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// Copyright (C) 2018 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#include <Eigen/SVD>
#include <Eigen/Cholesky>
#include "StOpt/regression/LaplacianLinearKernelRegression.h"
#include "StOpt/regression/nDDominanceKernel.h"
using namespace std ;
using namespace Eigen ;
namespace StOpt
{
LaplacianLinearKernelRegression::LaplacianLinearKernelRegression(const bool &p_bZeroDate,
const ArrayXXd &p_particles,
const ArrayXd &p_h):
BaseRegression(p_bZeroDate, p_particles, false), m_h(p_h), m_tree(p_particles)
{
}
LaplacianLinearKernelRegression::LaplacianLinearKernelRegression(const ArrayXd &p_h):
BaseRegression(false), m_h(p_h)
{
}
LaplacianLinearKernelRegression::LaplacianLinearKernelRegression(const bool &p_bZeroDate,
const ArrayXXd &p_particles):
BaseRegression(p_bZeroDate, p_particles, false), m_tree(p_particles)
{
}
void LaplacianLinearKernelRegression::updateSimulations(const bool &p_bZeroDate, const ArrayXXd &p_particles)
{
BaseRegression::updateSimulationsBase(p_bZeroDate, p_particles);
m_tree = KDTree(p_particles);
}
ArrayXXd LaplacianLinearKernelRegression::regressFunction(const ArrayXXd &p_fToRegress) const
{
// dimension
int nD = m_particles.rows();
// number of functions to calculate for regressions
int nbFuncReg = (nD + 1) * (nD + 2) / 2;
int nbFuncSecMem = (nD + 1) * p_fToRegress.rows() ;
// creation of the 2^d terms
int nbSum = pow(2, nD);
vector< shared_ptr<ArrayXXd> > vecToAdd(nbSum);
// calculate exp values
Eigen::ArrayXi iCoord(nD) ;
for (int i = 0; i < nbSum; ++i)
{
int ires = i;
for (int id = nD - 1 ; id >= 0 ; --id)
{
unsigned int idec = (ires >> id) ;
iCoord(id) = -(2 * idec - 1);
ires -= (idec << id);
}
vecToAdd[i] = make_shared<ArrayXXd>(nbFuncReg + nbFuncSecMem, m_particles.cols());
for (int is = 0; is < m_particles.cols(); ++is)
{
double ssum = 0;
for (int id = 0; id < nD; ++id)
ssum += iCoord(id) * m_particles(id, is) / m_h(id);
double expSum = exp(ssum);
int iloc = 0;
// lower triangular matrix
(*vecToAdd[i])(iloc++, is) = expSum;
for (int id = 0; id < nD; ++id)
{
(*vecToAdd[i])(iloc++, is) = expSum * m_particles(id, is);
for (int idd = 0; idd <= id; ++idd)
(*vecToAdd[i])(iloc++, is) = expSum * m_particles(id, is) * m_particles(idd, is) ;
}
for (int ifunc = 0; ifunc < p_fToRegress.rows(); ++ifunc)
{
(*vecToAdd[i])(iloc++, is) = expSum * p_fToRegress(ifunc, is);
for (int id = 0; id < nD ; ++id)
(*vecToAdd[i])(iloc++, is) = expSum * p_fToRegress(ifunc, is) * m_particles(id, is) ;
}
}
}
vector< shared_ptr<ArrayXXd> > fDomin(nbSum);
// kernel resolution
nDDominanceKernel(m_particles, vecToAdd, fDomin);
// reconstruction of the 2^d terms for each matrix term
ArrayXd forMatrix(nbFuncReg);
ArrayXd secMem(nbFuncSecMem);
MatrixXd matA(1 + nD, 1 + nD);
VectorXd vecB(1 + nD);
ArrayXXd ret(p_fToRegress.rows(), p_fToRegress.cols());
for (int is = 0; is < m_particles.cols(); ++is)
{
// calculate matrix Coeff
int iPosLoc = 0;
forMatrix(iPosLoc) = 1.;
for (int iSum = 0; iSum < nbSum; ++iSum)
{
forMatrix(iPosLoc) += (*fDomin[iSum])(0, is) * (*vecToAdd[nbSum - 1 - iSum])(0, is);
}
iPosLoc += 1;
for (int id = 0; id < nD; ++id)
{
forMatrix(iPosLoc) = m_particles(id, is);
for (int iSum = 0; iSum < nbSum; ++iSum)
forMatrix(iPosLoc) += (*fDomin[iSum])(iPosLoc, is) * (*vecToAdd[nbSum - 1 - iSum])(0, is);
iPosLoc += 1;
for (int idd = 0; idd <= id; ++idd)
{
forMatrix(iPosLoc) = m_particles(id, is) * m_particles(idd, is) ;
for (int iSum = 0; iSum < nbSum; ++iSum)
forMatrix(iPosLoc) += (*fDomin[iSum])(iPosLoc, is) * (*vecToAdd[nbSum - 1 - iSum])(0, is);
iPosLoc += 1;
}
}
// create second member
int iSecMem = 0 ;
for (int ifunc = 0 ; ifunc < p_fToRegress.rows(); ++ifunc)
{
secMem(iSecMem) = p_fToRegress(ifunc, is);
for (int iSum = 0; iSum < nbSum; ++iSum)
{
secMem(iSecMem) += (*fDomin[iSum])(nbFuncReg + iSecMem, is) * (*vecToAdd[nbSum - 1 - iSum])(0, is);
}
iSecMem += 1;
for (int id = 0; id < nD; ++id)
{
secMem(iSecMem) = p_fToRegress(ifunc, is) * m_particles(id, is) ;
for (int iSum = 0; iSum < nbSum; ++iSum)
{
secMem(iSecMem) += (*fDomin[iSum])(nbFuncReg + iSecMem, is) * (*vecToAdd[nbSum - 1 - iSum])(0, is);
}
iSecMem += 1;
}
}
// create regression matrix
int iloc = 0;
for (int id = 0; id <= nD; ++id)
for (int idd = 0; idd <= id; ++idd)
matA(id, idd) = forMatrix(iloc++);
for (int id = 0; id <= nD; ++id)
for (int idd = id + 1; idd <= nD; ++idd)
matA(id, idd) = matA(idd, id);
// second member and inverse
int iloc1 = 0;
// inverse
LLT<MatrixXd> lltA(matA);
for (int ifunc = 0 ; ifunc < p_fToRegress.rows(); ++ifunc)
{
for (int id = 0; id <= nD; ++id)
vecB(id) = secMem(iloc1++);
VectorXd coeff = lltA.solve(vecB);
ret(ifunc, is) = coeff(0);
for (int id = 0; id < nD; ++id)
ret(ifunc, is) += coeff(id + 1) * m_particles(id, is);
}
}
return ret;
}
ArrayXd LaplacianLinearKernelRegression::getCoordBasisFunction(const ArrayXd &p_fToRegress) const
{
if (!BaseRegression::m_bZeroDate)
{
const ArrayXXd fToRegress = Map<const ArrayXXd>(p_fToRegress.data(), 1, p_fToRegress.size()) ;
ArrayXXd regressed = regressFunction(fToRegress);
ArrayXd toReturn = Map<ArrayXd>(regressed.data(), regressed.size());
return toReturn;
}
else
{
ArrayXd retAverage(1);
retAverage(0) = p_fToRegress.mean();
return retAverage;
}
}
ArrayXXd LaplacianLinearKernelRegression::getCoordBasisFunctionMultiple(const ArrayXXd &p_fToRegress) const
{
if (!BaseRegression::m_bZeroDate)
{
return regressFunction(p_fToRegress);
}
else
{
ArrayXXd retAverage(p_fToRegress.rows(), 1);
for (int nsm = 0; nsm < p_fToRegress.rows(); ++nsm)
retAverage.row(nsm).setConstant(p_fToRegress.row(nsm).mean());
return retAverage;
}
}
ArrayXd LaplacianLinearKernelRegression::getAllSimulations(const ArrayXd &p_fToRegress) const
{
if (!BaseRegression::m_bZeroDate)
{
const ArrayXXd fToRegress = Map<const ArrayXXd>(p_fToRegress.data(), 1, p_fToRegress.size()) ;
ArrayXXd regressed = regressFunction(fToRegress);
ArrayXd toReturn = Map<ArrayXd>(regressed.data(), regressed.size());
return toReturn;
}
else
{
return ArrayXd::Constant(p_fToRegress.size(), p_fToRegress.mean());
}
}
ArrayXXd LaplacianLinearKernelRegression::getAllSimulationsMultiple(const ArrayXXd &p_fToRegress) const
{
if (!BaseRegression::m_bZeroDate)
{
return regressFunction(p_fToRegress);
}
else
{
ArrayXXd ret(p_fToRegress.rows(), p_fToRegress.cols());
for (int ism = 0; ism < p_fToRegress.rows(); ++ism)
ret.row(ism).setConstant(p_fToRegress.row(ism).mean());
return ret;
}
}
ArrayXd LaplacianLinearKernelRegression::reconstruction(const ArrayXd &p_basisCoefficients) const
{
if (!BaseRegression::m_bZeroDate)
return p_basisCoefficients; // basis function are here regressed values !
else
{
return ArrayXd::Constant(m_particles.cols(), p_basisCoefficients(0));
}
}
ArrayXXd LaplacianLinearKernelRegression::reconstructionMultiple(const ArrayXXd &p_basisCoefficients) const
{
if (!BaseRegression::m_bZeroDate)
{
return p_basisCoefficients; // basis function are here regressed values !
}
else
{
ArrayXXd retValue(p_basisCoefficients.rows(), m_particles.cols());
for (int nsm = 0; nsm < p_basisCoefficients.rows(); ++nsm)
retValue.row(nsm).setConstant(p_basisCoefficients(nsm, 0));
return retValue ;
}
}
double LaplacianLinearKernelRegression::reconstructionASim(const int &p_isim, const ArrayXd &p_basisCoefficients) const
{
double ret ;
if (!BaseRegression::m_bZeroDate)
{
ret = p_basisCoefficients(p_isim);
}
else
{
ret = p_basisCoefficients(0);
}
return ret ;
}
double LaplacianLinearKernelRegression::getValue(const ArrayXd &p_coordinates,
const ArrayXd &p_coordBasisFunction) const
{
double ret ;
if (!BaseRegression::m_bZeroDate)
{
// Use KDTree to find nearest point close to a given one and regress the associated
// regressed value
return p_coordBasisFunction(m_tree.nearestIndex(p_coordinates));
}
else
ret = p_coordBasisFunction(0);
return ret ;
}
double LaplacianLinearKernelRegression::getAValue(const ArrayXd &p_coordinates, const ArrayXd &p_ptOfStock,
const vector< shared_ptr<InterpolatorSpectral> > &p_interpFuncBasis) const
{
if (!BaseRegression::m_bZeroDate)
{
return p_interpFuncBasis[m_tree.nearestIndex(p_coordinates)]->apply(p_ptOfStock);
}
else
{
return p_interpFuncBasis[0]->apply(p_ptOfStock);
}
}
}
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