text: // Copyright (C) 2016-2019 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 DENSE_CHOLESKY_H
  #define DENSE_CHOLESKY_H
  
  #include <Eigen/Core>
  #include <Eigen/Cholesky>
  #include <stdexcept>
  #include "../Util/CompInfo.h"
  
  namespace Spectra {
  
  
  ///
  /// \ingroup MatOp
  ///
  /// This class defines the operations related to Cholesky decomposition on a
  /// positive definite matrix, \f$B=LL'\f$, where \f$L\f$ is a lower triangular
  /// matrix. It is mainly used in the SymGEigsSolver generalized eigen solver
  /// in the Cholesky decomposition mode.
  ///
  template <typename Scalar, int Uplo = Eigen::Lower>
  class DenseCholesky
  {
  private:
      typedef Eigen::Index Index;
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> Matrix;
      typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1> Vector;
      typedef Eigen::Map<const Matrix> MapConstMat;
      typedef Eigen::Map<const Vector> MapConstVec;
      typedef Eigen::Map<Vector> MapVec;
      typedef const Eigen::Ref<const Matrix> ConstGenericMatrix;
  
      const Index m_n;
      Eigen::LLT<Matrix, Uplo> m_decomp;
      int m_info;  // status of the decomposition
  
  public:
      ///
      /// Constructor to create the matrix operation object.
      ///
      /// \param mat An **Eigen** matrix object, whose type can be
      /// `Eigen::Matrix<Scalar, ...>` (e.g. `Eigen::MatrixXd` and
      /// `Eigen::MatrixXf`), or its mapped version
      /// (e.g. `Eigen::Map<Eigen::MatrixXd>`).
      ///
      DenseCholesky(ConstGenericMatrix& mat) :
          m_n(mat.rows()), m_info(NOT_COMPUTED)
      {
          if(mat.rows() != mat.cols())
              throw std::invalid_argument("DenseCholesky: matrix must be square");
  
          m_decomp.compute(mat);
          m_info = (m_decomp.info() == Eigen::Success) ?
                   SUCCESSFUL :
                   NUMERICAL_ISSUE;
      }
  
      ///
      /// Returns the number of rows of the underlying matrix.
      ///
      Index rows() const { return m_n; }
      ///
      /// Returns the number of columns of the underlying matrix.
      ///
      Index cols() const { return m_n; }
  
      ///
      /// Returns the status of the computation.
      /// The full list of enumeration values can be found in \ref Enumerations.
      ///
      int info() const { return m_info; }
  
      ///
      /// Performs the lower triangular solving operation \f$y=L^{-1}x\f$.
      ///
      /// \param x_in  Pointer to the \f$x\f$ vector.
      /// \param y_out Pointer to the \f$y\f$ vector.
      ///
      // y_out = inv(L) * x_in
      void lower_triangular_solve(const Scalar* x_in, Scalar* y_out) const
      {
          MapConstVec x(x_in,  m_n);
          MapVec      y(y_out, m_n);
          y.noalias() = m_decomp.matrixL().solve(x);
      }
  
      ///
      /// Performs the upper triangular solving operation \f$y=(L')^{-1}x\f$.
      ///
      /// \param x_in  Pointer to the \f$x\f$ vector.
      /// \param y_out Pointer to the \f$y\f$ vector.
      ///
      // y_out = inv(L') * x_in
      void upper_triangular_solve(const Scalar* x_in, Scalar* y_out) const
      {
          MapConstVec x(x_in,  m_n);
          MapVec      y(y_out, m_n);
          y.noalias() = m_decomp.matrixU().solve(x);
      }
  };
  
  
  } // namespace Spectra
  
  #endif // DENSE_CHOLESKY_H
  