libdeal.ii-dev 8.4.2-2+b1 / usr / include / deal.II / lac / slepc_solver.h

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// Copyright (C) 2009 - 2016 by the deal.II authors
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// This file is part of the deal.II library.
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// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
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#ifndef dealii__slepc_solver_h
#define dealii__slepc_solver_h

#include <deal.II/base/config.h>

#ifdef DEAL_II_WITH_SLEPC

#  include <deal.II/base/std_cxx11/shared_ptr.h>
#  include <deal.II/lac/exceptions.h>
#  include <deal.II/lac/solver_control.h>
#  include <deal.II/lac/petsc_matrix_base.h>
#  include <deal.II/lac/slepc_spectral_transformation.h>

#  include <petscconf.h>
#  include <petscksp.h>
#  include <slepceps.h>

DEAL_II_NAMESPACE_OPEN

/**
 * Base namespace for solver classes using the SLEPc solvers which are
 * selected based on flags passed to the eigenvalue problem solver context.
 * Derived classes set the right flags to set the right solver.
 *
 * The SLEPc solvers are intended to be used for solving the generalized
 * eigenspectrum problem $(A-\lambda B)x=0$, for $x\neq0$; where $A$ is a
 * system matrix, $B$ is a mass matrix, and $\lambda, x$ are a set of
 * eigenvalues and eigenvectors respectively. The emphasis is on methods and
 * techniques appropriate for problems in which the associated matrices are
 * sparse. Most of the methods offered by the SLEPc library are projection
 * methods or other methods with similar properties; and wrappers are provided
 * to interface to SLEPc solvers that handle both of these problem sets.
 *
 * SLEPcWrappers can be implemented in application codes in the following way:
 * @code
 *  SolverControl solver_control (1000, 1e-9);
 *  SolverArnoldi system (solver_control, mpi_communicator);
 *  system.solve (A, B, lambda, x, size_of_spectrum);
 * @endcode
 * for the generalized eigenvalue problem $Ax=B\lambda x$, where the variable
 * <code>const unsigned int size_of_spectrum</code> tells SLEPc the number of
 * eigenvector/eigenvalue pairs to solve for. Additional options and solver
 * parameters can be passed to the SLEPc solvers before calling
 * <code>solve()</code>. For example, if the matrices of the general
 * eigenspectrum problem are not hermitian and the lower eigenvalues are
 * wanted only, the following code can be implemented before calling
 * <code>solve()</code>:
 * @code
 *  system.set_problem_type (EPS_NHEP);
 *  system.set_which_eigenpairs (EPS_SMALLEST_REAL);
 * @endcode
 * These options can also be set at the command line.
 *
 * See also <code>step-36</code> for a hands-on example.
 *
 * For cases when spectral transformations are used in conjunction with
 * Krylov-type solvers or Davidson-type eigensolvers are employed one can
 * additionally specify which linear solver and preconditioner to use. This
 * can be achieved as follows
 * @code
 *   PETScWrappers::PreconditionBoomerAMG::AdditionalData data;
 *   data.symmetric_operator = true;
 *   PETScWrappers::PreconditionBoomerAMG preconditioner(mpi_communicator, data);
 *   SolverControl linear_solver_control (dof_handler.n_dofs(), 1e-12,false,false);
 *   PETScWrappers::SolverCG  linear_solver(linear_solver_control,mpi_communicator);
 *   linear_solver.initialize(preconditioner);
 *   SolverControl solver_control (100, 1e-9,false,false);
 *   SLEPcWrappers::SolverKrylovSchur eigensolver(solver_control,mpi_communicator);
 *   SLEPcWrappers::TransformationShift spectral_transformation(mpi_communicator);
 *   spectral_transformation.set_solver(linear_solver);
 *   eigensolver.set_transformation(spectral_transformation);
 *   eigensolver.solve (stiffness_matrix,mass_matrix,eigenvalues,eigenfunctions,eigenfunctions.size());
 * @endcode
 *
 * In order to support this usage case, different from PETSc wrappers, the
 * classes in this namespace are written in such a way that the underlying
 * SLEPc objects are initialized in constructors. By doing so one also avoid
 * caching of different settings (such as target eigenvalue or type of the
 * problem); instead those are applied straight away when the corresponding
 * functions of the wrapper classes are called.
 *
 * An alternative implementation to the one above is to use the API internals
 * directly within the application code. In this way the calling sequence
 * requires calling several of SolverBase functions rather than just one. This
 * freedom is intended for use of the SLEPcWrappers that require a greater
 * handle on the eigenvalue problem solver context. See also the API of, for
 * example:
 * @code
 * template <typename OutputVector>
 * void
 * SolverBase::solve (const PETScWrappers::MatrixBase &A,
 *                   const PETScWrappers::MatrixBase &B,
 *                   std::vector<PetscScalar>        &eigenvalues,
 *                   std::vector<OutputVector>       &eigenvectors,
 *                   const unsigned int               n_eigenpairs)
 * { ... }
 * @endcode
 * as an example on how to do this.
 *
 * For further information and explanations on handling the
 * @ref SLEPcWrappers "SLEPcWrappers",
 * see also the
 * @ref PETScWrappers "PETScWrappers",
 * on which they depend.
 *
 * @ingroup SLEPcWrappers
 *
 * @author Toby D. Young 2008, 2009, 2010, 2011, 2013; and Rickard Armiento
 * 2008; and Denis Davydov 2015.
 *
 * @note Various tweaks and enhancements contributed by Eloy Romero and Jose
 * E. Roman 2009, 2010.
 */
namespace SLEPcWrappers
{

  /**
   * Base class for solver classes using the SLEPc solvers. Since solvers in
   * SLEPc are selected based on flags passed to a generic solver object,
   * basically all the actual solver calls happen in this class, and derived
   * classes simply set the right flags to select one solver or another, or to
   * set certain parameters for individual solvers.
   */
  class SolverBase
  {
  public:
    /**
     * Constructor. Takes the MPI communicator over which parallel
     * computations are to happen.
     */
    SolverBase (SolverControl &cn,
                const MPI_Comm &mpi_communicator);

    /**
     * Destructor.
     */
    virtual ~SolverBase ();

    /**
     * Composite method that solves the eigensystem $Ax=\lambda x$. The
     * eigenvector sent in has to have at least one element that we can use as
     * a template when resizing, since we do not know the parameters of the
     * specific vector class used (i.e. local_dofs for MPI vectors). However,
     * while copying eigenvectors, at least twice the memory size of
     * <tt>eigenvectors</tt> is being used (and can be more). To avoid doing
     * this, the fairly standard calling sequence executed here is used: Set
     * up matrices for solving; Actually solve the system; Gather the
     * solution(s).
     *
     * @note Note that the number of converged eigenvectors can be larger than
     * the number of eigenvectors requested; this is due to a round off error
     * (success) of the eigenproblem solver context. If this is found to be
     * the case we simply do not bother with more eigenpairs than requested,
     * but handle that it may be more than specified by ignoring any extras.
     * By default one eigenvector/eigenvalue pair is computed.
     */
    template <typename OutputVector>
    void
    solve (const PETScWrappers::MatrixBase &A,
           std::vector<PetscScalar>        &eigenvalues,
           std::vector<OutputVector>       &eigenvectors,
           const unsigned int               n_eigenpairs = 1);

    /**
     * Same as above, but here a composite method for solving the system $A
     * x=\lambda B x$, for real matrices, vectors, and values $A, B, x,
     * \lambda$.
     */
    template <typename OutputVector>
    void
    solve (const PETScWrappers::MatrixBase &A,
           const PETScWrappers::MatrixBase &B,
           std::vector<PetscScalar>        &eigenvalues,
           std::vector<OutputVector>       &eigenvectors,
           const unsigned int               n_eigenpairs = 1);

    /**
     * Same as above, but here a composite method for solving the system $A
     * x=\lambda B x$ with real matrices $A, B$ and imaginary eigenpairs $x,
     * \lambda$.
     */
    template <typename OutputVector>
    void
    solve (const PETScWrappers::MatrixBase &A,
           const PETScWrappers::MatrixBase &B,
           std::vector<double>             &real_eigenvalues,
           std::vector<double>             &imag_eigenvalues,
           std::vector<OutputVector>       &real_eigenvectors,
           std::vector<OutputVector>       &imag_eigenvectors,
           const unsigned int               n_eigenpairs = 1);

    /**
     * Set the initial vector for the solver.
     */
    void
    set_initial_vector
    (const PETScWrappers::VectorBase &this_initial_vector) DEAL_II_DEPRECATED;

    /**
     * Set the initial vector space for the solver.
     *
     * By default, SLEPc initializes the starting vector or the initial
     * subspace randomly.
     */
    template <typename Vector>
    void
    set_initial_space
    (const std::vector<Vector> &initial_space);

    /**
     * Set the spectral transformation to be used.
     */
    void
    set_transformation (SLEPcWrappers::TransformationBase &this_transformation);

    /**
     * Set target eigenvalues in the spectrum to be computed. By default, no
     * target is set.
     */
    void
    set_target_eigenvalue (const PetscScalar &this_target);

    /**
     * Indicate which part of the spectrum is to be computed. By default
     * largest magnitude eigenvalues are computed.
     *
     * @note For other allowed values see the SLEPc documentation.
     */
    void
    set_which_eigenpairs (EPSWhich set_which);

    /**
     * Specify the type of the eigenspectrum problem. This can be used to
     * exploit known symmetries of the matrices that make up the
     * standard/generalized eigenspectrum problem.  By default a non-Hermitian
     * problem is assumed.
     *
     * @note For other allowed values see the SLEPc documentation.
     */
    void
    set_problem_type (EPSProblemType set_problem);

    /**
     * Take the information provided from SLEPc and checks it against
     * deal.II's own SolverControl objects to see if convergence has been
     * reached.
     */
    void
    get_solver_state (const SolverControl::State state);

    /**
     * Exception. Standard exception.
     */
    DeclException0 (ExcSLEPcWrappersUsageError);

    /**
     * Exception. SLEPc error with error number.
     */
    DeclException1 (ExcSLEPcError,
                    int,
                    << "    An error with error number " << arg1
                    << " occurred while calling a SLEPc function");

    /**
     * Exception. Convergence failure on the number of eigenvectors.
     */
    DeclException2 (ExcSLEPcEigenvectorConvergenceMismatchError,
                    int, int,
                    << "    The number of converged eigenvectors is " << arg1
                    << " but " << arg2 << " were requested. ");

    /**
     * Access to the object that controls convergence.
     */
    SolverControl &control () const;

  protected:

    /**
     * Reference to the object that controls convergence of the iterative
     * solver.
     */
    SolverControl &solver_control;

    /**
     * Copy of the MPI communicator object to be used for the solver.
     */
    const MPI_Comm mpi_communicator;

    /**
     * Solve the linear system for <code>n_eigenpairs</code> eigenstates.
     * Parameter <code>n_converged</code> contains the actual number of
     * eigenstates that have  converged; this can be both fewer or more than
     * n_eigenpairs, depending on the SLEPc eigensolver used.
     */
    void
    solve (const unsigned int n_eigenpairs,
           unsigned int *n_converged);

    /**
     * Access the real parts of solutions for a solved eigenvector problem,
     * pair index solutions, $\text{index}\,\in\,0\hdots
     * \text{n\_converged}-1$.
     */
    void
    get_eigenpair (const unsigned int         index,
                   PetscScalar               &eigenvalues,
                   PETScWrappers::VectorBase &eigenvectors);

    /**
     * Access the real and imaginary parts of solutions for a solved
     * eigenvector problem, pair index solutions, $\text{index}\,\in\,0\hdots
     * \text{n\_converged}-1$.
     */
    void
    get_eigenpair (const unsigned int         index,
                   double                    &real_eigenvalues,
                   double                    &imag_eigenvalues,
                   PETScWrappers::VectorBase &real_eigenvectors,
                   PETScWrappers::VectorBase &imag_eigenvectors);

    /**
     * Initialize solver for the linear system $Ax=\lambda x$. (Note: this is
     * required before calling solve ())
     */
    void
    set_matrices (const PETScWrappers::MatrixBase &A);

    /**
     * Same as above, but here initialize solver for the linear system $A
     * x=\lambda B x$.
     */
    void
    set_matrices (const PETScWrappers::MatrixBase &A,
                  const PETScWrappers::MatrixBase &B);

  protected:

    /**
     * Objects for Eigenvalue Problem Solver.
     */
    EPS eps;

  private:
    /**
     * Convergence reason.
     */
    EPSConvergedReason reason;


    /**
     * A function that can be used in SLEPc as a callback to check on
     * convergence.
     *
     * @note This function is not used currently.
     */
    static
    int
    convergence_test (EPS          eps,
                      PetscScalar  real_eigenvalue,
                      PetscScalar  imag_eigenvalue,
                      PetscReal    residual_norm,
                      PetscReal   *estimated_error,
                      void        *solver_control);
  };

  /**
   * An implementation of the solver interface using the SLEPc Krylov-Schur
   * solver. Usage: All spectrum, all problem types, complex.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2008
   */
  class SolverKrylovSchur : public SolverBase
  {
  public:

    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {};

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverKrylovSchur (SolverControl        &cn,
                       const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                       const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  /**
   * An implementation of the solver interface using the SLEPc Arnoldi solver.
   * Usage: All spectrum, all problem types, complex.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2008, 2011
   */
  class SolverArnoldi : public SolverBase
  {
  public:
    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {
      /**
       * Constructor. By default, set the option of delayed
       * reorthogonalization to false, i.e. don't do it.
       */
      AdditionalData (const bool delayed_reorthogonalization = false);

      /**
       * Flag for delayed reorthogonalization.
       */
      bool delayed_reorthogonalization;
    };

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverArnoldi (SolverControl        &cn,
                   const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                   const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  /**
   * An implementation of the solver interface using the SLEPc Lanczos solver.
   * Usage: All spectrum, all problem types, complex.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2009; and Denis Davydov 2015;
   */
  class SolverLanczos : public SolverBase
  {
  public:
    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {
      /**
       * The type of reorthogonalization used during the Lanczos iteration.
       */
      EPSLanczosReorthogType reorthog;

      /**
       * Constructor. By default sets the type of reorthogonalization used
       * during the Lanczos iteration to full.
       */
      AdditionalData(const EPSLanczosReorthogType r  = EPS_LANCZOS_REORTHOG_FULL);
    };

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverLanczos (SolverControl        &cn,
                   const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                   const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  /**
   * An implementation of the solver interface using the SLEPc Power solver.
   * Usage: Largest values of spectrum only, all problem types, complex.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2010
   */
  class SolverPower : public SolverBase
  {
  public:
    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {};

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverPower (SolverControl        &cn,
                 const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                 const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  /**
   * An implementation of the solver interface using the SLEPc Davidson
   * solver. Usage: All problem types.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2010; Denis Davydov 2015
   */
  class SolverGeneralizedDavidson : public SolverBase
  {
  public:
    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {
      /**
       * Use double expansion in search subspace.
       */
      bool double_expansion;

      /**
       * Constructor. By default set double_expansion to false.
       */
      AdditionalData(bool double_expansion = false);
    };

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverGeneralizedDavidson (SolverControl        &cn,
                               const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                               const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  /**
   * An implementation of the solver interface using the SLEPc Jacobi-Davidson
   * solver. Usage: All problem types.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2013
   */
  class SolverJacobiDavidson : public SolverBase
  {
  public:
    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {};

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverJacobiDavidson (SolverControl        &cn,
                          const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                          const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };


  /**
   * An implementation of the solver interface using the SLEPc LAPACK direct
   * solver.
   *
   * @ingroup SLEPcWrappers
   *
   * @author Toby D. Young 2013
   */
  class SolverLAPACK : public SolverBase
  {
  public:

    /**
     * Standardized data struct to pipe additional data to the solver, should
     * it be needed.
     */
    struct AdditionalData
    {};

    /**
     * SLEPc solvers will want to have an MPI communicator context over which
     * computations are parallelized. By default, this carries the same
     * behaviour as the PETScWrappers, but you can change that.
     */
    SolverLAPACK (SolverControl        &cn,
                  const MPI_Comm       &mpi_communicator = PETSC_COMM_SELF,
                  const AdditionalData &data = AdditionalData());

  protected:

    /**
     * Store a copy of the flags for this particular solver.
     */
    const AdditionalData additional_data;
  };

  // --------------------------- inline and template functions -----------
  /**
   * This is declared here to make it possible to take a std::vector of
   * different PETScWrappers vector types
   */
  // todo: The logic of these functions can be simplified without breaking backward compatibility...

  template <typename OutputVector>
  void
  SolverBase::solve (const PETScWrappers::MatrixBase &A,
                     std::vector<PetscScalar>        &eigenvalues,
                     std::vector<OutputVector>       &eigenvectors,
                     const unsigned int               n_eigenpairs)
  {
    // Panic if the number of eigenpairs wanted is out of bounds.
    AssertThrow ((n_eigenpairs > 0) && (n_eigenpairs <= A.m ()),
                 ExcSLEPcWrappersUsageError());

    // Set the matrices of the problem
    set_matrices (A);

    // and solve
    unsigned int n_converged = 0;
    solve (n_eigenpairs, &n_converged);

    if (n_converged > n_eigenpairs)
      n_converged = n_eigenpairs;
    AssertThrow (n_converged == n_eigenpairs,
                 ExcSLEPcEigenvectorConvergenceMismatchError(n_converged, n_eigenpairs));

    AssertThrow (eigenvectors.size() != 0, ExcSLEPcWrappersUsageError());
    eigenvectors.resize (n_converged, eigenvectors.front());
    eigenvalues.resize (n_converged);

    for (unsigned int index=0; index<n_converged; ++index)
      get_eigenpair (index, eigenvalues[index], eigenvectors[index]);
  }

  template <typename OutputVector>
  void
  SolverBase::solve (const PETScWrappers::MatrixBase &A,
                     const PETScWrappers::MatrixBase &B,
                     std::vector<PetscScalar>        &eigenvalues,
                     std::vector<OutputVector>       &eigenvectors,
                     const unsigned int                  n_eigenpairs)
  {
    // Guard against incompatible matrix sizes:
    AssertThrow (A.m() == B.m (), ExcDimensionMismatch(A.m(), B.m()));
    AssertThrow (A.n() == B.n (), ExcDimensionMismatch(A.n(), B.n()));

    // Panic if the number of eigenpairs wanted is out of bounds.
    AssertThrow ((n_eigenpairs>0) && (n_eigenpairs<=A.m ()),
                 ExcSLEPcWrappersUsageError());

    // Set the matrices of the problem
    set_matrices (A, B);

    // and solve
    unsigned int n_converged = 0;
    solve (n_eigenpairs, &n_converged);

    if (n_converged>=n_eigenpairs)
      n_converged = n_eigenpairs;

    AssertThrow (n_converged==n_eigenpairs,
                 ExcSLEPcEigenvectorConvergenceMismatchError(n_converged, n_eigenpairs));
    AssertThrow (eigenvectors.size() != 0, ExcSLEPcWrappersUsageError());

    eigenvectors.resize (n_converged, eigenvectors.front());
    eigenvalues.resize (n_converged);

    for (unsigned int index=0; index<n_converged; ++index)
      get_eigenpair (index, eigenvalues[index], eigenvectors[index]);
  }

  template <typename OutputVector>
  void
  SolverBase::solve (const PETScWrappers::MatrixBase &A,
                     const PETScWrappers::MatrixBase &B,
                     std::vector<double>             &real_eigenvalues,
                     std::vector<double>             &imag_eigenvalues,
                     std::vector<OutputVector>       &real_eigenvectors,
                     std::vector<OutputVector>       &imag_eigenvectors,
                     const unsigned int                  n_eigenpairs)
  {
    // Guard against incompatible matrix sizes:
    AssertThrow (A.m() == B.m (), ExcDimensionMismatch(A.m(), B.m()));
    AssertThrow (A.n() == B.n (), ExcDimensionMismatch(A.n(), B.n()));

    // and incompatible eigenvalue/eigenvector sizes
    AssertThrow (real_eigenvalues.size() == imag_eigenvalues.size(),
                 ExcDimensionMismatch(real_eigenvalues.size(), imag_eigenvalues.size()));
    AssertThrow (real_eigenvectors.size() == imag_eigenvectors.size (),
                 ExcDimensionMismatch(real_eigenvectors.size(), imag_eigenvectors.size()));

    // Panic if the number of eigenpairs wanted is out of bounds.
    AssertThrow ((n_eigenpairs>0) && (n_eigenpairs<=A.m ()),
                 ExcSLEPcWrappersUsageError());

    // Set the matrices of the problem
    set_matrices (A, B);

    // and solve
    unsigned int n_converged = 0;
    solve (n_eigenpairs, &n_converged);

    if (n_converged>=n_eigenpairs)
      n_converged = n_eigenpairs;

    AssertThrow (n_converged==n_eigenpairs,
                 ExcSLEPcEigenvectorConvergenceMismatchError(n_converged, n_eigenpairs));
    AssertThrow ((real_eigenvectors.size()!=0) && (imag_eigenvectors.size()!=0),
                 ExcSLEPcWrappersUsageError());

    real_eigenvectors.resize (n_converged, real_eigenvectors.front());
    imag_eigenvectors.resize (n_converged, imag_eigenvectors.front());
    real_eigenvalues.resize (n_converged);
    imag_eigenvalues.resize (n_converged);

    for (unsigned int index=0; index<n_converged; ++index)
      get_eigenpair (index,
                     real_eigenvalues[index], imag_eigenvalues[index],
                     real_eigenvectors[index], imag_eigenvectors[index]);
  }

  template <typename Vector>
  void
  SolverBase::set_initial_space(const std::vector<Vector> &this_initial_space)
  {
    int ierr;
    std::vector<Vec> vecs(this_initial_space.size());

    for (unsigned int i = 0; i < this_initial_space.size(); i++)
      {
        Assert(this_initial_space[i].l2_norm()>0.0,
               ExcMessage("Initial vectors should be nonzero."));
        vecs[i] = this_initial_space[i];
      }

    // if the eigensolver supports only a single initial vector, but several
    // guesses are provided, then all except the first one will be discarded.
    // One could still build a vector that is rich in the directions of all guesses,
    // by taking a linear combination of them. (TODO: make function virtual?)

#if DEAL_II_PETSC_VERSION_LT(3,1,0)
    ierr = EPSSetInitialVector (eps, &vecs[0]);
#else
    ierr = EPSSetInitialSpace (eps, vecs.size(), &vecs[0]);
#endif
    AssertThrow (ierr == 0, ExcSLEPcError(ierr));
  }

}

DEAL_II_NAMESPACE_CLOSE

#endif // DEAL_II_WITH_SLEPC

/*----------------------------   slepc_solver.h  ---------------------------*/

#endif

/*----------------------------   slepc_solver.h  ---------------------------*/