sgpp::base::ConvertPrewaveletToLinear Class Reference

Class that implements the transformation of a hierarchical prewavelet sparse grid to a hierarchical linear sparse grid. More...

#include <ConvertPrewaveletToLinear.hpp>

Public Member Functions
	ConvertPrewaveletToLinear (GridStorage &storage)
	Constructor, must be bind to a grid.
void	operator() (DataVector &source, DataVector &result, grid_iterator &index, size_t dim)
	Converts a given prewavelet base to a normal linear base.
	~ConvertPrewaveletToLinear ()
	Destructor.

Protected Types
typedef GridStorage::grid_iterator	grid_iterator
typedef index_t	index_type
typedef level_t	level_type

Protected Attributes
GridStorage &	storage
	the grid object

Detailed Description

Class that implements the transformation of a hierarchical prewavelet sparse grid to a hierarchical linear sparse grid.

Therefore the ()operator is implemented in order to use the sweep algorithm for the grid traversal. Let the coefficients from the hat basis be \( h_{l,i}\) and from the prewavelet basis \( u_{l,i} \). To calculate the surplusses, temp values are needed:

\[ (l,i)\neq G_{n}^{1}:t_{l,i}=-\frac{6}{10}u_{l,i\pm1}+t_{l+1,2i} \]

All temp values for levels greater than the maximal level of the grid are set to 0. The actual transformation is calculated as follows:

\begin{eqnarray*} h_{l,i}&=&u_{l,i}+\frac{1}{10}u_{l,i\pm2}+t_{l+1,2i}-\frac{1}{2}t_{l,i\pm1}\qquad\mbox{if \ensuremath{(l,i)} is an inner point}\\h_{l,i}&=&\frac{9}{10}u_{l,i}+\frac{1}{10}u_{l,i\pm2}+t_{l+1,2i}-\frac{1}{2}t_{l,i\pm1}\qquad\mbox{if \ensuremath{(l,i)} is at border} \end{eqnarray*}

The picture depicts all needed variables in oder to perform the transformation:

This picture shows all involved gridpoints (red crosses) and temp values (green circles) to calculate the new hierarchical coefficients (red arrows) and new temp values (green arrows).

Member Typedef Documentation

grid_iterator

typedef GridStorage::grid_iterator sgpp::base::ConvertPrewaveletToLinear::grid_iterator

protected

index_type

typedef index_t sgpp::base::ConvertPrewaveletToLinear::index_type

protected

level_type

typedef level_t sgpp::base::ConvertPrewaveletToLinear::level_type

protected

Constructor & Destructor Documentation

ConvertPrewaveletToLinear()

sgpp::base::ConvertPrewaveletToLinear::ConvertPrewaveletToLinear ( GridStorage &  storage )

explicit

Constructor, must be bind to a grid.

Parameters

storage

the grid storage object of the the grid, on which the hierarchisation should be executed

~ConvertPrewaveletToLinear()

sgpp::base::ConvertPrewaveletToLinear::~ConvertPrewaveletToLinear

(

)

Destructor.

Member Function Documentation

operator()()

void sgpp::base::ConvertPrewaveletToLinear::operator()	(	DataVector &	source,
		DataVector &	result,
		grid_iterator &	index,
		size_t	dim
	)

Converts a given prewavelet base to a normal linear base.

References sgpp::base::HashGridIterator::get(), sgpp::base::HashGridIterator::getGridDepth(), sgpp::base::HashGridStorage::isInvalidSequenceNumber(), level, sgpp::base::HashGridIterator::seq(), sgpp::base::HashGridIterator::set(), and storage.

Member Data Documentation

storage

GridStorage& sgpp::base::ConvertPrewaveletToLinear::storage

protected

the grid object

Referenced by operator()().

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

• base/src/sgpp/base/operation/hash/common/algorithm_sweep/ConvertPrewaveletToLinear.hpp
• base/src/sgpp/base/operation/hash/common/algorithm_sweep/ConvertPrewaveletToLinear.cpp