// ===========================================================================
//
//       Filename:  EMSchur3DBase.h
//
//        Created:  09/20/2013 04:35:57 PM
//       Compiler:  Tested with g++, icpc, and MSVC 2010
//
//         Author:  Trevor Irons (ti)
//
//   Organisation:  University of Utah,
//                  Colorado School of Mines
//                  US Geological Survey
//
//          Email:  Trevor.Irons@utah.edu
//
// ===========================================================================

/**
  @file
  @author   Trevor Irons
  @date     09/20/2013
  @version  $Id$
 **/
#pragma once

#ifndef  EMSCHUR3DBASE_INC
#define  EMSCHUR3DBASE_INC

#include <LemmaCore>
#include "EMSchur3DConfig.h"
#include <FDEM1D>


//#include "LemmaObject.h"
//#include "rectilineargrid.h"
//#include "RectilinearGridVTKExporter.h"
//#include "ASCIIParser.h"
//#include "AEMSurvey.h"
//#include "receiverpoints.h"
//#include "layeredearthem.h"
//#include "emearth1d.h"

#include "timer.h"
#include <Eigen/Sparse>

//#define  SPARSEMAJOR Eigen::ColMajor
#define  SPARSEMAJOR Eigen::RowMajor

// SPARSEMAJOR;
//typedef  Eigen::RowMajor  SPARSEMAJOR;

//#include "bicgstab.h"

// // Solvers
// #ifdef HAVE_PASTIX
// #include <Eigen/PaStiXSupport>
// #endif
//
// #ifdef HAVE_METIS
// #include <Eigen/MetisSupport>
// #endif
//
// #ifdef HAVE_SUPERLU
// #include <Eigen/SuperLUSupport>
// #endif
//
// #ifdef HAVE_SUPERLUMT
// #include <Eigen/SuperLUMTSupport>
// #endif
//
// #ifdef HAVE_SPQR
// #include <Eigen/SPQRSupport>
// #endif

// Cholmod Support won't compile typedef issue
// #ifdef HAVE_CHOLMOD
// #include <Eigen/CholmodSupport>
// #endif
//
// // Cholmod Support won't compile
// #ifdef HAVE_UMFPACK
// #include <Eigen/UmfPackSupport>
// #endif

namespace Lemma {

// Pardiso likes LOWER for Sym problem,
//         for non-symmetric, set both to 1
#define UPPER 1  // 1=true, 0=false
#define LOWER 1  // 1=true, 0=false

enum SOLVER{ SPARSELU, SimplicialLLT, SimplicialLDLT, BiCGStab, SparseQR };

/**
  \ingroup EMSchur3D
  \brief Provides a 3D solution to Maxwell's equations.
  \details 3D finite difference solution to maxwells equations
            using a SCHUR decomposition on a staggered grid.
  Performs a Schur decomposition on the vector scalar formulation of
  Maxwell's equations.
   \f[
  -\nabla^2 (\mathbf{A}) - \jmath \omega \mu \sigma  \mathbf{A} - \mu \sigma \nabla (\phi) = -  \mu  \mathbf{J}_s
   \f]

Which can be written in the functional form
\f[ \begin{pmatrix}
      -\nabla^2 + \jmath \omega \mu \sigma   & \mu \sigma \nabla  \\
       \nabla \cdot  & 0
    \end{pmatrix}
    \begin{pmatrix}   \mathbf{A} \\  \phi   \end{pmatrix}
     = \begin{pmatrix}      \mathbf{s}_E \\   0      \end{pmatrix}
\f]
Using the notation
\f[ \begin{pmatrix}
        \mathbf{C} & \mathbf{B} \\
        \mathbf{D} & \mathbf{0}
    \end{pmatrix}  \begin{pmatrix} \mathbf{A} \\ \phi \end{pmatrix} =
    \begin{pmatrix} \mathbf{s}_E \\ 0 \end{pmatrix}
\f]
Which is decomposed for seperate solutions to \f$ \mathbf{A}, \phi \f$ using a Schur decomposition
  \f[   \begin{matrix}
        \mathbf{D}\mathbf{C}^{-1}\mathbf{B} \phi & = \mathbf{D} \mathbf{C}^{-1} \mathbf{s}_E \\
        \mathbf{C}\mathbf{A}                     & = \mathbf{s}_E - \mathbf{G} \phi
        \end{matrix}
  \f]

Where \f$ \mathbf{B} = \mu \sigma \mathbf{D}^T \f$. Additional algorithmic details may be found at
@verbatim
@inproceedings{doi:10.1190/segam2012-0896.1,
  author = {Trevor Irons and Yaoguo Li and Jason R. McKenna},
  title = {3D frequency-domain electromagnetics modeling using decoupled scalar and vector potentials},
  booktitle = {SEG Technical Program Expanded Abstracts 2012},
  chapter = {112},
  year = {2012},
  pages = {1-6},
  doi = {10.1190/segam2012-0896.1},
  URL = {http://library.seg.org/doi/abs/10.1190/segam2012-0896.1},
  eprint = {http://library.seg.org/doi/pdf/10.1190/segam2012-0896.1}
}
@endverbatim
*/

//template< class Solver >
class EMSchur3DBase : public LemmaObject {

    friend std::ostream &operator<<(std::ostream &stream,
            const EMSchur3DBase &ob);

    protected:

    //template<typename U>
    //friend class EMSchur3D;

    public:

    // ====================  LIFECYCLE     =======================

    /** Default protected constructor, use New */
    explicit EMSchur3DBase ( const ctor_key&  );

    /** Default protected constructor, use New */
    explicit EMSchur3DBase ( const YAML::Node& node, const ctor_key& );

    /** Default protected destructor, use Delete */
    virtual ~EMSchur3DBase ( );

    /**
     * Initialises antenna to contain no points, with no current
     * and no frequency. NumberOfTurns set to 1
     */
    static std::shared_ptr<EMSchur3DBase> NewSP();

    /*
     * Provides deep copy
     */
    //virtual std::shared_ptr<EMSchur3DBase> Clone() const ;

    /**
     *  Uses YAML to serialize this object.
     *  @return a YAML::Node
     */
    YAML::Node Serialize() const;

    /**
     *   Constructs an object from a YAML::Node.
     */
     static std::shared_ptr<EMSchur3DBase> DeSerialize( const YAML::Node& node );

    // ====================  OPERATORS     =======================

    // ====================  OPERATIONS    =======================

    /* Performs the solution
     * This is thread safe. TODO, but where should the results go? Just to file?
     * Who does the parsing? Actually I think this method is the wrong place to talk
     * about that. This is just a big red button. The details should be worked out in private
     * methods, that this could well call. Still though, where should the damn results go. What if
     * someone wants to use them *right now*, and not go through file IO. This is a good cause for
     * fixing the model class. So the result will be a final RectGrid (or Model) where the results live.
     * THEN users can call a seperate WriteToVTK or whatever based on that.
     */
    void Solve( );

    // ====================  ACCESS        =======================

    /** Sets the RectilinearGrid to use
     *  @param[in] Grid is a pointer to the Grid to be used.
     */
    void SetRectilinearGrid( std::shared_ptr<RectilinearGrid> Grid);

    /** Sets the RectilinearGrid to use
     *  @param[in] Grid is a pointer to the Grid to be used.
     */
    void SetRectilinearGrid( vtkRectilinearGrid* vtkGrid );

    /** Sets the RectilinearGrid to use
     *  @param[in] Grid is a pointer to the Grid to be used.
     */
    void SetAEMSurvey( std::shared_ptr<AEMSurvey> Survey);

    /** Sets the prefix for results files (.log and .vtr) the source fiducial is added as well
     */
    void SetResFileName(const std::string& filename);

    /** Sets the solver to use to invert the C matrix. This is done many times. If you are reusing the same matrix
        for numerous simulations, it may be benefitial to use the direct (SPARSELU) solver. For one off calculations the BiCGSTAB
        is a good choice. Default is SPARSELU.
     */
    void SetCSolver(const SOLVER& CSOLVER);

    /**
     *  Sets the LayredEarthEM model that will be used for the primary field calculation as well as deterimining the
     *  bacground conductivity file.
     @  @param[in] LayModel is a pointer to the LayeredEarthEM model to use.
     */
    void SetLayeredEarthEM( std::shared_ptr<LayeredEarthEM> LayModel );

    /**
     * Loads a MeshTools conductivity model.
     * @param[in] fname is the file to load.
     */
    void LoadMeshToolsConductivityModel( const std::string& fname );

    /**
     *  Writes out results to into a vtkRectilinearGrid file
     *  @param[in] fname is the file name that is created, the .vtr suffix is added.
     */
    void WriteVTKResults( const std::string& fname, Eigen::Ref<VectorXcr> A,
          Eigen::Ref<VectorXcr> Se, Eigen::Ref<VectorXcr> E0, Eigen::Ref<VectorXcr> E,
          Eigen::Ref<VectorXcr> Phi, Eigen::Ref<VectorXcr> ADiv, Eigen::Ref<VectorXcr> ADiv2,
          Eigen::Ref<VectorXcr> B
        );

    // ====================  INQUIRY       =======================

    /** Returns the name of the underlying class, similiar to Python's type */
    virtual std::string GetName() const {
        return this->CName;
    }

    protected:

    // ====================  LIFECYCLE     =======================

    //private:

    /** Builds the C matrix */
    void BuildC( Real*** sigmax, Real*** sigmay, Real*** sigmaz, const int& iw);

    /* Builds the C matrix as a block real system. Benefits of this are the availability of an
     *  LDL^T decomposition. Also, as complex number in C++ are templates and will necessarily have
     *  real and imaginary parts, this formulation will have a reduced cost, due to less computations
     *  with the zero valued imaginary parts (off-diagonals)
     *  The \f$C \in I^3\f$ matrix is instead written as
     *   [  C_r   C_i ] [ x_r ] = [ b_r ]
     *   [  C_i  -C_r ] [ x_i ]   [ b_i ]
     */
    //void BuildCReal( Real*** sigmax, Real*** sigmay, Real*** sigmaz, const int& iw);

    /** Builds the C matrix */
    void BuildCPreconditioner( const int& iw);

    /** Builds the C matrix */
    virtual void BuildCDirectSolver( )=0;

    /** Fills the actual points on the grid that 1D primary field calculations need to be made.
        @todo  This is a little stupid as all threads share the same points. Stupid in that right now
               this is done for every calculation. Not a huge amount of time is spent here, I suppose some extra memory
               though. We need to extend
               EmEARTH to be able to input a grid so that points are not explicitly needed like
               this. This requires some care as calcs are made on faces.
               Alternatively, the bins function of FieldPoints could be extended quite easily.
               This may be the way to do this.
     */
    void FillPoints( std::shared_ptr<FieldPoints> Points );

    /** Builds D/G
     */
    void BuildD( );

    /** Used to manage tradititional C 3D array */
    template <typename T>
    void Allocate3DScalar(T ***&Array, T init) {
        Array  = new T**[nx];
        for (int ix=0; ix<nx; ix++){
            Array[ix] = new T*[ny];
            for (int iy=0; iy<ny; iy++){
                Array[ix][iy]  = new T[nz];
                for (int iz=0; iz<nz; iz++) Array[ix][iy][iz] = init;
            }
        }
        return;
    }

    /** Used to manage tradititional C 3D array */
    template <typename T>
    void Delete3DScalar(T ***&Array) {
        for (int ix=0; ix<nx; ix++){
            for (int iy=0; iy<ny; iy++){
                delete [] Array[ix][iy];
            }
            delete [] Array[ix];
        }
        delete [] Array;
        Array = NULL;
        return;
    }

    /**
     * This is called just before solve and gets all shared objects ready to go
     */
    void Setup( );

    /** Solves a single source problem. This method is thread safe.
     *  @param[in] Source is the source term for generating primary fields
     *  @param[in] isource is the source index
     */
    virtual void SolveSource( std::shared_ptr< DipoleSource > Source , const int& isource)=0;

    /** Computes the primary field
     */
    void PrimaryField( std::shared_ptr<DipoleSource> Source, std::shared_ptr<FieldPoints> dpoint);

    /**
     *  Fills the vectors that are called in
     */
    void FillSourceTerms(  Eigen::Ref<VectorXcr>  ms,
                                        Eigen::Ref<VectorXcr> Se, Eigen::Ref<VectorXcr> E0,
                                        std::shared_ptr<FieldPoints> dpoint, const Real& omega );

    /** Computes the curl of A on the staggered grid
     */
    VectorXcr StaggeredGridCurl(Eigen::Ref<VectorXcr> A);

    // ====================  DATA MEMBERS  =========================

    /** Grid over which operators are active */
    std::shared_ptr<RectilinearGrid>                    Grid;

    /* Used to help dump results */
    //std::shared_ptr<RectilinearGridVTKExporter>         VTKGridExporter;

    /** Class containing information about the AEM survey */
    std::shared_ptr<AEMSurvey>                          Survey;

    std::shared_ptr<LayeredEarthEM>                     LayModel;

    /** Matrix objects representing discrete operators
     */
    Eigen::SparseMatrix<Complex, SPARSEMAJOR>*                  Cvec;
    Eigen::SparseMatrix<Complex, SPARSEMAJOR>                   D;

    /** Squeezed matrices for reduced phi grid
     */
    Eigen::SparseMatrix<Complex, SPARSEMAJOR>*                  Cvec_s;
    Eigen::SparseMatrix<Complex, SPARSEMAJOR>                   D_s;

    /** number of cells in x, set when RectilinearGrid is attached */
    int nx;

    /** number of cells in y, set when RectilinearGrid is attached */
    int ny;

    /** number of cells in z, set when RectilinearGrid is attached */
    int nz;

    /** number of fields/faces in x, unwrapped x */
    int unx;

    /** number of fields/faces in y, unwrapped y */
    int uny;

    /** number of fields/faces in z, unwrapped z */
    int unz;

    /** number of cell centres, unwrapped scalars */
    int uns;

    /** name for log files and VTK files */
    std::string ResFile;

    /** frequency of source */
    VectorXr Omegas;

    /** Conductivity model */
    //Complex ***sigma_jwe;
    Real ***sigma;

    /** Conductivity model minus reference model */
    //Complex ***sigmap;
    Real ***sigmap;

    /** rectilinear grid spacing in x */
    VectorXr hx;

    /** rectilinear grid spacing in y */
    VectorXr hy;

    /** rectilinear grid spacing in z */
    VectorXr hz;

    /** inverse of hx */
    VectorXr ihx;

    /** inverse of hx squared */
    VectorXr ihx2;

    /** inverse of hy */
    VectorXr ihy;

    /** inverse of hy squared */
    VectorXr ihy2;

    /** inverse of hz */
    VectorXr ihz;

    /** inverse of hz squared */
    VectorXr ihz2;

    /** Marker for air cells */
    VectorXi MAC;

    /** Marker for air cells */
    std::vector<int> idx;

    /** Dirichlet on low X */
    bool DirichletXLO = true;
    //bool DirichletXLO = false;

    bool DirichletXHI = true;
    //bool DirichletXHI = false;

    bool DirichletYLO = true;
    //bool DirichletYLO = false;

    bool DirichletYHI = true;
    //bool DirichletYHI = false;

    bool DirichletZLO = true;
    //bool DirichletZLO = false;

    bool DirichletZHI = true;
    //bool DirichletZHI = false;

    private:

        static constexpr auto CName = "EMSchur3DBase";

}; // -----  end of class  EMSchur3DBase  -----

}

#endif   // ----- #ifndef EMSCHUR3BASE_INC  -----