AnasaziRTRBase.hpp

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// @HEADER
// *****************************************************************************
//                 Anasazi: Block Eigensolvers Package
//
// Copyright 2004 NTESS and the Anasazi contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER
 
#ifndef ANASAZI_RTRBASE_HPP
#define ANASAZI_RTRBASE_HPP
 
#include "AnasaziTypes.hpp"
 
#include "AnasaziEigensolver.hpp"
#include "AnasaziMultiVecTraits.hpp"
#include "AnasaziOperatorTraits.hpp"
#include "Teuchos_ScalarTraits.hpp"
 
#include "AnasaziGenOrthoManager.hpp"
#include "AnasaziSolverUtils.hpp"
 
#include "Teuchos_LAPACK.hpp"
#include "Teuchos_BLAS.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_TimeMonitor.hpp"
 
namespace Anasazi {
 
 
 
  template <class ScalarType, class MV>
  struct RTRState {
    Teuchos::RCP<const MV> X; 
    Teuchos::RCP<const MV> AX; 
    Teuchos::RCP<const MV> BX;
    Teuchos::RCP<const MV> R;
    Teuchos::RCP<const std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> > T;
    typename Teuchos::ScalarTraits<ScalarType>::magnitudeType rho;
    RTRState() : X(Teuchos::null),AX(Teuchos::null),BX(Teuchos::null),
                 R(Teuchos::null),T(Teuchos::null),rho(0) {};
  };
 
 
 
 
  class RTRRitzFailure : public AnasaziError {public:
    RTRRitzFailure(const std::string& what_arg) : AnasaziError(what_arg)
    {}};
 
  class RTRInitFailure : public AnasaziError {public:
    RTRInitFailure(const std::string& what_arg) : AnasaziError(what_arg)
    {}};
 
  class RTROrthoFailure : public AnasaziError {public:
    RTROrthoFailure(const std::string& what_arg) : AnasaziError(what_arg)
    {}};
 
 
 
 
  template <class ScalarType, class MV, class OP>
  class RTRBase : public Eigensolver<ScalarType,MV,OP> {
  public:
 
 
 
    RTRBase(const Teuchos::RCP<Eigenproblem<ScalarType,MV,OP> > &problem, 
            const Teuchos::RCP<SortManager<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> > &sorter,
            const Teuchos::RCP<OutputManager<ScalarType> > &printer,
            const Teuchos::RCP<StatusTest<ScalarType,MV,OP> > &tester,
            const Teuchos::RCP<GenOrthoManager<ScalarType,MV,OP> > &ortho,
                  Teuchos::ParameterList &params,
            const std::string &solverLabel, bool skinnySolver
           );
 
    virtual ~RTRBase() {};
 
 
 
 
    virtual void iterate() = 0;
 
    void initialize(RTRState<ScalarType,MV>& newstate);
 
    void initialize();
 
    bool isInitialized() const;
 
    RTRState<ScalarType,MV> getState() const;
 
 
 
 
    int getNumIters() const;
 
    void resetNumIters();
 
    Teuchos::RCP<const MV> getRitzVectors();
 
    std::vector<Value<ScalarType> > getRitzValues();
 
    std::vector<int> getRitzIndex();
 
    std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> getResNorms();
 
 
    std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> getRes2Norms();
 
 
    std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> getRitzRes2Norms();
 
 
    int getCurSubspaceDim() const;
 
    int getMaxSubspaceDim() const;
 
 
 
 
    void setStatusTest(Teuchos::RCP<StatusTest<ScalarType,MV,OP> > test);
 
    Teuchos::RCP<StatusTest<ScalarType,MV,OP> > getStatusTest() const;
 
    const Eigenproblem<ScalarType,MV,OP>& getProblem() const;
 
 
    void setBlockSize(int blockSize);
 
 
    int getBlockSize() const;
 
 
    void setAuxVecs(const Teuchos::Array<Teuchos::RCP<const MV> > &auxvecs);
 
    Teuchos::Array<Teuchos::RCP<const MV> > getAuxVecs() const;
 
 
 
 
    virtual void currentStatus(std::ostream &os);
 
 
  protected:
    //
    // Convenience typedefs
    //
    typedef SolverUtils<ScalarType,MV,OP> Utils;
    typedef MultiVecTraits<ScalarType,MV> MVT;
    typedef OperatorTraits<ScalarType,MV,OP> OPT;
    typedef Teuchos::ScalarTraits<ScalarType> SCT;
    typedef typename SCT::magnitudeType MagnitudeType;
    typedef Teuchos::ScalarTraits<MagnitudeType> MAT;
    const MagnitudeType ONE;  
    const MagnitudeType ZERO; 
    const MagnitudeType NANVAL;
    typedef typename std::vector<MagnitudeType>::iterator vecMTiter;
    typedef typename std::vector<ScalarType>::iterator    vecSTiter;
    //
    // Internal structs
    //
    struct CheckList {
      bool checkX, checkAX, checkBX;
      bool checkEta, checkAEta, checkBEta;
      bool checkR, checkQ, checkBR;
      bool checkZ, checkPBX;
      CheckList() : checkX(false),checkAX(false),checkBX(false),
                    checkEta(false),checkAEta(false),checkBEta(false),
                    checkR(false),checkQ(false),checkBR(false),
                    checkZ(false), checkPBX(false) {};
    };
    //
    // Internal methods
    //
    std::string accuracyCheck(const CheckList &chk, const std::string &where) const;
    // solves the model minimization
    virtual void solveTRSubproblem() = 0;
    // Riemannian metric
    typename Teuchos::ScalarTraits<ScalarType>::magnitudeType ginner(const MV &xi) const;
    typename Teuchos::ScalarTraits<ScalarType>::magnitudeType ginner(const MV &xi, const MV &zeta) const;
    void ginnersep(const MV &xi, std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType > &d) const;
    void ginnersep(const MV &xi, const MV &zeta, std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType > &d) const;
    //
    // Classes input through constructor that define the eigenproblem to be solved.
    //
    const Teuchos::RCP<Eigenproblem<ScalarType,MV,OP> >     problem_;
    const Teuchos::RCP<SortManager<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> >           sm_;
    const Teuchos::RCP<OutputManager<ScalarType> >          om_;
    Teuchos::RCP<StatusTest<ScalarType,MV,OP> >             tester_;
    const Teuchos::RCP<GenOrthoManager<ScalarType,MV,OP> >  orthman_;
    //
    // Information obtained from the eigenproblem
    //
    Teuchos::RCP<const OP> AOp_;
    Teuchos::RCP<const OP> BOp_;
    Teuchos::RCP<const OP> Prec_;
    bool hasBOp_, hasPrec_, olsenPrec_;
    //
    // Internal timers
    //
    Teuchos::RCP<Teuchos::Time> timerAOp_, timerBOp_, timerPrec_,
                                timerSort_, 
                                timerLocalProj_, timerDS_,
                                timerLocalUpdate_, timerCompRes_,
                                timerOrtho_, timerInit_;
    //
    // Counters
    //
    // Number of operator applications
    int counterAOp_, counterBOp_, counterPrec_;
 
    //
    // Algorithmic parameters.
    //
    // blockSize_ is the solver block size
    int blockSize_;
    //
    // Current solver state
    //
    // initialized_ specifies that the basis vectors have been initialized and the iterate() routine
    // is capable of running; _initialize is controlled  by the initialize() member method
    // For the implications of the state of initialized_, please see documentation for initialize()
    bool initialized_;
    //
    // nevLocal_ reflects how much of the current basis is valid (0 <= nevLocal_ <= blockSize_)
    // this tells us how many of the values in theta_ are valid Ritz values
    int nevLocal_;
    // 
    // are we implementing a skinny solver? (SkinnyIRTR)
    bool isSkinny_;
    // 
    // are we computing leftmost or rightmost eigenvalue?
    bool leftMost_;
    //
    // State Multivecs
    //
    // if we are implementing a skinny solver (SkinnyIRTR), 
    // then some of these will never be allocated
    // 
    // In order to handle auxiliary vectors, we need to handle the projector
    //   P_{[BQ BX],[BQ BX]}
    // Using an orthomanager with B-inner product, this requires calling with multivectors
    // [BQ,BX] and [Q,X].
    // These multivectors must be combined because <[BQ,BX],[Q,X]>_B != I
    // Hence, we will create two multivectors V and BV, which store
    //   V = [Q,X]
    //  BV = [BQ,BX]
    // 
    //  In the context of preconditioning, we may need to apply the projector
    //   P_{prec*[BQ,BX],[BQ,BX]}
    //  Because [BQ,BX] do not change during the supproblem solver, we will apply 
    //  the preconditioner to [BQ,BX] only once. This result is stored in PBV.
    // 
    // X,BX are views into V,BV
    // We don't need views for Q,BQ
    // Inside the subproblem solver, X,BX are constant, so we can allow these
    // views to exist alongside the full view of V,BV without violating
    // view semantics.
    // 
    // Skinny solver allocates 6/7/8 multivectors:
    //    V_, BV_ (if hasB)
    //    PBV_ (if hasPrec and olsenPrec)
    //    R_, Z_  (regardless of hasPrec)
    //    eta_, delta_, Hdelta_
    //
    // Hefty solver allocates 10/11/12/13 multivectors:
    //    V_, AX_, BV_ (if hasB)
    //    PBV_ (if hasPrec and olsenPrec)
    //    R_, Z_ (if hasPrec)
    //    eta_, Aeta_, Beta_
    //    delta_, Adelta_, Bdelta_, Hdelta_
    //
    Teuchos::RCP<MV> V_, BV_, PBV_,                     // V = [Q,X]; B*V; Prec*B*V
                     AX_, R_,                           // A*X_; residual, gradient, and residual of model minimization
                     eta_, Aeta_, Beta_,                // update vector from model minimization
                     delta_, Adelta_, Bdelta_, Hdelta_, // search direction in model minimization
                     Z_;                                // preconditioned residual
    Teuchos::RCP<const MV> X_, BX_;
    // 
    // auxiliary vectors
    Teuchos::Array<Teuchos::RCP<const MV> > auxVecs_;
    int numAuxVecs_;
    //
    // Number of iterations that have been performed.
    int iter_;
    // 
    // Current eigenvalues, residual norms
    std::vector<MagnitudeType> theta_, Rnorms_, R2norms_, ritz2norms_;
    // 
    // are the residual norms current with the residual?
    bool Rnorms_current_, R2norms_current_;
    // 
    // parameters solver and inner solver
    MagnitudeType conv_kappa_, conv_theta_;
    MagnitudeType rho_;
    // 
    // current objective function value
    MagnitudeType fx_;
  };
 
 
 
 
  // Constructor
  template <class ScalarType, class MV, class OP>
  RTRBase<ScalarType,MV,OP>::RTRBase(
        const Teuchos::RCP<Eigenproblem<ScalarType,MV,OP> >    &problem, 
        const Teuchos::RCP<SortManager<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> > &sorter,
        const Teuchos::RCP<OutputManager<ScalarType> >         &printer,
        const Teuchos::RCP<StatusTest<ScalarType,MV,OP> >      &tester,
        const Teuchos::RCP<GenOrthoManager<ScalarType,MV,OP> > &ortho,
        Teuchos::ParameterList                                 &params,
        const std::string &solverLabel, bool skinnySolver
        ) :
    ONE(Teuchos::ScalarTraits<MagnitudeType>::one()),
    ZERO(Teuchos::ScalarTraits<MagnitudeType>::zero()),
    NANVAL(Teuchos::ScalarTraits<MagnitudeType>::nan()),
    // problem, tools
    problem_(problem), 
    sm_(sorter),
    om_(printer),
    tester_(tester),
    orthman_(ortho),
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
    timerAOp_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Operation A*x")),
    timerBOp_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Operation B*x")),
    timerPrec_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Operation Prec*x")),
    timerSort_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Sorting eigenvalues")),
    timerLocalProj_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Local projection")),
    timerDS_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Direct solve")),
    timerLocalUpdate_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Local update")),
    timerCompRes_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Computing residuals")),
    timerOrtho_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Orthogonalization")),
    timerInit_(Teuchos::TimeMonitor::getNewTimer("Anasazi: "+solverLabel+"::Initialization")),
#endif
    counterAOp_(0),
    counterBOp_(0),
    counterPrec_(0),
    // internal data
    blockSize_(0),
    initialized_(false),
    nevLocal_(0),
    isSkinny_(skinnySolver),
    leftMost_(true),
    auxVecs_( Teuchos::Array<Teuchos::RCP<const MV> >(0) ), 
    numAuxVecs_(0),
    iter_(0),
    Rnorms_current_(false),
    R2norms_current_(false),
    conv_kappa_(.1), 
    conv_theta_(1),
    rho_( MAT::nan() ),
    fx_( MAT::nan() )
  {
    TEUCHOS_TEST_FOR_EXCEPTION(problem_ == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::constructor: user passed null problem pointer.");
    TEUCHOS_TEST_FOR_EXCEPTION(sm_ == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::constructor: user passed null sort manager pointer.");
    TEUCHOS_TEST_FOR_EXCEPTION(om_ == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::constructor: user passed null output manager pointer.");
    TEUCHOS_TEST_FOR_EXCEPTION(tester_ == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::constructor: user passed null status test pointer.");
    TEUCHOS_TEST_FOR_EXCEPTION(orthman_ == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::constructor: user passed null orthogonalization manager pointer.");
    TEUCHOS_TEST_FOR_EXCEPTION(problem_->isProblemSet() == false, std::invalid_argument,
        "Anasazi::RTRBase::constructor: problem is not set.");
    TEUCHOS_TEST_FOR_EXCEPTION(problem_->isHermitian() == false, std::invalid_argument,
        "Anasazi::RTRBase::constructor: problem is not Hermitian.");
 
    // get the problem operators
    AOp_   = problem_->getOperator();
    TEUCHOS_TEST_FOR_EXCEPTION(AOp_ == Teuchos::null, std::invalid_argument,
                       "Anasazi::RTRBase::constructor: problem provides no A matrix.");
    BOp_  = problem_->getM();
    Prec_ = problem_->getPrec();
    hasBOp_ = (BOp_ != Teuchos::null);
    hasPrec_ = (Prec_ != Teuchos::null);
    olsenPrec_ = params.get<bool>("Olsen Prec", true);
 
    TEUCHOS_TEST_FOR_EXCEPTION(orthman_->getOp() != BOp_,std::invalid_argument,
        "Anasazi::RTRBase::constructor: orthogonalization manager must use mass matrix for inner product.");
 
    // set the block size and allocate data
    int bs = params.get("Block Size", problem_->getNEV());
    setBlockSize(bs);
 
    // leftmost or rightmost?
    leftMost_ = params.get("Leftmost",leftMost_);
 
    conv_kappa_ = params.get("Kappa Convergence",conv_kappa_);
    TEUCHOS_TEST_FOR_EXCEPTION(conv_kappa_ <= 0 || conv_kappa_ >= 1,std::invalid_argument,
                       "Anasazi::RTRBase::constructor: kappa must be in (0,1).");
    conv_theta_ = params.get("Theta Convergence",conv_theta_);
    TEUCHOS_TEST_FOR_EXCEPTION(conv_theta_ <= 0,std::invalid_argument,
                       "Anasazi::RTRBase::constructor: theta must be strictly postitive.");
  }
 
 
  // Set the block size and make necessary adjustments.
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::setBlockSize (int blockSize) 
  {
    // time spent here counts towards timerInit_
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
    Teuchos::TimeMonitor lcltimer( *timerInit_ );
#endif
 
    // This routine only allocates space; it doesn't not perform any computation
    // if solver is initialized and size is to be decreased, take the first blockSize vectors of all to preserve state
    // otherwise, shrink/grow/allocate space and set solver to unitialized
 
    Teuchos::RCP<const MV> tmp;
    // grab some Multivector to Clone
    // in practice, getInitVec() should always provide this, but it is possible to use a 
    // Eigenproblem with nothing in getInitVec() by manually initializing with initialize(); 
    // in case of that strange scenario, we will try to Clone from R_
    // we like R_ for this, because it has minimal size (blockSize_), as opposed to V_ (blockSize_+numAuxVecs_)
    if (blockSize_ > 0) {
      tmp = R_;
    }
    else {
      tmp = problem_->getInitVec();
      TEUCHOS_TEST_FOR_EXCEPTION(tmp == Teuchos::null,std::logic_error,
          "Anasazi::RTRBase::setBlockSize(): Eigenproblem did not specify initial vectors to clone from");
    }
 
    TEUCHOS_TEST_FOR_EXCEPTION(blockSize <= 0 || blockSize > MVT::GetGlobalLength(*tmp), std::invalid_argument, 
        "Anasazi::RTRBase::setBlockSize was passed a non-positive block size");
 
    // last chance to quit before causing side-effects
    if (blockSize == blockSize_) {
      // do nothing
      return;
    }
 
    // clear views
    X_  = Teuchos::null;
    BX_ = Teuchos::null;
 
    // regardless of whether we preserve any data, any content in V, BV and PBV corresponding to the
    // auxiliary vectors must be retained
    // go ahead and do these first
    // 
    // two cases here: 
    // * we are growing (possibly, from empty) 
    //   any aux data must be copied over, nothing from X need copying
    // * we are shrinking
    //   any aux data must be copied over, go ahead and copy X material (initialized or not)
    //
    if (blockSize > blockSize_)
    {
      // GROWING 
      // get a pointer for Q-related material, and an index for extracting/setting it
      Teuchos::RCP<const MV> Q;
      std::vector<int> indQ(numAuxVecs_);
      for (int i=0; i<numAuxVecs_; i++) indQ[i] = i;
      // if numAuxVecs_ > 0, then necessarily blockSize_ > 0 (we have already been allocated once)
      TEUCHOS_TEST_FOR_EXCEPTION(numAuxVecs_ > 0 && blockSize_ == 0, std::logic_error,
          "Anasazi::RTRBase::setSize(): logic error. Please contact Anasazi team.");
      // V
      if (numAuxVecs_ > 0) Q = MVT::CloneView(*V_,indQ);
      V_ = MVT::Clone(*tmp,numAuxVecs_ + blockSize);
      if (numAuxVecs_ > 0) MVT::SetBlock(*Q,indQ,*V_);
      // BV
      if (hasBOp_) {
        if (numAuxVecs_ > 0) Q = MVT::CloneView(*BV_,indQ);
        BV_ = MVT::Clone(*tmp,numAuxVecs_ + blockSize);
        if (numAuxVecs_ > 0) MVT::SetBlock(*Q,indQ,*BV_);
      }
      else {
        BV_ = V_;
      }
      // PBV
      if (hasPrec_ && olsenPrec_) {
        if (numAuxVecs_ > 0) Q = MVT::CloneView(*PBV_,indQ);
        PBV_ = MVT::Clone(*tmp,numAuxVecs_ + blockSize);
        if (numAuxVecs_ > 0) MVT::SetBlock(*Q,indQ,*PBV_);
      }
    }
    else 
    {
      // SHRINKING
      std::vector<int> indV(numAuxVecs_+blockSize);
      for (int i=0; i<numAuxVecs_+blockSize; i++) indV[i] = i;
      // V
      V_ = MVT::CloneCopy(*V_,indV);
      // BV
      if (hasBOp_) {
        BV_ = MVT::CloneCopy(*BV_,indV);
      }
      else {
        BV_ = V_;
      }
      // PBV
      if (hasPrec_ && olsenPrec_) {
        PBV_ = MVT::CloneCopy(*PBV_,indV);
      }
    }
 
    if (blockSize < blockSize_) {
      // shrink vectors
      blockSize_ = blockSize;
 
      theta_.resize(blockSize_);
      ritz2norms_.resize(blockSize_);
      Rnorms_.resize(blockSize_);
      R2norms_.resize(blockSize_);
 
      if (initialized_) {
        // shrink multivectors with copy
        std::vector<int> ind(blockSize_);
        for (int i=0; i<blockSize_; i++) ind[i] = i;
 
        // Z can be deleted, no important info there
        Z_ = Teuchos::null;
        
        // we will not use tmp for cloning, clear it and free some space
        tmp = Teuchos::null;
 
        R_      = MVT::CloneCopy(*R_     ,ind);
        eta_    = MVT::CloneCopy(*eta_   ,ind);
        delta_  = MVT::CloneCopy(*delta_ ,ind);
        Hdelta_ = MVT::CloneCopy(*Hdelta_,ind);
        if (!isSkinny_) {
          AX_     = MVT::CloneCopy(*AX_    ,ind);
          Aeta_   = MVT::CloneCopy(*Aeta_  ,ind);
          Adelta_ = MVT::CloneCopy(*Adelta_,ind);
        }
        else {
          AX_     = Teuchos::null;
          Aeta_   = Teuchos::null;
          Adelta_ = Teuchos::null;
        }
 
        if (hasBOp_) {
          if (!isSkinny_) {
            Beta_   = MVT::CloneCopy(*Beta_,ind);
            Bdelta_ = MVT::CloneCopy(*Bdelta_,ind);
          }
          else {
            Beta_   = Teuchos::null;
            Bdelta_ = Teuchos::null;
          }
        }
        else {
          Beta_   = eta_;
          Bdelta_ = delta_;
        }
        
        // we need Z if we have a preconditioner
        // we also use Z for temp storage in the skinny solvers
        if (hasPrec_ || isSkinny_) {
          Z_ = MVT::Clone(*V_,blockSize_);
        }
        else {
          Z_ = R_;
        }
 
      }
      else {
        // release previous multivectors
        // shrink multivectors without copying
        AX_     = Teuchos::null;
        R_      = Teuchos::null;
        eta_    = Teuchos::null;
        Aeta_   = Teuchos::null;
        delta_  = Teuchos::null;
        Adelta_ = Teuchos::null;
        Hdelta_ = Teuchos::null;
        Beta_   = Teuchos::null;
        Bdelta_ = Teuchos::null;
        Z_      = Teuchos::null;
 
        R_      = MVT::Clone(*tmp,blockSize_);
        eta_    = MVT::Clone(*tmp,blockSize_);
        delta_  = MVT::Clone(*tmp,blockSize_);
        Hdelta_ = MVT::Clone(*tmp,blockSize_);
        if (!isSkinny_) {
          AX_     = MVT::Clone(*tmp,blockSize_);
          Aeta_   = MVT::Clone(*tmp,blockSize_);
          Adelta_ = MVT::Clone(*tmp,blockSize_);
        }
 
        if (hasBOp_) {
          if (!isSkinny_) {
            Beta_   = MVT::Clone(*tmp,blockSize_);
            Bdelta_ = MVT::Clone(*tmp,blockSize_);
          }
        }
        else {
          Beta_   = eta_;
          Bdelta_ = delta_;
        }
 
        // we need Z if we have a preconditioner
        // we also use Z for temp storage in the skinny solvers
        if (hasPrec_ || isSkinny_) {
          Z_ = MVT::Clone(*tmp,blockSize_);
        }
        else {
          Z_ = R_;
        }
      } // if initialized_
    } // if blockSize is shrinking
    else {  // if blockSize > blockSize_
      // this is also the scenario for our initial call to setBlockSize(), in the constructor
      initialized_ = false;
 
      // grow/allocate vectors
      theta_.resize(blockSize,NANVAL);
      ritz2norms_.resize(blockSize,NANVAL);
      Rnorms_.resize(blockSize,NANVAL);
      R2norms_.resize(blockSize,NANVAL);
 
      // deallocate old multivectors
      AX_     = Teuchos::null;
      R_      = Teuchos::null;
      eta_    = Teuchos::null;
      Aeta_   = Teuchos::null;
      delta_  = Teuchos::null;
      Adelta_ = Teuchos::null;
      Hdelta_ = Teuchos::null;
      Beta_   = Teuchos::null;
      Bdelta_ = Teuchos::null;
      Z_      = Teuchos::null;
 
      // clone multivectors off of tmp
      R_      = MVT::Clone(*tmp,blockSize);
      eta_    = MVT::Clone(*tmp,blockSize);
      delta_  = MVT::Clone(*tmp,blockSize);
      Hdelta_ = MVT::Clone(*tmp,blockSize);
      if (!isSkinny_) {
        AX_     = MVT::Clone(*tmp,blockSize);
        Aeta_   = MVT::Clone(*tmp,blockSize);
        Adelta_ = MVT::Clone(*tmp,blockSize);
      }
 
      if (hasBOp_) {
        if (!isSkinny_) {
          Beta_   = MVT::Clone(*tmp,blockSize);
          Bdelta_ = MVT::Clone(*tmp,blockSize);
        }
      }
      else {
        Beta_   = eta_;
        Bdelta_ = delta_;
      }
      if (hasPrec_ || isSkinny_) {
        Z_ = MVT::Clone(*tmp,blockSize);
      }
      else {
        Z_ = R_;
      }
      blockSize_ = blockSize;
    }
 
    // get view of X from V, BX from BV
    // these are located after the first numAuxVecs columns
    {
      std::vector<int> indX(blockSize_);
      for (int i=0; i<blockSize_; i++) indX[i] = numAuxVecs_+i;
      X_ = MVT::CloneView(*V_,indX);
      if (hasBOp_) {
        BX_ = MVT::CloneView(*BV_,indX);
      }
      else {
        BX_ = X_;
      }
    }
  }
 
 
  // Set a new StatusTest for the solver.
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::setStatusTest(Teuchos::RCP<StatusTest<ScalarType,MV,OP> > test) {
    TEUCHOS_TEST_FOR_EXCEPTION(test == Teuchos::null,std::invalid_argument,
        "Anasazi::RTRBase::setStatusTest() was passed a null StatusTest.");
    tester_ = test;
  }
 
 
  // Get the current StatusTest used by the solver.
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<StatusTest<ScalarType,MV,OP> > RTRBase<ScalarType,MV,OP>::getStatusTest() const {
    return tester_;
  }
  
 
  // Set the auxiliary vectors
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::setAuxVecs(const Teuchos::Array<Teuchos::RCP<const MV> > &auxvecs) {
    typedef typename Teuchos::Array<Teuchos::RCP<const MV> >::const_iterator tarcpmv;
 
    // set new auxiliary vectors
    auxVecs_.resize(0);
    auxVecs_.reserve(auxvecs.size());
 
    numAuxVecs_ = 0;
    for (tarcpmv v=auxvecs.begin(); v != auxvecs.end(); ++v) {
      numAuxVecs_ += MVT::GetNumberVecs(**v);
    }
 
    // If the solver has been initialized, X is not necessarily orthogonal to new auxiliary vectors
    if (numAuxVecs_ > 0 && initialized_) {
      initialized_ = false;
    }
 
    // clear X,BX views
    X_   = Teuchos::null;
    BX_  = Teuchos::null;
    // deallocate, we'll clone off R_ below
    V_   = Teuchos::null;
    BV_  = Teuchos::null;
    PBV_ = Teuchos::null;
 
    // put auxvecs into V, update BV and PBV if necessary
    if (numAuxVecs_ > 0) {
      V_ = MVT::Clone(*R_,numAuxVecs_ + blockSize_);
      int numsofar = 0;
      for (tarcpmv v=auxvecs.begin(); v != auxvecs.end(); ++v) {
        std::vector<int> ind(MVT::GetNumberVecs(**v));
        for (size_t j=0; j<ind.size(); j++) ind[j] = numsofar++;
        MVT::SetBlock(**v,ind,*V_);
        auxVecs_.push_back(MVT::CloneView(*Teuchos::rcp_static_cast<const MV>(V_),ind));
      }
      TEUCHOS_TEST_FOR_EXCEPTION(numsofar != numAuxVecs_, std::logic_error,
          "Anasazi::RTRBase::setAuxVecs(): Logic error. Please contact Anasazi team.");
      // compute B*V, Prec*B*V
      if (hasBOp_) {
        BV_ = MVT::Clone(*R_,numAuxVecs_ + blockSize_);
        OPT::Apply(*BOp_,*V_,*BV_);
      }
      else {
        BV_ = V_;
      }
      if (hasPrec_ && olsenPrec_) {
        PBV_ = MVT::Clone(*R_,numAuxVecs_ + blockSize_);
        OPT::Apply(*Prec_,*BV_,*V_);
      }
    }
    // 
 
    if (om_->isVerbosity( Debug ) ) {
      // Check almost everything here
      CheckList chk;
      chk.checkQ = true;
      om_->print( Debug, accuracyCheck(chk, "in setAuxVecs()") );
    }
  }
 
 
  /* Initialize the state of the solver
   * 
   * POST-CONDITIONS:
   *
   * initialized_ == true
   * X is orthonormal, orthogonal to auxVecs_
   * AX = A*X if not skinnny
   * BX = B*X if hasBOp_
   * theta_ contains Ritz values of X
   * R = AX - BX*diag(theta_)
   */
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::initialize(RTRState<ScalarType,MV>& newstate)
  {
    // NOTE: memory has been allocated by setBlockSize(). Use SetBlock below; do not Clone
    // NOTE: Overall time spent in this routine is counted to timerInit_; portions will also be counted towards other primitives
 
    // clear const views to X,BX in V,BV
    // work with temporary non-const views
    X_  = Teuchos::null;
    BX_ = Teuchos::null;
    Teuchos::RCP<MV> X, BX;
    {
      std::vector<int> ind(blockSize_);
      for (int i=0; i<blockSize_; ++i) ind[i] = numAuxVecs_+i;
      X = MVT::CloneViewNonConst(*V_,ind);
      if (hasBOp_) {
        BX = MVT::CloneViewNonConst(*BV_,ind);
      }
      else {
        BX = X;
      }
    }
 
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
    Teuchos::TimeMonitor inittimer( *timerInit_ );
#endif
 
    std::vector<int> bsind(blockSize_);
    for (int i=0; i<blockSize_; i++) bsind[i] = i;
 
    // in RTR, X (the subspace iterate) is primary
    // the order of dependence follows like so.
    // --init->                 X
    //    --op apply->          AX,BX
    //       --ritz analysis->  theta
    // 
    // if the user specifies all data for a level, we will accept it.
    // otherwise, we will generate the whole level, and all subsequent levels.
    //
    // the data members are ordered based on dependence, and the levels are
    // partitioned according to the amount of work required to produce the
    // items in a level.
    //
    // inconsitent multivectors widths and lengths will not be tolerated, and
    // will be treated with exceptions.
 
    // set up X, AX, BX: get them from "state" if user specified them
    if (newstate.X != Teuchos::null) {
      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength(*newstate.X) != MVT::GetGlobalLength(*X),
                          std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): vector length of newstate.X not correct." );
      // newstate.X must have blockSize_ vectors; any more will be ignored
      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.X) < blockSize_,
                          std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): newstate.X must have at least block size vectors.");
 
      // put data in X
      MVT::SetBlock(*newstate.X,bsind,*X);
 
      // put data in AX
      // if we are implementing a skinny solver, then we don't have memory allocated for AX
      // in this case, point AX at Z (skinny solvers allocate Z) and use it for temporary storage
      // we will clear the pointer later
      if (isSkinny_) {
        AX_ = Z_;
      }
      if (newstate.AX != Teuchos::null) {
        TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength(*newstate.AX) != MVT::GetGlobalLength(*X),
                            std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): vector length of newstate.AX not correct." );
        // newstate.AX must have blockSize_ vectors; any more will be ignored
        TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.AX) < blockSize_,
                            std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): newstate.AX must have at least block size vectors.");
        MVT::SetBlock(*newstate.AX,bsind,*AX_);
      }
      else {
        {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
          Teuchos::TimeMonitor lcltimer( *timerAOp_ );
#endif
          OPT::Apply(*AOp_,*X,*AX_);
          counterAOp_ += blockSize_;
        }
        // we generated AX; we will generate R as well
        newstate.R = Teuchos::null;
      }
 
      // put data in BX
      // skinny solvers always allocate BX if hasB, so this is unconditionally appropriate
      if (hasBOp_) {
        if (newstate.BX != Teuchos::null) {
          TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength(*newstate.BX) != MVT::GetGlobalLength(*X),
                              std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): vector length of newstate.BX not correct." );
          // newstate.BX must have blockSize_ vectors; any more will be ignored
          TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.BX) < blockSize_,
                              std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): newstate.BX must have at least block size vectors.");
          MVT::SetBlock(*newstate.BX,bsind,*BX);
        }
        else {
          {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
            Teuchos::TimeMonitor lcltimer( *timerBOp_ );
#endif
            OPT::Apply(*BOp_,*X,*BX);
            counterBOp_ += blockSize_;
          }
          // we generated BX; we will generate R as well
          newstate.R = Teuchos::null;
        }
      }
      else {
        // the assignment BX_==X_ would be redundant; take advantage of this opportunity to debug a little
        TEUCHOS_TEST_FOR_EXCEPTION(BX != X, std::logic_error, "Anasazi::RTRBase::initialize(): solver invariant not satisfied (BX==X).");
      }
 
    }
    else {
      // user did not specify X
 
      // clear state so we won't use any data from it below
      newstate.R  = Teuchos::null;
      newstate.T  = Teuchos::null;
 
      // generate something and projectAndNormalize
      Teuchos::RCP<const MV> ivec = problem_->getInitVec();
      TEUCHOS_TEST_FOR_EXCEPTION(ivec == Teuchos::null,std::logic_error,
                         "Anasazi::RTRBase::initialize(): Eigenproblem did not specify initial vectors to clone from.");
 
      int initSize = MVT::GetNumberVecs(*ivec);
      if (initSize > blockSize_) {
        // we need only the first blockSize_ vectors from ivec; get a view of them
        initSize = blockSize_;
        std::vector<int> ind(blockSize_);
        for (int i=0; i<blockSize_; i++) ind[i] = i;
        ivec = MVT::CloneView(*ivec,ind);
      }
 
      // assign ivec to first part of X
      if (initSize > 0) {
        std::vector<int> ind(initSize);
        for (int i=0; i<initSize; i++) ind[i] = i;
        MVT::SetBlock(*ivec,ind,*X);
      }
      // fill the rest of X with random
      if (blockSize_ > initSize) {
        std::vector<int> ind(blockSize_ - initSize);
        for (int i=0; i<blockSize_ - initSize; i++) ind[i] = initSize + i;
        Teuchos::RCP<MV> rX = MVT::CloneViewNonConst(*X,ind);
        MVT::MvRandom(*rX);
        rX = Teuchos::null;
      }
 
      // put data in BX
      if (hasBOp_) {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerBOp_ );
#endif
        OPT::Apply(*BOp_,*X,*BX);
        counterBOp_ += blockSize_;
      }
      else {
        // the assignment BX==X would be redundant; take advantage of this opportunity to debug a little
        TEUCHOS_TEST_FOR_EXCEPTION(BX != X, std::logic_error, "Anasazi::RTRBase::initialize(): solver invariant not satisfied (BX==X).");
      }
  
      // remove auxVecs from X and normalize it
      if (numAuxVecs_ > 0) {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerOrtho_ );
#endif
        Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > dummyC;
        int rank = orthman_->projectAndNormalizeMat(*X,auxVecs_,dummyC,Teuchos::null,BX);
        TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_, RTRInitFailure,
                           "Anasazi::RTRBase::initialize(): Couldn't generate initial basis of full rank.");
      }
      else {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerOrtho_ );
#endif
        int rank = orthman_->normalizeMat(*X,Teuchos::null,BX);
        TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_, RTRInitFailure,
                           "Anasazi::RTRBase::initialize(): Couldn't generate initial basis of full rank.");
      }
 
      // put data in AX
      if (isSkinny_) {
        AX_ = Z_;
      }
      {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerAOp_ );
#endif
        OPT::Apply(*AOp_,*X,*AX_);
        counterAOp_ += blockSize_;
      }
 
    } // end if (newstate.X != Teuchos::null)
 
 
    // set up Ritz values
    if (newstate.T != Teuchos::null) {
      TEUCHOS_TEST_FOR_EXCEPTION( (signed int)(newstate.T->size()) < blockSize_,
                          std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): newstate.T must contain at least block size Ritz values.");
      for (int i=0; i<blockSize_; i++) {
        theta_[i] = (*newstate.T)[i];
      }
    }
    else {
      // get ritz vecs/vals
      Teuchos::SerialDenseMatrix<int,ScalarType> AA(blockSize_,blockSize_),
                                                 BB(blockSize_,blockSize_),
                                                  S(blockSize_,blockSize_);
      // project A
      {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerLocalProj_ );
#endif
        MVT::MvTransMv(ONE,*X,*AX_,AA);
        if (hasBOp_) {
          MVT::MvTransMv(ONE,*X,*BX,BB);
        }
      }
      nevLocal_ = blockSize_;
 
      // solve the projected problem
      // project B
      int ret;
      if (hasBOp_) {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerDS_ );
#endif
        ret = Utils::directSolver(blockSize_,AA,Teuchos::rcpFromRef(BB),S,theta_,nevLocal_,1);
      }
      else {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerDS_ );
#endif
        ret = Utils::directSolver(blockSize_,AA,Teuchos::null,S,theta_,nevLocal_,10);
      }
      TEUCHOS_TEST_FOR_EXCEPTION(ret != 0,RTRInitFailure,
          "Anasazi::RTRBase::initialize(): failure solving projected eigenproblem after retraction. LAPACK returns " << ret);
      TEUCHOS_TEST_FOR_EXCEPTION(nevLocal_ != blockSize_,RTRInitFailure,"Anasazi::RTRBase::initialize(): retracted iterate failed in Ritz analysis.");
 
      // We only have blockSize_ ritz pairs, ergo we do not need to select.
      // However, we still require them to be ordered correctly
      {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerSort_ );
#endif
        
        std::vector<int> order(blockSize_);
        // 
        // sort the first blockSize_ values in theta_
        sm_->sort(theta_, Teuchos::rcpFromRef(order), blockSize_);   // don't catch exception
        //
        // apply the same ordering to the primitive ritz vectors
        Utils::permuteVectors(order,S);
      }
 
      // compute ritz residual norms
      {
        Teuchos::BLAS<int,ScalarType> blas;
        Teuchos::SerialDenseMatrix<int,ScalarType> RR(blockSize_,blockSize_);
        // RR = AA*S - BB*S*diag(theta)
        int info;
        if (hasBOp_) {
          info = RR.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,ONE,BB,S,ZERO);
          TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error, "Anasazi::RTRBase::initialize(): Logic error calling SerialDenseMatrix::multiply.");
        }
        else {
          RR.assign(S);
        }
        for (int i=0; i<blockSize_; i++) {
          blas.SCAL(blockSize_,theta_[i],RR[i],1);
        }
        info = RR.multiply(Teuchos::NO_TRANS,Teuchos::NO_TRANS,ONE,AA,S,-ONE);
        TEUCHOS_TEST_FOR_EXCEPTION(info != 0, std::logic_error, "Anasazi::RTRBase::initialize(): Logic error calling SerialDenseMatrix::multiply.");
        for (int i=0; i<blockSize_; i++) {
          ritz2norms_[i] = blas.NRM2(blockSize_,RR[i],1);
        }
      }
 
      // update the solution
      // use R as local work space
      // Z may already be in use as work space (holding AX if isSkinny)
      {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
        Teuchos::TimeMonitor lcltimer( *timerLocalUpdate_ );
#endif
        // X <- X*S
        MVT::MvAddMv( ONE, *X, ZERO, *X, *R_ );        
        MVT::MvTimesMatAddMv( ONE, *R_, S, ZERO, *X );
        // AX <- AX*S
        MVT::MvAddMv( ONE, *AX_, ZERO, *AX_, *R_ );        
        MVT::MvTimesMatAddMv( ONE, *R_, S, ZERO, *AX_ );
        if (hasBOp_) {
          // BX <- BX*S
          MVT::MvAddMv( ONE, *BX, ZERO, *BX, *R_ );        
          MVT::MvTimesMatAddMv( ONE, *R_, S, ZERO, *BX );
        }
      }
    }
    
    // done modifying X,BX; clear temp views and setup const views
    X  = Teuchos::null;
    BX = Teuchos::null;
    {
      std::vector<int> ind(blockSize_);
      for (int i=0; i<blockSize_; ++i) ind[i] = numAuxVecs_+i;
      this->X_ = MVT::CloneView(static_cast<const MV&>(*V_),ind);
      if (hasBOp_) {
        this->BX_ = MVT::CloneView(static_cast<const MV&>(*BV_),ind);
      }
      else {
        this->BX_ = this->X_;
      }
    }
 
 
    // get objective function value
    fx_ = std::accumulate(theta_.begin(),theta_.end(),ZERO);
 
    // set up R
    if (newstate.R != Teuchos::null) {
      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.R) < blockSize_,
                          std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): newstate.R must have blockSize number of vectors." );
      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength(*newstate.R) != MVT::GetGlobalLength(*R_),
                          std::invalid_argument, "Anasazi::RTRBase::initialize(newstate): vector length of newstate.R not correct." );
      MVT::SetBlock(*newstate.R,bsind,*R_);
    }
    else {
#ifdef ANASAZI_TEUCHOS_TIME_MONITOR
      Teuchos::TimeMonitor lcltimer( *timerCompRes_ );
#endif
      // form R <- AX - BX*T
      MVT::MvAddMv(ZERO,*AX_,ONE,*AX_,*R_);
      Teuchos::SerialDenseMatrix<int,ScalarType> T(blockSize_,blockSize_);
      T.putScalar(ZERO);
      for (int i=0; i<blockSize_; i++) T(i,i) = theta_[i];
      MVT::MvTimesMatAddMv(-ONE,*BX_,T,ONE,*R_);
    }
 
    // R has been updated; mark the norms as out-of-date
    Rnorms_current_ = false;
    R2norms_current_ = false;
 
    // if isSkinny, then AX currently points to Z for temp storage
    // set AX back to null
    if (isSkinny_) {
      AX_ = Teuchos::null;
    }
 
    // finally, we are initialized
    initialized_ = true;
 
    if (om_->isVerbosity( Debug ) ) {
      // Check almost everything here
      CheckList chk;
      chk.checkX = true;
      chk.checkAX = true;
      chk.checkBX = true;
      chk.checkR = true;
      chk.checkQ = true;
      om_->print( Debug, accuracyCheck(chk, "after initialize()") );
    }
  }
 
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::initialize()
  {
    RTRState<ScalarType,MV> empty;
    initialize(empty);
  }
 
 
 
 
  // compute/return residual B-norms
  template <class ScalarType, class MV, class OP>
  std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> 
  RTRBase<ScalarType,MV,OP>::getResNorms() {
    if (Rnorms_current_ == false) {
      // Update the residual norms
      orthman_->norm(*R_,Rnorms_);
      Rnorms_current_ = true;
    }
    return Rnorms_;
  }
 
  
  // compute/return residual 2-norms
  template <class ScalarType, class MV, class OP>
  std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> 
  RTRBase<ScalarType,MV,OP>::getRes2Norms() {
    if (R2norms_current_ == false) {
      // Update the residual 2-norms 
      MVT::MvNorm(*R_,R2norms_);
      R2norms_current_ = true;
    }
    return R2norms_;
  }
 
 
 
 
  // Check accuracy, orthogonality, and other debugging stuff
  // 
  // bools specify which tests we want to run (instead of running more than we actually care about)
  //
  // we don't bother checking the following because they are computed explicitly:
  //   AH == A*H
  //
  // 
  // checkX    : X orthonormal
  //             orthogonal to auxvecs
  // checkAX   : check AX == A*X
  // checkBX   : check BX == B*X
  // checkEta  : check that Eta'*B*X == 0
  //             orthogonal to auxvecs
  // checkAEta : check that AEta = A*Eta
  // checkBEta : check that BEta = B*Eta
  // checkR    : check R orthogonal to X
  // checkBR   : check R B-orthogonal to X, valid in and immediately after solveTRSubproblem
  // checkQ    : check that auxiliary vectors are actually orthonormal
  //
  // TODO: 
  //  add checkTheta 
  //
  template <class ScalarType, class MV, class OP>
  std::string RTRBase<ScalarType,MV,OP>::accuracyCheck( const CheckList &chk, const std::string &where ) const 
  {
    using std::setprecision;
    using std::scientific;
    using std::setw;
    using std::endl;
    std::stringstream os;
    MagnitudeType tmp;
 
    os << " Debugging checks: " << where << endl;
 
    // X and friends
    if (chk.checkX && initialized_) {
      tmp = orthman_->orthonormError(*X_);
      os << " >> Error in X^H B X == I :    " << scientific << setprecision(10) << tmp << endl;
      for (Array_size_type i=0; i<auxVecs_.size(); i++) {
        tmp = orthman_->orthogError(*X_,*auxVecs_[i]);
        os << " >> Error in X^H B Q[" << i << "] == 0 : " << scientific << setprecision(10) << tmp << endl;
      }
    }
    if (chk.checkAX && !isSkinny_ && initialized_) {
      tmp = Utils::errorEquality(*X_, *AX_, AOp_);
      os << " >> Error in AX == A*X    :    " << scientific << setprecision(10) << tmp << endl;
    }
    if (chk.checkBX && hasBOp_ && initialized_) {
      Teuchos::RCP<MV> BX = MVT::Clone(*this->X_,this->blockSize_);
      OPT::Apply(*BOp_,*this->X_,*BX);
      tmp = Utils::errorEquality(*BX, *BX_);
      os << " >> Error in BX == B*X    :    " << scientific << setprecision(10) << tmp << endl;
    }
 
    // Eta and friends
    if (chk.checkEta && initialized_) {
      tmp = orthman_->orthogError(*X_,*eta_);
      os << " >> Error in X^H B Eta == 0 :  " << scientific << setprecision(10) << tmp << endl;
      for (Array_size_type i=0; i<auxVecs_.size(); i++) {
        tmp = orthman_->orthogError(*eta_,*auxVecs_[i]);
        os << " >> Error in Eta^H B Q[" << i << "]==0 : " << scientific << setprecision(10) << tmp << endl;
      }
    }
    if (chk.checkAEta && !isSkinny_ && initialized_) {
      tmp = Utils::errorEquality(*eta_, *Aeta_, AOp_);
      os << " >> Error in AEta == A*Eta    :    " << scientific << setprecision(10) << tmp << endl;
    }
    if (chk.checkBEta && !isSkinny_ && hasBOp_ && initialized_) {
      tmp = Utils::errorEquality(*eta_, *Beta_, BOp_);
      os << " >> Error in BEta == B*Eta    :    " << scientific << setprecision(10) << tmp << endl;
    }
 
    // R: this is not B-orthogonality, but standard euclidean orthogonality
    if (chk.checkR && initialized_) {
      Teuchos::SerialDenseMatrix<int,ScalarType> xTx(blockSize_,blockSize_);
      MVT::MvTransMv(ONE,*X_,*R_,xTx);
      tmp = xTx.normFrobenius();
      os << " >> Error in X^H R == 0   :    " << scientific << setprecision(10) << tmp << endl;
    }
 
    // BR: this is B-orthogonality: this is only valid inside and immediately after solveTRSubproblem 
    // only check if B != I, otherwise, it is equivalent to the above test
    if (chk.checkBR && hasBOp_ && initialized_) {
      Teuchos::SerialDenseMatrix<int,ScalarType> xTx(blockSize_,blockSize_);
      MVT::MvTransMv(ONE,*BX_,*R_,xTx);
      tmp = xTx.normFrobenius();
      os << " >> Error in X^H B R == 0 :    " << scientific << setprecision(10) << tmp << endl;
    }
 
    // Z: Z is preconditioned R, should be on tangent plane
    if (chk.checkZ && initialized_) {
      Teuchos::SerialDenseMatrix<int,ScalarType> xTx(blockSize_,blockSize_);
      MVT::MvTransMv(ONE,*BX_,*Z_,xTx);
      tmp = xTx.normFrobenius();
      os << " >> Error in X^H B Z == 0 :    " << scientific << setprecision(10) << tmp << endl;
    }
 
    // Q
    if (chk.checkQ) {
      for (Array_size_type i=0; i<auxVecs_.size(); i++) {
        tmp = orthman_->orthonormError(*auxVecs_[i]);
        os << " >> Error in Q[" << i << "]^H B Q[" << i << "]==I: " << scientific << setprecision(10) << tmp << endl;
        for (Array_size_type j=i+1; j<auxVecs_.size(); j++) {
          tmp = orthman_->orthogError(*auxVecs_[i],*auxVecs_[j]);
          os << " >> Error in Q[" << i << "]^H B Q[" << j << "]==0: " << scientific << setprecision(10) << tmp << endl;
        }
      }
    }
    os << endl;
    return os.str();
  }
 
 
  // Print the current status of the solver
  template <class ScalarType, class MV, class OP>
  void 
  RTRBase<ScalarType,MV,OP>::currentStatus(std::ostream &os) 
  {
    using std::setprecision;
    using std::scientific;
    using std::setw;
    using std::endl;
 
    os <<endl;
    os <<"================================================================================" << endl;
    os << endl;
    os <<"                              RTRBase Solver Status" << endl;
    os << endl;
    os <<"The solver is "<<(initialized_ ? "initialized." : "not initialized.") << endl;
    os <<"The number of iterations performed is " << iter_       << endl;
    os <<"The current block size is             " << blockSize_  << endl;
    os <<"The number of auxiliary vectors is    " << numAuxVecs_ << endl;
    os <<"The number of operations A*x    is " << counterAOp_   << endl;
    os <<"The number of operations B*x    is " << counterBOp_    << endl;
    os <<"The number of operations Prec*x is " << counterPrec_ << endl;
    os <<"The most recent rho was " << scientific << setprecision(10) << rho_ << endl;
    os <<"The current value of f(x) is " << scientific << setprecision(10) << fx_ << endl;
 
    if (initialized_) {
      os << endl;
      os <<"CURRENT EIGENVALUE ESTIMATES             "<<endl;
      os << setw(20) << "Eigenvalue" 
         << setw(20) << "Residual(B)"
         << setw(20) << "Residual(2)"
         << endl;
      os <<"--------------------------------------------------------------------------------"<<endl;
      for (int i=0; i<blockSize_; i++) {
        os << scientific << setprecision(10) << setw(20) << theta_[i];
        if (Rnorms_current_) os << scientific << setprecision(10) << setw(20) << Rnorms_[i];
        else os << scientific << setprecision(10) << setw(20) << "not current";
        if (R2norms_current_) os << scientific << setprecision(10) << setw(20) << R2norms_[i];
        else os << scientific << setprecision(10) << setw(20) << "not current";
        os << endl;
      }
    }
    os <<"================================================================================" << endl;
    os << endl;
  }
 
 
  // Inner product 1
  template <class ScalarType, class MV, class OP>
  typename Teuchos::ScalarTraits<ScalarType>::magnitudeType 
  RTRBase<ScalarType,MV,OP>::ginner(const MV &xi) const 
  {
    std::vector<MagnitudeType> d(MVT::GetNumberVecs(xi));
    MVT::MvNorm(xi,d);
    MagnitudeType ret = 0;
    for (vecMTiter i=d.begin(); i != d.end(); ++i) {
      ret += (*i)*(*i);
    }
    return ret;
  }
 
 
  // Inner product 2
  template <class ScalarType, class MV, class OP>
  typename Teuchos::ScalarTraits<ScalarType>::magnitudeType 
  RTRBase<ScalarType,MV,OP>::ginner(const MV &xi, const MV &zeta) const 
  {
    std::vector<ScalarType> d(MVT::GetNumberVecs(xi));
    MVT::MvDot(xi,zeta,d);
    return SCT::real(std::accumulate(d.begin(),d.end(),SCT::zero()));
  }
 
 
  // Inner product 1 without trace accumulation
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::ginnersep(
      const MV &xi, 
      std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> &d) const 
  {
    MVT::MvNorm(xi,d);
    for (vecMTiter i=d.begin(); i != d.end(); ++i) {
      (*i) = (*i)*(*i);
    }
  }
 
 
  // Inner product 2 without trace accumulation
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::ginnersep(
      const MV &xi, const MV &zeta, 
      std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> &d) const 
  {
    std::vector<ScalarType> dC(MVT::GetNumberVecs(xi));
    MVT::MvDot(xi,zeta,dC);
    vecMTiter iR=d.begin(); 
    vecSTiter iS=dC.begin();
    for (; iR != d.end(); iR++, iS++) {
      (*iR) = SCT::real(*iS);
    }
  }
 
  template <class ScalarType, class MV, class OP>
  Teuchos::Array<Teuchos::RCP<const MV> > RTRBase<ScalarType,MV,OP>::getAuxVecs() const {
    return auxVecs_;
  }
 
  template <class ScalarType, class MV, class OP>
  int RTRBase<ScalarType,MV,OP>::getBlockSize() const { 
    return(blockSize_); 
  }
 
  template <class ScalarType, class MV, class OP>
  const Eigenproblem<ScalarType,MV,OP>& RTRBase<ScalarType,MV,OP>::getProblem() const { 
    return(*problem_); 
  }
 
  template <class ScalarType, class MV, class OP>
  int RTRBase<ScalarType,MV,OP>::getMaxSubspaceDim() const {
    return blockSize_;
  }
 
  template <class ScalarType, class MV, class OP>
  int RTRBase<ScalarType,MV,OP>::getCurSubspaceDim() const 
  {
    if (!initialized_) return 0;
    return nevLocal_;
  }
 
  template <class ScalarType, class MV, class OP>
  std::vector<typename Teuchos::ScalarTraits<ScalarType>::magnitudeType> 
  RTRBase<ScalarType,MV,OP>::getRitzRes2Norms() 
  {
    std::vector<MagnitudeType> ret = ritz2norms_;
    ret.resize(nevLocal_);
    return ret;
  }
 
  template <class ScalarType, class MV, class OP>
  std::vector<Value<ScalarType> > 
  RTRBase<ScalarType,MV,OP>::getRitzValues() 
  {
    std::vector<Value<ScalarType> > ret(nevLocal_);
    for (int i=0; i<nevLocal_; i++) {
      ret[i].realpart = theta_[i];
      ret[i].imagpart = ZERO;
    }
    return ret;
  }
 
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<const MV> 
  RTRBase<ScalarType,MV,OP>::getRitzVectors() 
  {
    return X_;
  }
 
  template <class ScalarType, class MV, class OP>
  void RTRBase<ScalarType,MV,OP>::resetNumIters() 
  { 
    iter_=0; 
  }
 
  template <class ScalarType, class MV, class OP>
  int RTRBase<ScalarType,MV,OP>::getNumIters() const 
  { 
    return iter_; 
  }
 
  template <class ScalarType, class MV, class OP>
  RTRState<ScalarType,MV> RTRBase<ScalarType,MV,OP>::getState() const 
  {
    RTRState<ScalarType,MV> state;
    state.X = X_;
    state.AX = AX_;
    if (hasBOp_) {
      state.BX = BX_;
    }
    else {
      state.BX = Teuchos::null;
    }
    state.rho = rho_;
    state.R = R_;
    state.T = Teuchos::rcp(new std::vector<MagnitudeType>(theta_));
    return state;
  }
 
  template <class ScalarType, class MV, class OP>
  bool RTRBase<ScalarType,MV,OP>::isInitialized() const 
  { 
    return initialized_; 
  }
 
  template <class ScalarType, class MV, class OP>
  std::vector<int> RTRBase<ScalarType,MV,OP>::getRitzIndex() 
  {
    std::vector<int> ret(nevLocal_,0);
    return ret;
  }
 
 
} // end Anasazi namespace
 
#endif // ANASAZI_RTRBASE_HPP