text: // Copyright (C) 2016-2018 Yixuan Qiu <yixuan.qiu@cos.name>
  //
  // This Source Code Form is subject to the terms of the Mozilla
  // Public License v. 2.0. If a copy of the MPL was not distributed
  // with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
  
  #ifndef SPARSE_GEN_REAL_SHIFT_SOLVE_H
  #define SPARSE_GEN_REAL_SHIFT_SOLVE_H
  
  #include <Eigen/Core>
  #include <Eigen/SparseCore>
  #include <Eigen/SparseLU>
  #include <stdexcept>
  
  namespace Spectra {
  
  
  ///
  /// \ingroup MatOp
  ///
  /// This class defines the shift-solve operation on a sparse real matrix \f$A\f$,
  /// i.e., calculating \f$y=(A-\sigma I)^{-1}x\f$ for any real \f$\sigma\f$ and
  /// vector \f$x\f$. It is mainly used in the GenEigsRealShiftSolver eigen solver.
  ///
  template <typename Scalar,int Flags = 0, typename StorageIndex = int>
  class SparseGenRealShiftSolve
  {
  private:
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
      typedef Eigen::Map<const Vector> MapConstVec;
      typedef Eigen::Map<Vector> MapVec;
      typedef Eigen::SparseMatrix<Scalar, Flags, StorageIndex> SparseMatrix;
      typedef const Eigen::Ref<const SparseMatrix> ConstGenericSparseMatrix;
  
      ConstGenericSparseMatrix m_mat;
      const int m_n;
      Eigen::SparseLU<SparseMatrix> m_solver;
  
  public:
      ///
      /// Constructor to create the matrix operation object.
      ///
      /// \param mat An **Eigen** sparse matrix object, whose type can be
      /// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
      /// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
      ///
      SparseGenRealShiftSolve(ConstGenericSparseMatrix& mat) :
          m_mat(mat), m_n(mat.rows())
      {
          if(mat.rows() != mat.cols())
              throw std::invalid_argument("SparseGenRealShiftSolve: matrix must be square");
      }
  
      ///
      /// Return the number of rows of the underlying matrix.
      ///
      int rows() const { return m_n; }
      ///
      /// Return the number of columns of the underlying matrix.
      ///
      int cols() const { return m_n; }
  
      ///
      /// Set the real shift \f$\sigma\f$.
      ///
      void set_shift(Scalar sigma)
      {
          SparseMatrix I(m_n, m_n);
          I.setIdentity();
  
          m_solver.compute(m_mat - sigma * I);
      }
  
      ///
      /// Perform the shift-solve operation \f$y=(A-\sigma I)^{-1}x\f$.
      ///
      /// \param x_in  Pointer to the \f$x\f$ vector.
      /// \param y_out Pointer to the \f$y\f$ vector.
      ///
      // y_out = inv(A - sigma * I) * x_in
      void perform_op(const Scalar* x_in, Scalar* y_out) const
      {
          MapConstVec x(x_in,  m_n);
          MapVec      y(y_out, m_n);
          y.noalias() = m_solver.solve(x);
      }
  };
  
  
  } // namespace Spectra
  
  #endif // SPARSE_GEN_REAL_SHIFT_SOLVE_H
  