Basic algorithm for getting all affected basis functions. More...

#include <AlgorithmEvaluationTransposed.hpp>

Public Member Functions
	AlgorithmEvaluationTransposed (GridStorage &storage)

void	operator() (BASIS &basis, const DataVector &point, double alpha, DataVector &result)
	Returns evaluations of all basis functions that are non-zero at a given evaluation point. More...

	~AlgorithmEvaluationTransposed ()

Protected Member Functions
void	rec (BASIS &basis, DataVector &point, size_t current_dim, double value, GridStorage::grid_iterator &working, index_t *source, double alpha, DataVector &result)
	Recursive traversal of the "tree" of basis functions for evaluation, used in operator(). More...

Protected Attributes
GridStorage &	storage

Detailed Description

template<class BASIS>
class sgpp::base::AlgorithmEvaluationTransposed< BASIS >

Basic algorithm for getting all affected basis functions.

This implicitly assumes a tensor-product approach and local support. No grid points on the border are supported.

Constructor & Destructor Documentation

◆ AlgorithmEvaluationTransposed()

template<class BASIS >

sgpp::base::AlgorithmEvaluationTransposed< BASIS >::AlgorithmEvaluationTransposed ( GridStorage & storage )

inlineexplicit

◆ ~AlgorithmEvaluationTransposed()

template<class BASIS >

sgpp::base::AlgorithmEvaluationTransposed< BASIS >::~AlgorithmEvaluationTransposed ( )

inline

Member Function Documentation

◆ operator()()

template<class BASIS >

void sgpp::base::AlgorithmEvaluationTransposed< BASIS >::operator()	(	BASIS &	basis,
		const DataVector &	point,
		double	alpha,
		DataVector &	result
	)

inline

Returns evaluations of all basis functions that are non-zero at a given evaluation point.

For a given evaluation point \(x\), it stores tuples (std::pair) of \((i,\phi_i(x))\) in the result vector for all basis functions that are non-zero. If one wants to evaluate \(f_N(x)\), one only has to compute

\[ \sum_{r\in\mathbf{result}} \alpha[r\rightarrow\mathbf{first}] \cdot r\rightarrow\mathbf{second}. \]

Parameters

basis	a sparse grid basis
point	evaluation point within the domain
alpha	the coefficient of the regarded ansatzfunction
result	vector that will contain the local support of the given ansatzfuction for all evaluations points

References chess::dim, sgpp::base::HashGridStorage::getBoundingBox(), sgpp::base::HashGridStorage::getDimension(), sgpp::base::BoundingBox::isContainingPoint(), sgpp::base::AlgorithmEvaluationTransposed< BASIS >::rec(), sgpp::base::AlgorithmEvaluationTransposed< BASIS >::storage, and sgpp::base::BoundingBox::transformPointToUnitCube().

◆ rec()

template<class BASIS >

void sgpp::base::AlgorithmEvaluationTransposed< BASIS >::rec	(	BASIS &	basis,
		DataVector &	point,
		size_t	current_dim,
		double	value,
		GridStorage::grid_iterator &	working,
		index_t *	source,
		double	alpha,
		DataVector &	result
	)

inlineprotected

Recursive traversal of the "tree" of basis functions for evaluation, used in operator().

For a given evaluation point \(x\), it stores tuples (std::pair) of \((i,\phi_i(x))\) in the result vector for all basis functions that are non-zero.

Parameters

basis	a sparse grid basis
point	evaluation point within the domain
current_dim	the dimension currently looked at (recursion parameter)
value	the value of the evaluation of the current basis function up to (excluding) dimension current_dim (product of the evaluations of the one-dimensional ones)
working	iterator working on the GridStorage of the basis
source	array of indices for each dimension (identifying the indices of the current grid point)
alpha	the coefficient of current ansatzfunction
result	vector that will contain the local support of the given ansatzfuction for all evaluations points