text: // This file is part of Eigen, a lightweight C++ template library
  // for linear algebra.
  //
  // Copyright (C) 2012 David Harmon <dharmon@gmail.com>
  //
  // 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 http://mozilla.org/MPL/2.0/.
  
  #ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
  #define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
  
  #include "../../../../Eigen/Dense"
  
  #include "./InternalHeaderCheck.h"
  
  namespace Eigen { 
  
  namespace internal {
    template<typename Scalar, typename RealScalar> struct arpack_wrapper;
    template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;
  }
  
  
  
  template<typename MatrixType, typename MatrixSolver=SimplicialLLT<MatrixType>, bool BisSPD=false>
  class ArpackGeneralizedSelfAdjointEigenSolver
  {
  public:
    //typedef typename MatrixSolver::MatrixType MatrixType;
  
    /** \brief Scalar type for matrices of type \p MatrixType. */
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::Index Index;
  
    /** \brief Real scalar type for \p MatrixType.
     *
     * This is just \c Scalar if #Scalar is real (e.g., \c float or
     * \c Scalar), and the type of the real part of \c Scalar if #Scalar is
     * complex.
     */
    typedef typename NumTraits<Scalar>::Real RealScalar;
  
    /** \brief Type for vector of eigenvalues as returned by eigenvalues().
     *
     * This is a column vector with entries of type #RealScalar.
     * The length of the vector is the size of \p nbrEigenvalues.
     */
    typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;
  
    /** \brief Default constructor.
     *
     * The default constructor is for cases in which the user intends to
     * perform decompositions via compute().
     *
     */
    ArpackGeneralizedSelfAdjointEigenSolver()
     : m_eivec(),
       m_eivalues(),
       m_isInitialized(false),
       m_eigenvectorsOk(false),
       m_nbrConverged(0),
       m_nbrIterations(0)
    { }
  
    /** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
     *
     * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
     *    computed. By default, the upper triangular part is used, but can be changed
     *    through the template parameter.
     * \param[in] B Self-adjoint matrix for the generalized eigenvalue problem.
     * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
     *    Must be less than the size of the input matrix, or an error is returned.
     * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
     *    respective meanings to find the largest magnitude , smallest magnitude,
     *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
     *    value can contain floating point value in string form, in which case the
     *    eigenvalues closest to this value will be found.
     * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
     * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
     *    means machine precision.
     *
     * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)
     * to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if
     * \p options equals #ComputeEigenvectors.
     *
     */
    ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A, const MatrixType& B,
                                            Index nbrEigenvalues, std::string eigs_sigma="LM",
                                 int options=ComputeEigenvectors, RealScalar tol=0.0)
      : m_eivec(),
        m_eivalues(),
        m_isInitialized(false),
        m_eigenvectorsOk(false),
        m_nbrConverged(0),
        m_nbrIterations(0)
    {
      compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
    }
  
    /** \brief Constructor; computes eigenvalues of given matrix.
     *
     * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
     *    computed. By default, the upper triangular part is used, but can be changed
     *    through the template parameter.
     * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
     *    Must be less than the size of the input matrix, or an error is returned.
     * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
     *    respective meanings to find the largest magnitude , smallest magnitude,
     *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
     *    value can contain floating point value in string form, in which case the
     *    eigenvalues closest to this value will be found.
     * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
     * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
     *    means machine precision.
     *
     * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)
     * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
     * \p options equals #ComputeEigenvectors.
     *
     */
  
    ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
                                            Index nbrEigenvalues, std::string eigs_sigma="LM",
                                 int options=ComputeEigenvectors, RealScalar tol=0.0)
      : m_eivec(),
        m_eivalues(),
        m_isInitialized(false),
        m_eigenvectorsOk(false),
        m_nbrConverged(0),
        m_nbrIterations(0)
    {
      compute(A, nbrEigenvalues, eigs_sigma, options, tol);
    }
  
  
    /** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
     *
     * \param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.
     * \param[in]  B  Selfadjoint matrix for generalized eigenvalues.
     * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
     *    Must be less than the size of the input matrix, or an error is returned.
     * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
     *    respective meanings to find the largest magnitude , smallest magnitude,
     *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
     *    value can contain floating point value in string form, in which case the
     *    eigenvalues closest to this value will be found.
     * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
     * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
     *    means machine precision.
     *
     * \returns    Reference to \c *this
     *
     * This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK.  The eigenvalues()
     * function can be used to retrieve them.  If \p options equals #ComputeEigenvectors,
     * then the eigenvectors are also computed and can be retrieved by
     * calling eigenvectors().
     *
     */
    ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A, const MatrixType& B,
                                                     Index nbrEigenvalues, std::string eigs_sigma="LM",
                                          int options=ComputeEigenvectors, RealScalar tol=0.0);
    
    /** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
     *
     * \param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.
     * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
     *    Must be less than the size of the input matrix, or an error is returned.
     * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
     *    respective meanings to find the largest magnitude , smallest magnitude,
     *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
     *    value can contain floating point value in string form, in which case the
     *    eigenvalues closest to this value will be found.
     * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
     * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
     *    means machine precision.
     *
     * \returns    Reference to \c *this
     *
     * This function computes the eigenvalues of \p A using ARPACK.  The eigenvalues()
     * function can be used to retrieve them.  If \p options equals #ComputeEigenvectors,
     * then the eigenvectors are also computed and can be retrieved by
     * calling eigenvectors().
     *
     */
    ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
                                                     Index nbrEigenvalues, std::string eigs_sigma="LM",
                                          int options=ComputeEigenvectors, RealScalar tol=0.0);
  
  
    /** \brief Returns the eigenvectors of given matrix.
     *
     * \returns  A const reference to the matrix whose columns are the eigenvectors.
     *
     * \pre The eigenvectors have been computed before.
     *
     * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
     * to eigenvalue number \f$ k \f$ as returned by eigenvalues().  The
     * eigenvectors are normalized to have (Euclidean) norm equal to one. If
     * this object was used to solve the eigenproblem for the selfadjoint
     * matrix \f$ A \f$, then the matrix returned by this function is the
     * matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$.
     * For the generalized eigenproblem, the matrix returned is the solution \f$ A V = D B V \f$
     *
     * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
     * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
     *
     * \sa eigenvalues()
     */
    const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const
    {
      eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
      eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
      return m_eivec;
    }
  
    /** \brief Returns the eigenvalues of given matrix.
     *
     * \returns A const reference to the column vector containing the eigenvalues.
     *
     * \pre The eigenvalues have been computed before.
     *
     * The eigenvalues are repeated according to their algebraic multiplicity,
     * so there are as many eigenvalues as rows in the matrix. The eigenvalues
     * are sorted in increasing order.
     *
     * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
     * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
     *
     * \sa eigenvectors(), MatrixBase::eigenvalues()
     */
    const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
    {
      eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
      return m_eivalues;
    }
  
    /** \brief Computes the positive-definite square root of the matrix.
     *
     * \returns the positive-definite square root of the matrix
     *
     * \pre The eigenvalues and eigenvectors of a positive-definite matrix
     * have been computed before.
     *
     * The square root of a positive-definite matrix \f$ A \f$ is the
     * positive-definite matrix whose square equals \f$ A \f$. This function
     * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
     * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
     *
     * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
     * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
     *
     * \sa operatorInverseSqrt(),
     *     \ref MatrixFunctions_Module "MatrixFunctions Module"
     */
    Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const
    {
      eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
      eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
      return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
    }
  
    /** \brief Computes the inverse square root of the matrix.
     *
     * \returns the inverse positive-definite square root of the matrix
     *
     * \pre The eigenvalues and eigenvectors of a positive-definite matrix
     * have been computed before.
     *
     * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
     * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
     * cheaper than first computing the square root with operatorSqrt() and
     * then its inverse with MatrixBase::inverse().
     *
     * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
     * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
     *
     * \sa operatorSqrt(), MatrixBase::inverse(),
     *     \ref MatrixFunctions_Module "MatrixFunctions Module"
     */
    Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const
    {
      eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
      eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
      return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
    }
  
    /** \brief Reports whether previous computation was successful.
     *
     * \returns \c Success if computation was successful, \c NoConvergence otherwise.
     */
    ComputationInfo info() const
    {
      eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
      return m_info;
    }
  
    size_t getNbrConvergedEigenValues() const
    { return m_nbrConverged; }
  
    size_t getNbrIterations() const
    { return m_nbrIterations; }
  
  protected:
    Matrix<Scalar, Dynamic, Dynamic> m_eivec;
    Matrix<Scalar, Dynamic, 1> m_eivalues;
    ComputationInfo m_info;
    bool m_isInitialized;
    bool m_eigenvectorsOk;
  
    size_t m_nbrConverged;
    size_t m_nbrIterations;
  };
  
  
  
  
  
  template<typename MatrixType, typename MatrixSolver, bool BisSPD>
  ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
      ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
  ::compute(const MatrixType& A, Index nbrEigenvalues,
            std::string eigs_sigma, int options, RealScalar tol)
  {
      MatrixType B(0,0);
      compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
      
      return *this;
  }
  
  
  template<typename MatrixType, typename MatrixSolver, bool BisSPD>
  ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
      ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>
  ::compute(const MatrixType& A, const MatrixType& B, Index nbrEigenvalues,
            std::string eigs_sigma, int options, RealScalar tol)
  {
    eigen_assert(A.cols() == A.rows());
    eigen_assert(B.cols() == B.rows());
    eigen_assert(B.rows() == 0 || A.cols() == B.rows());
    eigen_assert((options &~ (EigVecMask | GenEigMask)) == 0
              && (options & EigVecMask) != EigVecMask
              && "invalid option parameter");
  
    bool isBempty = (B.rows() == 0) || (B.cols() == 0);
  
    // For clarity, all parameters match their ARPACK name
    //
    // Always 0 on the first call
    //
    int ido = 0;
  
    int n = (int)A.cols();
  
    // User options: "LA", "SA", "SM", "LM", "BE"
    //
    char whch[3] = "LM";
      
    // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }
    //
    RealScalar sigma = 0.0;
  
    if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))
    {
        eigs_sigma[0] = toupper(eigs_sigma[0]);
        eigs_sigma[1] = toupper(eigs_sigma[1]);
  
        // In the following special case we're going to invert the problem, since solving
        // for larger magnitude is much much faster
        // i.e., if 'SM' is specified, we're going to really use 'LM', the default
        //
        if (eigs_sigma.substr(0,2) != "SM")
        {
            whch[0] = eigs_sigma[0];
            whch[1] = eigs_sigma[1];
        }
    }
    else
    {
        eigen_assert(false && "Specifying clustered eigenvalues is not yet supported!");
  
        // If it's not scalar values, then the user may be explicitly
        // specifying the sigma value to cluster the evs around
        //
        sigma = atof(eigs_sigma.c_str());
  
        // If atof fails, it returns 0.0, which is a fine default
        //
    }
  
    // "I" means normal eigenvalue problem, "G" means generalized
    //
    char bmat[2] = "I";
    if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))
        bmat[0] = 'G';
  
    // Now we determine the mode to use
    //
    int mode = (bmat[0] == 'G') + 1;
    if (eigs_sigma.substr(0,2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))
    {
        // We're going to use shift-and-invert mode, and basically find
        // the largest eigenvalues of the inverse operator
        //
        mode = 3;
    }
  
    // The user-specified number of eigenvalues/vectors to compute
    //
    int nev = (int)nbrEigenvalues;
  
    // Allocate space for ARPACK to store the residual
    //
    Scalar *resid = new Scalar[n];
  
    // Number of Lanczos vectors, must satisfy nev < ncv <= n
    // Note that this indicates that nev != n, and we cannot compute
    // all eigenvalues of a mtrix
    //
    int ncv = std::min(std::max(2*nev, 20), n);
  
    // The working n x ncv matrix, also store the final eigenvectors (if computed)
    //
    Scalar *v = new Scalar[n*ncv];
    int ldv = n;
  
    // Working space
    //
    Scalar *workd = new Scalar[3*n];
    int lworkl = ncv*ncv+8*ncv; // Must be at least this length
    Scalar *workl = new Scalar[lworkl];
  
    int *iparam= new int[11];
    iparam[0] = 1; // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it
    iparam[2] = std::max(300, (int)std::ceil(2*n/std::max(ncv,1)));
    iparam[6] = mode; // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert
  
    // Used during reverse communicate to notify where arrays start
    //
    int *ipntr = new int[11]; 
  
    // Error codes are returned in here, initial value of 0 indicates a random initial
    // residual vector is used, any other values means resid contains the initial residual
    // vector, possibly from a previous run
    //
    int info = 0;
  
    Scalar scale = 1.0;
    //if (!isBempty)
    //{
    //Scalar scale = B.norm() / std::sqrt(n);
    //scale = std::pow(2, std::floor(std::log(scale+1)));
    ////M /= scale;
    //for (size_t i=0; i<(size_t)B.outerSize(); i++)
    //    for (typename MatrixType::InnerIterator it(B, i); it; ++it)
    //        it.valueRef() /= scale;
    //}
  
    MatrixSolver OP;
    if (mode == 1 || mode == 2)
    {
        if (!isBempty)
            OP.compute(B);
    }
    else if (mode == 3)
    {
        if (sigma == 0.0)
        {
            OP.compute(A);
        }
        else
        {
            // Note: We will never enter here because sigma must be 0.0
            //
            if (isBempty)
            {
              MatrixType AminusSigmaB(A);
              for (Index i=0; i<A.rows(); ++i)
                  AminusSigmaB.coeffRef(i,i) -= sigma;
              
              OP.compute(AminusSigmaB);
            }
            else
            {
                MatrixType AminusSigmaB = A - sigma * B;
                OP.compute(AminusSigmaB);
            }
        }
    }
   
    if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
        std::cout << "Error factoring matrix" << std::endl;
  
    do
    {
      internal::arpack_wrapper<Scalar, RealScalar>::saupd(&ido, bmat, &n, whch, &nev, &tol, resid, 
                                                          &ncv, v, &ldv, iparam, ipntr, workd, workl,
                                                          &lworkl, &info);
  
      if (ido == -1 || ido == 1)
      {
        Scalar *in  = workd + ipntr[0] - 1;
        Scalar *out = workd + ipntr[1] - 1;
  
        if (ido == 1 && mode != 2)
        {
            Scalar *out2 = workd + ipntr[2] - 1;
            if (isBempty || mode == 1)
              Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
            else
              Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
            
            in = workd + ipntr[2] - 1;
        }
  
        if (mode == 1)
        {
          if (isBempty)
          {
            // OP = A
            //
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
          }
          else
          {
            // OP = L^{-1}AL^{-T}
            //
            internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);
          }
        }
        else if (mode == 2)
        {
          if (ido == 1)
            Matrix<Scalar, Dynamic, 1>::Map(in, n)  = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
          
          // OP = B^{-1} A
          //
          Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
        }
        else if (mode == 3)
        {
          // OP = (A-\sigmaB)B (\sigma could be 0, and B could be I)
          // The B * in is already computed and stored at in if ido == 1
          //
          if (ido == 1 || isBempty)
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
          else
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));
        }
      }
      else if (ido == 2)
      {
        Scalar *in  = workd + ipntr[0] - 1;
        Scalar *out = workd + ipntr[1] - 1;
  
        if (isBempty || mode == 1)
          Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
        else
          Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
      }
    } while (ido != 99);
  
    if (info == 1)
      m_info = NoConvergence;
    else if (info == 3)
      m_info = NumericalIssue;
    else if (info < 0)
      m_info = InvalidInput;
    else if (info != 0)
      eigen_assert(false && "Unknown ARPACK return value!");
    else
    {
      // Do we compute eigenvectors or not?
      //
      int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;
  
      // "A" means "All", use "S" to choose specific eigenvalues (not yet supported in ARPACK))
      //
      char howmny[2] = "A"; 
  
      // if howmny == "S", specifies the eigenvalues to compute (not implemented in ARPACK)
      //
      int *select = new int[ncv];
  
      // Final eigenvalues
      //
      m_eivalues.resize(nev, 1);
  
      internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec, howmny, select, m_eivalues.data(), v, &ldv,
                                                          &sigma, bmat, &n, whch, &nev, &tol, resid, &ncv,
                                                          v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);
  
      if (info == -14)
        m_info = NoConvergence;
      else if (info != 0)
        m_info = InvalidInput;
      else
      {
        if (rvec)
        {
          m_eivec.resize(A.rows(), nev);
          for (int i=0; i<nev; i++)
            for (int j=0; j<n; j++)
              m_eivec(j,i) = v[i*n+j] / scale;
        
          if (mode == 1 && !isBempty && BisSPD)
            internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());
  
          m_eigenvectorsOk = true;
        }
  
        m_nbrIterations = iparam[2];
        m_nbrConverged  = iparam[4];
  
        m_info = Success;
      }
  
      delete[] select;
    }
  
    delete[] v;
    delete[] iparam;
    delete[] ipntr;
    delete[] workd;
    delete[] workl;
    delete[] resid;
  
    m_isInitialized = true;
  
    return *this;
  }
  
  
  // Single precision
  //
  extern "C" void ssaupd_(int *ido, char *bmat, int *n, char *which,
      int *nev, float *tol, float *resid, int *ncv,
      float *v, int *ldv, int *iparam, int *ipntr,
      float *workd, float *workl, int *lworkl,
      int *info);
  
  extern "C" void sseupd_(int *rvec, char *All, int *select, float *d,
      float *z, int *ldz, float *sigma, 
      char *bmat, int *n, char *which, int *nev,
      float *tol, float *resid, int *ncv, float *v,
      int *ldv, int *iparam, int *ipntr, float *workd,
      float *workl, int *lworkl, int *ierr);
  
  // Double precision
  //
  extern "C" void dsaupd_(int *ido, char *bmat, int *n, char *which,
      int *nev, double *tol, double *resid, int *ncv,
      double *v, int *ldv, int *iparam, int *ipntr,
      double *workd, double *workl, int *lworkl,
      int *info);
  
  extern "C" void dseupd_(int *rvec, char *All, int *select, double *d,
      double *z, int *ldz, double *sigma, 
      char *bmat, int *n, char *which, int *nev,
      double *tol, double *resid, int *ncv, double *v,
      int *ldv, int *iparam, int *ipntr, double *workd,
      double *workl, int *lworkl, int *ierr);
  
  
  namespace internal {
  
  template<typename Scalar, typename RealScalar> struct arpack_wrapper
  {
    static inline void saupd(int *ido, char *bmat, int *n, char *which,
        int *nev, RealScalar *tol, Scalar *resid, int *ncv,
        Scalar *v, int *ldv, int *iparam, int *ipntr,
        Scalar *workd, Scalar *workl, int *lworkl, int *info)
    { 
      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
    }
  
    static inline void seupd(int *rvec, char *All, int *select, Scalar *d,
        Scalar *z, int *ldz, RealScalar *sigma,
        char *bmat, int *n, char *which, int *nev,
        RealScalar *tol, Scalar *resid, int *ncv, Scalar *v,
        int *ldv, int *iparam, int *ipntr, Scalar *workd,
        Scalar *workl, int *lworkl, int *ierr)
    {
      EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
    }
  };
  
  template <> struct arpack_wrapper<float, float>
  {
    static inline void saupd(int *ido, char *bmat, int *n, char *which,
        int *nev, float *tol, float *resid, int *ncv,
        float *v, int *ldv, int *iparam, int *ipntr,
        float *workd, float *workl, int *lworkl, int *info)
    {
      ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
    }
  
    static inline void seupd(int *rvec, char *All, int *select, float *d,
        float *z, int *ldz, float *sigma,
        char *bmat, int *n, char *which, int *nev,
        float *tol, float *resid, int *ncv, float *v,
        int *ldv, int *iparam, int *ipntr, float *workd,
        float *workl, int *lworkl, int *ierr)
    {
      sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
          workd, workl, lworkl, ierr);
    }
  };
  
  template <> struct arpack_wrapper<double, double>
  {
    static inline void saupd(int *ido, char *bmat, int *n, char *which,
        int *nev, double *tol, double *resid, int *ncv,
        double *v, int *ldv, int *iparam, int *ipntr,
        double *workd, double *workl, int *lworkl, int *info)
    {
      dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
    }
  
    static inline void seupd(int *rvec, char *All, int *select, double *d,
        double *z, int *ldz, double *sigma,
        char *bmat, int *n, char *which, int *nev,
        double *tol, double *resid, int *ncv, double *v,
        int *ldv, int *iparam, int *ipntr, double *workd,
        double *workl, int *lworkl, int *ierr)
    {
      dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr,
          workd, workl, lworkl, ierr);
    }
  };
  
  
  template<typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD>
  struct OP
  {
      static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out);
      static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs);
  };
  
  template<typename MatrixSolver, typename MatrixType, typename Scalar>
  struct OP<MatrixSolver, MatrixType, Scalar, true>
  {
    static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
  {
      // OP = L^{-1} A L^{-T}  (B = LL^T)
      //
      // First solve L^T out = in
      //
      Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
      Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
  
      // Then compute out = A out
      //
      Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);
  
      // Then solve L out = out
      //
      Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
      Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));
  }
  
    static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
  {
      // Solve L^T out = in
      //
      Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));
      Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);
  }
  
  };
  
  template<typename MatrixSolver, typename MatrixType, typename Scalar>
  struct OP<MatrixSolver, MatrixType, Scalar, false>
  {
    static inline void applyOP(MatrixSolver &OP, const MatrixType &A, int n, Scalar *in, Scalar *out)
  {
      eigen_assert(false && "Should never be in here...");
  }
  
    static inline void project(MatrixSolver &OP, int n, int k, Scalar *vecs)
  {
      eigen_assert(false && "Should never be in here...");
  }
  
  };
  
  } // end namespace internal
  
  } // end namespace Eigen
  
  #endif // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H
  
  