Added ARPACK support for standard and generalized eigenvalue problems. Currently self-adjoint only.

1 files changed, 799 insertions, 0 deletions

diff --git a/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
new file mode 100644
index 000000000..2f1bb7c50
--- /dev/null
+++ b/unsupported/Eigen/src/Eigenvalues/ArpackSelfAdjointEigenSolver.h
@@ -0,0 +1,799 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2012 David Harmon <dharmon@gmail.com>
+//
+// Eigen is free software; 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.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
+#define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_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
+   *
+   * 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 succesful, \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);
+}
+
+
+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(false, static_assertion<true>::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(false, static_assertion<true>::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
+