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// Copyright (C) 2021 EDF
// All Rights Reserved
// This code is published under the GNU Lesser General Public License (GNU LGPL)
#ifndef LOCALLINEARDISCRLASTDIMREGRESSION_H
#define LOCALLINEARDISCRLASTDIMREGRESSION_H
#include <vector>
#include <memory>
#include <array>
#include <Eigen/Dense>
#include "StOpt/regression/LocalDiscrLastDimRegression.h"
#include "StOpt/core/grids/InterpolatorSpectral.h"
/** \file LocalLinearDiscrLastDimRegression.h
* \brief Compute conditional expectations by using local regressions.
* See article "Monte-Carlo valorisation of American options: facts and new algorithms to improve existing methods"
* by Bouchard, Warin in "Numerical methods in finance", Springer,2012
* Here the approximation in the last dimension has discrete values gathered in constant approximation in the lasty dimension.
* \author Xavier Warin
*/
namespace StOpt
{
/**
* \defgroup LocalLinearDiscrLastDim Piecewise linear regression
* \brief It implements local linear functions for performing local regression
* using P-1 finite elements.
*@{
*/
/// \class LocalLinearDiscrLastDimRegression LocalLinearDiscrLastDimRegression.h
/// To be used in Monte Carlo methods. LinearDiscrLastDim regression on each cell which is constructed such that each cell has
/// roughly the same number of particles, except in last dimension with discrete values.
class LocalLinearDiscrLastDimRegression : public LocalDiscrLastDimRegression
{
protected :
Eigen::ArrayXXd m_matReg ; ///< Regression matrix (rank \f$ (n_d+1)^2 \f$ by the number of meshes ). Also store lower part of factorized matrix.
Eigen::ArrayXXd m_diagReg ; ///< Diagonal part of the factorized matrix during Choleski factorization
public :
/// \brief Default constructor
LocalLinearDiscrLastDimRegression() {}
/// \brief Constructor
/// \param p_nbMesh discretization in each direction
/// \param p_bRotationAndRecale do we use SVD
LocalLinearDiscrLastDimRegression(const Eigen::ArrayXi &p_nbMesh, bool p_bRotationAndRecale = false);
/// \brief Constructor for object constructed at each time step
/// \param p_bZeroDate first date is 0?
/// \param p_particles particles used for the meshes.
/// First dimension : dimension of the problem,
/// second dimension : the number of particles
/// \param p_nbMesh discretization in each direction
/// \param p_bRotationAndRecale do we use SVD
LocalLinearDiscrLastDimRegression(const bool &p_bZeroDate,
const Eigen::ArrayXXd &p_particles,
const Eigen::ArrayXi &p_nbMesh,
bool p_bRotationAndRecale = false);
/// \brief Second constructor , only to be used in simulation
/// \param p_bRotationAndRecale do we use SVD
LocalLinearDiscrLastDimRegression(const bool &p_bZeroDate,
const Eigen::ArrayXi &p_nbMesh,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh,
const std::vector< std::shared_ptr< Eigen::ArrayXd > > &p_mesh1D, const Eigen::ArrayXd &p_meanX,
const Eigen::ArrayXd &p_etypX, const Eigen::MatrixXd &p_svdMatrix,
const bool &p_bRotationAndRecale) ;
/// \brief Copy constructor
/// \param p_objet object to copy
LocalLinearDiscrLastDimRegression(const LocalLinearDiscrLastDimRegression &p_objet);
/// \brief update the particles used in regression and construct the matrices
/// \param p_bZeroDate first date is 0?
/// \param p_particles particles used for the meshes.
/// First dimension : dimension of the problem,
/// second dimension : the number of particles
void updateSimulations(const bool &p_bZeroDate, const Eigen::ArrayXXd &p_particles);
/// \brief Get some local accessors
///@{
inline const Eigen::ArrayXXd &getMatReg() const
{
return m_matReg;
}
inline const Eigen::ArrayXXd &getDiagReg() const
{
return m_diagReg;
}
///@}
/// \brief conditional expectation basis function coefficient calculation
/// \param p_fToRegress function to regress associated to each simulation used in optimization
/// \return regression coordinates on the basis (size : number of meshes multiplied by the dimension plus one)
/// @{
Eigen::ArrayXd getCoordBasisFunction(const Eigen::ArrayXd &p_fToRegress) const;
///@}
/// \brief conditional expectation basis function coefficient calculation for multiple functions to regress
/// \param p_fToRegress function to regress associated to each simulation used in optimization (size : number of functions to regress \times the number of Monte Carlo simulations)
/// \return regression coordinates on the basis (size : number of function to regress \times number of meshes multiplied by the dimension plus one)
/// @{
Eigen::ArrayXXd getCoordBasisFunctionMultiple(const Eigen::ArrayXXd &p_fToRegress) const ;
///@}
/// \brief conditional expectation calculation
/// \param p_fToRegress simulations to regress used in optimization
/// \return regressed value function
/// @{
Eigen::ArrayXd getAllSimulations(const Eigen::ArrayXd &p_fToRegress) const ;
Eigen::ArrayXXd getAllSimulationsMultiple(const Eigen::ArrayXXd &p_fToRegress) const;
///@}
/// \brief Use basis functions to reconstruct the solution
/// \param p_basisCoefficients basis coefficients
///@{
Eigen::ArrayXd reconstruction(const Eigen::ArrayXd &p_basisCoefficients) const;
Eigen::ArrayXXd reconstructionMultiple(const Eigen::ArrayXXd &p_basisCoefficients) const;
/// @}
/// \brief use basis function to reconstruct a given simulation
/// \param p_isim simulation number
/// \param p_basisCoefficients basis coefficients to reconstruct a given conditional expectation
double reconstructionASim(const int &p_isim, const Eigen::ArrayXd &p_basisCoefficients) const ;
/// \brief conditional expectation reconstruction
/// \param p_coordinates coordinates to interpolate (uncertainty sample)
/// \param p_coordBasisFunction regression coordinates on the basis (size: number of meshes multiplied by the dimension plus one)
/// \return regressed value function reconstructed for each simulation
double getValue(const Eigen::ArrayXd &p_coordinates,
const Eigen::ArrayXd &p_coordBasisFunction) const;
/// \brief permits to reconstruct a function with basis functions coefficients values given on a grid
/// \param p_coordinates coordinates (uncertainty sample)
/// \param p_ptOfStock grid point
/// \param p_interpFuncBasis spectral interpolator to interpolate the basis functions coefficients used in regression on the grid (given for each basis function)
double getAValue(const Eigen::ArrayXd &p_coordinates, const Eigen::ArrayXd &p_ptOfStock,
const std::vector< std::shared_ptr<InterpolatorSpectral> > &p_interpFuncBasis) const;
/// \brief get the number of basis functions
inline int getNumberOfFunction() const
{
if (m_bZeroDate)
return 1;
else
return m_nbMesh.prod() * (m_nbMesh.size() + 1);
}
/// \brief Clone the regressor
std::shared_ptr<BaseRegression> clone() const
{
return std::static_pointer_cast<BaseRegression>(std::make_shared<LocalLinearDiscrLastDimRegression>(*this));
}
/// \brief conditional expectation basis function coefficient calculation for a special cell
/// \param p_iCell cell number
/// \param p_fToRegress function to regress associated to each simulation used in optimization and corresponding to the cell
/// \return regression coordinates on the basis (size : the dimension of the problem plus one)
/// @{
Eigen::ArrayXd getCoordBasisFunctionOneCell(const int &p_iCell, const Eigen::ArrayXd &p_fToRegress) const ;
Eigen::ArrayXXd getCoordBasisFunctionMultipleOneCell(const int &p_iCell, const Eigen::ArrayXXd &p_fToRegress) const ;
///@}
/// \brief Given a particle and the coordinates of the mesh it belongs to, get back the conditional expectation
/// \param p_oneParticle The particle generated
/// \param p_cell the cell it belongs to
/// \param p_foncBasisCoef function basis on the current cell (the row is the number of reconstruction to achieve, the columns the number of function basis)
/// \return send back the array of conditional expectations
Eigen::ArrayXd getValuesOneCell(const Eigen::ArrayXd &p_oneParticle, const int &p_cell, const Eigen::ArrayXXd &p_foncBasisCoef) const;
};
/**@}*/
}
#endif /*LOCALLINEARDISCRLASTDIMREGRESSION_H*/
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