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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 LOCALLINEARMATRIXOPERATION_H
#define LOCALLINEARMATRIXOPERATION_H
/** \file localLinearMatrixOperation.h
* \brief Develop the normal operators for regression, permits inversion by Choleski of \f$ A^tA x = A^t b \f$ and reconstruct the solution
* \author Xavier Warin
*/
#include <vector>
#include <array>
#include <memory>
#include <Eigen/Dense>
#include "StOpt/core/grids/InterpolatorSpectral.h"
namespace StOpt
{
/**
* \addtogroup LocalLinear
* @{
*/
/// \brief Regression matrix calculation for local linear functions
/// \param p_particles Particles used for regression
/// \param p_simToCell To each particle associates the cell it belongs to.
/// \param p_mesh Description of the mesh coordinates for each mesh
/// \return Regression matrix to calculate
Eigen::ArrayXXd localLinearMatrixCalculation(const Eigen::ArrayXXd &p_particles,
const Eigen::ArrayXi &p_simToCell,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh);
/// \brief Calculate the second member of the normal problem \f$ A^t b \f$
/// \param p_particles Particles used for regression
/// \param p_simToCell To each particle associates the cell it belongs to.
/// \param p_mesh Description of the mesh coordinates for each mesh
/// \param p_fToRegress simulations to regress
/// \return parameters of the regressed function (
Eigen::ArrayXXd localLinearSecondMemberCalculation(const Eigen::ArrayXXd &p_particles,
const Eigen::ArrayXi &p_simToCell,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh,
const Eigen::ArrayXXd &p_fToRegress);
/// \brief Calculate the second member of the normal problem \f$ A^t b \f$
/// \param p_particles Particles used for regression
/// \param p_SimulBelongingToCell simulations belonging to the cell
/// \param p_mesh Description of coordinates of the cell
/// \param p_fToRegress simulations to regress corresponding to particles belonging to the cell
/// \return parameters of the regressed function (
Eigen::ArrayXXd localLinearSecondMemberCalculationOneCell(const Eigen::ArrayXXd &p_particles,
const std::vector<int> &p_SimulBelongingToCell,
const Eigen::Ref<const Eigen::Array< std::array<double, 2 >, Eigen::Dynamic, 1 > > &p_mesh,
const Eigen::ArrayXXd &p_fToRegress);
/// \brief Choleski factorization for linear per cell representation of regressions
/// \param p_mat matrix is factorized \f$ LL^T = \f$ p_mat using superior part of p_mat. The \f$L\f$ part is put in p_mat except for diagonal
/// \param p_diag diagonal part of factorization
/// \param p_bSingular true for a cell is the corresponding matrix is singular
void localLinearCholeski(Eigen::ArrayXXd &p_mat, Eigen::ArrayXXd &p_diag, Eigen::Array<bool, Eigen::Dynamic, 1> &p_bSingular);
/// \brief Inversion using Choleski factorization (factorized matrix by localLinearCholeski)
/// \param p_mat Factorized matrix by Choleski ($L$ in lower part of p_mat)
/// \param p_diag diagonal of the factorized matrix
/// \param p_secMember Second member fo invert
/// \return solution of the inversion
Eigen::ArrayXd localLinearCholeskiInversion(const Eigen::ArrayXXd &p_mat, const Eigen::ArrayXXd &p_diag, const Eigen::ArrayXd &p_secMember);
/// \brief Reconstruct the conditional expectation for the simulations used in the optimization part (multiple functions possible)
/// \param p_particles Particles used for regression
/// \param p_simToCell To each particle associates the cell it belongs to.
/// \param p_mesh Description of the mesh coordinates for each mesh
/// \param p_foncBasisCoef Coefficients associated to each function basis (first dimension is the function number)
/// \return Reconstructed conditional expectation for each simulation (first dimension is the function number)
Eigen::ArrayXXd localLinearReconstruction(const Eigen::ArrayXXd &p_particles, const Eigen::ArrayXi &p_simToCell,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh,
const Eigen::ArrayXXd &p_foncBasisCoef);
/// \brief Reconstruct the conditional expectation for a given simulation used in the optimization part
/// \param p_isim Particle number used
/// \param p_particles Particles used for regression
/// \param p_simToCell To each particle associates the cell it belongs to.
/// \param p_mesh Description of the mesh coordinates for each mesh
/// \param p_foncBasisCoef Coefficients associated to the function basis
/// \return Reconstructed conditional expectation for the current simulation
double localLinearReconstructionASim(const int &p_isim, const Eigen::ArrayXXd &p_particles, const Eigen::ArrayXi &p_simToCell,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh,
const Eigen::ArrayXd &p_foncBasisCoef);
/// \brief Inversion using Choleski factorization (factorized matrix by localLinearCholeski) for only one cell
/// \param p_iCell Inversion for one cell
/// \param p_mat Factorized matrix by Choleski ($L$ in lower part of p_mat)
/// \param p_diag diagonal of the factorized matrix
/// \param p_secMember Second member to invert
/// \return solution of the inversion
Eigen::ArrayXd localLinearCholeskiInversionOneCell(const int &p_iCell, const Eigen::ArrayXXd &p_mat, const Eigen::ArrayXXd &p_diag, const Eigen::ArrayXd &p_secMember);
/// \brief Calculate conditional expectation for one particular particle
/// \param p_oneParticle One point where to calculate the conditional expectation (multiple functions possible)
/// \param p_mesh1D Discretization of the domain in each dimension
/// \param p_foncBasisCoef Coefficients associated to each function basis (first dimension is the function number)
/// \return Solution calculated for each function
Eigen::ArrayXd localLinearReconstructionOnePoint(const Eigen::ArrayXd &p_oneParticle,
const std::vector< std::shared_ptr< Eigen::ArrayXd > > &p_mesh1D,
const Eigen::ArrayXXd &p_foncBasisCoef);
/// \brief Permit to reconstruct a value for a state (pt_stock, uncertainty) : the uncertainty and pt_stock are
/// given and interpolator are given to interpolate function basis at pt_stock
/// \param p_oneParticle One uncertainty point where to calculate the function (using regression)
/// \param p_stock One stock point where to calculate the function
/// \param p_interpBaseFunc spectral interpolator to interpolate the basis functions used in regression at p_stock
/// \param p_mesh1D Discretization of the domain in each dimension
/// \return Solution calculated at (pt_stock, uncertainty)
double localLinearReconsOnePointSimStock(const Eigen::ArrayXd &p_oneParticle, const Eigen::ArrayXd &p_stock,
const std::vector< std::shared_ptr<InterpolatorSpectral> > &p_interpBaseFunc,
const std::vector< std::shared_ptr< Eigen::ArrayXd > > &p_mesh1D);
/// \brief Given a particle and the coordinates of the mesh it belongs to, reconstruct the regressed value
/// \param p_oneParticle The particle generated
/// \param p_mesh the mesh it belongs to (each coordinate of the particle should be inside the low and max coordinate of the cell in each dimension)
/// In each dimension gives the low and high coordinates values
/// \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 reconstructed values
Eigen::ArrayXd localLinearReconstructionOnePointOneCell(const Eigen::ArrayXd &p_oneParticle,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, 1 > &p_mesh,
const Eigen::ArrayXXd &p_foncBasisCoef);
/// \brief Calculate for each particule the cell it belongs too such that
/// on this cell the value regressed is above all linear reconstruction
/// using the linear representation on others cells : first step of a
/// convex representation of the conditional expectation
/// (see "Convex piecewise-linear fitting" by Alessandro Magnani ยท Stephen P. Boyd, Optim Eng (2009))
/// \param p_particles Particles used for regression
/// \param p_mesh Description of the mesh coordinates for each mesh
/// \param p_foncBasisCoef Coefficients associated to each function basis (first dimension is the function number)
/// \param p_nbCell number of regression cells for the process
/// \param p_simToCell To each particle associates the cell it belongs to.
void localLinearConvexHull(const Eigen::ArrayXXd &p_particles,
const Eigen::Array< std::array< double, 2>, Eigen::Dynamic, Eigen::Dynamic > &p_mesh,
const Eigen::ArrayXXd &p_foncBasisCoef,
const int &p_nbCell,
Eigen::ArrayXi &p_simToCell);
/**@}*/
}
#endif /*LOCALLINEARMATRIXOPERATION_H*/
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