BelosGCRODRSolMgr.hpp

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// @HEADER
// *****************************************************************************
//                 Belos: Block Linear Solvers Package
//
// Copyright 2004 NTESS and the Belos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef BELOS_GCRODR_SOLMGR_HPP
#define BELOS_GCRODR_SOLMGR_HPP

 
#include "BelosConfigDefs.hpp"
#include "BelosOrthoManagerFactory.hpp"
#include "BelosSolverManager.hpp"
#include "BelosLinearProblem.hpp"
#include "BelosTypes.hpp"
 
#include "BelosGCRODRIter.hpp"
#include "BelosFGCRODRIter.hpp"
#include "BelosStatusTestMaxIters.hpp"
#include "BelosStatusTestGenResNorm.hpp"
#include "BelosStatusTestCombo.hpp"
#include "BelosStatusTestOutputFactory.hpp"
#include "BelosOutputManager.hpp"
#include "Teuchos_BLAS.hpp" // includes Teuchos_ConfigDefs.hpp
#include "Teuchos_LAPACK.hpp"
#include "Teuchos_as.hpp"
 
#ifdef BELOS_TEUCHOS_TIME_MONITOR
#  include "Teuchos_TimeMonitor.hpp"
#endif // BELOS_TEUCHOS_TIME_MONITOR
 
#if defined(HAVE_TEUCHOSCORE_CXX11)
#  include <type_traits>
#  if defined(HAVE_TEUCHOS_COMPLEX)
#include "Kokkos_Complex.hpp"
#  endif
#endif // defined(HAVE_TEUCHOSCORE_CXX11)

 
namespace Belos {



  class GCRODRSolMgrLinearProblemFailure : public BelosError {
    public:
      GCRODRSolMgrLinearProblemFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };

  class GCRODRSolMgrOrthoFailure : public BelosError {
    public:
      GCRODRSolMgrOrthoFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };

  class GCRODRSolMgrLAPACKFailure : public BelosError {
    public:
      GCRODRSolMgrLAPACKFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };

  class GCRODRSolMgrRecyclingFailure : public BelosError {
    public:
      GCRODRSolMgrRecyclingFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };


 
  template<class ScalarType, class MV, class OP, class DM = DefaultDenseMatrix<int,ScalarType>,
           const bool lapackSupportsScalarType =
           Belos::Details::LapackSupportsScalar<ScalarType>::value>
  class GCRODRSolMgr :
    public Details::SolverManagerRequiresLapack<ScalarType,MV,OP,DM>
  {
    static const bool requiresLapack =
      Belos::Details::LapackSupportsScalar<ScalarType>::value;
    typedef Details::SolverManagerRequiresLapack<ScalarType, MV, OP,DM,
                                                 requiresLapack> base_type;
 
  public:
    GCRODRSolMgr () :
      base_type ()
    {}
    GCRODRSolMgr (const Teuchos::RCP<LinearProblem<ScalarType,MV,OP,DM> >& problem,
                  const Teuchos::RCP<Teuchos::ParameterList>& pl) :
      base_type ()
    {}
    virtual ~GCRODRSolMgr () {}
  };

  template<class ScalarType, class MV, class OP, class DM>
  class GCRODRSolMgr<ScalarType, MV, OP, DM, true> :
    public Details::SolverManagerRequiresLapack<ScalarType, MV, OP, DM, true>
  {
 
#if defined(HAVE_TEUCHOSCORE_CXX11)
#  if defined(HAVE_TEUCHOS_COMPLEX)
      #if defined(HAVE_TEUCHOS_LONG_DOUBLE) 
        static_assert (std::is_same<ScalarType, std::complex<float> >::value ||
                       std::is_same<ScalarType, std::complex<double> >::value ||
                       std::is_same<ScalarType, Kokkos::complex<double> >::value ||
                       std::is_same<ScalarType, float>::value ||
                       std::is_same<ScalarType, double>::value ||
                       std::is_same<ScalarType, long double>::value,
                       "Belos::GCRODRSolMgr: ScalarType must be one of the four "
                       "types (S,D,C,Z) supported by LAPACK or long double (largely not impl'd).");
       #else
        static_assert (std::is_same<ScalarType, std::complex<float> >::value ||
                       std::is_same<ScalarType, std::complex<double> >::value ||
                       std::is_same<ScalarType, Kokkos::complex<double> >::value ||
                       std::is_same<ScalarType, float>::value ||
                       std::is_same<ScalarType, double>::value,
                       "Belos::GCRODRSolMgr: ScalarType must be one of the four "
                       "types (S,D,C,Z) supported by LAPACK.");
       #endif 
#  else
      #if defined(HAVE_TEUCHOS_LONG_DOUBLE) 
        static_assert (std::is_same<ScalarType, float>::value ||
                       std::is_same<ScalarType, double>::value ||
                       std::is_same<ScalarType, long double>::value,
                       "Belos::GCRODRSolMgr: ScalarType must be float, double or long double.  "
                       "Complex arithmetic support is currently disabled.  To "
                       "enable it, set Teuchos_ENABLE_COMPLEX=ON.");
      #else
        static_assert (std::is_same<ScalarType, float>::value ||
                       std::is_same<ScalarType, double>::value,
                       "Belos::GCRODRSolMgr: ScalarType must be float or double.  "
                       "Complex arithmetic support is currently disabled.  To "
                       "enable it, set Teuchos_ENABLE_COMPLEX=ON.");
      #endif  
#  endif // defined(HAVE_TEUCHOS_COMPLEX)
#endif // defined(HAVE_TEUCHOSCORE_CXX11)
 
  private:
    typedef MultiVecTraits<ScalarType,MV,DM> MVT;
    typedef OperatorTraits<ScalarType,MV,OP> OPT;
    typedef DenseMatTraits<ScalarType,DM>    DMT;
    typedef Teuchos::ScalarTraits<ScalarType> SCT;
    typedef typename Teuchos::ScalarTraits<ScalarType>::magnitudeType MagnitudeType;
    typedef Teuchos::ScalarTraits<MagnitudeType> MT;
    typedef OrthoManagerFactory<ScalarType, MV, OP, DM> ortho_factory_type;
 
  public:


     GCRODRSolMgr();

    GCRODRSolMgr (const Teuchos::RCP<LinearProblem<ScalarType,MV,OP,DM> > &problem,
                  const Teuchos::RCP<Teuchos::ParameterList> &pl);

    virtual ~GCRODRSolMgr() {};

    Teuchos::RCP<SolverManager<ScalarType, MV, OP, DM> > clone () const override {
      return Teuchos::rcp(new GCRODRSolMgr<ScalarType,MV,OP,DM,true>);
    }




    const LinearProblem<ScalarType,MV,OP,DM>& getProblem() const override {
      return *problem_;
    }

    Teuchos::RCP<const Teuchos::ParameterList> getValidParameters() const override;

    Teuchos::RCP<const Teuchos::ParameterList> getCurrentParameters() const override {
      return params_;
    }

    Teuchos::Array<Teuchos::RCP<Teuchos::Time> > getTimers() const {
      return Teuchos::tuple(timerSolve_);
    }

    MagnitudeType achievedTol() const override {
      return achievedTol_;
    }

    int getNumIters() const override {
      return numIters_;
    }

    bool isLOADetected() const override { return false; }




    void setProblem( const Teuchos::RCP<LinearProblem<ScalarType,MV,OP,DM> > &problem ) override {
      problem_ = problem;
      // Force the status tests to be rebuilt on the next solve() so that a
      // status test installed via setDebugStatusTest() is wired into sTest_.
      isSet_ = false;
    }

    void setParameters( const Teuchos::RCP<Teuchos::ParameterList> &params ) override;

    void setDebugStatusTest( const Teuchos::RCP<StatusTest<ScalarType,MV,OP,DM> > &debugStatusTest ) override {
      debugStatusTest_ = debugStatusTest;
      // Force the status-test tree to be rebuilt on the next solve() so the
      // debug test gets OR-combined into sTest_.
      isSet_ = false;
    }




    void reset( const ResetType type ) override {
      if ((type & Belos::Problem) && !Teuchos::is_null(problem_)) {
        bool set = problem_->setProblem();
        if  (!set)
          throw "Could not set problem.";
      }
      else if (type & Belos::RecycleSubspace) {
        keff = 0;
      }
    }




    ReturnType solve() override;



    std::string description() const override;

 
  private:
 
    // Called by all constructors; Contains init instructions common to all constructors
    void init();
 
    // Initialize solver state storage
    void initializeStateStorage();
 
    // Compute updated recycle space given existing recycle space and newly generated Krylov space
    void buildRecycleSpace2(Teuchos::RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_iter);
 
    void buildFlexibleRecycleSpace2(Teuchos::RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_iter);
 
    void computeGCRODRResidual();
 
    void updateSolutionWithUpdate(const Teuchos::RCP<MV>& update);
 
    //  Computes harmonic eigenpairs of projected matrix created during the priming solve.
    //  HH is the projected problem from the initial cycle of Gmres, it is (at least) of dimension m+1 x m.
    //  PP contains the harmonic eigenvectors corresponding to the recycledBlocks eigenvalues of smallest magnitude.
    //  The return value is the number of vectors needed to be stored, recycledBlocks or recycledBlocks+1.
    int getHarmonicVecs1(int m, const DM& HH, DM& PP);
 
    //  Computes harmonic eigenpairs of projected matrix created during one cycle.
    //  HH is the total block projected problem from the GCRO-DR algorithm, it is (at least) of dimension keff+m+1 x keff+m.
    //  VV is the Krylov vectors from the projected GMRES algorithm, which has (at least) m+1 vectors.
    //  PP contains the harmonic eigenvectors corresponding to the recycledBlocks eigenvalues of smallest magnitude.
    //  The return value is the number of vectors needed to be stored, recycledBlocks or recycledBlocks+1.
    int getHarmonicVecs2(int keff, int m, const DM& HH,
                         const Teuchos::RCP<const MV>& VV, DM& PP);
 
    int getFlexibleHarmonicVecs2(int keff, int m, const DM& HH,
                         const Teuchos::RCP<const MV>& VV, DM& PP);
 
    // Sort list of n floating-point numbers and return permutation vector
    void sort(std::vector<MagnitudeType>& dlist, int n, std::vector<int>& iperm);
 
    // Lapack interface
    Teuchos::LAPACK<int,ScalarType> lapack;
 
    // Linear problem.
    Teuchos::RCP<LinearProblem<ScalarType,MV,OP,DM> > problem_;
 
    // Output manager.
    Teuchos::RCP<OutputManager<ScalarType> > printer_;
    Teuchos::RCP<std::ostream> outputStream_;
 
    // Status test.
    Teuchos::RCP<StatusTest<ScalarType,MV,OP,DM> > sTest_;
    Teuchos::RCP<StatusTestMaxIters<ScalarType,MV,OP,DM> > maxIterTest_;
    Teuchos::RCP<StatusTest<ScalarType,MV,OP,DM> > convTest_;
    Teuchos::RCP<StatusTestGenResNorm<ScalarType,MV,OP,DM> > expConvTest_, impConvTest_;
    Teuchos::RCP<StatusTestOutput<ScalarType,MV,OP,DM> > outputTest_;
    Teuchos::RCP<StatusTest<ScalarType,MV,OP,DM> > debugStatusTest_;

    Teuchos::RCP<MatOrthoManager<ScalarType,MV,OP,DM> > ortho_;
 
    // Current parameter list.
    Teuchos::RCP<Teuchos::ParameterList> params_;
 
    // Default solver values.
    static constexpr double orthoKappa_default_ = 0.0;
    static constexpr int maxRestarts_default_ = 100;
    static constexpr int maxIters_default_ = 1000;
    static constexpr int numBlocks_default_ = 50;
    static constexpr int blockSize_default_ = 1;
    static constexpr int recycledBlocks_default_ = 5;
    static constexpr bool flexibleGCRODR_default_ = false;
    static constexpr int verbosity_default_ = Belos::Errors;
    static constexpr int outputStyle_default_ = Belos::General;
    static constexpr int outputFreq_default_ = -1;
    static constexpr const char * impResScale_default_ = "Norm of Preconditioned Initial Residual";
    static constexpr const char * expResScale_default_ = "Norm of Initial Residual";
    static constexpr const char * label_default_ = "Belos";
    static constexpr const char * orthoType_default_ = "ICGS";
 
    // Current solver values.
    MagnitudeType convTol_, orthoKappa_, achievedTol_;
    int maxRestarts_, maxIters_, numIters_;
    int verbosity_, outputStyle_, outputFreq_;
    bool isFlexible_;
    std::string orthoType_;
    std::string impResScale_, expResScale_;

    // Solver State Storage
    //
    // The number of blocks and recycle blocks (m and k, respectively)
    int numBlocks_, recycledBlocks_;
    // Current size of recycled subspace
    int keff;
    //
    // Residual vector
    Teuchos::RCP<MV> r_;
    //
    // Search space
    Teuchos::RCP<MV> V_;
    // Flexible correction basis for current cycle.
    Teuchos::RCP<MV> Z_;
    //
    // Recycled subspace and its image
    Teuchos::RCP<MV> U_, C_;
    // Auxiliary W recycle basis used by the FGCRODR harmonic projection.
    Teuchos::RCP<MV> W_, W1_;
    //
    // Updated recycle space and its image
    Teuchos::RCP<MV> U1_, C1_;
    //
    // Storage used in constructing harmonic Ritz values/vectors
    Teuchos::RCP<DM> H2_;
    Teuchos::RCP<DM> H_;
    Teuchos::RCP<DM> PP_;
    Teuchos::RCP<DM> HP_;
    std::vector<ScalarType> tau_;
    std::vector<ScalarType> work_;
    Teuchos::RCP<DM> R_;
    std::vector<int> ipiv_;
 
    // Timers.
    std::string label_;
    Teuchos::RCP<Teuchos::Time> timerSolve_;
 
    // Internal state variables.
    bool isSet_;
 
    // Have we generated or regenerated a recycle space yet this solve?
    bool builtRecycleSpace_;
  };
 
 
// Empty Constructor
template<class ScalarType, class MV, class OP, class DM>
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::GCRODRSolMgr():
  achievedTol_(0.0),
  numIters_(0)
{
  init ();
}
 
 
// Basic Constructor
template<class ScalarType, class MV, class OP, class DM>
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::
GCRODRSolMgr(const Teuchos::RCP<LinearProblem<ScalarType,MV,OP,DM> >& problem,
             const Teuchos::RCP<Teuchos::ParameterList>& pl):
  achievedTol_(0.0),
  numIters_(0)
{
  // Initialize local pointers to null, and initialize local variables
  // to default values.
  init ();
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    problem == Teuchos::null, std::invalid_argument,
    "Belos::GCRODRSolMgr constructor: The solver manager's "
    "constructor needs the linear problem argument 'problem' "
    "to be non-null.");
  problem_ = problem;
 
  // Set the parameters using the list that was passed in.  If null,
  // we defer initialization until a non-null list is set (by the
  // client calling setParameters(), or by calling solve() -- in
  // either case, a null parameter list indicates that default
  // parameters should be used).
  if (! pl.is_null ()) {
    setParameters (pl);
  }
}
 
// Common instructions executed in all constructors
template<class ScalarType, class MV, class OP, class DM>
void GCRODRSolMgr<ScalarType,MV,OP,DM,true>::init () {
  outputStream_ = Teuchos::rcpFromRef(std::cout);
  convTol_ = DefaultSolverParameters::convTol;
  orthoKappa_ = orthoKappa_default_;
  maxRestarts_ = maxRestarts_default_;
  maxIters_ = maxIters_default_;
  numBlocks_ = numBlocks_default_;
  recycledBlocks_ = recycledBlocks_default_;
  verbosity_ = verbosity_default_;
  outputStyle_ = outputStyle_default_;
  outputFreq_ = outputFreq_default_;
  isFlexible_ = flexibleGCRODR_default_;
  orthoType_ = orthoType_default_;
  impResScale_ = impResScale_default_;
  expResScale_ = expResScale_default_;
  label_ = label_default_;
  isSet_ = false;
  builtRecycleSpace_ = false;
  keff = 0;
  r_ = Teuchos::null;
  V_ = Teuchos::null;
  Z_ = Teuchos::null;
  U_ = Teuchos::null;
  C_ = Teuchos::null;
  W_ = Teuchos::null;
  W1_ = Teuchos::null;
  U1_ = Teuchos::null;
  C1_ = Teuchos::null;
  PP_ = Teuchos::null;
  HP_ = Teuchos::null;
  H2_ = Teuchos::null;
  R_ = Teuchos::null;
  H_ = Teuchos::null;
}
 
template<class ScalarType, class MV, class OP, class DM>
void GCRODRSolMgr<ScalarType,MV,OP,DM,true>::
setParameters (const Teuchos::RCP<Teuchos::ParameterList> &params)
{
  using Teuchos::isParameterType;
  using Teuchos::getParameter;
  using Teuchos::null;
  using Teuchos::ParameterList;
  using Teuchos::parameterList;
  using Teuchos::RCP;
  using Teuchos::rcp;
  using Teuchos::rcp_dynamic_cast;
  using Teuchos::rcpFromRef;
  using Teuchos::Exceptions::InvalidParameter;
  using Teuchos::Exceptions::InvalidParameterName;
  using Teuchos::Exceptions::InvalidParameterType;
 
  // The default parameter list contains all parameters that
  // GCRODRSolMgr understands, and none that it doesn't understand.
  RCP<const ParameterList> defaultParams = getValidParameters();
 
  // Create the internal parameter list if one doesn't already exist.
  //
  // (mfh 28 Feb 2011, 10 Mar 2011) At the time this code was written,
  // ParameterList did not have validators or validateParameters().
  // This is why the code below carefully validates the parameters one
  // by one and fills in defaults.  This code could be made a lot
  // shorter by using validators.  To do so, we would have to define
  // appropriate validators for all the parameters.  (This would more
  // or less just move all that validation code out of this routine
  // into to getValidParameters().)
  //
  // For an analogous reason, GCRODRSolMgr defines default parameter
  // values as class data, as well as in the default ParameterList.
  // This redundancy could be removed by defining the default
  // parameter values only in the default ParameterList (which
  // documents each parameter as well -- handy!).
  if (params_.is_null()) {
    params_ = parameterList (*defaultParams);
  } else {
    // A common case for setParameters() is for it to be called at the
    // beginning of the solve() routine.  This follows the Belos
    // pattern of delaying initialization until the last possible
    // moment (when the user asks Belos to perform the solve).  In
    // this common case, we save ourselves a deep copy of the input
    // parameter list.
    if (params_ != params) {
      // Make a deep copy of the input parameter list.  This allows
      // the caller to modify or change params later, without
      // affecting the behavior of this solver.  This solver will then
      // only change its internal parameters if setParameters() is
      // called again.
      params_ = parameterList (*params);
    }
 
    // Fill in any missing parameters and their default values.  Also,
    // throw an exception if the parameter list has any misspelled or
    // "extra" parameters.  If you don't like this behavior, you'll
    // want to replace the line of code below with your desired
    // validation scheme.  Note that Teuchos currently only implements
    // two options:
    //
    // 1. validateParameters() requires that params_ has all the
    //    parameters that the default list has, and none that it
    //    doesn't have.
    //
    // 2. validateParametersAndSetDefaults() fills in missing
    //    parameters in params_ using the default list, but requires
    //    that any parameter provided in params_ is also in the
    //    default list.
    //
    // Here is an easy way to ignore any "extra" or misspelled
    // parameters: Make a deep copy of the default list, fill in any
    // "missing" parameters from the _input_ list, and then validate
    // the input list using the deep copy of the default list.  We
    // show this in code:
    //
    // RCP<ParameterList> defaultCopy = parameterList (*getValidParameters ());
    // defaultCopy->validateParametersAndSetDefaults (params);
    // params->validateParametersAndSetDefaults (defaultCopy);
    //
    // This method is not entirely robust, because the input list may
    // have incorrect validators set for existing parameters in the
    // default list.  This would then cause "validation" of the
    // default list to throw an exception.  As a result, we've chosen
    // for now to be intolerant of misspellings and "extra" parameters
    // in the input list.
    params_->validateParametersAndSetDefaults (*defaultParams);
  }
 
  // Check for maximum number of restarts.
  if (params->isParameter ("Maximum Restarts")) {
    maxRestarts_ = params->get("Maximum Restarts", maxRestarts_default_);
 
    // Update parameter in our list.
    params_->set ("Maximum Restarts", maxRestarts_);
  }
 
  // Check for maximum number of iterations
  if (params->isParameter ("Maximum Iterations")) {
    maxIters_ = params->get ("Maximum Iterations", maxIters_default_);
 
    // Update parameter in our list and in status test.
    params_->set ("Maximum Iterations", maxIters_);
    if (! maxIterTest_.is_null())
      maxIterTest_->setMaxIters (maxIters_);
  }
 
  // Check for the maximum number of blocks.
  if (params->isParameter ("Num Blocks")) {
    numBlocks_ = params->get ("Num Blocks", numBlocks_default_);
    TEUCHOS_TEST_FOR_EXCEPTION(numBlocks_ <= 0, std::invalid_argument,
                       "Belos::GCRODRSolMgr: The \"Num Blocks\" parameter must "
                       "be strictly positive, but you specified a value of "
                       << numBlocks_ << ".");
    // Update parameter in our list.
    params_->set ("Num Blocks", numBlocks_);
  }
 
  // Check for the maximum number of blocks.
  if (params->isParameter ("Num Recycled Blocks")) {
    recycledBlocks_ = params->get ("Num Recycled Blocks",
                                   recycledBlocks_default_);
    TEUCHOS_TEST_FOR_EXCEPTION(recycledBlocks_ <= 0, std::invalid_argument,
                       "Belos::GCRODRSolMgr: The \"Num Recycled Blocks\" "
                       "parameter must be strictly positive, but you specified "
                       "a value of " << recycledBlocks_ << ".");
    TEUCHOS_TEST_FOR_EXCEPTION(recycledBlocks_ >= numBlocks_, std::invalid_argument,
                       "Belos::GCRODRSolMgr: The \"Num Recycled Blocks\" "
                       "parameter must be less than the \"Num Blocks\" "
                       "parameter, but you specified \"Num Recycled Blocks\" "
                       "= " << recycledBlocks_ << " and \"Num Blocks\" = "
                       << numBlocks_ << ".");
    // Update parameter in our list.
    params_->set("Num Recycled Blocks", recycledBlocks_);
  }
 
  if (params->isParameter("Flexible GCRODR")) {
    const bool newFlexible =
      params->get("Flexible GCRODR", flexibleGCRODR_default_);
    if (newFlexible != isFlexible_) {
      impConvTest_ = null;
      expConvTest_ = null;
      convTest_ = null;
      outputTest_ = null;
    }
    isFlexible_ = newFlexible;
    params_->set("Flexible GCRODR", isFlexible_);
  }
 
  // Check to see if the timer label changed.  If it did, update it in
  // the parameter list, and create a new timer with that label (if
  // Belos was compiled with timers enabled).
  if (params->isParameter ("Timer Label")) {
    std::string tempLabel = params->get ("Timer Label", label_default_);
 
    // Update parameter in our list and solver timer
    if (tempLabel != label_) {
      label_ = tempLabel;
      params_->set ("Timer Label", label_);
      std::string solveLabel = label_ + ": GCRODRSolMgr total solve time";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
      timerSolve_ = Teuchos::TimeMonitor::getNewCounter (solveLabel);
#endif
      if (ortho_ != Teuchos::null) {
        ortho_->setLabel( label_ );
      }
    }
  }
 
  // Check for a change in verbosity level
  if (params->isParameter ("Verbosity")) {
    if (isParameterType<int> (*params, "Verbosity")) {
      verbosity_ = params->get ("Verbosity", verbosity_default_);
    } else {
      verbosity_ = (int) getParameter<Belos::MsgType> (*params, "Verbosity");
    }
    // Update parameter in our list.
    params_->set ("Verbosity", verbosity_);
    // If the output manager (printer_) is null, then we will
    // instantiate it later with the correct verbosity.
    if (! printer_.is_null())
      printer_->setVerbosity (verbosity_);
  }
 
  // Check for a change in output style
  if (params->isParameter ("Output Style")) {
    if (isParameterType<int> (*params, "Output Style")) {
      outputStyle_ = params->get ("Output Style", outputStyle_default_);
    } else {
      outputStyle_ = (int) getParameter<OutputType> (*params, "Output Style");
    }
 
    // Update parameter in our list.
    params_->set ("Output Style", outputStyle_);
    // We will (re)instantiate the output status test afresh below.
    outputTest_ = null;
  }
 
  // Get the output stream for the output manager.
  //
  // While storing the output stream in the parameter list (either as
  // an RCP or as a nonconst reference) is convenient and safe for
  // programming, it makes it impossible to serialize the parameter
  // list, read it back in from the serialized representation, and get
  // the same output stream as before.  This is because output streams
  // may be arbitrary constructed objects.
  //
  // In case the user tried reading in the parameter list from a
  // serialized representation and the output stream can't be read
  // back in, we set the output stream to point to std::cout.  This
  // ensures reasonable behavior.
  if (params->isParameter ("Output Stream")) {
    try {
      outputStream_ = getParameter<RCP<std::ostream> > (*params, "Output Stream");
    } catch (InvalidParameter&) {
      outputStream_ = rcpFromRef (std::cout);
    }
    // We assume that a null output stream indicates that the user
    // doesn't want to print anything, so we replace it with a "black
    // hole" stream that prints nothing sent to it.  (We can't use a
    // null output stream, since the output manager always sends
    // things it wants to print to the output stream.)
    if (outputStream_.is_null()) {
      outputStream_ = rcp (new Teuchos::oblackholestream);
    }
    // Update parameter in our list.
    params_->set ("Output Stream", outputStream_);
    // If the output manager (printer_) is null, then we will
    // instantiate it later with the correct output stream.
    if (! printer_.is_null()) {
      printer_->setOStream (outputStream_);
    }
  }
 
  // frequency level
  if (verbosity_ & Belos::StatusTestDetails) {
    if (params->isParameter ("Output Frequency")) {
      outputFreq_ = params->get ("Output Frequency", outputFreq_default_);
    }
 
    // Update parameter in out list and output status test.
    params_->set("Output Frequency", outputFreq_);
    if (! outputTest_.is_null())
      outputTest_->setOutputFrequency (outputFreq_);
  }
 
  // Create output manager if we need to, using the verbosity level
  // and output stream that we fetched above.  We do this here because
  // instantiating an OrthoManager using OrthoManagerFactory requires
  // a valid OutputManager.
  if (printer_.is_null()) {
    printer_ = rcp (new OutputManager<ScalarType> (verbosity_, outputStream_));
  }
 
  // Get the orthogonalization manager name ("Orthogonalization").
  //
  // Getting default values for the orthogonalization manager
  // parameters ("Orthogonalization Parameters") requires knowing the
  // orthogonalization manager name.  Save it for later, and also
  // record whether it's different than before.
  OrthoManagerFactory<ScalarType, MV, OP, DM> factory;
  bool changedOrthoType = false;
  if (params->isParameter ("Orthogonalization")) {
    const std::string& tempOrthoType =
      params->get ("Orthogonalization", orthoType_default_);
    // Ensure that the specified orthogonalization type is valid.
    if (! factory.isValidName (tempOrthoType)) {
      std::ostringstream os;
      os << "Belos::GCRODRSolMgr: Invalid orthogonalization name \""
         << tempOrthoType << "\".  The following are valid options "
         << "for the \"Orthogonalization\" name parameter: ";
      factory.printValidNames (os);
      throw std::invalid_argument (os.str());
    }
    if (tempOrthoType != orthoType_) {
      changedOrthoType = true;
      orthoType_ = tempOrthoType;
      // Update parameter in our list.
      params_->set ("Orthogonalization", orthoType_);
    }
  }
 
  // Get any parameters for the orthogonalization ("Orthogonalization
  // Parameters").  If not supplied, the orthogonalization manager
  // factory will supply default values.
  //
  // NOTE (mfh 12 Jan 2011) For the sake of backwards compatibility,
  // if params has an "Orthogonalization Constant" parameter and the
  // DGKS orthogonalization manager is to be used, the value of this
  // parameter will override DGKS's "depTol" parameter.
  //
  // Users must supply the orthogonalization manager parameters as a
  // sublist (supplying it as an RCP<ParameterList> would make the
  // resulting parameter list not serializable).
  RCP<ParameterList> orthoParams;
  { // The nonmember function sublist() returns an RCP<ParameterList>,
    // which is what we want here.
    using Teuchos::sublist;
    // Abbreviation to avoid typos.
    const std::string paramName ("Orthogonalization Parameters");
 
    try {
      orthoParams = sublist (params_, paramName, true);
    } catch (InvalidParameter&) {
      // We didn't get the parameter list from params, so get a
      // default parameter list from the OrthoManagerFactory.  Modify
      // params_ so that it has the default parameter list, and set
      // orthoParams to ensure it's a sublist of params_ (and not just
      // a copy of one).
      params_->set (paramName, factory.getDefaultParameters (orthoType_));
      orthoParams = sublist (params_, paramName, true);
    }
  }
  TEUCHOS_TEST_FOR_EXCEPTION(orthoParams.is_null(), std::logic_error,
                             "Failed to get orthogonalization parameters.  "
                             "Please report this bug to the Belos developers.");
 
  // Instantiate a new MatOrthoManager subclass instance if necessary.
  // If not necessary, then tell the existing instance about the new
  // parameters.
  if (ortho_.is_null() || changedOrthoType) {
    // We definitely need to make a new MatOrthoManager, since either
    // we haven't made one yet, or we've changed orthogonalization
    // methods.  Creating the orthogonalization manager requires that
    // the OutputManager (printer_) already be initialized.
    ortho_ = factory.makeMatOrthoManager (orthoType_, null, printer_,
                                          label_, orthoParams);
  } else {
    // If the MatOrthoManager implements the ParameterListAcceptor
    // mix-in interface, we can propagate changes to its parameters
    // without reinstantiating the MatOrthoManager.
    //
    // We recommend that all MatOrthoManager subclasses implement
    // Teuchos::ParameterListAcceptor, but do not (yet) require this.
    typedef Teuchos::ParameterListAcceptor PLA;
    RCP<PLA> pla = rcp_dynamic_cast<PLA> (ortho_);
    if (pla.is_null()) {
      // Oops, it's not a ParameterListAcceptor.  We have to
      // reinstantiate the MatOrthoManager in order to pass in the
      // possibly new parameters.
      ortho_ = factory.makeMatOrthoManager (orthoType_, null, printer_,
                                            label_, orthoParams);
    } else {
      pla->setParameterList (orthoParams);
    }
  }
 
  // The DGKS orthogonalization accepts a "Orthogonalization Constant"
  // parameter (also called kappa in the code, but not in the
  // parameter list).  If its value is provided in the given parameter
  // list, and its value is positive, use it.  Ignore negative values.
  //
  // NOTE (mfh 12 Jan 2011) This overrides the "depTol" parameter that
  // may have been specified in "Orthogonalization Parameters".  We
  // retain this behavior for backwards compatibility.
  if (params->isParameter ("Orthogonalization Constant")) {
    MagnitudeType orthoKappa = orthoKappa_default_;
    if (params->isType<MagnitudeType> ("Orthogonalization Constant")) {
      orthoKappa = params->get ("Orthogonalization Constant", orthoKappa);
    }
    else {
      orthoKappa = params->get ("Orthogonalization Constant", orthoKappa_default_);
    }
 
    if (orthoKappa > 0) {
      orthoKappa_ = orthoKappa;
      // Update parameter in our list.
      params_->set("Orthogonalization Constant", orthoKappa_);
      // Only DGKS currently accepts this parameter.
      if (orthoType_ == "DGKS" && ! ortho_.is_null()) {
        typedef DGKSOrthoManager<ScalarType, MV, OP, DM> ortho_man_type;
        // This cast should always succeed; it's a bug
        // otherwise.  (If the cast fails, then orthoType_
        // doesn't correspond to the OrthoManager subclass
        // instance that we think we have, so we initialized the
        // wrong subclass somehow.)
        rcp_dynamic_cast<ortho_man_type>(ortho_)->setDepTol (orthoKappa_);
      }
    }
  }
 
  // Convergence
  typedef Belos::StatusTestCombo<ScalarType,MV,OP,DM>  StatusTestCombo_t;
  typedef Belos::StatusTestGenResNorm<ScalarType,MV,OP,DM>  StatusTestResNorm_t;
 
  // Check for convergence tolerance
  if (params->isParameter("Convergence Tolerance")) {
    if (params->isType<MagnitudeType> ("Convergence Tolerance")) {
      convTol_ = params->get ("Convergence Tolerance",
                              static_cast<MagnitudeType> (DefaultSolverParameters::convTol));
    }
    else {
      convTol_ = params->get ("Convergence Tolerance", DefaultSolverParameters::convTol);
    }
 
    // Update parameter in our list and residual tests.
    params_->set ("Convergence Tolerance", convTol_);
    if (! impConvTest_.is_null())
      impConvTest_->setTolerance (convTol_);
    if (! expConvTest_.is_null())
      expConvTest_->setTolerance (convTol_);
  }
 
  // Check for a change in scaling, if so we need to build new residual tests.
  if (params->isParameter ("Implicit Residual Scaling")) {
    std::string tempImpResScale =
      getParameter<std::string> (*params, "Implicit Residual Scaling");
 
    // Only update the scaling if it's different.
    if (impResScale_ != tempImpResScale) {
      ScaleType impResScaleType = convertStringToScaleType (tempImpResScale);
      impResScale_ = tempImpResScale;
 
      // Update parameter in our list and residual tests
      params_->set("Implicit Residual Scaling", impResScale_);
      // NOTE (mfh 28 Feb 2011) StatusTestImpResNorm only lets you
      // call defineScaleForm() once.  The code below attempts to call
      // defineScaleForm(); if the scale form has already been
      // defined, it constructs a new StatusTestImpResNorm instance.
      // StatusTestImpResNorm really should not expose the
      // defineScaleForm() method, since it's serving an
      // initialization purpose; all initialization should happen in
      // the constructor whenever possible.  In that case, the code
      // below could be simplified into a single (re)instantiation.
      if (! impConvTest_.is_null()) {
        try {
          impConvTest_->defineScaleForm (impResScaleType, Belos::TwoNorm);
        }
        catch (StatusTestError&) {
          // Delete the convergence test so it gets constructed again.
          impConvTest_ = null;
          convTest_ = null;
        }
      }
    }
  }
 
  if (params->isParameter("Explicit Residual Scaling")) {
    std::string tempExpResScale =
      getParameter<std::string> (*params, "Explicit Residual Scaling");
 
    // Only update the scaling if it's different.
    if (expResScale_ != tempExpResScale) {
      ScaleType expResScaleType = convertStringToScaleType (tempExpResScale);
      expResScale_ = tempExpResScale;
 
      // Update parameter in our list and residual tests
      params_->set("Explicit Residual Scaling", expResScale_);
      // NOTE (mfh 28 Feb 2011) See note above on the (re)construction
      // of StatusTestImpResNorm.
      if (! expConvTest_.is_null()) {
        try {
          expConvTest_->defineScaleForm (expResScaleType, Belos::TwoNorm);
        }
        catch (StatusTestError&) {
          // Delete the convergence test so it gets constructed again.
          expConvTest_ = null;
          convTest_ = null;
        }
      }
    }
  }
  //
  // Create iteration stopping criteria ("status tests") if we need
  // to, by combining three different stopping criteria.
  //
  // First, construct maximum-number-of-iterations stopping criterion.
  if (maxIterTest_.is_null())
    maxIterTest_ = rcp (new StatusTestMaxIters<ScalarType,MV,OP,DM> (maxIters_));
 
  if (isFlexible_) {
    // Flexible GCRODR stores the correction basis Z and computes updates
    // directly in solution space.  The generic explicit residual status
    // test machinery is not safe here unless it is made flexible-aware.
    // This follows BlockGmresSolMgr's flexible GMRES behavior: use the
    // native / implicit residual for convergence, then the solver manager
    // applies the final flexible update directly.
    if (impConvTest_.is_null()) {
      impConvTest_ = rcp (new StatusTestResNorm_t (convTol_));
      impConvTest_->defineScaleForm (convertStringToScaleType (impResScale_),
                                     Belos::TwoNorm);
    }
 
    expConvTest_ = impConvTest_;
    convTest_ = impConvTest_;
  }
  else {
    // Implicit residual test, using the native residual to determine if
    // convergence was achieved.
    if (impConvTest_.is_null()) {
      impConvTest_ = rcp (new StatusTestResNorm_t (convTol_));
      impConvTest_->defineScaleForm (convertStringToScaleType (impResScale_),
                                     Belos::TwoNorm);
    }
 
    // Explicit residual test once the native residual is below the tolerance.
    if (expConvTest_.is_null()) {
      expConvTest_ = rcp (new StatusTestResNorm_t (convTol_));
      expConvTest_->defineResForm (StatusTestResNorm_t::Explicit, Belos::TwoNorm);
      expConvTest_->defineScaleForm (convertStringToScaleType (expResScale_),
                                     Belos::TwoNorm);
    }
 
    // Convergence test first tests the implicit residual, then the
    // explicit residual if the implicit residual test passes.
    if (convTest_.is_null()) {
      convTest_ = rcp (new StatusTestCombo_t (StatusTestCombo_t::SEQ,
                                              impConvTest_,
                                              expConvTest_));
    }
  }
  // Construct the complete iteration stopping criterion:
  //
  // "Stop iterating if the maximum number of iterations has been
  // reached, or if the convergence test passes."
  sTest_ = rcp (new StatusTestCombo_t (StatusTestCombo_t::OR,
                                       maxIterTest_,
                                       convTest_));
 
  // Add a debug status test if one was provided (e.g. a wall-clock time limit).
  // OR-combining it into the top-level test lets it stop the solve; the
  // dispatch in solve() treats such a stop as an unconverged (recoverable)
  // termination.
  if (Teuchos::nonnull(debugStatusTest_)) {
    sTest_ = rcp (new StatusTestCombo_t (StatusTestCombo_t::OR,
                                         sTest_,
                                         debugStatusTest_));
  }
 
  // Create the status test output class.
  // This class manages and formats the output from the status test.
  StatusTestOutputFactory<ScalarType,MV,OP,DM> stoFactory (outputStyle_);
  outputTest_ = stoFactory.create (printer_, sTest_, outputFreq_,
                                   Passed+Failed+Undefined);
 
  // Set the solver string for the output test
  std::string solverDesc = " GCRODR ";
  if (isFlexible_)
    solverDesc = "Flexible" + solverDesc;
  outputTest_->setSolverDesc( solverDesc );
 
  // Create the timer if we need to.
  if (timerSolve_.is_null()) {
    std::string solveLabel = label_ + ": GCRODRSolMgr total solve time";
#ifdef BELOS_TEUCHOS_TIME_MONITOR
    timerSolve_ = Teuchos::TimeMonitor::getNewCounter(solveLabel);
#endif
  }
 
  // Inform the solver manager that the current parameters were set.
  isSet_ = true;
}
 
 
template<class ScalarType, class MV, class OP, class DM>
Teuchos::RCP<const Teuchos::ParameterList>
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::getValidParameters() const
{
  using Teuchos::ParameterList;
  using Teuchos::parameterList;
  using Teuchos::RCP;
 
  static RCP<const ParameterList> validPL;
  if (is_null(validPL)) {
    RCP<ParameterList> pl = parameterList ();
 
    // Set all the valid parameters and their default values.
    pl->set("Convergence Tolerance", static_cast<MagnitudeType>(DefaultSolverParameters::convTol),
      "The relative residual tolerance that needs to be achieved by the\n"
      "iterative solver in order for the linear system to be declared converged.");
    pl->set("Maximum Restarts", static_cast<int>(maxRestarts_default_),
      "The maximum number of cycles allowed for each\n"
      "set of RHS solved.");
    pl->set("Maximum Iterations", static_cast<int>(maxIters_default_),
      "The maximum number of iterations allowed for each\n"
      "set of RHS solved.");
    // mfh 25 Oct 2010: "Block Size" must be 1 because GCRODR is
    // currently not a block method: i.e., it does not work on
    // multiple right-hand sides at once.
    pl->set("Block Size", static_cast<int>(blockSize_default_),
      "Block Size Parameter -- currently must be 1 for GCRODR");
    pl->set("Num Blocks", static_cast<int>(numBlocks_default_),
      "The maximum number of vectors allowed in the Krylov subspace\n"
      "for each set of RHS solved.");
    pl->set("Num Recycled Blocks", static_cast<int>(recycledBlocks_default_),
      "The maximum number of vectors in the recycled subspace." );
    pl->set("Flexible GCRODR", static_cast<bool>(flexibleGCRODR_default_),
      "Whether to use the flexible variant of GCRODR.  The flexible variant stores the right-preconditioned correction basis Z.");
    pl->set("Verbosity", static_cast<int>(verbosity_default_),
      "What type(s) of solver information should be outputted\n"
      "to the output stream.");
    pl->set("Output Style", static_cast<int>(outputStyle_default_),
      "What style is used for the solver information outputted\n"
      "to the output stream.");
    pl->set("Output Frequency", static_cast<int>(outputFreq_default_),
      "How often convergence information should be outputted\n"
      "to the output stream.");
    pl->set("Output Stream", Teuchos::rcpFromRef(std::cout),
      "A reference-counted pointer to the output stream where all\n"
      "solver output is sent.");
    pl->set("Implicit Residual Scaling", static_cast<const char *>(impResScale_default_),
      "The type of scaling used in the implicit residual convergence test.");
    pl->set("Explicit Residual Scaling", static_cast<const char *>(expResScale_default_),
      "The type of scaling used in the explicit residual convergence test.");
    pl->set("Timer Label", static_cast<const char *>(label_default_),
      "The string to use as a prefix for the timer labels.");
    {
      OrthoManagerFactory<ScalarType, MV, OP, DM> factory;
      pl->set("Orthogonalization", static_cast<const char *>(orthoType_default_),
              "The type of orthogonalization to use.  Valid options: " +
              factory.validNamesString());
      RCP<const ParameterList> orthoParams =
        factory.getDefaultParameters (orthoType_default_);
      pl->set ("Orthogonalization Parameters", *orthoParams,
               "Parameters specific to the type of orthogonalization used.");
    }
    pl->set("Orthogonalization Constant",static_cast<MagnitudeType>(orthoKappa_default_),
            "When using DGKS orthogonalization: the \"depTol\" constant, used "
            "to determine whether another step of classical Gram-Schmidt is "
            "necessary.  Otherwise ignored.");
    validPL = pl;
  }
  return validPL;
}
 
// initializeStateStorage
template<class ScalarType, class MV, class OP, class DM>
void GCRODRSolMgr<ScalarType,MV,OP,DM,true>::initializeStateStorage() {
 
    ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
 
    // Check if there is any multivector to clone from.
    Teuchos::RCP<const MV> rhsMV = problem_->getRHS();
    if (rhsMV == Teuchos::null) {
      // Nothing to do
      return;
    }
    else {
 
      // Initialize the state storage
      TEUCHOS_TEST_FOR_EXCEPTION(static_cast<ptrdiff_t>(numBlocks_) > MVT::GetGlobalLength(*rhsMV),std::invalid_argument,
                         "Belos::GCRODRSolMgr::initializeStateStorage(): Cannot generate a Krylov basis with dimension larger the operator!");
 
      // If the subspace has not been initialized before, generate it using the RHS from lp_.
      if (U_ == Teuchos::null) {
        U_ = MVT::Clone( *rhsMV, recycledBlocks_+1 );
      }
      else {
        // Generate U_ by cloning itself ONLY if more space is needed.
        if (MVT::GetNumberVecs(*U_) < recycledBlocks_+1) {
          Teuchos::RCP<const MV> tmp = U_;
          U_ = MVT::Clone( *tmp, recycledBlocks_+1 );
        }
      }
 
      // If the subspace has not been initialized before, generate it using the RHS from lp_.
      if (C_ == Teuchos::null) {
        C_ = MVT::Clone( *rhsMV, recycledBlocks_+1 );
      }
      else {
        // Generate C_ by cloning itself ONLY if more space is needed.
        if (MVT::GetNumberVecs(*C_) < recycledBlocks_+1) {
          Teuchos::RCP<const MV> tmp = C_;
          C_ = MVT::Clone( *tmp, recycledBlocks_+1 );
        }
      }
 
      // If the subspace has not been initialized before, generate it using the RHS from lp_.
      if (V_ == Teuchos::null) {
        V_ = MVT::Clone( *rhsMV, numBlocks_+1 );
      }
      else {
        // Generate V_ by cloning itself ONLY if more space is needed.
        if (MVT::GetNumberVecs(*V_) < numBlocks_+1) {
          Teuchos::RCP<const MV> tmp = V_;
          V_ = MVT::Clone( *tmp, numBlocks_+1 );
        }
      }
 
      // If the subspace has not been initialized before, generate it using the RHS from lp_.
      if (U1_ == Teuchos::null) {
        U1_ = MVT::Clone( *rhsMV, recycledBlocks_+1 );
      }
      else {
        // Generate U1_ by cloning itself ONLY if more space is needed.
        if (MVT::GetNumberVecs(*U1_) < recycledBlocks_+1) {
          Teuchos::RCP<const MV> tmp = U1_;
          U1_ = MVT::Clone( *tmp, recycledBlocks_+1 );
        }
      }
 
      // If the subspace has not been initialized before, generate it using the RHS from lp_.
      if (C1_ == Teuchos::null) {
        C1_ = MVT::Clone( *rhsMV, recycledBlocks_+1 );
      }
      else {
        // Generate C1_ by cloning itself ONLY if more space is needed.
        if (MVT::GetNumberVecs(*C1_) < recycledBlocks_+1) {
          Teuchos::RCP<const MV> tmp = C1_;
          C1_ = MVT::Clone( *tmp, recycledBlocks_+1 );
        }
      }
 
 
      if (isFlexible_) {
        if (Z_ == Teuchos::null) {
          Z_ = MVT::Clone(*rhsMV, numBlocks_+1);
        }
        else {
          if (MVT::GetNumberVecs(*Z_) < numBlocks_+1) {
            Teuchos::RCP<const MV> tmp = Z_;
            Z_ = MVT::Clone(*tmp, numBlocks_+1);
          }
        }
 
        if (W_ == Teuchos::null) {
          W_ = MVT::Clone(*rhsMV, recycledBlocks_+1);
        }
        else {
          if (MVT::GetNumberVecs(*W_) < recycledBlocks_+1) {
            Teuchos::RCP<const MV> tmp = W_;
            W_ = MVT::Clone(*tmp, recycledBlocks_+1);
          }
        }
 
        if (W1_ == Teuchos::null) {
          W1_ = MVT::Clone(*rhsMV, recycledBlocks_+1);
        }
        else {
          if (MVT::GetNumberVecs(*W1_) < recycledBlocks_+1) {
            Teuchos::RCP<const MV> tmp = W1_;
            W1_ = MVT::Clone(*tmp, recycledBlocks_+1);
          }
        }
      }
 
      // Generate r_ only if it doesn't exist
      if (r_ == Teuchos::null)
        r_ = MVT::Clone( *rhsMV, 1 );
 
      // Size of tau_ will change during computation, so just be sure it starts with appropriate size
      tau_.resize(recycledBlocks_+1);
 
      // Size of work_ will change during computation, so just be sure it starts with appropriate size
      work_.resize(recycledBlocks_+1);
 
      // Size of ipiv_ will change during computation, so just be sure it starts with appropriate size
      ipiv_.resize(recycledBlocks_+1);
 
      // Generate H2_ only if it doesn't exist, otherwise resize it.
      if (H2_ == Teuchos::null)
        H2_ = DMT::Create( numBlocks_+recycledBlocks_+2, numBlocks_+recycledBlocks_+1 );
      else {
        if ( (DMT::GetNumRows(*H2_) != numBlocks_+recycledBlocks_+2) || (DMT::GetNumCols(*H2_) != numBlocks_+recycledBlocks_+1) )
          DMT::Reshape( *H2_, numBlocks_+recycledBlocks_+2, numBlocks_+recycledBlocks_+1 );
      }
      DMT::PutScalar(*H2_, zero);
 
      // Generate R_ only if it doesn't exist, otherwise resize it.
      if (R_ == Teuchos::null)
        R_ = DMT::Create( recycledBlocks_+1, recycledBlocks_+1 );
      else {
        if ( (DMT::GetNumRows(*R_) != recycledBlocks_+1) || (DMT::GetNumCols(*R_) != recycledBlocks_+1) )
          DMT::Reshape( *R_, recycledBlocks_+1, recycledBlocks_+1 );
      }
      DMT::PutScalar(*R_,zero);
 
      // Generate PP_ only if it doesn't exist, otherwise resize it.
      if (PP_ == Teuchos::null)
        PP_ = DMT::Create( numBlocks_+recycledBlocks_+2, recycledBlocks_+1 );
      else {
        if ( (DMT::GetNumRows(*PP_) != numBlocks_+recycledBlocks_+2) || (DMT::GetNumCols(*PP_) != recycledBlocks_+1) )
          DMT::Reshape( *PP_, numBlocks_+recycledBlocks_+2, recycledBlocks_+1 );
      }
 
      // Generate HP_ only if it doesn't exist, otherwise resize it.
      if (HP_ == Teuchos::null)
        HP_ = DMT::Create( numBlocks_+recycledBlocks_+2, numBlocks_+recycledBlocks_+1 );
      else {
        if ( (DMT::GetNumRows(*HP_) != numBlocks_+recycledBlocks_+2) || (DMT::GetNumCols(*HP_) != numBlocks_+recycledBlocks_+1) )
          DMT::Reshape( *HP_, numBlocks_+recycledBlocks_+2, numBlocks_+recycledBlocks_+1 );
      }
 
    } // end else
}
 
 
 
template<class ScalarType, class MV, class OP, class DM>
void
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::computeGCRODRResidual()
{
  if (isFlexible_) {
    problem_->computeCurrResVec(&*r_);
  }
  else {
    problem_->computeCurrPrecResVec(&*r_);
  }
}
 
template<class ScalarType, class MV, class OP, class DM>
void
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::
updateSolutionWithUpdate(const Teuchos::RCP<MV>& update)
{
  if (update == Teuchos::null) {
    return;
  }
 
  const ScalarType one = SCT::one();
 
  if (isFlexible_) {
    Teuchos::RCP<MV> curX = problem_->getCurrLHSVec();
    MVT::MvAddMv(one, *curX, one, *update, *curX);
  }
  else {
    problem_->updateSolution(update, true);
  }
}
 
 
// solve()
template<class ScalarType, class MV, class OP, class DM>
ReturnType GCRODRSolMgr<ScalarType,MV,OP,DM,true>::solve() {
  using Teuchos::RCP;
  using Teuchos::rcp;
 
  ReturnType retType = Undetermined;
 
  // Set the current parameters if they were not set before.
  // NOTE:  This may occur if the user generated the solver manager with the default constructor and
  // then didn't set any parameters using setParameters().
  if (!isSet_) { setParameters( params_ ); }
 
  ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
  ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
  std::vector<int> index(numBlocks_+1);
 
  TEUCHOS_TEST_FOR_EXCEPTION(problem_ == Teuchos::null,GCRODRSolMgrLinearProblemFailure, "Belos::GCRODRSolMgr::solve(): Linear problem is not a valid object.");
 
  TEUCHOS_TEST_FOR_EXCEPTION(!problem_->isProblemSet(),GCRODRSolMgrLinearProblemFailure,"Belos::GCRODRSolMgr::solve(): Linear problem is not ready, setProblem() has not been called.");
 
  if (isFlexible_) {
    TEUCHOS_TEST_FOR_EXCEPTION(
      !Teuchos::is_null(problem_->getLeftPrec()),
      GCRODRSolMgrLinearProblemFailure,
      "Belos::GCRODRSolMgr::solve(): Flexible GCRODR does not support left preconditioning; use no preconditioner or a right preconditioner.");
  }
 
  // Create indices for the linear systems to be solved.
  int numRHS2Solve = MVT::GetNumberVecs( *(problem_->getRHS()) );
  std::vector<int> currIdx(1);
  currIdx[0] = 0;
 
  // Inform the linear problem of the current linear system to solve.
  problem_->setLSIndex( currIdx );
 
  // Check the number of blocks and change them is necessary.
  ptrdiff_t dim = MVT::GetGlobalLength( *(problem_->getRHS()) );
  if (static_cast<ptrdiff_t>(numBlocks_) > dim) {
    numBlocks_ = Teuchos::as<int>(dim);
    printer_->stream(Warnings) <<
      "Warning! Requested Krylov subspace dimension is larger than operator dimension!" << std::endl <<
      " The maximum number of blocks allowed for the Krylov subspace will be adjusted to " << numBlocks_ << std::endl;
    params_->set("Num Blocks", numBlocks_);
  }
 
  // Assume convergence is achieved, then let any failed convergence set this to false.
  bool isConverged = true;
 
  // Initialize storage for all state variables
  initializeStateStorage();

  // Parameter list
  Teuchos::ParameterList plist;
 
  plist.set("Num Blocks",numBlocks_);
  plist.set("Recycled Blocks",recycledBlocks_);

  // GCRODR solver
 
  RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_iter;
  if (isFlexible_) {
    gcrodr_iter = rcp(new FGCRODRIter<ScalarType,MV,OP,DM>(problem_,printer_,outputTest_,ortho_,plist));
  }
  else {
    gcrodr_iter = rcp(new GCRODRIter<ScalarType,MV,OP,DM>(problem_,printer_,outputTest_,ortho_,plist));
  }
  // Number of iterations required to generate initial recycle space (if needed)
  int prime_iterations = 0;
 
  // Enter solve() iterations
  {
#ifdef BELOS_TEUCHOS_TIME_MONITOR
    Teuchos::TimeMonitor slvtimer(*timerSolve_);
#endif
 
    while ( numRHS2Solve > 0 ) {
 
      // Set flag indicating recycle space has not been generated this solve
      builtRecycleSpace_ = false;
 
      // Reset the status test.
      outputTest_->reset();

      // Initialize recycled subspace for GCRODR
 
      // If there is a subspace to recycle, recycle it, otherwise generate the initial recycled subspace.
      if (keff > 0) {
        TEUCHOS_TEST_FOR_EXCEPTION(keff < recycledBlocks_,GCRODRSolMgrRecyclingFailure,
                           "Belos::GCRODRSolMgr::solve(): Requested size of recycled subspace is not consistent with the current recycle subspace.");
 
        printer_->stream(Debug) << " Now solving RHS index " << currIdx[0] << " using recycled subspace of dimension " << keff << std::endl << std::endl;
        // Compute image of U_ under the new operator
        index.resize(keff);
        for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
        RCP<const MV> Utmp  = MVT::CloneView( *U_, index );
        RCP<MV> Ctmp  = MVT::CloneViewNonConst( *C_, index );
        if (isFlexible_) {
          problem_->applyOp(*Utmp, *Ctmp);
        }
        else {
          problem_->apply(*Utmp, *Ctmp);
        }
 
        RCP<MV> U1tmp = MVT::CloneViewNonConst( *U1_, index );
 
        // Orthogonalize this block
        // Get a matrix to hold the orthonormalization coefficients.
  Teuchos::RCP<DM> Rtmp = DMT::Subview( *R_, keff, keff );
        int rank = ortho_->normalize(*Ctmp, Rtmp);
        // Throw an error if we could not orthogonalize this block
        TEUCHOS_TEST_FOR_EXCEPTION(rank != keff,GCRODRSolMgrOrthoFailure,"Belos::GCRODRSolMgr::solve(): Failed to compute orthonormal basis for initial recycled subspace.");
 
  // Synchronize R_ before calling LAPACK
        DMT::SyncDeviceToHost(*R_);
 
  // U_ = U_*R^{-1}
        // First, compute LU factorization of R
        int info = 0;
        ipiv_.resize(DMT::GetNumRows(*Rtmp));
  lapack.GETRF(DMT::GetNumRows(*Rtmp), DMT::GetNumCols(*Rtmp), DMT::GetRawHostPtr(*Rtmp), DMT::GetStride(*Rtmp), &ipiv_[0], &info);
        TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure,"Belos::GCRODRSolMgr::solve(): LAPACK _GETRF failed to compute an LU factorization.");
 
        // Now, form inv(R)
        int lwork = DMT::GetNumRows(*Rtmp);
        work_.resize(lwork);
        lapack.GETRI(DMT::GetNumRows(*Rtmp), DMT::GetRawHostPtr(*Rtmp), DMT::GetStride(*Rtmp), &ipiv_[0], &work_[0], lwork, &info);
        TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure,"Belos::GCRODRSolMgr::solve(): LAPACK _GETRI failed to invert triangular matrix.");
 
  DMT::SyncHostToDevice(*R_);
 
        // U_ = U1_; (via a swap)
        MVT::MvTimesMatAddMv( one, *Utmp, *Rtmp, zero, *U1tmp );
        if (isFlexible_) {
          Teuchos::RCP<const MV> Wtmp = MVT::CloneView(*W_, index);
          Teuchos::RCP<MV> W1tmp = MVT::CloneViewNonConst(*W1_, index);
          MVT::MvTimesMatAddMv(one, *Wtmp, *Rtmp, zero, *W1tmp);
          std::swap(W_, W1_);
        }
        std::swap(U_, U1_);
 
        // Must reinitialize after swap
        index.resize(keff);
        for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
        Ctmp  = MVT::CloneViewNonConst( *C_, index );
        Utmp  = MVT::CloneView( *U_, index );
 
        // Compute C_'*r_
        Teuchos::RCP<DM> Ctr = DMT::Create(keff, 1);
        computeGCRODRResidual();
        MVT::MvTransMv( one, *Ctmp, *r_, *Ctr );
 
        // Update solution ( x += U_*C_'*r_ )
        RCP<MV> update = MVT::Clone( *problem_->getCurrLHSVec(), 1 );
        MVT::MvInit( *update, 0.0 );
        MVT::MvTimesMatAddMv( one, *Utmp, *Ctr, one, *update );
        updateSolutionWithUpdate(update);
 
        // Update residual norm ( r -= C_*C_'*r_ )
        MVT::MvTimesMatAddMv( -one, *Ctmp, *Ctr, one, *r_ );
 
        // We recycled space from previous call
        prime_iterations = 0;
 
      }
      else {
 
        // Do one cycle of Gmres to "prime the pump" if there is no subspace to recycle
        printer_->stream(Debug) << " No recycled subspace available for RHS index " << currIdx[0] << std::endl << std::endl;
 
        Teuchos::ParameterList primeList;
        primeList.set("Num Blocks",numBlocks_);
        primeList.set("Recycled Blocks",recycledBlocks_);
 
        //  Create GCRODR iterator object to perform one cycle of GMRES.
        RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_prime_iter;
        if (isFlexible_) {
          gcrodr_prime_iter = rcp(new FGCRODRIter<ScalarType,MV,OP,DM>(problem_,printer_,outputTest_,ortho_,primeList));
        }
        else {
          gcrodr_prime_iter = rcp(new GCRODRIter<ScalarType,MV,OP,DM>(problem_,printer_,outputTest_,ortho_,primeList));
        }
 
        // Create the first block in the current Krylov basis (residual).
  computeGCRODRResidual();
        index.resize( 1 ); index[0] = 0;
        RCP<MV> v0 =  MVT::CloneViewNonConst( *V_,  index );
        MVT::SetBlock(*r_,index,*v0); // V(:,0) = r
 
        // Set the new state and initialize the solver.
        GCRODRIterState<ScalarType,MV,DM> newstate;
        index.resize( numBlocks_+1 );
        for (int ii=0; ii<(numBlocks_+1); ++ii) { index[ii] = ii; }
        newstate.V = MVT::CloneViewNonConst( *V_,  index );
        if (isFlexible_) newstate.Z = MVT::CloneViewNonConst( *Z_, index );
        newstate.U = Teuchos::null;
        newstate.C = Teuchos::null;
        newstate.H2 = H2_;
        newstate.curDim = 0;
        gcrodr_prime_iter->initialize(newstate);
 
        // Perform one cycle of GMRES
        bool primeConverged = false;
        bool debugTestPassed = false;
        try {
          gcrodr_prime_iter->iterate();
 
          // Check convergence first
          if ( convTest_->getStatus() == Passed ) {
            // we have convergence
            primeConverged = true;
          }
          // Check whether a debug status test requested termination while
          // building the initial recycle space.  This is a valid early exit from
          // iterate(), not an inconsistent solver state.
          else if (Teuchos::nonnull(debugStatusTest_) &&
                   debugStatusTest_->getStatus() == Passed) {
            retType = Unconverged;
            isConverged = false;
            debugTestPassed = true;
          }
        }
        catch (const GCRODRIterOrthoFailure &e) {
          // Try to recover the most recent least-squares solution
          gcrodr_prime_iter->updateLSQR( gcrodr_prime_iter->getCurSubspaceDim() );
 
          // Check to see if the most recent least-squares solution yielded convergence.
          sTest_->checkStatus( &*gcrodr_prime_iter );
          if (convTest_->getStatus() == Passed)
            primeConverged = true;
        }
        catch (const StatusTestNaNError& e) {
          // A NaN was detected in the solver.  Set the solution to zero and return unconverged.
          retType = NaNDetected;
          achievedTol_ = MT::one();
          Teuchos::RCP<MV> X = problem_->getLHS();
          MVT::MvInit( *X, SCT::zero() );
          printer_->stream(Warnings) << "Belos::GCRODRSolMgr::solve(): Warning! NaN has been detected!" 
                                     << std::endl;
          return retType; 
        }
        catch (const std::exception &e) {
          retType = NonspecificException;
          printer_->stream(Errors) << "Error! Caught exception in GCRODRIter::iterate() at iteration "
                                   << gcrodr_prime_iter->getNumIters() << std::endl
                                   << e.what() << std::endl;
          throw;
        }
        // Record number of iterations in generating initial recycle spacec
        prime_iterations = gcrodr_prime_iter->getNumIters();
 
        if (debugTestPassed) {
          break;
        }
 
        // Update the linear problem.
        RCP<MV> update = gcrodr_prime_iter->getCurrentUpdate();
        updateSolutionWithUpdate(update);
 
        // Get the state.
        newstate = gcrodr_prime_iter->getState();
        int p = newstate.curDim;
 
        // Compute harmonic Ritz vectors
        // NOTE:  The storage for the harmonic Ritz vectors (PP) is made one column larger
        //        just in case we split a complex conjugate pair.
        // NOTE:  Generate a recycled subspace only if we have enough vectors.  If we converged
        //        too early, move on to the next linear system and try to generate a subspace again.
        if (recycledBlocks_ < p+1) {
          int info = 0;
          
    // Synchronize before calling getHarmonicVecs1; H2_ is const
    DMT::SyncDeviceToHost( *H2_ );
          DMT::SyncDeviceToHost( *PP_ );
    RCP<DM> PPtmp = DMT::Subview( *PP_, p, recycledBlocks_+1 );
 
          // getHarmonicVecs1 assumes PP has recycledBlocks_+1 columns available
    keff = getHarmonicVecs1( p, *newstate.H, *PPtmp );
 
    // Synchronize before forming U (the subspace to recycle)
          DMT::SyncHostToDevice( *PP_ );
    // Hereafter, only keff columns of PP are needed
          PPtmp = DMT::Subview( *PP_, p, keff );
 
    // Now get views into C, U, V
          index.resize(keff);
          for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
          RCP<MV> Ctmp  = MVT::CloneViewNonConst( *C_, index );
          RCP<MV> Utmp  = MVT::CloneViewNonConst( *U_, index );
          RCP<MV> U1tmp = MVT::CloneViewNonConst( *U1_, index );
          index.resize(p);
          for (int ii=0; ii < p; ++ii) { index[ii] = ii; }
          RCP<const MV> Vtmp = MVT::CloneView( *V_, index );
 
          // Form U (the subspace to recycle).
          // Standard GCRODR: U = V_m * P.
          // Flexible GCRODR: U = Z_m * P and W = V_m * P.
          if (isFlexible_) {
            RCP<const MV> Ztmp = MVT::CloneView(*Z_, index);
            MVT::MvTimesMatAddMv(one, *Ztmp, *PPtmp, zero, *U1tmp);
            std::vector<int> wind(keff);
            for (int wi = 0; wi < keff; ++wi) wind[wi] = wi;
            RCP<MV> W1tmp = MVT::CloneViewNonConst(*W1_, wind);
            MVT::MvTimesMatAddMv(one, *Vtmp, *PPtmp, zero, *W1tmp);
          }
          else {
            MVT::MvTimesMatAddMv( one, *Vtmp, *PPtmp, zero, *U1tmp );
          }
 
          // Form orthonormalized C and adjust U so that C = A*U
 
          // First, compute [Q, R] = qr(H*P);
 
          // Step #1: Form HP = H*P
    DMT::SyncDeviceToHost( *HP_ );
 
          RCP<DM> Htmp = DMT::Subview( *H2_, p+1, p, recycledBlocks_+1,recycledBlocks_+1 );
          RCP<DM> HPtmp = DMT::Subview( *HP_, p+1, keff );
 
          Teuchos::BLAS<int,ScalarType> blas;
    blas.GEMM( Teuchos::NO_TRANS, Teuchos::NO_TRANS, p+1, keff, p, one,
                   DMT::GetConstRawHostPtr(*Htmp), DMT::GetStride(*Htmp),
                   DMT::GetConstRawHostPtr(*PPtmp), DMT::GetStride(*PPtmp),
                   zero, DMT::GetRawHostPtr(*HPtmp), DMT::GetStride(*HPtmp));
 
    // Step #1.5: Perform workspace size query for QR
          // factorization of HP.  On input, lwork must be -1.
          // _GEQRF will put the workspace size in work_[0].
          int lwork = -1;
          tau_.resize (keff);
          lapack.GEQRF (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetRawHostPtr(*HPtmp),
                        DMT::GetStride(*HPtmp), &tau_[0], &work_[0], lwork, &info);
          TEUCHOS_TEST_FOR_EXCEPTION(
            info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve:"
            " LAPACK's _GEQRF failed to compute a workspace size.");
 
          // Step #2: Compute QR factorization of HP
          //
          // NOTE (mfh 17 Apr 2014) LAPACK promises that the value of
          // work_[0] after the workspace query will fit in int.  This
          // justifies the cast.  We call real() first because
          // static_cast from std::complex to int doesn't work.
          lwork = std::abs (static_cast<int> (Teuchos::ScalarTraits<ScalarType>::real (work_[0])));
          work_.resize (lwork); // Allocate workspace for the QR factorization
          lapack.GEQRF (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetRawHostPtr(*HPtmp),
                        DMT::GetStride(*HPtmp), &tau_[0], &work_[0], lwork, &info);
          TEUCHOS_TEST_FOR_EXCEPTION(
            info != 0, GCRODRSolMgrLAPACKFailure,  "Belos::GCRODRSolMgr::solve:"
            " LAPACK's _GEQRF failed to compute a QR factorization.");
 
          // Step #3: Explicitly construct Q and R factors
          // NOTE:  The upper triangular part of HP is copied into R and HP becomes Q.
          // Synchronize R_ before and after copying over diagonal of HP
    DMT::SyncDeviceToHost( *R_ );
          RCP<DM> Rtmp = DMT::Subview( *R_, keff, keff );
          for (int ii = 0; ii < keff; ++ii) {
            for (int jj = ii; jj < keff; ++jj) {
              DMT::Value(*Rtmp,ii,jj) = DMT::ValueConst(*HPtmp,ii,jj);
      }
          }
          DMT::SyncHostToDevice( *R_ );
    // NOTE (mfh 17 Apr 2014): Teuchos::LAPACK's wrapper for
          // UNGQR dispatches to the correct Scalar-specific routine.
          // It calls {S,D}ORGQR if Scalar is real, and {C,Z}UNGQR if
          // Scalar is complex.
          lapack.UNGQR (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetNumCols(*HPtmp),
                        DMT::GetRawHostPtr(*HPtmp), DMT::GetStride(*HPtmp), &tau_[0], &work_[0],
                        lwork, &info);
          TEUCHOS_TEST_FOR_EXCEPTION(
            info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
            "LAPACK's _UNGQR failed to construct the Q factor.");
 
          // Now we have [Q,R] = qr(H*P)
          // Synchronize HP_ after call to LAPACK
    DMT::SyncHostToDevice( *HP_ );
 
          // Now compute C = V(:,1:p+1) * Q
          index.resize (p + 1);
          for (int ii = 0; ii < (p+1); ++ii) {
            index[ii] = ii;
          }
          Vtmp = MVT::CloneView( *V_, index ); // need new view into V (p+1 vectors now; needed p above)
          MVT::MvTimesMatAddMv( one, *Vtmp, *HPtmp, zero, *Ctmp );
 
          // Finally, compute U = U*R^{-1}.
          // This unfortuntely requires me to form R^{-1} explicitly and execute U = U * R^{-1}, as
          // backsolve capabilities don't exist in the Belos::MultiVec class
 
          // Step #1: First, compute LU factorization of R
          ipiv_.resize(DMT::GetNumRows(*Rtmp));
          lapack.GETRF(DMT::GetNumRows(*Rtmp), DMT::GetNumCols(*Rtmp), DMT::GetRawHostPtr(*Rtmp),
           DMT::GetStride(*Rtmp), &ipiv_[0], &info);
          TEUCHOS_TEST_FOR_EXCEPTION(
            info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
            "LAPACK's _GETRF failed to compute an LU factorization.");
 
          // FIXME (mfh 17 Apr 2014) We have to compute the explicit
          // inverse of R here because Belos::MultiVecTraits doesn't
          // have a triangular solve (where the triangular matrix is
          // globally replicated and the "right-hand side" is the
          // distributed MultiVector).
 
          // Step #2: Form inv(R)
          lwork = DMT::GetNumRows(*Rtmp);
          work_.resize(lwork);
          lapack.GETRI(DMT::GetNumRows(*Rtmp), DMT::GetRawHostPtr(*Rtmp), DMT::GetStride(*Rtmp), 
           &ipiv_[0], &work_[0], lwork, &info);
          TEUCHOS_TEST_FOR_EXCEPTION(
            info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
            "LAPACK's _GETRI failed to invert triangular matrix.");
 
    DMT::SyncHostToDevice( *R_ );
 
          // Step #3: Let U = U * R^{-1}
          MVT::MvTimesMatAddMv( one, *U1tmp, *Rtmp, zero, *Utmp );
          if (isFlexible_) {
            std::vector<int> wind(keff);
            for (int wi = 0; wi < keff; ++wi) wind[wi] = wi;
            RCP<const MV> W1tmp = MVT::CloneView(*W1_, wind);
            RCP<MV> Wtmp = MVT::CloneViewNonConst(*W_, wind);
            MVT::MvTimesMatAddMv(one, *W1tmp, *Rtmp, zero, *Wtmp);
          }
 
          printer_->stream(Debug)
            << " Generated recycled subspace using RHS index " << currIdx[0]
            << " of dimension " << keff << std::endl << std::endl;
 
        }  // if (recycledBlocks_ < p+1)
 
        // Return to outer loop if the priming solve converged, set the next linear system.
        if (primeConverged) {
          // Inform the linear problem that we are finished with this block linear system.
          problem_->setCurrLS();
 
          // Update indices for the linear systems to be solved.
          numRHS2Solve -= 1;
          if (numRHS2Solve > 0) {
            currIdx[0]++;
            problem_->setLSIndex (currIdx); // Set the next indices
          }
          else {
            currIdx.resize (numRHS2Solve);
          }
 
          continue;
        }
      } // if (keff > 0) ...
 
      // Prepare for the Gmres iterations with the recycled subspace.
 
      // Set the current number of recycled blocks and subspace dimension with the GCRO-DR iteration.
      gcrodr_iter->setSize( keff, numBlocks_ );
 
      // Reset the number of iterations.
      gcrodr_iter->resetNumIters(prime_iterations);
 
      // Reset the number of calls that the status test output knows about.
      outputTest_->resetNumCalls();
 
      // Compute the residual after the priming solve, it will be the first block in the current Krylov basis.
      computeGCRODRResidual();
      index.resize( 1 ); index[0] = 0;
      RCP<MV> v0 =  MVT::CloneViewNonConst( *V_,  index );
      MVT::SetBlock(*r_,index,*v0); // V(:,0) = r
 
      // Set the new state and initialize the solver.
      DMT::SyncDeviceToHost( *H2_ );
      GCRODRIterState<ScalarType,MV,DM> newstate;
      index.resize( numBlocks_+1 );
      for (int ii=0; ii<(numBlocks_+1); ++ii) { index[ii] = ii; }
      newstate.V  = MVT::CloneViewNonConst( *V_,  index );
      if (isFlexible_) newstate.Z = MVT::CloneViewNonConst( *Z_, index );
      index.resize( keff );
      for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
      newstate.C  = MVT::CloneViewNonConst( *C_,  index );
      newstate.U  = MVT::CloneViewNonConst( *U_,  index );
      newstate.H2 = H2_;
      newstate.curDim = 0;
      gcrodr_iter->initialize(newstate);
 
      // variables needed for inner loop
      int numRestarts = 0;
      while(1) {
 
        // tell gcrodr_iter to iterate
        try {
          gcrodr_iter->iterate();

          //
          // check convergence first
          //
          if ( convTest_->getStatus() == Passed ) {
            // we have convergence
            break;  // break from while(1){gcrodr_iter->iterate()}
          }
          //
          // check for maximum iterations
          //
          else if ( maxIterTest_->getStatus() == Passed ) {
            // we don't have convergence
            retType = MaxItersReached;
            isConverged = false;
            break;  // break from while(1){gcrodr_iter->iterate()}
          }
          //
          // check for restarting, i.e. the subspace is full
          //
          else if ( gcrodr_iter->getCurSubspaceDim() == gcrodr_iter->getMaxSubspaceDim() ) {
 
            // Update the recycled subspace even if we have hit the maximum number of restarts.
 
            // Update the linear problem.
            RCP<MV> update = gcrodr_iter->getCurrentUpdate();
            updateSolutionWithUpdate(update);
 
            buildRecycleSpace2(gcrodr_iter);
 
            printer_->stream(Debug)
              << " Generated new recycled subspace using RHS index "
              << currIdx[0] << " of dimension " << keff << std::endl
              << std::endl;
 
            // NOTE:  If we have hit the maximum number of restarts then quit
            if (numRestarts >= maxRestarts_) {
              retType = MaxRestartsReached;
              isConverged = false;
              break; // break from while(1){gcrodr_iter->iterate()}
            }
            numRestarts++;
 
            printer_->stream(Debug)
              << " Performing restart number " << numRestarts << " of "
              << maxRestarts_ << std::endl << std::endl;
 
            // Create the restart vector (first block in the current Krylov basis)
            computeGCRODRResidual();
            index.resize( 1 ); index[0] = 0;
            RCP<MV> v00 =  MVT::CloneViewNonConst( *V_,  index );
            MVT::SetBlock(*r_,index,*v00); // V(:,0) = r
 
            // Set the new state and initialize the solver.
      DMT::SyncDeviceToHost( *H2_ );
            GCRODRIterState<ScalarType,MV,DM> restartState;
            index.resize( numBlocks_+1 );
            for (int ii=0; ii<(numBlocks_+1); ++ii) { index[ii] = ii; }
            restartState.V  = MVT::CloneViewNonConst( *V_,  index );
            if (isFlexible_) restartState.Z = MVT::CloneViewNonConst( *Z_, index );
            index.resize( keff );
            for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
            restartState.U = MVT::CloneViewNonConst( *U_,  index );
            restartState.C = MVT::CloneViewNonConst( *C_,  index );
            restartState.H2 = H2_;
            restartState.curDim = 0;
            gcrodr_iter->initialize(restartState);
 
 
          } // end of restarting

          //
          // check for a debug status test requesting termination
          //
          else if (Teuchos::nonnull(debugStatusTest_) &&
                   debugStatusTest_->getStatus() == Passed) {
            // A debug status test (e.g. a wall-clock time limit) stopped the
            // iteration. Treat as an unconverged termination rather than an
            // inconsistent state.
            retType = Unconverged;
            isConverged = false;
            break; // break from while(1){gcrodr_iter->iterate()}
          }
          //
          // we returned from iterate(), but none of our status tests Passed.
          // something is wrong, and it is probably our fault.
          //
 
          else {
            retType = InconsistentState;
            TEUCHOS_TEST_FOR_EXCEPTION(true,
              std::logic_error, "Belos::GCRODRSolMgr::solve: "
              "Invalid return from GCRODRIter::iterate().");
          }
        }
        catch (const GCRODRIterOrthoFailure &e) {
          // Try to recover the most recent least-squares solution
          gcrodr_iter->updateLSQR( gcrodr_iter->getCurSubspaceDim() );
 
          // Check to see if the most recent least-squares solution yielded convergence.
          sTest_->checkStatus( &*gcrodr_iter );
          if (convTest_->getStatus() != Passed) {
            retType = OrthonormFailure;
            isConverged = false;
          }
          break;
        }
        catch (const std::exception& e) {
          retType = NonspecificException;
          printer_->stream(Errors)
            << "Error! Caught exception in GCRODRIter::iterate() at iteration "
            << gcrodr_iter->getNumIters() << std::endl << e.what() << std::endl;
          throw;
        }
      }
 
      // Compute the current solution.
      // Update the linear problem.
      RCP<MV> update = gcrodr_iter->getCurrentUpdate();
      updateSolutionWithUpdate(update);
 
      // Inform the linear problem that we are finished with this block linear system.
      problem_->setCurrLS();
 
      // If we didn't build a recycle space this solve but ran at least k iterations,
      // force build of new recycle space
 
      if (!builtRecycleSpace_) {
        buildRecycleSpace2(gcrodr_iter);
        printer_->stream(Debug)
          << " Generated new recycled subspace using RHS index " << currIdx[0]
          << " of dimension " << keff << std::endl << std::endl;
      }
 
      // Update indices for the linear systems to be solved.
      numRHS2Solve -= 1;
      if (numRHS2Solve > 0) {
        currIdx[0]++;
        problem_->setLSIndex (currIdx); // Set the next indices
      }
      else {
        currIdx.resize (numRHS2Solve);
      }
    } // while (numRHS2Solve > 0)
  }
 
  sTest_->print (printer_->stream (FinalSummary)); // print final summary
 
  // print timing information
#ifdef BELOS_TEUCHOS_TIME_MONITOR
  // Calling summarize() can be expensive, so don't call unless the
  // user wants to print out timing details.  summarize() will do all
  // the work even if it's passed a "black hole" output stream.
  if (verbosity_ & TimingDetails)
    Teuchos::TimeMonitor::summarize( printer_->stream(TimingDetails) );
#endif // BELOS_TEUCHOS_TIME_MONITOR
 
  // get iteration information for this solve
  numIters_ = maxIterTest_->getNumIters ();
 
  // Save the convergence test value ("achieved tolerance") for this
  // solve.  This solver (unlike BlockGmresSolMgr) always has two
  // residual norm status tests: an explicit and an implicit test.
  // The master convergence test convTest_ is a SEQ combo of the
  // implicit resp. explicit tests.  If the implicit test never
  // passes, then the explicit test won't ever be executed.  This
  // manifests as expConvTest_->getTestValue()->size() < 1.  We deal
  // with this case by using the values returned by
  // impConvTest_->getTestValue().
  {
    const std::vector<MagnitudeType>* pTestValues = NULL;
    if (! expConvTest_.is_null()) {
      pTestValues = expConvTest_->getTestValue();
    }
    if (pTestValues == NULL || pTestValues->size() < 1) {
      pTestValues = impConvTest_->getTestValue();
    }
    TEUCHOS_TEST_FOR_EXCEPTION(pTestValues == NULL, std::logic_error,
      "Belos::GCRODRSolMgr::solve(): The implicit convergence test's getTestValue() "
      "method returned NULL.  Please report this bug to the Belos developers.");
    TEUCHOS_TEST_FOR_EXCEPTION(pTestValues->size() < 1, std::logic_error,
      "Belos::GCRODRSolMgr::solve(): The implicit convergence test's getTestValue() "
      "method returned a vector of length zero.  Please report this bug to the "
      "Belos developers.");
 
    // FIXME (mfh 12 Dec 2011) Does pTestValues really contain the
    // achieved tolerances for all vectors in the current solve(), or
    // just for the vectors from the last deflation?
    achievedTol_ = *std::max_element (pTestValues->begin(), pTestValues->end());
  }
 
  if (!isConverged) {
    return retType; // return from solve()
  }
  return Converged; // return from solve()
}
 
//  Given existing recycle space and Krylov space, build new recycle space
template<class ScalarType, class MV, class OP, class DM>
void GCRODRSolMgr<ScalarType,MV,OP,DM,true>::buildRecycleSpace2(Teuchos::RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_iter) {
 
  if (isFlexible_) {
    buildFlexibleRecycleSpace2(gcrodr_iter);
    return;
  }
 
  MagnitudeType one = Teuchos::ScalarTraits<MagnitudeType>::one();
  ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
 
  std::vector<MagnitudeType> d(keff);
  std::vector<ScalarType> dscalar(keff);
  std::vector<int> index(numBlocks_+1);
 
  // Get the state
  GCRODRIterState<ScalarType,MV,DM> oldState = gcrodr_iter->getState();
  int p = oldState.curDim;
 
  // insufficient new information to update recycle space
  if (p<1) return;
 
  // Take the norm of the recycled vectors
  {
    index.resize(keff);
    for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
    Teuchos::RCP<MV> Utmp  = MVT::CloneViewNonConst( *U_, index );
    d.resize(keff);
    dscalar.resize(keff);
    MVT::MvNorm( *Utmp, d );
    for (int i=0; i<keff; ++i) {
      d[i] = one / d[i];
      dscalar[i] = (ScalarType)d[i];
    }
    MVT::MvScale( *Utmp, dscalar );
  }
 
  // Get view into current "full" upper Hessenburg matrix
  DMT::SyncDeviceToHost( *H2_ );
  Teuchos::RCP<DM> H2tmp = DMT::Subview( *H2_, p+keff+1, p+keff );
 
  // Insert D into the leading keff x keff  block of H2
  for (int i=0; i<keff; ++i) {
    DMT::Value(*H2tmp,i,i) = d[i];
  }
 
  DMT::SyncHostToDevice( *H2_ );
 
  // Compute the harmoic Ritz pairs for the generalized eigenproblem
  // getHarmonicVecs2 assumes PP has recycledBlocks_+1 columns available
  int keff_new;
  {
    DMT::SyncDeviceToHost( *PP_ );
    Teuchos::RCP<DM> PPtmp = DMT::Subview( *PP_, p+keff, recycledBlocks_+1 );
    keff_new = getHarmonicVecs2( keff, p, *H2tmp, oldState.V, *PPtmp );
    DMT::SyncHostToDevice( *PP_ );
  }
 
  // Code to form new U, C
  // U = [U V(:,1:p)] * P; (in two steps)
 
  // U(:,1:keff) = matmul(U(:,1:keff_old),PP(1:keff_old,1:keff)) (step 1)
  Teuchos::RCP<MV> U1tmp;
  {
    index.resize( keff );
    for (int ii=0; ii<keff; ++ii) { index[ii] = ii; }
    Teuchos::RCP<const MV> Utmp  = MVT::CloneView( *U_,  index );
    index.resize( keff_new );
    for (int ii=0; ii<keff_new; ++ii) { index[ii] = ii; }
    U1tmp  = MVT::CloneViewNonConst( *U1_,  index );
    Teuchos::RCP<const DM> PPtmp = DMT::SubviewConst( *PP_, keff, keff_new );
    MVT::MvTimesMatAddMv( one, *Utmp, *PPtmp, zero, *U1tmp );
  }
 
  // U(:,1:keff) = U(:,1:keff) + matmul(V(:,1:m-k),PP(keff_old+1:m-k+keff_old,1:keff)) (step 2)
  {
    index.resize(p);
    for (int ii=0; ii < p; ii++) { index[ii] = ii; }
    Teuchos::RCP<const MV> Vtmp = MVT::CloneView( *V_, index );
    Teuchos::RCP<const DM> PPtmp = DMT::SubviewConst( *PP_, p, keff_new, keff );
    MVT::MvTimesMatAddMv( one, *Vtmp, *PPtmp, one, *U1tmp );
  }
 
  // Form HP = H*P
  DMT::SyncDeviceToHost( *HP_ );
  Teuchos::RCP<DM> HPtmp = DMT::Subview( *HP_, p+keff+1, keff_new );
  {
    DMT::SyncDeviceToHost( *PP_ );
    Teuchos::RCP<DM> PPtmp = DMT::Subview( *PP_, p+keff, keff_new );
 
    Teuchos::BLAS<int,ScalarType> blas;
    blas.GEMM( Teuchos::NO_TRANS, Teuchos::NO_TRANS, p+keff+1, keff_new, p+keff, one,
                   DMT::GetConstRawHostPtr(*H2tmp), DMT::GetStride(*H2tmp),
                   DMT::GetConstRawHostPtr(*PPtmp), DMT::GetStride(*PPtmp),
                   zero, DMT::GetRawHostPtr(*HPtmp), DMT::GetStride(*HPtmp));
  }
 
  // Workspace size query for QR factorization of HP (the worksize will be placed in work_[0])
  int info = 0, lwork = -1;
  tau_.resize (keff_new);
  lapack.GEQRF (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetRawHostPtr(*HPtmp),
                DMT::GetStride(*HPtmp), &tau_[0], &work_[0], lwork, &info);
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
    "LAPACK's _GEQRF failed to compute a workspace size.");
 
  // NOTE (mfh 18 Apr 2014) LAPACK promises that the value of work_[0]
  // after the workspace query will fit in int.  This justifies the
  // cast.  We call real() first because static_cast from std::complex
  // to int doesn't work.
  lwork = std::abs (static_cast<int> (Teuchos::ScalarTraits<ScalarType>::real (work_[0])));
  work_.resize (lwork); // Allocate workspace for the QR factorization
  lapack.GEQRF (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetRawHostPtr(*HPtmp),
                DMT::GetStride(*HPtmp), &tau_[0], &work_[0], lwork, &info);
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
    "LAPACK's _GEQRF failed to compute a QR factorization.");
 
  // Explicitly construct Q and R factors
  // NOTE:  The upper triangular part of HP is copied into R and HP becomes Q.
  DMT::SyncDeviceToHost( *R_ );
  Teuchos::RCP<DM> Rtmp = DMT::Subview( *R_, keff_new, keff_new );
  for(int i=0;i<keff_new;i++) { for(int j=i;j<keff_new;j++) DMT::Value(*Rtmp,i,j) = DMT::ValueConst(*HPtmp,i,j); }
 
  // NOTE (mfh 18 Apr 2014): Teuchos::LAPACK's wrapper for UNGQR
  // dispatches to the correct Scalar-specific routine.  It calls
  // {S,D}ORGQR if Scalar is real, and {C,Z}UNGQR if Scalar is
  // complex.
  lapack.UNGQR (DMT::GetNumRows(*HPtmp), DMT::GetNumCols(*HPtmp), DMT::GetNumCols(*HPtmp),
                DMT::GetRawHostPtr(*HPtmp), DMT::GetStride(*HPtmp), &tau_[0], &work_[0],
                lwork, &info);
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve: "
    "LAPACK's _UNGQR failed to construct the Q factor.");
 
  DMT::SyncHostToDevice( *HP_ );
  HPtmp = Teuchos::null;
 
  // Form orthonormalized C and adjust U accordingly so that C = A*U
  // C = [C V] * Q;
 
  // C(:,1:keff) = matmul(C(:,1:keff_old),QQ(1:keff_old,1:keff))
  {
    Teuchos::RCP<MV> C1tmp;
    {
      index.resize(keff);
      for (int i=0; i < keff; i++) { index[i] = i; }
      Teuchos::RCP<const MV> Ctmp  = MVT::CloneView( *C_,  index );
      index.resize(keff_new);
      for (int i=0; i < keff_new; i++) { index[i] = i; }
      C1tmp  = MVT::CloneViewNonConst( *C1_,  index );
      Teuchos::RCP<const DM> PPtmp = DMT::SubviewConst( *HP_, keff, keff_new );
      MVT::MvTimesMatAddMv( one, *Ctmp, *PPtmp, zero, *C1tmp );
    }
    // Now compute C += V(:,1:p+1) * Q
    {
      index.resize( p+1 );
      for (int i=0; i < p+1; ++i) { index[i] = i; }
      Teuchos::RCP<const MV> Vtmp = MVT::CloneView( *V_, index );
      Teuchos::RCP<const DM> PPtmp = DMT::SubviewConst( *HP_, p+1, keff_new, keff, 0 );
      MVT::MvTimesMatAddMv( one, *Vtmp, *PPtmp, one, *C1tmp );
    }
  }
 
  // C_ = C1_; (via a swap)
  std::swap(C_, C1_);
 
  // Finally, compute U_ = U_*R^{-1}
  // First, compute LU factorization of R
  ipiv_.resize(DMT::GetNumRows(*Rtmp));
  lapack.GETRF(DMT::GetNumRows(*Rtmp),DMT::GetNumCols(*Rtmp),DMT::GetRawHostPtr(*Rtmp),DMT::GetStride(*Rtmp),&ipiv_[0],&info);
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0,GCRODRSolMgrLAPACKFailure,"Belos::GCRODRSolMgr::buildRecycleSpace2(): LAPACK _GETRF failed to compute an LU factorization.");
 
  // Now, form inv(R)
  lwork = DMT::GetNumRows(*Rtmp);
  work_.resize(lwork);
  lapack.GETRI(DMT::GetNumRows(*Rtmp),DMT::GetRawHostPtr(*Rtmp),DMT::GetStride(*Rtmp),&ipiv_[0],&work_[0],lwork,&info);
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure,"Belos::GCRODRSolMgr::buildRecycleSpace2(): LAPACK _GETRI failed to compute an LU factorization.");
 
  DMT::SyncHostToDevice(*R_);
 
  {
    index.resize(keff_new);
    for (int i=0; i < keff_new; i++) { index[i] = i; }
    Teuchos::RCP<MV> Utmp  = MVT::CloneViewNonConst( *U_,  index );
    MVT::MvTimesMatAddMv( one, *U1tmp, *Rtmp, zero, *Utmp );
  }
 
  // Set the current number of recycled blocks and subspace dimension with the GCRO-DR iteration.
  if (keff != keff_new) {
    keff = keff_new;
    gcrodr_iter->setSize( keff, numBlocks_ );
    // Important to zero this out before next cyle
    Teuchos::RCP<DM> b1 = DMT::Subview( *H2_, recycledBlocks_+2, 1, 0, recycledBlocks_ );
    DMT::PutScalar( *b1, zero );
  }
 
}
 
// Given existing recycle space and flexible Krylov space, build new recycle space.
// Flexible version:
//   correction basis: [U, Z]
//   image basis:      [C, V]
//   auxiliary basis:  [W, V_m]
template<class ScalarType, class MV, class OP, class DM>
void
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::
buildFlexibleRecycleSpace2(Teuchos::RCP<GCRODRIteration<ScalarType,MV,OP,DM> > gcrodr_iter)
{
  MagnitudeType magOne = Teuchos::ScalarTraits<MagnitudeType>::one();
  ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
  ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
 
  std::vector<MagnitudeType> d(keff);
  std::vector<ScalarType> dscalar(keff);
  std::vector<int> index(numBlocks_+1);
 
  GCRODRIterState<ScalarType,MV,DM> oldState = gcrodr_iter->getState();
  int p = oldState.curDim;
 
  if (p < 1) return;
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    oldState.Z == Teuchos::null,
    GCRODRSolMgrRecyclingFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): oldState.Z is null.");
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    W_ == Teuchos::null,
    GCRODRSolMgrRecyclingFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): W_ is null.");
 
  // Scale U and W consistently.
  {
    index.resize(keff);
    for (int ii=0; ii<keff; ++ii) index[ii] = ii;
 
    Teuchos::RCP<MV> Utmp = MVT::CloneViewNonConst(*U_, index);
    Teuchos::RCP<MV> Wtmp = MVT::CloneViewNonConst(*W_, index);
 
    d.resize(keff);
    dscalar.resize(keff);
 
    MVT::MvNorm(*Utmp, d);
    for (int i=0; i<keff; ++i) {
      d[i] = magOne / d[i];
      dscalar[i] = static_cast<ScalarType>(d[i]);
    }
 
    MVT::MvScale(*Utmp, dscalar);
    MVT::MvScale(*Wtmp, dscalar);
  }
 
  // Get view into current full projected matrix.
  DMT::SyncDeviceToHost(*H2_);
  Teuchos::RCP<DM> H2tmp = DMT::Subview(*H2_, p+keff+1, p+keff);
 
  // Insert D into the leading keff x keff block of H2.
  for (int i=0; i<keff; ++i) {
    DMT::Value(*H2tmp, i, i) = d[i];
  }
 
  DMT::SyncHostToDevice(*H2_);
 
  // Compute flexible harmonic Ritz vectors.
  int keff_new;
  {
    DMT::SyncDeviceToHost(*PP_);
    Teuchos::RCP<DM> PPtmp = DMT::Subview(*PP_, p+keff, recycledBlocks_+1);
    keff_new = getFlexibleHarmonicVecs2(keff, p, *H2tmp, oldState.V, *PPtmp);
    DMT::SyncHostToDevice(*PP_);
  }
 
  // U1 = [U, Z] * P.
  Teuchos::RCP<MV> U1tmp;
  {
    index.resize(keff);
    for (int ii=0; ii<keff; ++ii) index[ii] = ii;
 
    Teuchos::RCP<const MV> Utmp = MVT::CloneView(*U_, index);
 
    index.resize(keff_new);
    for (int ii=0; ii<keff_new; ++ii) index[ii] = ii;
 
    U1tmp = MVT::CloneViewNonConst(*U1_, index);
 
    Teuchos::RCP<const DM> PPtop = DMT::SubviewConst(*PP_, keff, keff_new);
    MVT::MvTimesMatAddMv(one, *Utmp, *PPtop, zero, *U1tmp);
  }
 
  {
    index.resize(p);
    for (int ii=0; ii<p; ++ii) index[ii] = ii;
 
    Teuchos::RCP<const MV> Ztmp = MVT::CloneView(*oldState.Z, index);
    Teuchos::RCP<const DM> PPbottom = DMT::SubviewConst(*PP_, p, keff_new, keff);
 
    MVT::MvTimesMatAddMv(one, *Ztmp, *PPbottom, one, *U1tmp);
  }
 
  // W1 = [W, V_m] * P.
  Teuchos::RCP<MV> W1tmp;
  {
    index.resize(keff);
    for (int ii=0; ii<keff; ++ii) index[ii] = ii;
 
    Teuchos::RCP<const MV> Wtmp = MVT::CloneView(*W_, index);
 
    index.resize(keff_new);
    for (int ii=0; ii<keff_new; ++ii) index[ii] = ii;
 
    W1tmp = MVT::CloneViewNonConst(*W1_, index);
 
    Teuchos::RCP<const DM> PPtop = DMT::SubviewConst(*PP_, keff, keff_new);
    MVT::MvTimesMatAddMv(one, *Wtmp, *PPtop, zero, *W1tmp);
  }
 
  {
    index.resize(p);
    for (int ii=0; ii<p; ++ii) index[ii] = ii;
 
    Teuchos::RCP<const MV> Vtmp = MVT::CloneView(*oldState.V, index);
    Teuchos::RCP<const DM> PPbottom = DMT::SubviewConst(*PP_, p, keff_new, keff);
 
    MVT::MvTimesMatAddMv(one, *Vtmp, *PPbottom, one, *W1tmp);
  }
 
  // HP = H * P.
  DMT::SyncDeviceToHost(*HP_);
  Teuchos::RCP<DM> HPtmp = DMT::Subview(*HP_, p+keff+1, keff_new);
 
  {
    DMT::SyncDeviceToHost(*PP_);
    DMT::SyncDeviceToHost(*H2_);
    Teuchos::RCP<DM> PPtmp = DMT::Subview(*PP_, p+keff, keff_new);
 
    Teuchos::BLAS<int,ScalarType> blas;
    blas.GEMM(Teuchos::NO_TRANS, Teuchos::NO_TRANS,
              p+keff+1, keff_new, p+keff,
              one,
              DMT::GetConstRawHostPtr(*H2tmp), DMT::GetStride(*H2tmp),
              DMT::GetConstRawHostPtr(*PPtmp), DMT::GetStride(*PPtmp),
              zero,
              DMT::GetRawHostPtr(*HPtmp), DMT::GetStride(*HPtmp));
  }
 
  // QR factorization of HP.
  int info = 0;
  int lwork = -1;
 
  tau_.resize(keff_new);
  if (work_.size() < 1) work_.resize(1);
 
  lapack.GEQRF(DMT::GetNumRows(*HPtmp),
               DMT::GetNumCols(*HPtmp),
               DMT::GetRawHostPtr(*HPtmp),
               DMT::GetStride(*HPtmp),
               &tau_[0], &work_[0], lwork, &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): LAPACK GEQRF workspace query failed.");
 
  lwork = std::abs(static_cast<int>(Teuchos::ScalarTraits<ScalarType>::real(work_[0])));
  work_.resize(lwork);
 
  lapack.GEQRF(DMT::GetNumRows(*HPtmp),
               DMT::GetNumCols(*HPtmp),
               DMT::GetRawHostPtr(*HPtmp),
               DMT::GetStride(*HPtmp),
               &tau_[0], &work_[0], lwork, &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): LAPACK GEQRF failed.");
 
  // Copy R from upper triangular part of HP.
  DMT::SyncDeviceToHost(*R_);
  Teuchos::RCP<DM> Rtmp = DMT::Subview(*R_, keff_new, keff_new);
 
  for (int i=0; i<keff_new; ++i) {
    for (int j=i; j<keff_new; ++j) {
      DMT::Value(*Rtmp, i, j) = DMT::ValueConst(*HPtmp, i, j);
    }
  }
 
  // Form Q explicitly in HPtmp.
  lapack.UNGQR(DMT::GetNumRows(*HPtmp),
               DMT::GetNumCols(*HPtmp),
               DMT::GetNumCols(*HPtmp),
               DMT::GetRawHostPtr(*HPtmp),
               DMT::GetStride(*HPtmp),
               &tau_[0], &work_[0], lwork, &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): LAPACK UNGQR failed.");
 
  DMT::SyncHostToDevice(*HP_);
 
  // C1 = [C, V_{p+1}] * Q.
  {
    Teuchos::RCP<MV> C1tmp;
 
    {
      index.resize(keff);
      for (int i=0; i<keff; ++i) index[i] = i;
 
      Teuchos::RCP<const MV> Ctmp = MVT::CloneView(*C_, index);
 
      index.resize(keff_new);
      for (int i=0; i<keff_new; ++i) index[i] = i;
 
      C1tmp = MVT::CloneViewNonConst(*C1_, index);
 
      Teuchos::RCP<const DM> Qtop = DMT::SubviewConst(*HP_, keff, keff_new);
      MVT::MvTimesMatAddMv(one, *Ctmp, *Qtop, zero, *C1tmp);
    }
 
    {
      index.resize(p+1);
      for (int i=0; i<p+1; ++i) index[i] = i;
 
      Teuchos::RCP<const MV> Vtmp = MVT::CloneView(*oldState.V, index);
      Teuchos::RCP<const DM> Qbottom = DMT::SubviewConst(*HP_, p+1, keff_new, keff, 0);
 
      MVT::MvTimesMatAddMv(one, *Vtmp, *Qbottom, one, *C1tmp);
    }
  }
 
  std::swap(C_, C1_);
 
  // Compute R^{-1}.
  ipiv_.resize(DMT::GetNumRows(*Rtmp));
 
  lapack.GETRF(DMT::GetNumRows(*Rtmp),
               DMT::GetNumCols(*Rtmp),
               DMT::GetRawHostPtr(*Rtmp),
               DMT::GetStride(*Rtmp),
               &ipiv_[0], &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): LAPACK GETRF failed.");
 
  lwork = DMT::GetNumRows(*Rtmp);
  work_.resize(lwork);
 
  lapack.GETRI(DMT::GetNumRows(*Rtmp),
               DMT::GetRawHostPtr(*Rtmp),
               DMT::GetStride(*Rtmp),
               &ipiv_[0], &work_[0], lwork, &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::buildFlexibleRecycleSpace2(): LAPACK GETRI failed.");
 
  DMT::SyncHostToDevice(*R_);
 
  {
    index.resize(keff_new);
    for (int i=0; i<keff_new; ++i) index[i] = i;
 
    Teuchos::RCP<MV> Utmp = MVT::CloneViewNonConst(*U_, index);
    Teuchos::RCP<const MV> U1tmpConst = MVT::CloneView(*U1_, index);
    MVT::MvTimesMatAddMv(one, *U1tmpConst, *Rtmp, zero, *Utmp);
 
    Teuchos::RCP<MV> Wtmp = MVT::CloneViewNonConst(*W_, index);
    Teuchos::RCP<const MV> W1tmpConst = MVT::CloneView(*W1_, index);
    MVT::MvTimesMatAddMv(one, *W1tmpConst, *Rtmp, zero, *Wtmp);
  }
 
  if (keff != keff_new) {
    keff = keff_new;
    gcrodr_iter->setSize(keff, numBlocks_);
 
    Teuchos::RCP<DM> b1 = DMT::Subview(*H2_, recycledBlocks_+2, 1, 0, recycledBlocks_);
    DMT::PutScalar(*b1, zero);
  }
}
 
 
//  Compute the harmonic eigenpairs of the projected, dense system.
template<class ScalarType, class MV, class OP, class DM>
int GCRODRSolMgr<ScalarType,MV,OP,DM,true>::getHarmonicVecs1(int m, const DM& HH, DM& PP) {
 
  int i, j;
  bool xtraVec = false;
  ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
 
  // Real and imaginary eigenvalue components
  std::vector<MagnitudeType> wr(m), wi(m);
 
  // Real and imaginary (right) eigenvectors; Don't zero out matrix when constructing
  Teuchos::RCP<DM> vr = DMT::Create(m,m,false);
 
  // Magnitude of harmonic Ritz values
  std::vector<MagnitudeType> w(m);
 
  // Sorted order of harmonic Ritz values, also used for GEEV
  std::vector<int> iperm(m);
 
  // Output info
  int info = 0;
 
  // Set flag indicating recycle space has been generated this solve
  builtRecycleSpace_ = true;
 
  // Solve linear system:  H_m^{-H}*e_m
  Teuchos::RCP<DM> HHt = DMT::CreateCopy( HH, true );
  Teuchos::RCP<DM> e_m = DMT::Create( m, 1 );
  DMT::SyncDeviceToHost( *HHt );
 
  DMT::Value( *e_m, m-1, 0 ) = one;
  lapack.GESV(m, 1, DMT::GetRawHostPtr(*HHt), DMT::GetStride(*HHt), &iperm[0], DMT::GetRawHostPtr(*e_m), DMT::GetStride(*e_m), &info);
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve(): LAPACK GESV failed to compute a solution.");
 
  // Compute H_m + d*H_m^{-H}*e_m*e_m^H
  Teuchos::RCP<DM> tmpHH = DMT::CreateCopy( HH );
  DMT::SyncDeviceToHost( *tmpHH );
 
  ScalarType d = DMT::ValueConst(*tmpHH, m, m-1) * DMT::ValueConst(*tmpHH, m, m-1);
  Teuchos::RCP<DM> harmHH = DMT::Subview( *tmpHH, m, m );
  for( i=0; i<m; ++i )
    DMT::Value(*harmHH, i, m-1) += d * DMT::ValueConst(*e_m, i, 0);
 
  // Revise to do query for optimal workspace first
  // Create simple storage for the left eigenvectors, which we don't care about.
  const int ldvl = 1;
  ScalarType* vl = 0;
 
  // Size of workspace and workspace for GEEV
  int lwork = -1;
  std::vector<ScalarType> work(1);
  std::vector<MagnitudeType> rwork(2*m);
 
  // First query GEEV for the optimal workspace size
  lapack.GEEV('N', 'V', m, DMT::GetRawHostPtr(*harmHH), DMT::GetStride(*harmHH), &wr[0], &wi[0],
              vl, ldvl, DMT::GetRawHostPtr(*vr), DMT::GetStride(*vr), &work[0], lwork, &rwork[0], &info);
 
  lwork = std::abs (static_cast<int> (Teuchos::ScalarTraits<ScalarType>::real (work[0])));
  work.resize( lwork );
 
  lapack.GEEV('N', 'V', m, DMT::GetRawHostPtr(*harmHH), DMT::GetStride(*harmHH), &wr[0], &wi[0],
              vl, ldvl, DMT::GetRawHostPtr(*vr), DMT::GetStride(*vr), &work[0], lwork, &rwork[0], &info);
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure,"Belos::GCRODRSolMgr::solve(): LAPACK GEEV failed to compute eigensolutions.");
 
  // Construct magnitude of each harmonic Ritz value
  for( i=0; i<m; ++i )
    w[i] = Teuchos::ScalarTraits<MagnitudeType>::squareroot( wr[i]*wr[i] + wi[i]*wi[i] );
 
  // Construct magnitude of each harmonic Ritz value
  this->sort(w, m, iperm);
 
  const bool scalarTypeIsComplex = Teuchos::ScalarTraits<ScalarType>::isComplex;
 
  // Select recycledBlocks_ smallest eigenvectors
  for( i=0; i<recycledBlocks_; ++i ) {
    for( j=0; j<m; j++ ) {
      DMT::Value(PP,j,i) = DMT::ValueConst(*vr,j,iperm[i]);
    }
  }
 
  if(!scalarTypeIsComplex) {
 
    // Determine exact size for PP (i.e., determine if we need to store an additional vector)
    if (wi[iperm[recycledBlocks_-1]] != 0.0) {
      int countImag = 0;
      for ( i=0; i<recycledBlocks_; ++i ) {
        if (wi[iperm[i]] != 0.0)
          countImag++;
      }
      // Check to see if this count is even or odd:
      if (countImag % 2)
        xtraVec = true;
    }
 
    if (xtraVec) { // we need to store one more vector
      if (wi[iperm[recycledBlocks_-1]] > 0.0) { // I picked the "real" component
        for( j=0; j<m; ++j ) {   // so get the "imag" component
    DMT::Value(PP,j,recycledBlocks_) = DMT::ValueConst(*vr,j,iperm[recycledBlocks_-1]+1);
        }
      }
      else { //  I picked the "imag" component
        for( j=0; j<m; ++j ) {   // so get the "real" component
    DMT::Value(PP,j,recycledBlocks_) = DMT::ValueConst(*vr,j,iperm[recycledBlocks_-1]-1);
        }
      }
    }
 
  }
 
  // Return whether we needed to store an additional vector
  if (xtraVec) {
    return recycledBlocks_+1;
  }
  else {
    return recycledBlocks_;
  }
 
}
 
//  Compute the harmonic eigenpairs of the projected, dense system.
template<class ScalarType, class MV, class OP, class DM>
int GCRODRSolMgr<ScalarType,MV,OP,DM,true>::getHarmonicVecs2(int keffloc, int m,
                                                     const DM& HH,
                                                     const Teuchos::RCP<const MV>& VV,
                                                     DM& PP) {
  int i, j;
  int m2 = DMT::GetNumCols(HH);
  bool xtraVec = false;
  ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
  ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
  std::vector<int> index;
 
  // Real and imaginary eigenvalue components
  std::vector<MagnitudeType> wr(m2), wi(m2);
 
  // Magnitude of harmonic Ritz values
  std::vector<MagnitudeType> w(m2);
 
  // Real and imaginary (right) eigenvectors; Don't zero out matrix when constructing
  Teuchos::RCP<DM> vr = DMT::Create(m2,m2,false);
 
  // Sorted order of harmonic Ritz values
  std::vector<int> iperm(m2);
 
  // Set flag indicating recycle space has been generated this solve
  builtRecycleSpace_ = true;
 
  // Form matrices for generalized eigenproblem
 
  // B = H2' * H2; Don't zero out matrix when constructing
  Teuchos::RCP<DM> B = DMT::Create(m2,m2,false);
 
  Teuchos::BLAS<int,ScalarType> blas;
  blas.GEMM( Teuchos::TRANS, Teuchos::NO_TRANS, m2, m2, DMT::GetNumRows(HH), one,
             DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
             DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
             zero, DMT::GetRawHostPtr(*B), DMT::GetStride(*B));
 
  // A_tmp = | C'*U        0 |
  //         | V_{m+1}'*U  I |
  Teuchos::RCP<DM> A_tmp = DMT::Create( keffloc+m+1, keffloc+m );
 
  // A_tmp(1:keffloc,1:keffloc) = C' * U;
  index.resize(keffloc);
  for (i=0; i<keffloc; ++i) { index[i] = i; }
  Teuchos::RCP<const MV> Ctmp  = MVT::CloneView( *C_, index );
  Teuchos::RCP<const MV> Utmp  = MVT::CloneView( *U_, index );
  Teuchos::RCP<DM> A11 = DMT::Subview( *A_tmp, keffloc, keffloc );
  MVT::MvTransMv( one, *Ctmp, *Utmp, *A11 );
 
  // A_tmp(keffloc+1:m-k+keffloc+1,1:keffloc) = V' * U;
  Teuchos::RCP<DM> A21 = DMT::Subview( *A_tmp, m+1, keffloc, keffloc );
  index.resize(m+1);
  for (i=0; i < m+1; i++) { index[i] = i; }
  Teuchos::RCP<const MV> Vp = MVT::CloneView( *VV, index );
  MVT::MvTransMv( one, *Vp, *Utmp, *A21 );
 
  A11 = Teuchos::null;
  A21 = Teuchos::null;
  DMT::SyncDeviceToHost(*A_tmp);
 
  // A_tmp(keffloc+1:m-k+keffloc,keffloc+1:m-k+keffloc) = eye(m-k);
  for( i=keffloc; i<keffloc+m; i++ ) {
    DMT::Value(*A_tmp,i,i) = one;
  }
 
  // A = H2' * A_tmp;
  Teuchos::RCP<DM> A = DMT::Create( m2, DMT::GetNumCols(*A_tmp) );
  blas.GEMM( Teuchos::TRANS, Teuchos::NO_TRANS, m2, DMT::GetNumCols(*A_tmp), DMT::GetNumRows(*A_tmp),
             one, DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
       DMT::GetConstRawHostPtr(*A_tmp), DMT::GetStride(*A_tmp),
       zero, DMT::GetRawHostPtr(*A), DMT::GetStride(*A) );
 
  // Compute k smallest harmonic Ritz pairs
  // SUBROUTINE DGGEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, B, LDB,
  //                   ALPHAR, ALPHAI, BETA, VL, LDVL, VR, LDVR, ILO,
  //                   IHI, LSCALE, RSCALE, ABNRM, BBNRM, RCONDE,
  //                   RCONDV, WORK, LWORK, IWORK, BWORK, INFO )
  // MLP: 'SCALING' in DGGEVX generates incorrect eigenvalues. Therefore, only permuting
  char balanc='P', jobvl='N', jobvr='V', sense='N';
  int ld = DMT::GetNumRows(*A);
  int lwork = 6*ld;
  int ldvl = ld, ldvr = ld;
  int info = 0,ilo = 0,ihi = 0;
  MagnitudeType abnrm = 0.0, bbnrm = 0.0;
  ScalarType *vl = 0; // This is never referenced by dggevx if jobvl == 'N'
  std::vector<ScalarType> beta(ld);
  std::vector<ScalarType> work(lwork);
  std::vector<MagnitudeType> rwork(lwork);
  std::vector<MagnitudeType> lscale(ld), rscale(ld);
  std::vector<MagnitudeType> rconde(ld), rcondv(ld);
  std::vector<int> iwork(ld+6);
  int *bwork = 0; // If sense == 'N', bwork is never referenced
  //lapack.GGEVX(balanc, jobvl, jobvr, sense, ld, A.values(), ld, B.values(), ld, &wr[0], &wi[0],
  //             &beta[0], vl, ldvl, vr.values(), ldvr, &ilo, &ihi, &lscale[0], &rscale[0],
  //             &abnrm, &bbnrm, &rconde[0], &rcondv[0], &work[0], lwork, &iwork[0], bwork, &info);
  lapack.GGEVX(balanc, jobvl, jobvr, sense, ld, DMT::GetRawHostPtr(*A), ld, DMT::GetRawHostPtr(*B), 
         ld, &wr[0], &wi[0], &beta[0], vl, ldvl, DMT::GetRawHostPtr(*vr), ldvr, &ilo, &ihi, 
         &lscale[0], &rscale[0], &abnrm, &bbnrm, &rconde[0], &rcondv[0], &work[0], lwork, &rwork[0],
               &iwork[0], bwork, &info);
  TEUCHOS_TEST_FOR_EXCEPTION(info != 0, GCRODRSolMgrLAPACKFailure, "Belos::GCRODRSolMgr::solve(): LAPACK GGEVX failed to compute eigensolutions.");
 
  // Construct magnitude of each harmonic Ritz value
  // NOTE : Forming alpha/beta *should* be okay here, given assumptions on construction of matrix pencil above
  for( i=0; i<ld; i++ ) {
    w[i] = Teuchos::ScalarTraits<MagnitudeType>::squareroot (wr[i]*wr[i] + wi[i]*wi[i]) /
      Teuchos::ScalarTraits<ScalarType>::magnitude (beta[i]);
  }
 
  // Construct magnitude of each harmonic Ritz value
  this->sort(w,ld,iperm);
 
  const bool scalarTypeIsComplex = Teuchos::ScalarTraits<ScalarType>::isComplex;
 
  // Select recycledBlocks_ smallest eigenvectors
  for( i=0; i<recycledBlocks_; i++ ) {
    for( j=0; j<ld; j++ ) {
      DMT::Value(PP,j,i) = DMT::ValueConst(*vr,j,iperm[ld-recycledBlocks_+i]);
    }
  }
 
  if(!scalarTypeIsComplex) {
 
    // Determine exact size for PP (i.e., determine if we need to store an additional vector)
    if (wi[iperm[ld-recycledBlocks_]] != 0.0) {
      int countImag = 0;
      for ( i=ld-recycledBlocks_; i<ld; i++ ) {
        if (wi[iperm[i]] != 0.0)
          countImag++;
      }
      // Check to see if this count is even or odd:
      if (countImag % 2)
        xtraVec = true;
    }
 
    if (xtraVec) { // we need to store one more vector
      if (wi[iperm[ld-recycledBlocks_]] > 0.0) { // I picked the "real" component
        for( j=0; j<ld; j++ ) {   // so get the "imag" component
    DMT::Value(PP,j,recycledBlocks_) = DMT::ValueConst(*vr,j,iperm[ld-recycledBlocks_]+1);
        }
      }
      else { // I picked the "imag" component
        for( j=0; j<ld; j++ ) {   // so get the "real" component
    DMT::Value(PP,j,recycledBlocks_) = DMT::ValueConst(*vr,j,iperm[ld-recycledBlocks_]-1);
        }
      }
    }
 
  }
 
  // Return whether we needed to store an additional vector
  if (xtraVec) {
    return recycledBlocks_+1;
  }
  else {
    return recycledBlocks_;
  }
 
}
 
 
 
// Compute harmonic Ritz vectors for flexible GCRODR.
//
// This uses the paper-compatible auxiliary space W:
//   T     = [C, V_{m+1}]
//   Wfull = [W, V_m]
// and forms the small projected pencil
//   H^H H p = theta H^H (T^H Wfull) p.
template<class ScalarType, class MV, class OP, class DM>
int
GCRODRSolMgr<ScalarType,MV,OP,DM,true>::
getFlexibleHarmonicVecs2(int keffloc, int m,
                         const DM& HH,
                         const Teuchos::RCP<const MV>& VV,
                         DM& PP)
{
  int i, j;
  int m2 = DMT::GetNumCols(HH);
  bool xtraVec = false;
 
  ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
  ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
 
  std::vector<int> index;
 
  std::vector<MagnitudeType> wr(m2), wi(m2);
  std::vector<MagnitudeType> w(m2);
 
  Teuchos::RCP<DM> vr = DMT::Create(m2, m2, false);
 
  std::vector<int> iperm(m2);
 
  builtRecycleSpace_ = true;
 
  // B = H^H H.
  Teuchos::RCP<DM> B = DMT::Create(m2, m2, false);
 
  Teuchos::BLAS<int,ScalarType> blas;
  blas.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS,
            m2, m2, DMT::GetNumRows(HH),
            one,
            DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
            DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
            zero,
            DMT::GetRawHostPtr(*B), DMT::GetStride(*B));
 
  // A_tmp = T^H Wfull.
  Teuchos::RCP<DM> A_tmp = DMT::Create(keffloc + m + 1, keffloc + m);
  DMT::PutScalar(*A_tmp, zero);
 
  // A11 = C^H W.
  index.resize(keffloc);
  for (i=0; i<keffloc; ++i) index[i] = i;
 
  Teuchos::RCP<const MV> Ctmp = MVT::CloneView(*C_, index);
  Teuchos::RCP<const MV> Wtmp = MVT::CloneView(*W_, index);
  Teuchos::RCP<DM> A11 = DMT::Subview(*A_tmp, keffloc, keffloc);
 
  MVT::MvTransMv(one, *Ctmp, *Wtmp, *A11);
 
  // A21 = V_{m+1}^H W.
  Teuchos::RCP<DM> A21 = DMT::Subview(*A_tmp, m+1, keffloc, keffloc);
 
  index.resize(m+1);
  for (i=0; i<m+1; ++i) index[i] = i;
 
  Teuchos::RCP<const MV> Vp = MVT::CloneView(*VV, index);
 
  index.resize(keffloc);
  for (i=0; i<keffloc; ++i) index[i] = i;
 
  Wtmp = MVT::CloneView(*W_, index);
 
  MVT::MvTransMv(one, *Vp, *Wtmp, *A21);
 
  A11 = Teuchos::null;
  A21 = Teuchos::null;
 
  DMT::SyncDeviceToHost(*A_tmp);
 
  // A22 = V_{m+1}^H V_m = [I; 0].
  for (i=0; i<m; ++i) {
    DMT::Value(*A_tmp, keffloc+i, keffloc+i) = one;
  }
 
  // A = H^H A_tmp.
  Teuchos::RCP<DM> A = DMT::Create(m2, DMT::GetNumCols(*A_tmp));
 
  blas.GEMM(Teuchos::TRANS, Teuchos::NO_TRANS,
            m2, DMT::GetNumCols(*A_tmp), DMT::GetNumRows(*A_tmp),
            one,
            DMT::GetConstRawHostPtr(HH), DMT::GetStride(HH),
            DMT::GetConstRawHostPtr(*A_tmp), DMT::GetStride(*A_tmp),
            zero,
            DMT::GetRawHostPtr(*A), DMT::GetStride(*A));
 
  char balanc = 'P', jobvl = 'N', jobvr = 'V', sense = 'N';
 
  int ld = DMT::GetNumRows(*A);
  int lwork = 6 * ld;
  int ldvl = ld, ldvr = ld;
  int info = 0, ilo = 0, ihi = 0;
 
  MagnitudeType abnrm = 0.0, bbnrm = 0.0;
  ScalarType* vl = 0;
 
  std::vector<ScalarType> beta(ld);
  std::vector<ScalarType> work(lwork);
  std::vector<MagnitudeType> rwork(lwork);
  std::vector<MagnitudeType> lscale(ld), rscale(ld);
  std::vector<MagnitudeType> rconde(ld), rcondv(ld);
  std::vector<int> iwork(ld+6);
  int* bwork = 0;
 
  lapack.GGEVX(balanc, jobvl, jobvr, sense, ld,
               DMT::GetRawHostPtr(*A), ld,
               DMT::GetRawHostPtr(*B), ld,
               &wr[0], &wi[0], &beta[0],
               vl, ldvl,
               DMT::GetRawHostPtr(*vr), ldvr,
               &ilo, &ihi,
               &lscale[0], &rscale[0],
               &abnrm, &bbnrm,
               &rconde[0], &rcondv[0],
               &work[0], lwork, &rwork[0],
               &iwork[0], bwork, &info);
 
  TEUCHOS_TEST_FOR_EXCEPTION(
    info != 0,
    GCRODRSolMgrLAPACKFailure,
    "Belos::GCRODRSolMgr::getFlexibleHarmonicVecs2(): LAPACK GGEVX failed to compute eigensolutions.");
 
  for (i=0; i<ld; ++i) {
    w[i] =
      Teuchos::ScalarTraits<MagnitudeType>::squareroot(wr[i]*wr[i] + wi[i]*wi[i]) /
      Teuchos::ScalarTraits<ScalarType>::magnitude(beta[i]);
  }
 
  this->sort(w, ld, iperm);
 
  const bool scalarTypeIsComplex = Teuchos::ScalarTraits<ScalarType>::isComplex;
 
  for (i=0; i<recycledBlocks_; ++i) {
    for (j=0; j<ld; ++j) {
      DMT::Value(PP, j, i) =
        DMT::ValueConst(*vr, j, iperm[ld-recycledBlocks_+i]);
    }
  }
 
  if (!scalarTypeIsComplex) {
    if (wi[iperm[ld-recycledBlocks_]] != 0.0) {
      int countImag = 0;
      for (i=ld-recycledBlocks_; i<ld; ++i) {
        if (wi[iperm[i]] != 0.0) {
          countImag++;
        }
      }
 
      if (countImag % 2) {
        xtraVec = true;
      }
    }
 
    if (xtraVec) {
      if (wi[iperm[ld-recycledBlocks_]] > 0.0) {
        for (j=0; j<ld; ++j) {
          DMT::Value(PP, j, recycledBlocks_) =
            DMT::ValueConst(*vr, j, iperm[ld-recycledBlocks_]+1);
        }
      }
      else {
        for (j=0; j<ld; ++j) {
          DMT::Value(PP, j, recycledBlocks_) =
            DMT::ValueConst(*vr, j, iperm[ld-recycledBlocks_]-1);
        }
      }
    }
  }
 
  if (xtraVec) {
    return recycledBlocks_ + 1;
  }
  else {
    return recycledBlocks_;
  }
}
 
 
// This method sorts list of n floating-point numbers and return permutation vector
template<class ScalarType, class MV, class OP, class DM>
void GCRODRSolMgr<ScalarType,MV,OP,DM,true>::sort(std::vector<MagnitudeType>& dlist, int n, std::vector<int>& iperm) {
  int l, r, j, i, flag;
  int    RR2;
  MagnitudeType dRR, dK;
 
  // Initialize the permutation vector.
  for(j=0;j<n;j++)
    iperm[j] = j;
 
  if (n <= 1) return;
 
  l    = n / 2 + 1;
  r    = n - 1;
  l    = l - 1;
  dRR  = dlist[l - 1];
  dK   = dlist[l - 1];
 
  RR2 = iperm[l - 1];
  while (r != 0) {
    j = l;
    flag = 1;
 
    while (flag == 1) {
      i = j;
      j = j + j;
 
      if (j > r + 1)
        flag = 0;
      else {
        if (j < r + 1)
          if (dlist[j] > dlist[j - 1]) j = j + 1;
 
        if (dlist[j - 1] > dK) {
          dlist[i - 1] = dlist[j - 1];
          iperm[i - 1] = iperm[j - 1];
        }
        else {
          flag = 0;
        }
      }
    }
    dlist[i - 1] = dRR;
    iperm[i - 1] = RR2;
 
    if (l == 1) {
      dRR  = dlist [r];
      RR2 = iperm[r];
      dK = dlist[r];
      dlist[r] = dlist[0];
      iperm[r] = iperm[0];
      r = r - 1;
    }
    else {
      l   = l - 1;
      dRR  = dlist[l - 1];
      RR2  = iperm[l - 1];
      dK   = dlist[l - 1];
    }
  }
  dlist[0] = dRR;
  iperm[0] = RR2;
}
 
 
template<class ScalarType, class MV, class OP, class DM>
std::string GCRODRSolMgr<ScalarType,MV,OP,DM,true>::description () const {
  std::ostringstream out;
  out << "Belos::GCRODRSolMgr<...,"<<Teuchos::ScalarTraits<ScalarType>::name()<<">";
  out << "{";
  out << "Ortho Type: \"" << orthoType_ << "\"";
  out << ", Flexible: " << (isFlexible_ ? "true" : "false");
  out << ", Num Blocks: " <<numBlocks_;
  out << ", Num Recycle Blocks: " << recycledBlocks_;
  out << ", Max Restarts: " << maxRestarts_;
  out << "}";
  return out.str ();
}
 
} // namespace Belos
 
#ifdef HAVE_BELOS_TPETRA
#include "BelosTpetraETIHelpers.hpp"
 
#define BELOS_TPETRA_GCRODRSOLMGR_NOEXTERN_CALL(SC, LO, GO, NT)            \
  BELOS_TPETRA_CALL(Belos::GCRODRSolMgr, SC, LO, GO, NT)
 
#define BELOS_TPETRA_GCRODRSOLMGR_EXTERN_CALL(SC, LO, GO, NT)              \
  BELOS_TPETRA_EXTERN_CALL(Belos::GCRODRSolMgr, SC, LO, GO, NT)
 
TPETRA_INSTANTIATE_SLGN_NO_ORDINAL_SCALAR(BELOS_TPETRA_GCRODRSOLMGR_EXTERN_CALL)
#endif
 
 
#endif /* BELOS_GCRODR_SOLMGR_HPP */