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// Copyright (C) 2017 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#ifndef GRIDKERNELREGRESSION_H
#define GRIDKERNELREGRESSION_H
#include <vector>
#include <memory>
#include <Eigen/Dense>
#include <boost/multi_array.hpp>
#include "StOpt/core/grids/InterpolatorSpectral.h"
/// \file gridKernelConstruction.h
namespace StOpt
{
/// \brief calculate the regressed values on the grid p_z
/// \param p_newX renormalized particle
/// \param p_y second member to regress
/// \param p_z grid points for regressions (in each dimension)
/// \param p_h bandwith for each point in p_z (in each dimension)
/// \param p_g storing all point in p_z + /- p_h (in each dimension)
/// \param p_xG permits to affect each particle to a slice defined by p_g in each direction
/// \param p_zl for each dimension, indicate in which point in p_g correspond a point in p_z-p_h
/// \param p_zr for each dimension, indicate in which point in p_g correspond a point in p_z+p_h
/// \param p_tick tick to help regresssion matrix
/// \param p_bLinear true if we use linear regressions
/// \return An array with all the regressed value at p_z points
Eigen::ArrayXd gridKernelRegressedValuesOnGrid(const Eigen::ArrayXXd &p_newX,
const Eigen::ArrayXd &p_y,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_h,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_g,
const Eigen::ArrayXXi &p_xG,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zl,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zr,
const bool &p_bLinear,
double p_tick = 1e-7) ;
/// \brief calculate he regressed values on the grid p_z
/// \param p_newX renormalized particle
/// \param p_y second member to regress
/// \param p_z grid points for regressions (in each dimension)
/// \param p_h bandwith for each point in p_z (in each dimension)
/// \param p_g storing all point in p_z + /- p_h (in each dimension)
/// \param p_xG permits to affect each particle to a slice defined by p_g in each direction
/// \param p_zl for each dimension, indicate in which point in p_g correspond a point in p_z-p_h
/// \param p_zr for each dimension, indicate in which point in p_g correspond a point in p_z+p_h
/// \param p_bLinear true if we use linear regressions
/// \param p_tick tick to help regresssion matrix
/// \return An array with all the regressed value at p_z points
Eigen::ArrayXd gridKernelRegressedValuesOnGridStable(const Eigen::ArrayXXd &p_newX,
const Eigen::ArrayXd &p_y,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_h,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_g,
const Eigen::ArrayXXi &p_xG,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zl,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zr,
const bool &p_bLinear,
double p_tick = 1e-7) ;
/// \brief calculate the regressed values associated to (p_newX,p_y)
/// \param p_newX renormalized particle
/// \param p_newY renormalized second member to regress
/// \param p_z grid points for regressions (in each dimension)
/// \param p_h bandwith for each point in p_z (in each dimension)
/// \param p_g storing all point in p_z + /- p_h (in each dimension)
/// \param p_xG permits to affect each particle to a slice defined by p_g in each direction
/// \param p_zl for each dimension, indicate in which point in p_g correspond a point in p_z-p_h
/// \param p_zr for each dimension, indicate in which point in p_g correspond a point in p_z+p_h
/// \param p_iSort in each direction sorted particles by their number
/// \param p_tick tick to help regresssion matrix
/// \param p_bLinear true if linear regression
/// \return An array with all the regressed value at p_z points
Eigen::ArrayXd gridKernelRegressedValues(const Eigen::ArrayXXd &p_newX,
const Eigen::ArrayXd &p_y,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_h,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_g,
const Eigen::ArrayXXi &p_xG,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zl,
const std::vector< std::shared_ptr<Eigen::ArrayXi> > &p_zr,
const Eigen::ArrayXXi &p_iSort,
const bool &p_bLinear,
double p_tick = 1e-7) ;
/// \brief General Subroutine : naive implementation for all points
/// \param p_X sample point
/// \param p_Y sample point to regress with respect to p_X
/// \param p_prop Proportion of point taken by each local regression (bandwith)
/// \param p_bLinear do we use linera regressions
/// \param p_q p_q by number of simulations correspond to the number of points in the grid
Eigen::ArrayXd locAdapRegNaive(const Eigen::ArrayXXd &p_X, const Eigen::ArrayXd &p_Y, const double &p_prop, const bool &p_bLinear, double p_q = 1., double p_tick = 1e-7);
/// \brief General Subroutine : fast sum implementation for all points
/// \param p_X sample point
/// \param p_Y sample point to regress with respect to p_X
/// \param p_prop Proportion of point taken by each local regression (bandwith)
/// \param p_bLinear do we use linera regressions
/// \param p_q p_q by number of simulations correspond to the number of points in the grid
Eigen::ArrayXd locAdapReg(const Eigen::ArrayXXd &p_X, const Eigen::ArrayXd &p_Y, const double &p_prop, const bool &p_bLinear, double p_q = 1., double p_tick = 1e-7);
/// \brief General Subroutine : naive implementation for all points
/// \param p_X sample point
/// \param p_Y sample point to regress with respect to p_X
/// \param p_prop Proportion of point taken by each local regression (bandwith)
/// \param p_bLinear do we use linera regressions
/// \param p_q p_q by number of simulations correspond to the number of points in the grid
Eigen::ArrayXd locAdapRegNaiveOnGrid(const Eigen::ArrayXXd &p_X, const Eigen::ArrayXd &p_Y, const double &p_prop, const bool &p_bLinear, double p_q = 1., double p_tick = 1e-7);
/// \brief General Subroutine : naive implementation for all points (stabilized version)
/// \param p_X sample point
/// \param p_Y sample point to regress with respect to p_X
/// \param p_prop Proportion of point taken by each local regression (bandwith)
/// \param p_bLinear do we use linera regressions
/// \param p_q p_q by number of simulations correspond to the number of points in the grid
Eigen::ArrayXd locAdapRegNaiveOnGridStab(const Eigen::ArrayXXd &p_X, const Eigen::ArrayXd &p_Y, const double &p_prop, const bool &p_bLinear, double p_q = 1., double p_tick = 1e-7);
/// \brief Calculate for all points used by the kernel method the regressed values from the interplated values on the grid
/// \param p_newX renormalized particle
/// \param p_yHatZ regressed values on the grid defined by p_z plus scaling (mean, std)
/// \param p_z grid points for regressions (in each dimension)
/// \param p_iSort in each direction sorted particles by their number
/// \return An array with all the regressed value for the particle p_newX
Eigen::ArrayXd fromGridValuesGetRegAllSim(const Eigen::ArrayXXd &p_newX,
const Eigen::ArrayXd &p_yHatZ,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z,
const Eigen::ArrayXXi &p_iSort);
/// \brief Calculate for one point used by the kernel method the regressed value from the interpolated values on the grid
/// by a naive method
/// \param p_newX renormalized particle
/// \param p_yHatZ regressed values on the grid defined by p_z plus scaling (mean, std)
/// \param p_z grid points for regressions (in each dimension)
/// \return the interpolated value
double fromGridValuesGetRegASim(const Eigen::ArrayXd &p_newX,
const Eigen::ArrayXd &p_yHatZ,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z);
/// \brief Calculate for one point used by the kernel method the regressed value from the interpolated values on the grid
/// Used to avoid costly interpolation on all function basis
/// \param p_newX renormalized particle
/// \param p_yHatZ regressed values on the grid defined by p_z plus scaling (mean, std)
/// \param p_z grid points for regressions (in each dimension)
/// \param p_ptOfStock grid point
/// \param p_interpFuncBasis spectral interpolator to interpolate on the basis the function value (regressed functions on all grid with
/// spectral representation)
/// \return the interpolated value
double fromGridValuesGetRegASimOnBasis(const Eigen::ArrayXd &p_newX,
const std::vector< std::shared_ptr<Eigen::ArrayXd> > &p_z,
const Eigen::ArrayXd &p_ptOfStock,
const std::vector< std::shared_ptr<InterpolatorSpectral> > &p_interpFuncBasis);
}
#endif /* GRIDKERNELREGRESSION_H */
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