the coefficients of the B-spline interpolation. More...

sgpp::combigrid::GridFunction	BSplineTensorCoefficientGridFunction (sgpp::combigrid::MultiFunction func, sgpp::combigrid::CombiHierarchies::Collection grids, size_t degree)
	Creates the GridFunction that calculates the coefficients of the B-spline interpolation. More...

std::vector< double >	createdeg1Knots (std::vector< double > const &xValues)
	Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1. More...

std::vector< double >	createdeg3NakKnots (std::vector< double > const &xValues)
	Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1. More...

std::vector< double >	createdeg5NakKnots (std::vector< double > const &xValues)
	Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1. More...

std::vector< double >	createNakKnots (std::vector< double > const &xValues, size_t const &degree)
	interface for creating the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degrees i n{1,3,5} More...

size_t	getUniqueIndex (size_t level, size_t index)
	unique index for level index pair More...

Function Documentation

◆ BSplineCoefficientGridFunction()

sgpp::combigrid::GridFunction BSplineCoefficientGridFunction	(	sgpp::combigrid::MultiFunction	func,
		sgpp::combigrid::CombiHierarchies::Collection	grids,
		size_t	degree
	)

Creates the GridFunction that calculates the coefficients of the B-spline interpolation.

The coefficients for each B-Spline are saved in a TreeStorage encoded by a MultiIndex The Grid Functions coefficients are used as well for quadrature.

Parameters

func	the objective function that shall be interpolated
grids	vector of one dimensional grids
degree	degree of the B spline basis functions

References sgpp::combigrid::CombiEvaluators::BSplineInterpolation(), chess::dim, sgpp::optimization::Printer::getInstance(), sgpp::combigrid::MultiIndexIterator::getMultiIndex(), grid(), python.statsfileInfo::i, level, sgpp::base::DataMatrix::set(), sgpp::optimization::Printer::setVerbosity(), and sgpp::optimization::sle_solver::Auto::solve().

Referenced by sgpp::combigrid::CombigridOperation::auxiliaryBsplineFunction(), sgpp::combigrid::CombigridMultiOperation::createBsplineLinearRefinementOperation(), sgpp::combigrid::CombigridMultiOperation::createBsplineVarianceRefinementOperation(), sgpp::combigrid::CombigridMultiOperation::createExpUniformBoundaryBsplineInterpolation(), sgpp::combigrid::CombigridMultiOperation::createExpUniformBoundaryBsplineQuadrature(), and sgpp::combigrid::CombigridMultiOperation::createExpUniformBoundaryBsplineSquareQuadrature().

◆ BSplineTensorCoefficientGridFunction()

sgpp::combigrid::GridFunction BSplineTensorCoefficientGridFunction	(	sgpp::combigrid::MultiFunction	func,
		sgpp::combigrid::CombiHierarchies::Collection	grids,
		size_t	degree
	)

Creates the GridFunction that calculates the coefficients of the B-spline interpolation.

The coefficients for each B-Spline are saved in a TreeStorage encoded by a MultiIndex The Grid Functions coefficients are used as well for quadrature.

Parameters

func	the objective function that shall be interpolated
grids	vector of one dimensional grids
degree	degree of the B spline basis functions

References chess::dim, sgpp::optimization::Printer::getInstance(), sgpp::combigrid::MultiIndexIterator::getMultiIndex(), getUniqueIndex(), grid(), python.statsfileInfo::i, level, sgpp::base::DataMatrix::set(), sgpp::base::DataMatrix::setAll(), sgpp::optimization::Printer::setVerbosity(), sgpp::optimization::sle_solver::Auto::solve(), and sgpp::combigrid::CombiEvaluators::tensorBSplineInterpolation().

Referenced by sgpp::combigrid::CombigridTensorOperation::createExpUniformBoundaryBSplineInterpolation().

◆ createdeg1Knots()

std::vector<double> createdeg1Knots ( std::vector< double > const & xValues )

Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1.

Parameters

xValues grid points inside [0,1]

References python.statsfileInfo::i.

Referenced by createNakKnots().

◆ createdeg3NakKnots()

std::vector<double> createdeg3NakKnots ( std::vector< double > const & xValues )

Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1.

For dealing with the boundaries at 0 and 1 not a knot knots are used. In the case of degree 3 this means that the knot directly to the right/left of 0/1 are removed.

Parameters

xValues grid points inside [0,1]

References python.statsfileInfo::i.

Referenced by createNakKnots().

◆ createdeg5NakKnots()

std::vector<double> createdeg5NakKnots ( std::vector< double > const & xValues )

Creates the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degree 1 by adding the necessary point outisde [0,1] by mirroring at 0 and 1.

For dealing with the boundaries at 0 and 1 not a knot knots are used. In the case of degree 3 this means that the two knots directly to the right/left of 0/1 are removed.

Parameters

xValues grid points inside [0,1]

References python.statsfileInfo::i.

Referenced by createNakKnots().

◆ createNakKnots()

std::vector<double> createNakKnots	(	std::vector< double > const &	xValues,
		size_t const &	degree
	)

interface for creating the knot sequence xi needed for the evaluation of B-splines from the evaluation points xValues for B splines of degrees i n{1,3,5}

Parameters

xValues	grid points inside [0,1]
degree	degree of the B spline basis functions

References createdeg1Knots(), createdeg3NakKnots(), and createdeg5NakKnots().

◆ getUniqueIndex()

size_t getUniqueIndex	(	size_t	level,
		size_t	index
	)

unique index for level index pair

Parameters

level
index

Returns

References sgpp::combigrid::pow().

Referenced by BSplineTensorCoefficientGridFunction(), and sgpp::combigrid::BSplineInterpolationCoefficientEvaluator::setGridPoints().