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// Copyright (C) 2016 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#ifndef SPARSEGRIDCUBICBOUND_H
#define SPARSEGRIDCUBICBOUND_H
#include <Eigen/Dense>
#include "StOpt/core/sparse/sparseGridTypes.h"
#include "StOpt/core/sparse/SparseGridHierarDehierarBound.h"
/** \file SparseGridCubicBound.h
* \brief cubicSparseBound Regroup hierarchization and dehierarchization for cubic sparse grids eliminating boundary points
* \author Xavier Warin
*/
namespace StOpt
{
/// \defgroup Cubic Hierarchization and Deheriarchization with boundary points
/// \brief Regroup function used in hierarchization and dehierarchization for sparse grids without any points on the boundary and a cubic approximation per mesh
///@{
/// \class Hierar1DCubicBound SparseGridCubicBound.h
/// Hierarchization
class Hierar1DCubicBound: public HierarDehierarBound
{
protected :
/// \brief Hierarchization in given dimension in 1D : general cubic
/// \param p_levelCurrent Current level of the point
/// \param p_positionCurrent Current position of the point
/// \param p_iterLevel Iteration on level
/// \param p_idim Current dimension
/// \param p_leftParentNodalValue Left parent nodal value
/// \param p_rightParentNodalValue Right parent nodal value
/// \param p_parentLinearHierarValue Linear Hierarchical value of parent
/// \param p_grandParentLinearHierarValue Linear Hierarchical value of grandparent
/// \param p_dataSet Data structure with all the points
/// \param p_nodalValues Nodal values
/// \param p_hierarValues Hierarchical values
template< class T, class TT>
void recursive1DHierarchization(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentNodalValue,
const T &p_rightParentNodalValue,
const T &p_parentLinearHierarValue,
const T &p_grandParentLinearHierarValue,
const SparseSet &p_dataSet,
const TT &p_nodalValues,
TT &p_hierarValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T valueMidle = DoubleOrArray()(p_nodalValues, iposPoint);
// hierarchization
T LinearHierar = valueMidle - 0.5 * (p_leftParentNodalValue + p_rightParentNodalValue);
int iBaseType = iNodeToFunc[p_positionCurrent(p_idim) % 4];
// begin by linear
DoubleOrArray().affect(p_hierarValues, iposPoint, LinearHierar + weightParent[iBaseType]*p_parentLinearHierarValue + weightGrandParent[iBaseType]*p_grandParentLinearHierarValue);
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 2 * oldPosition;
recursive1DHierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentNodalValue, valueMidle, LinearHierar, p_parentLinearHierarValue, p_dataSet, p_nodalValues,
p_hierarValues);
// right
p_positionCurrent(p_idim) += 1;
recursive1DHierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentNodalValue, LinearHierar, p_parentLinearHierarValue, p_dataSet, p_nodalValues,
p_hierarValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
/// \brief Hierarchization in given dimension in 1D quadratic
/// \param p_levelCurrent Current level of the point
/// \param p_positionCurrent Current position of the point
/// \param p_iterLevel Iteration on level
/// \param p_idim Current dimension
/// \param p_leftParentNodalValue Left parent nodal value
/// \param p_rightParentNodalValue Right parent nodal value
/// \param p_parentLinearHierarValue Linear Hierarchical value of parent
/// \param p_dataSet Data structure with all the points
/// \param p_nodalValues Nodal values
/// \param p_hierarValues Hierarchical values
template< class T, class TT>
void hierarchizationStep2(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentNodalValue,
const T &p_rightParentNodalValue,
const T &p_parentLinearHierarValue,
const SparseSet &p_dataSet,
const TT &p_nodalValues,
TT &p_hierarValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T valueMidle = DoubleOrArray()(p_nodalValues, iposPoint);
// hierarchization
T LinearHierar = valueMidle - 0.5 * (p_leftParentNodalValue + p_rightParentNodalValue);
// quadratic
DoubleOrArray().affect(p_hierarValues, iposPoint, LinearHierar - 0.25 * p_parentLinearHierarValue) ;
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 2 * oldPosition;
recursive1DHierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentNodalValue, valueMidle, LinearHierar, p_parentLinearHierarValue,
p_dataSet, p_nodalValues, p_hierarValues);
// right
p_positionCurrent(p_idim) += 1;
recursive1DHierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentNodalValue, LinearHierar, p_parentLinearHierarValue,
p_dataSet, p_nodalValues, p_hierarValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
/// \brief Hierarchization in given dimension in 1D (first step : subtract constant value)
/// \param p_levelCurrent Current level of the point
/// \param p_positionCurrent Current position of the point
/// \param p_iterLevel Iteration on level
/// \param p_idim Current dimension
/// \param p_leftParentNodalValue Left parent nodal value
/// \param p_rightParentNodalValue Right parent nodal value
/// \param p_dataSet Data structure with all the points
/// \param p_nodalValues Nodal values
/// \param p_hierarValues Hierarchical values
template< class T, class TT>
void hierarchizationStep1(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentNodalValue,
const T &p_rightParentNodalValue,
const SparseSet &p_dataSet,
const TT &p_nodalValues,
TT &p_hierarValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T valueMidle = DoubleOrArray()(p_nodalValues, iposPoint);
// hierarchization
T LinearHierar = valueMidle - 0.5 * (p_leftParentNodalValue + p_rightParentNodalValue);
// cubic
DoubleOrArray().affect(p_hierarValues, iposPoint, LinearHierar) ;
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 0;
hierarchizationStep2<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentNodalValue, valueMidle, LinearHierar, p_dataSet, p_nodalValues, p_hierarValues);
// right
p_positionCurrent(p_idim) = 1;
hierarchizationStep2<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentNodalValue, LinearHierar, p_dataSet, p_nodalValues, p_hierarValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
public :
// default
Hierar1DCubicBound() {}
// operator for 1D Hierarchization
/// \brief Hierarchization in given dimension in 1D
/// \param p_levelCurrent Current index of the point
/// \param p_positionCurrent Current level of the point
/// \param p_iterLevel Iterator on current level
/// \param p_idim Current dimension
/// \param p_dataSet Data structure with all the points
/// \param p_nodalValues Nodal values
/// \param p_hierarValues Hierarchical values
template< class T, class TT>
void operator()(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const SparseSet &p_dataSet,
const TT &p_nodalValues,
TT &p_hierarValues)
{
// get back boundary key in the dimension
T leftValue ;
T rightValue ;
Eigen::ArrayXui leftBound(p_positionCurrent) ;
leftBound(p_idim) = 0;
SparseLevel::const_iterator iterLeft = p_iterLevel->second.find(leftBound);
if (iterLeft != p_iterLevel->second.end())
leftValue = DoubleOrArray()(p_nodalValues, iterLeft->second);
Eigen::ArrayXui rightBound(p_positionCurrent);
rightBound(p_idim) = 2;
SparseLevel::const_iterator iterRight = p_iterLevel->second.find(rightBound);
if (iterRight != p_iterLevel->second.end())
rightValue = DoubleOrArray()(p_nodalValues, iterRight->second);
hierarchizationStep1<T, TT>(p_levelCurrent, p_positionCurrent, p_iterLevel, p_idim, leftValue, rightValue,
p_dataSet, p_nodalValues, p_hierarValues);
}
};
/// \class Dehierar1DCubicBound SparseGridCubicBound.h
/// Dehierarchization for cubic with boundary points
class Dehierar1DCubicBound: public HierarDehierarBound
{
protected :
/// \brief Dehierarchization 1D in given dimension (modified bound) (cubic so available after two level)
/// \param p_levelCurrent Current index of the point
/// \param p_positionCurrent Current level of the point
/// \param p_iterLevel Iterator on current level
/// \param p_idim Current dimension
/// \param p_leftParentHierarValue Left parent nodal value
/// \param p_rightParentHierarValue Right parent nodal value
/// \param p_linearHierarParent Linear hierarchical value of parent
/// \param p_linearHierarGrandParent Linear Hierarchical value of parent
/// \param p_dataSet Data structure with all the points
/// \param p_hierarValues Hierarchical values
/// \param p_nodalValues Nodal values
template< class T, class TT>
void recursive1DDehierarchization(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentHierarValue,
const T &p_rightParentHierarValue,
const T &p_linearHierarParent,
const T &p_linearHierarGrandParent,
const SparseSet &p_dataSet,
const TT &p_hierarValues,
TT &p_nodalValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
// position
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T valueMidle = DoubleOrArray()(p_hierarValues, iposPoint);
// do dehierarchization
// calculation linear hierarchical coefficient
int iBaseType = iNodeToFunc[p_positionCurrent(p_idim) % 4];
T LinearHierarchical = valueMidle - (weightParent[iBaseType] * p_linearHierarParent + weightGrandParent[iBaseType] * p_linearHierarGrandParent);
valueMidle = LinearHierarchical + 0.5 * (p_leftParentHierarValue + p_rightParentHierarValue);
DoubleOrArray().affect(p_nodalValues, iposPoint, valueMidle);
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 2 * oldPosition;
recursive1DDehierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentHierarValue, valueMidle, LinearHierarchical, p_linearHierarParent,
p_dataSet, p_hierarValues, p_nodalValues);
// right
p_positionCurrent(p_idim) += 1;
recursive1DDehierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentHierarValue, LinearHierarchical, p_linearHierarParent,
p_dataSet, p_hierarValues, p_nodalValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
/// \brief Dehierarchization 1D in given dimension (modified bound, step 2 quadratic)
/// \param p_levelCurrent Current index of the point
/// \param p_positionCurrent Current level of the point
/// \param p_iterLevel Iterator on current level
/// \param p_idim Current dimension
/// \param p_leftParentHierarValue Left parent nodal value
/// \param p_rightParentHierarValue Right parent nodal value
/// \param p_linearHierarParent Linear hierarchical value of parent
/// \param p_dataSet Data structure with all the points
/// \param p_hierarValues Hierarchical values
/// \param p_nodalValues Nodal values
template< class T, class TT>
void dehierarchizationStep2(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentHierarValue,
const T &p_rightParentHierarValue,
const T &p_linearHierarParent,
const SparseSet &p_dataSet,
const TT &p_hierarValues,
TT &p_nodalValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
// position
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T valueMidle = DoubleOrArray()(p_hierarValues, iposPoint);
// do dehierarchization
// calculation linear hierarchical coefficient
T LinearHierarchical = valueMidle + 0.25 * p_linearHierarParent;
valueMidle = LinearHierarchical + 0.5 * (p_leftParentHierarValue + p_rightParentHierarValue);
DoubleOrArray().affect(p_nodalValues, iposPoint, valueMidle);
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 2 * oldPosition;
recursive1DDehierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentHierarValue, valueMidle, LinearHierarchical, p_linearHierarParent,
p_dataSet, p_hierarValues, p_nodalValues);
// right
p_positionCurrent(p_idim) += 1;
recursive1DDehierarchization<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentHierarValue, LinearHierarchical, p_linearHierarParent,
p_dataSet, p_hierarValues, p_nodalValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
/// \brief Dehierarchization 1D in given dimension (modified bound, step 2 quadratic)
/// \param p_levelCurrent Current level of the point
/// \param p_positionCurrent Current position of the point
/// \param p_iterLevel Iteration on level
/// \param p_idim Current dimension
/// \param p_leftParentHierarValue Left parent nodal value
/// \param p_rightParentHierarValue Right parent nodal value
/// \param p_dataSet Data structure with all the points
/// \param p_hierarValues Hierarchical values
/// \param p_nodalValues Nodal values
template< class T, class TT>
void dehierarchizationStep1(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const T &p_leftParentHierarValue,
const T &p_rightParentHierarValue,
const SparseSet &p_dataSet,
const TT &p_hierarValues,
TT &p_nodalValues)
{
if (p_iterLevel == p_dataSet.end())
return ;
// position
SparseLevel::const_iterator iterPosition = p_iterLevel->second.find(p_positionCurrent);
if (iterPosition == p_iterLevel->second.end())
return ;
// position
int iposPoint = iterPosition->second;
T LinearHierarchical = DoubleOrArray()(p_hierarValues, iposPoint);
// do dehierarchization
// calculation linear hierarchical coefficient
T valueMidle = LinearHierarchical + 0.5 * (p_leftParentHierarValue + p_rightParentHierarValue);
DoubleOrArray().affect(p_nodalValues, iposPoint, valueMidle);
char oldLevel = p_levelCurrent(p_idim);
unsigned int oldPosition = p_positionCurrent(p_idim);
// child level
p_levelCurrent(p_idim) += 1;
SparseSet::const_iterator iterLevelChild = p_dataSet.find(p_levelCurrent);
// left
p_positionCurrent(p_idim) = 0;
dehierarchizationStep2<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, p_leftParentHierarValue, valueMidle, LinearHierarchical,
p_dataSet, p_hierarValues, p_nodalValues);
// right
p_positionCurrent(p_idim) = 1;
dehierarchizationStep2<T, TT>(p_levelCurrent, p_positionCurrent, iterLevelChild, p_idim, valueMidle, p_rightParentHierarValue, LinearHierarchical,
p_dataSet, p_hierarValues, p_nodalValues);
p_positionCurrent(p_idim) = oldPosition;
p_levelCurrent(p_idim) = oldLevel;
}
public :
Dehierar1DCubicBound() {}
/// \brief Dehierarchization 1D in given dimension
/// \param p_levelCurrent Current level of the point
/// \param p_positionCurrent Current position of the point
/// \param p_iterLevel Iteration on level
/// \param p_idim Current dimension
/// \param p_dataSet Data structure with all the points
/// \param p_hierarValues Hierarchical values
/// \param p_nodalValues Nodal values
template< class T, class TT>
void operator()(Eigen::ArrayXc &p_levelCurrent,
Eigen::ArrayXui &p_positionCurrent,
const SparseSet::const_iterator &p_iterLevel,
const unsigned int &p_idim,
const SparseSet &p_dataSet,
const TT &p_hierarValues,
TT &p_nodalValues)
{
// get back boundary key in the dimension
T leftValue ;
T rightValue ;
Eigen::ArrayXui leftBound(p_positionCurrent) ;
leftBound(p_idim) = 0;
SparseLevel::const_iterator iterLeft = p_iterLevel->second.find(leftBound);
if (iterLeft != p_iterLevel->second.end())
leftValue = DoubleOrArray()(p_hierarValues, iterLeft->second);
Eigen::ArrayXui rightBound(p_positionCurrent);
rightBound(p_idim) = 2;
SparseLevel::const_iterator iterRight = p_iterLevel->second.find(rightBound);
if (iterRight != p_iterLevel->second.end())
rightValue = DoubleOrArray()(p_hierarValues, iterRight->second); // get back boundary key in the dimension
dehierarchizationStep1<T, TT>(p_levelCurrent, p_positionCurrent, p_iterLevel, p_idim, leftValue, rightValue, p_dataSet, p_hierarValues, p_nodalValues);
}
};
///@}
}
#endif /* SPARSEGRIDCUBICNONOUND_H */
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