// Copyright (c) 2012  INRIA Bordeaux Sud-Ouest (France), All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
// SPDX-License-Identifier: LGPL-3.0+
//
// Author(s)     : Gael Guennebaud

#ifndef CGAL_EIGEN_MATRIX_H
#define CGAL_EIGEN_MATRIX_H

#include <CGAL/basic.h> // include basic.h before testing #defines

#include <Eigen/Sparse>

namespace CGAL {

/*!
\ingroup PkgSolver

The class `Eigen_sparse_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type
<a href="http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html">`Eigen::SparseMatrix`</a>
that represents general matrices, be they symmetric or not.

\cgalModels `SparseLinearAlgebraTraits_d::Matrix`

\tparam T Number type.

\sa `CGAL::Eigen_vector<T>`
\sa `CGAL::Eigen_matrix<T>`
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
*/
template<class T>
struct Eigen_sparse_matrix
{
  // Public types
public:
  /// \name Types
  /// @{

  /// The internal matrix type from \ref thirdpartyEigen "Eigen".
  typedef Eigen::SparseMatrix<T>      EigenType;

  typedef T                           NT;
  /// @}

  // Public operations
public:
  /// Create a square matrix initialized with zeros.
  Eigen_sparse_matrix(std::size_t  dim,           ///< Matrix dimension.
                      bool is_symmetric = false)  ///< Symmetric/hermitian?
    :
      m_is_already_built(false),
      m_matrix(static_cast<int>(dim), static_cast<int>(dim))
  {
    CGAL_precondition(dim > 0);

    m_is_symmetric = is_symmetric;
    m_triplets.reserve(dim); // reserve memory for a regular 3D grid
  }

  /// Create a square matrix initialized with zeros.
  Eigen_sparse_matrix(int dim,                    ///< Matrix dimension.
                      bool is_symmetric = false)  ///< Symmetric/hermitian?
    : m_is_already_built(false),
      m_matrix(dim, dim)
  {
    CGAL_precondition(dim > 0);

    m_is_symmetric = is_symmetric;
    // reserve memory for a regular 3D grid
    m_triplets.reserve(dim);
  }

  /// Create a rectangular matrix initialized with zeros.
  ///
  /// \pre rows == columns if `is_symmetric` is true.
  Eigen_sparse_matrix(std::size_t rows,          ///< Number of rows.
                      std::size_t columns,       ///< Number of columns.
                      bool is_symmetric = false) ///< Symmetric/hermitian?
    : m_is_already_built(false),
      m_matrix(static_cast<int>(rows), static_cast<int>(columns))
  {
    CGAL_precondition(rows > 0);
    CGAL_precondition(columns > 0);
    if(m_is_symmetric)
    {
      CGAL_precondition(rows == columns);
    }

    m_is_symmetric = is_symmetric;
    // reserve memory for a regular 3D grid
    m_triplets.reserve(rows);
  }

  /// Delete this object and the wrapped matrix.
  ~Eigen_sparse_matrix() { }

  /// Create a rectangular matrix initialized with zeros.
  ///
  /// \pre rows == columns if `is_symmetric` is true.
  Eigen_sparse_matrix(int rows,                  ///< Number of rows.
                      int columns,               ///< Number of columns.
                      bool is_symmetric = false) ///< Symmetric/hermitian?
    : m_is_already_built(false),
      m_matrix(rows,columns)
  {
    CGAL_precondition(rows > 0);
    CGAL_precondition(columns > 0);
    if(is_symmetric)
    {
      CGAL_precondition(rows == columns);
    }

    m_is_symmetric = is_symmetric;
    // reserve memory for a regular 3D grid
    m_triplets.reserve(rows);
  }

  /// Return the matrix number of rows
  int row_dimension() const { return static_cast<int>(m_matrix.rows()); }
  /// Return the matrix number of columns
  int column_dimension() const { return static_cast<int>(m_matrix.cols()); }

  /// Write access to a matrix coefficient: a_ij <- val.
  ///
  /// Users can optimize calls to this function by setting 'new_coef' to `true`
  /// if the coefficient does not already exist in the matrix.
  ///
  /// \warning For symmetric matrices, `Eigen_sparse_matrix` only stores the lower triangle
  ///   and `set_coef()` does nothing if (i, j) belongs to the upper triangle.
  ///
  /// \pre 0 <= i < row_dimension().
  /// \pre 0 <= j < column_dimension().
  void set_coef(std::size_t i_, std::size_t j_, T val, bool new_coef = false)
  {
    int i = static_cast<int>(i_);
    int j = static_cast<int>(j_);
    CGAL_precondition(i < row_dimension());
    CGAL_precondition(j < column_dimension());

    if (m_is_symmetric && (j > i))
      return;

    if(m_is_already_built)
    {
      m_matrix.coeffRef(i,j) = val;
    }
    else
    {
      if(new_coef == false)
      {
        assemble_matrix();
        m_matrix.coeffRef(i,j) = val;
      }
      else
      {
        m_triplets.push_back(Triplet(i,j,val));
      }
    }
  }

  /// Write access to a matrix coefficient: a_ij <- a_ij + val.
  ///
  /// \warning For symmetric matrices, Eigen_sparse_matrix only stores the lower triangle
  /// `add_coef()` does nothing if (i, j) belongs to the upper triangle.
  ///
  /// \pre 0 <= i < row_dimension().
  /// \pre 0 <= j < column_dimension().
  void add_coef(int i, int j, T  val)
  {
    CGAL_precondition(i < row_dimension());
    CGAL_precondition(j < column_dimension());

    if(m_is_symmetric && (j > i))
      return;

    if(m_is_already_built)
      m_matrix.coeffRef(i,j) += val;
    else
      m_triplets.push_back(Triplet(i,j,val));
  }

  /// Read access to a matrix coefficient.
  ///
  /// \warning Complexity:
  /// - O(log(n)) if the matrix is already built.
  /// - O(n) if the matrix is not built.
  /// `n` being the number of entries in the matrix.
  ///
  /// \pre 0 <= i < row_dimension().
  /// \pre 0 <= j < column_dimension().
  NT get_coef (unsigned int i, unsigned int j) const
  {
    CGAL_precondition(i < row_dimension());
    CGAL_precondition(j < column_dimension());

    if(m_is_symmetric && j > i)
      std::swap(i, j);

    if (m_is_already_built)
      return m_matrix.coeffRef(i,j);
    else
    {
      NT val = 0;
      for(std::size_t t=0; t<m_triplets.size(); ++t)
      {
        if(m_triplets[t].col() == j &&
           m_triplets[t].row() == i)
          val += m_triplets[t].value();
      }
      return val;
    }
  }

  /// \cond SKIP_IN_MANUAL
  void assemble_matrix() const
  {
    m_matrix.setFromTriplets(m_triplets.begin(), m_triplets.end());
    m_is_already_built = true;
    m_triplets.clear(); // the matrix is built and will not be rebuilt
  }
  /// \endcond

  /// Return the internal matrix, with type `EigenType`.
  const EigenType& eigen_object() const
  {
    if(!m_is_already_built)
      assemble_matrix();

    // turns the matrix into compressed mode:
    //  -> release some memory
    //  -> required for some external solvers
    m_matrix.makeCompressed();
    return m_matrix;
  }

private:
  /// Eigen_sparse_matrix cannot be copied (yet)
  Eigen_sparse_matrix(const Eigen_sparse_matrix& rhs);
  Eigen_sparse_matrix& operator=(const Eigen_sparse_matrix& rhs);

  // Fields
private:
  mutable bool m_is_already_built;

  typedef Eigen::Triplet<T,int> Triplet;
  mutable std::vector<Triplet> m_triplets;

  mutable EigenType m_matrix;

  // Symmetric/hermitian?
  bool m_is_symmetric;
}; // Eigen_sparse_matrix

/*!
\ingroup PkgSolver

The class `Eigen_sparse_symmetric_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type
<a href="http://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html">`Eigen::SparseMatrix` </a>

Since the matrix is symmetric, only the lower triangle part is stored.

\cgalModels `SparseLinearAlgebraTraits_d::Matrix`

\tparam T Number type.

\sa `CGAL::Eigen_vector<T>`
\sa `CGAL::Eigen_sparse_matrix<T>`
*/

template<class T>
struct Eigen_sparse_symmetric_matrix
  : public Eigen_sparse_matrix<T>
{
  /// Create a square *symmetric* matrix initialized with zeros.
  Eigen_sparse_symmetric_matrix(int dim)                  ///< Matrix dimension.
    : Eigen_sparse_matrix<T>(dim, true /* symmetric */)
  {
  }

  /// Create a square *symmetric* matrix initialized with zeros.
  ///
  /// \pre rows == columns.
  Eigen_sparse_symmetric_matrix(int rows,                 ///< Number of rows.
                                int columns)              ///< Number of columns.
    : Eigen_sparse_matrix<T>(rows, columns, true /* symmetric */)
  {
  }
};

/*!
\ingroup PkgSolver

The class `Eigen_matrix` is a wrapper around \ref thirdpartyEigen "Eigen" matrix type
<a href="http://eigen.tuxfamily.org/dox/classEigen_1_1Matrix.html">`Eigen::Matrix`</a>.

\cgalModels `SvdTraits::Matrix` 

\tparam T Number type.

\sa `CGAL::Eigen_vector<T>`
\sa `CGAL::Eigen_sparse_matrix<T>`
\sa `CGAL::Eigen_sparse_symmetric_matrix<T>`
*/
template <class FT>
struct Eigen_matrix
  : public ::Eigen::Matrix<FT, ::Eigen::Dynamic, ::Eigen::Dynamic>
{
  /// The internal matrix type from \ref thirdpartyEigen "Eigen".
  typedef ::Eigen::Matrix<FT, ::Eigen::Dynamic, ::Eigen::Dynamic> EigenType;

  /// Construct a matrix with `nr` rows and `nc` columns.
  Eigen_matrix(std::size_t nr, std::size_t nc) : EigenType(nr, nc) { }

  /// Return the matrix number of rows.
  std::size_t number_of_rows() const { return this->rows(); }
  /// Return the matrix number of columns.
  std::size_t number_of_columns() const { return this->cols(); }

  /// Return the value of the matrix at position (i,j).
  FT operator()( std::size_t i , std::size_t j ) const { return EigenType::operator()(i,j); }

  /// Write access to a matrix coefficient: `a_ij` <- `val`.
  void set(std::size_t i, std::size_t j, FT value) { this->coeffRef(i,j) = value; }

  /// Return the internal matrix, with type `EigenType`.
  const EigenType& eigen_object() const { return static_cast<const EigenType&>(*this); }
};

} //namespace CGAL

#endif // CGAL_EIGEN_MATRIX_H