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/// Copyright (C) 2021 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <vector>
#include <array>
#include <iostream>
#include <Eigen/Dense>
#include "StOpt/core/utils/types.h"
#include "StOpt/core/utils/constant.h"
#include "StOpt/core/grids/InterpolatorSpectral.h"
using namespace std;
using namespace Eigen;
namespace StOpt
{
// Only upper part is filled in
ArrayXXd localLinearDiscrLastDimMatrixCalculation(const ArrayXXd &p_particles,
const ArrayXi &p_simToCell,
const Array< array< double, 2>, Dynamic, Dynamic > &p_mesh)
{
int nbSimul = p_simToCell.size();
int nBase = p_particles.rows() ;
int nbCell = p_mesh.cols();
//to store fuction basis values
ArrayXd FBase(nBase);
// initialization
ArrayXXd matReg = ArrayXXd::Zero(nBase * nBase, nbCell);
for (int is = 0; is < nbSimul ; ++is)
{
// cell number
int ncell = p_simToCell(is) ;
// calculate basis function values
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
double xPosMin = p_mesh(id, ncell)[0];
double xPosMax = p_mesh(id, ncell)[1] ;
FBase(id + 1) = (p_particles(id, is) - xPosMin) / (xPosMax - xPosMin);
}
for (int k = 0 ; k < nBase ; ++k)
for (int kk = k ; kk < nBase ; ++kk)
matReg(k + kk * nBase, ncell) += FBase(k) * FBase(kk);
}
// normalization
matReg /= nbSimul ;
return matReg;
}
ArrayXXd localLinearDiscrLastDimSecondMemberCalculation(const ArrayXXd &p_particles,
const ArrayXi &p_simToCell,
const Array< array< double, 2>, Dynamic, Dynamic > &p_mesh,
const ArrayXXd &p_fToRegress)
{
int nbSimul = p_simToCell.size();
int nBase = p_particles.rows() ;
int nbCell = p_mesh.cols();
// number of function to regress
int iSecMem = p_fToRegress.rows();
ArrayXd FBase(nBase);
ArrayXXd secMember = ArrayXXd::Zero(p_fToRegress.rows(), nbCell * nBase);
for (int is = 0; is < nbSimul ; ++is)
{
int nCell = p_simToCell(is);
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1; id++)
{
double xPosMin = p_mesh(id, nCell)[0] ;
double xPosMax = p_mesh(id, nCell)[1] ;
FBase(id + 1) = (p_particles(id, is) - xPosMin) / (xPosMax - xPosMin);
}
int idec = nCell * nBase;
// nest on second members
for (int nsm = 0 ; nsm < iSecMem ; ++nsm)
{
double xtemp = p_fToRegress(nsm, is) ;
// second member of the regression problem
for (int id = 0 ; id < nBase ; ++id)
secMember(nsm, idec + id) += xtemp * FBase(id);
}
}
// normalization
secMember /= nbSimul;
return secMember;
}
ArrayXXd localLinearDiscrLastDimSecondMemberCalculationOneCell(const ArrayXXd &p_particles,
const std::vector<int> &p_SimulBelongingToCell,
const Eigen::Ref<const Eigen::Array< array<double, 2 >, Eigen::Dynamic, 1 > > &p_mesh,
const ArrayXXd &p_fToRegress)
{
int nbSimul = p_SimulBelongingToCell.size();
int nBase = p_particles.rows() ;
// number of function to regress
int iSecMem = p_fToRegress.rows();
ArrayXd FBase(nBase);
ArrayXXd secMember = ArrayXXd::Zero(p_fToRegress.rows(), nBase);
for (int is = 0; is < nbSimul ; ++is)
{
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1; id++)
{
double xPosMin = p_mesh(id)[0] ;
double xPosMax = p_mesh(id)[1] ;
FBase(id + 1) = (p_particles(id, p_SimulBelongingToCell[is]) - xPosMin) / (xPosMax - xPosMin);
}
// nest on second members
for (int nsm = 0 ; nsm < iSecMem ; ++nsm)
{
double xtemp = p_fToRegress(nsm, is) ;
// second member of the regression problem
for (int id = 0 ; id < nBase ; ++id)
secMember(nsm, id) += xtemp * FBase(id);
}
}
// no normalization
return secMember;
}
ArrayXXd localLinearDiscrLastDimReconstruction(const ArrayXXd &p_particles, const ArrayXi &p_simToCell,
const Array< array< double, 2>, Dynamic, Dynamic > &p_mesh,
const ArrayXXd &p_foncBasisCoef)
{
int nbSimul = p_simToCell.size();
int nBase = p_particles.rows();
// basis
ArrayXd FBase(nBase);
// initialization
ArrayXXd solution = ArrayXXd::Zero(p_foncBasisCoef.rows(), nbSimul) ;
for (int is = 0; is < nbSimul ; ++is)
{
int nCell = p_simToCell(is) ;
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
double xPosMin = p_mesh(id, nCell)[0] ;
double xPosMax = p_mesh(id, nCell)[1] ;
FBase(id + 1) = (p_particles(id, is) - xPosMin) / (xPosMax - xPosMin);
}
int idec = nCell * nBase ;
for (int isecMem = 0; isecMem < p_foncBasisCoef.rows(); ++isecMem)
for (int id = 0 ; id < nBase ; ++id)
solution(isecMem, is) += p_foncBasisCoef(isecMem, idec + id) * FBase(id);
}
return solution;
}
double localLinearDiscrLastDimReconstructionASim(const int &p_isim, const ArrayXXd &p_particles, const ArrayXi &p_simToCell,
const Array< array< double, 2>, Dynamic, Dynamic > &p_mesh,
const ArrayXd &p_foncBasisCoef)
{
int nBase = p_particles.rows() ;
// basis
ArrayXd FBase(nBase);
// initialization
double solution = 0 ;
int nCell = p_simToCell(p_isim) ;
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
double xPosMin = p_mesh(id, nCell)[0] ;
double xPosMax = p_mesh(id, nCell)[1] ;
FBase(id + 1) = (p_particles(id, p_isim) - xPosMin) / (xPosMax - xPosMin);
}
int idec = nCell * nBase ;
for (int id = 0 ; id < nBase ; ++id)
solution += p_foncBasisCoef(idec + id) * FBase(id);
return solution;
}
ArrayXd localLinearDiscrLastDimReconstructionOnePoint(const ArrayXd &p_oneParticle,
const vector< shared_ptr< ArrayXd > > &p_mesh1D,
const ArrayXXd &p_foncBasisCoef)
{
int nBase = p_oneParticle.size();
ArrayXd FBase(nBase);
// Values of the functon basis and position of the particle in the mesh
FBase(0) = 1;
int iCell = 0 ;
int idecCell = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
int iMesh = 1 ;
while ((p_oneParticle(id) > (*p_mesh1D[id])(iMesh)) && (iMesh < p_mesh1D[id]->size() - 1)) iMesh++;
double xPosMin = (*p_mesh1D[id])(iMesh - 1) ;
double xPosMax = (*p_mesh1D[id])(iMesh) ;
FBase(id + 1) = (p_oneParticle(id) - xPosMin) / (xPosMax - xPosMin);
iCell += (iMesh - 1) * idecCell;
idecCell *= p_mesh1D[id]->size() - 1;
}
// position last dimension
int iMesh = 1 ;
while ((p_oneParticle(nBase - 1) > (*p_mesh1D[nBase - 1])(iMesh)) && (iMesh < p_mesh1D[nBase - 1]->size() - 1)) iMesh++;
iCell += (iMesh - 1) * idecCell;
// reconstruction
int idec = nBase * iCell ;
ArrayXd solution = ArrayXd::Zero(p_foncBasisCoef.rows());
for (int isecMem = 0; isecMem < solution.size(); ++isecMem)
for (int id = 0 ; id < nBase ; ++id)
solution(isecMem) += p_foncBasisCoef(isecMem, idec + id) * FBase(id);
return solution;
}
double localLinearDiscrLastDimReconsOnePointSimStock(const ArrayXd &p_oneParticle, const ArrayXd &p_stock,
const std::vector< std::shared_ptr<InterpolatorSpectral> > &p_interpBaseFunc,
const std::vector< std::shared_ptr< ArrayXd > > &p_mesh1D)
{
int nBase = p_oneParticle.size();
ArrayXd FBase(nBase);
// Values of the functon basis and position of the particle in the mesh
FBase(0) = 1;
int iCell = 0 ;
int idecCell = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
int iMesh = 1 ;
while ((p_oneParticle(id) > (*p_mesh1D[id])(iMesh)) && (iMesh < p_mesh1D[id]->size() - 1)) iMesh++;
double xPosMin = (*p_mesh1D[id])(iMesh - 1) ;
double xPosMax = (*p_mesh1D[id])(iMesh) ;
FBase(id + 1) = (p_oneParticle(id) - xPosMin) / (xPosMax - xPosMin);
iCell += (iMesh - 1) * idecCell;
idecCell *= p_mesh1D[id]->size() - 1;
}
// position last dimension
int iMesh = 1 ;
while ((p_oneParticle(nBase - 1) > (*p_mesh1D[nBase - 1])(iMesh)) && (iMesh < p_mesh1D[nBase - 1]->size() - 1)) iMesh++;
iCell += (iMesh - 1) * idecCell;
// reconstruction
int idec = nBase * iCell ;
double solution = 0;
for (int id = 0 ; id < nBase ; ++id)
solution += p_interpBaseFunc[idec + id]->apply(p_stock) * FBase(id);
return solution;
}
ArrayXd localLinearDiscrLastDimReconstructionOnePointOneCell(const ArrayXd &p_oneParticle,
const Array< array< double, 2>, Dynamic, 1 > &p_mesh,
const ArrayXXd &p_foncBasisCoef)
{
int nBase = p_foncBasisCoef.cols();
// basis
ArrayXd FBase(nBase);
// initialization
ArrayXd solution = ArrayXd::Zero(p_foncBasisCoef.rows()) ;
FBase(0) = 1;
for (int id = 0 ; id < nBase - 1 ; id++)
{
double xPosMin = p_mesh(id)[0] ;
double xPosMax = p_mesh(id)[1] ;
FBase(id + 1) = (p_oneParticle(id) - xPosMin) / (xPosMax - xPosMin);
}
for (int isecMem = 0; isecMem < p_foncBasisCoef.rows(); ++isecMem)
for (int id = 0 ; id < nBase ; ++id)
solution(isecMem) += p_foncBasisCoef(isecMem, id) * FBase(id);
return solution;
}
}
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