BelosBlockGmresIter.hpp

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//
//                 Belos: Block Linear Solvers Package
//                 Copyright (2004) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
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// Questions? Contact Michael A. Heroux (maherou@sandia.gov)
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#ifndef BELOS_BLOCK_GMRES_ITER_HPP
#define BELOS_BLOCK_GMRES_ITER_HPP

#include "BelosConfigDefs.hpp"
#include "BelosTypes.hpp"
#include "BelosGmresIteration.hpp"

#include "BelosLinearProblem.hpp"
#include "BelosMatOrthoManager.hpp"
#include "BelosOutputManager.hpp"
#include "BelosStatusTest.hpp"
#include "BelosOperatorTraits.hpp"
#include "BelosMultiVecTraits.hpp"

#include "Teuchos_BLAS.hpp"
#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_ScalarTraits.hpp"
#include "Teuchos_ParameterList.hpp"
#include "Teuchos_TimeMonitor.hpp"

namespace Belos {
  
template<class ScalarType, class MV, class OP>
class BlockGmresIter : virtual public GmresIteration<ScalarType,MV,OP> {

  public:
    
  //
  // Convenience typedefs
  //
  typedef MultiVecTraits<ScalarType,MV> MVT;
  typedef OperatorTraits<ScalarType,MV,OP> OPT;
  typedef Teuchos::ScalarTraits<ScalarType> SCT;
  typedef typename SCT::magnitudeType MagnitudeType;



  BlockGmresIter( const Teuchos::RCP<LinearProblem<ScalarType,MV,OP> > &problem, 
      const Teuchos::RCP<OutputManager<ScalarType> > &printer,
      const Teuchos::RCP<StatusTest<ScalarType,MV,OP> > &tester,
      const Teuchos::RCP<MatOrthoManager<ScalarType,MV,OP> > &ortho,
      Teuchos::ParameterList &params );

  virtual ~BlockGmresIter() {};



  
  void iterate();

  void initializeGmres(GmresIterationState<ScalarType,MV> newstate);

  void initialize()
  {
    GmresIterationState<ScalarType,MV> empty;
    initializeGmres(empty);
  }
  
  GmresIterationState<ScalarType,MV> getState() const {
    GmresIterationState<ScalarType,MV> state;
    state.curDim = curDim_;
    state.V = V_;
    state.H = H_;
    state.R = R_;
    state.z = z_;
    return state;
  }


  


  int getNumIters() const { return iter_; }
  
  void resetNumIters( int iter = 0 ) { iter_ = iter; }

  Teuchos::RCP<const MV> getNativeResiduals( std::vector<MagnitudeType> *norms ) const;


  Teuchos::RCP<MV> getCurrentUpdate() const;


  void updateLSQR( int dim = -1 );

  int getCurSubspaceDim() const { 
    if (!initialized_) return 0;
    return curDim_;
  };

  int getMaxSubspaceDim() const { return blockSize_*numBlocks_; }


  


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

  int getBlockSize() const { return blockSize_; }
  
  void setBlockSize(int blockSize) { setSize( blockSize, numBlocks_ ); }
  
  int getNumBlocks() const { return numBlocks_; }
  
  void setNumBlocks(int numBlocks) { setSize( blockSize_, numBlocks ); }
  
  void setSize(int blockSize, int numBlocks);

  bool isInitialized() { return initialized_; }


  private:

  //
  // Internal methods
  //
  void setStateSize();
  
  //
  // Classes inputed through constructor that define the linear problem to be solved.
  //
  const Teuchos::RCP<LinearProblem<ScalarType,MV,OP> >    lp_;
  const Teuchos::RCP<OutputManager<ScalarType> >          om_;
  const Teuchos::RCP<StatusTest<ScalarType,MV,OP> >       stest_;
  const Teuchos::RCP<OrthoManager<ScalarType,MV> >        ortho_;

  //
  // Algorithmic parameters
  //  
  // blockSize_ is the solver block size.
  // It controls the number of vectors added to the basis on each iteration.
  int blockSize_;
  // numBlocks_ is the size of the allocated space for the Krylov basis, in blocks.
  int numBlocks_; 
  
  // Storage for QR factorization of the least squares system.
  Teuchos::SerialDenseVector<int,ScalarType> beta, sn;
  Teuchos::SerialDenseVector<int,MagnitudeType> cs;
  
  // 
  // 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_;

  // stateStorageInitialized_ specifies that the state storage has be initialized to the current
  // blockSize_ and numBlocks_.  This initialization may be postponed if the linear problem was
  // generated without the right-hand side or solution vectors.
  bool stateStorageInitialized_;

  // keepHessenberg_ specifies that the iteration must keep the Hessenberg matrix formed via the 
  // Arnoldi factorization and the upper triangular matrix that is the Hessenberg matrix reduced via
  // QR factorization separate.
  bool keepHessenberg_;

  // initHessenberg_ specifies that the iteration should reinitialize the Hessenberg matrix by zeroing
  // out all entries before an iteration is started.
  bool initHessenberg_;
 
  // Current subspace dimension, and number of iterations performed.
  int curDim_, iter_;
  
  // 
  // State Storage
  //
  Teuchos::RCP<MV> V_;
  //
  // Projected matrices
  // H_ : Projected matrix from the Krylov factorization AV = VH + FE^T
  //
  Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > H_;
  // 
  // QR decomposition of Projected matrices for solving the least squares system HY = B.
  // R_: Upper triangular reduction of H
  // z_: Q applied to right-hand side of the least squares system
  Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > R_;
  Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > z_;  
};

  // Constructor.
  template<class ScalarType, class MV, class OP>
  BlockGmresIter<ScalarType,MV,OP>::BlockGmresIter(const Teuchos::RCP<LinearProblem<ScalarType,MV,OP> > &problem, 
               const Teuchos::RCP<OutputManager<ScalarType> > &printer,
               const Teuchos::RCP<StatusTest<ScalarType,MV,OP> > &tester,
               const Teuchos::RCP<MatOrthoManager<ScalarType,MV,OP> > &ortho,
               Teuchos::ParameterList &params ):
    lp_(problem),
    om_(printer),
    stest_(tester),
    ortho_(ortho),
    blockSize_(0),
    numBlocks_(0),
    initialized_(false),
    stateStorageInitialized_(false),
    keepHessenberg_(false),
    initHessenberg_(false),
    curDim_(0),
    iter_(0)
  {
    // Find out whether we are saving the Hessenberg matrix.
    keepHessenberg_ = params.get("Keep Hessenberg", false);

    // Find out whether we are initializing the Hessenberg matrix.
    initHessenberg_ = params.get("Initialize Hessenberg", false);

    // Get the maximum number of blocks allowed for this Krylov subspace
    TEST_FOR_EXCEPTION(!params.isParameter("Num Blocks"), std::invalid_argument,
                       "Belos::BlockGmresIter::constructor: mandatory parameter 'Num Blocks' is not specified.");
    int nb = Teuchos::getParameter<int>(params, "Num Blocks");

    // Set the block size and allocate data
    int bs = params.get("Block Size", 1);
    setSize( bs, nb );
  }

  // Set the block size and make necessary adjustments.
  template <class ScalarType, class MV, class OP>
  void BlockGmresIter<ScalarType,MV,OP>::setSize (int blockSize, int numBlocks)
  {
    // This routine only allocates space; it doesn't not perform any computation
    // any change in size will invalidate the state of the solver.

    TEST_FOR_EXCEPTION(numBlocks <= 0 || blockSize <= 0, std::invalid_argument, "Belos::BlockGmresIter::setSize was passed a non-positive argument.");
    if (blockSize == blockSize_ && numBlocks == numBlocks_) {
      // do nothing
      return;
    }

    if (blockSize!=blockSize_ || numBlocks!=numBlocks_)
      stateStorageInitialized_ = false;

    blockSize_ = blockSize;
    numBlocks_ = numBlocks;

    initialized_ = false;
    curDim_ = 0;

    // Use the current blockSize_ and numBlocks_ to initialize the state storage.    
    setStateSize();
    
  }

  // Setup the state storage.
  template <class ScalarType, class MV, class OP>
  void BlockGmresIter<ScalarType,MV,OP>::setStateSize ()
  {
    if (!stateStorageInitialized_) {

      // Check if there is any multivector to clone from.
      Teuchos::RCP<const MV> lhsMV = lp_->getLHS();
      Teuchos::RCP<const MV> rhsMV = lp_->getRHS();
      if (lhsMV == Teuchos::null && rhsMV == Teuchos::null) {
  stateStorageInitialized_ = false;
  return;
      }
      else {
  
  // blockSize*numBlocks dependent
  //
  int newsd = blockSize_*(numBlocks_+1);
  
  if (blockSize_==1) {
    cs.resize( newsd );
    sn.resize( newsd );
  }
  else {
    beta.resize( newsd );
  }
  
  // Initialize the state storage
        TEST_FOR_EXCEPTION(blockSize_*numBlocks_ > MVT::GetVecLength(*rhsMV),std::invalid_argument,
                           "Belos::BlockGmresIter::setStateSize(): Cannot generate a Krylov basis with dimension larger the operator!");

  // If the subspace has not be initialized before, generate it using the LHS or RHS from lp_.
  if (V_ == Teuchos::null) {
    // Get the multivector that is not null.
    Teuchos::RCP<const MV> tmp = ( (rhsMV!=Teuchos::null)? rhsMV: lhsMV );
    TEST_FOR_EXCEPTION(tmp == Teuchos::null,std::invalid_argument,
           "Belos::BlockGmresIter::setStateSize(): linear problem does not specify multivectors to clone from.");
    V_ = MVT::Clone( *tmp, newsd );
  }
  else {
    // Generate V_ by cloning itself ONLY if more space is needed.
    if (MVT::GetNumberVecs(*V_) < newsd) {
      Teuchos::RCP<const MV> tmp = V_;
      V_ = MVT::Clone( *tmp, newsd );
    }
  }
  
  // Generate R_ only if it doesn't exist, otherwise resize it.
  if (R_ == Teuchos::null) {
    R_ = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>() );
        }
        if (initHessenberg_) {
          R_->shape( newsd, newsd-blockSize_ );
        }
        else {
          if (R_->numRows() < newsd || R_->numCols() < newsd-blockSize_) {
      R_->shapeUninitialized( newsd, newsd-blockSize_ );
    }
        }
  
  // Generate H_ only if it doesn't exist, and we are keeping the upper Hessenberg matrix.
  if (keepHessenberg_) {
    if (H_ == Teuchos::null) {
      H_ = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>() );
          }
          if (initHessenberg_) {
            H_->shape( newsd, newsd-blockSize_ );
          }
          else {
            if (H_->numRows() < newsd || H_->numCols() < newsd-blockSize_) {
        H_->shapeUninitialized( newsd, newsd-blockSize_ );
      }
          }
  }
  else {
    // Point H_ and R_ at the same object.
    H_ = R_;
  }
  
  // Generate z_ only if it doesn't exist, otherwise resize it.
  if (z_ == Teuchos::null) {
    z_ = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>() );
        }
        if (z_-> numRows() < newsd || z_->numCols() < blockSize_) {
    z_->shapeUninitialized( newsd, blockSize_ );
  }
  
  // State storage has now been initialized.
  stateStorageInitialized_ = true;
      }
    }
  }

  // Get the current update from this subspace.
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<MV> BlockGmresIter<ScalarType,MV,OP>::getCurrentUpdate() const
  {
    //
    // If this is the first iteration of the Arnoldi factorization, 
    // there is no update, so return Teuchos::null. 
    //
    RCP<MV> currentUpdate = Teuchos::null;
    if (curDim_==0) { 
      return currentUpdate; 
    } else {
      const ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
      const ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
      Teuchos::BLAS<int,ScalarType> blas;
      currentUpdate = MVT::Clone( *V_, blockSize_ );
      //
      //  Make a view and then copy the RHS of the least squares problem.  DON'T OVERWRITE IT!
      //
      Teuchos::SerialDenseMatrix<int,ScalarType> y( Teuchos::Copy, *z_, curDim_, blockSize_ );
      //
      //  Solve the least squares problem.
      //
      blas.TRSM( Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::NO_TRANS,
     Teuchos::NON_UNIT_DIAG, curDim_, blockSize_, one,  
     R_->values(), R_->stride(), y.values(), y.stride() );
      //
      //  Compute the current update.
      //
      std::vector<int> index(curDim_);
      for ( int i=0; i<curDim_; i++ ) {   
        index[i] = i;
      }
      RCP<const MV> Vjp1 = MVT::CloneView( *V_, index );
      MVT::MvTimesMatAddMv( one, *Vjp1, y, zero, *currentUpdate );
    }
    return currentUpdate;
  }


  // Get the native residuals stored in this iteration.  
  // Note:  No residual std::vector will be returned by Gmres.
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<const MV> BlockGmresIter<ScalarType,MV,OP>::getNativeResiduals( std::vector<MagnitudeType> *norms ) const 
  {
    //
    // NOTE: Make sure the incoming std::vector is the correct size!
    //
    if ( norms && (int)norms->size() < blockSize_ )                         
      norms->resize( blockSize_ );                                          
    
    if (norms) {
      Teuchos::BLAS<int,ScalarType> blas;
      for (int j=0; j<blockSize_; j++) {
        (*norms)[j] = blas.NRM2( blockSize_, &(*z_)(curDim_, j), 1);
      }
    }
    return Teuchos::null;
  }

  

  // Initialize this iteration object
  template <class ScalarType, class MV, class OP>
  void BlockGmresIter<ScalarType,MV,OP>::initializeGmres(GmresIterationState<ScalarType,MV> newstate)
  {
    // Initialize the state storage if it isn't already.
    if (!stateStorageInitialized_) 
      setStateSize();

    TEST_FOR_EXCEPTION(!stateStorageInitialized_,std::invalid_argument,
           "Belos::BlockGmresIter::initialize(): Cannot initialize state storage!");
    
    // NOTE:  In BlockGmresIter, V and Z are required!!!  
    // inconsitent multivectors widths and lengths will not be tolerated, and
    // will be treated with exceptions.
    //
    std::string errstr("Belos::BlockGmresIter::initialize(): Specified multivectors must have a consistent length and width.");

    if (newstate.V != Teuchos::null && newstate.z != Teuchos::null) {

      // initialize V_,z_, and curDim_

      TEST_FOR_EXCEPTION( MVT::GetVecLength(*newstate.V) != MVT::GetVecLength(*V_),
                          std::invalid_argument, errstr );
      TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.V) < blockSize_,
                          std::invalid_argument, errstr );
      TEST_FOR_EXCEPTION( newstate.curDim > blockSize_*(numBlocks_+1),
                          std::invalid_argument, errstr );

      curDim_ = newstate.curDim;
      int lclDim = MVT::GetNumberVecs(*newstate.V);

      // check size of Z
      TEST_FOR_EXCEPTION(newstate.z->numRows() < curDim_ || newstate.z->numCols() < blockSize_, std::invalid_argument, errstr);
      

      // copy basis vectors from newstate into V
      if (newstate.V != V_) {
        // only copy over the first block and print a warning.
        if (curDim_ == 0 && lclDim > blockSize_) {
    om_->stream(Warnings) << "Belos::BlockGmresIter::initialize(): the solver was initialized with a kernel of " << lclDim << std::endl
        << "The block size however is only " << blockSize_ << std::endl
        << "The last " << lclDim - blockSize_ << " vectors will be discarded." << std::endl;
  }
        std::vector<int> nevind(curDim_+blockSize_);
        for (int i=0; i<curDim_+blockSize_; i++) nevind[i] = i;
  Teuchos::RCP<const MV> newV = MVT::CloneView( *newstate.V, nevind );
  Teuchos::RCP<MV> lclV = MVT::CloneView( *V_, nevind );
        MVT::MvAddMv( 1.0, *newV, 0.0, *newV, *lclV );

        // done with local pointers
        lclV = Teuchos::null;
      }

      // put data into z_, make sure old information is not still hanging around.
      if (newstate.z != z_) {
        z_->putScalar();
        Teuchos::SerialDenseMatrix<int,ScalarType> newZ(Teuchos::View,*newstate.z,curDim_+blockSize_,blockSize_);
        Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > lclZ;
        lclZ = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>(Teuchos::View,*z_,curDim_+blockSize_,blockSize_) );
        lclZ->assign(newZ);

        // done with local pointers
        lclZ = Teuchos::null;
      }

    }
    else {

      TEST_FOR_EXCEPTION(newstate.V == Teuchos::null,std::invalid_argument,
                         "Belos::BlockGmresIter::initialize(): BlockGmresStateIterState does not have initial kernel V_0.");

      TEST_FOR_EXCEPTION(newstate.z == Teuchos::null,std::invalid_argument,
                         "Belos::BlockGmresIter::initialize(): BlockGmresStateIterState does not have initial norms z_0.");
    }

    // the solver is initialized
    initialized_ = true;

    /*
    if (om_->isVerbosity( Debug ) ) {
      // Check almost everything here
      CheckList chk;
      chk.checkV = true;
      chk.checkArn = true;
      chk.checkAux = true;
      om_->print( Debug, accuracyCheck(chk, ": after initialize()") );
    }
    */

  }


  // Iterate until the status test informs us we should stop.
  template <class ScalarType, class MV, class OP>
  void BlockGmresIter<ScalarType,MV,OP>::iterate()
  {
    //
    // Allocate/initialize data structures
    //
    if (initialized_ == false) {
      initialize();
    }
    
    // Compute the current search dimension. 
    int searchDim = blockSize_*numBlocks_;

    // iterate until the status test tells us to stop.
    //
    // also break if our basis is full
    //
    while (stest_->checkStatus(this) != Passed && curDim_+blockSize_ <= searchDim) {

      iter_++;

      // F can be found at the curDim_ block, but the next block is at curDim_ + blockSize_.
      int lclDim = curDim_ + blockSize_; 

      // Get the current part of the basis.
      std::vector<int> curind(blockSize_);
      for (int i=0; i<blockSize_; i++) { curind[i] = lclDim + i; }
      Teuchos::RCP<MV> Vnext = MVT::CloneView(*V_,curind);

      // Get a view of the previous vectors.
      // This is used for orthogonalization and for computing V^H K H
      for (int i=0; i<blockSize_; i++) { curind[i] = curDim_ + i; }
      Teuchos::RCP<MV> Vprev = MVT::CloneView(*V_,curind);

      // Compute the next std::vector in the Krylov basis:  Vnext = Op*Vprev
      lp_->apply(*Vprev,*Vnext);
      Vprev = Teuchos::null;
      
      // Remove all previous Krylov basis vectors from Vnext      
      // Get a view of all the previous vectors
      std::vector<int> prevind(lclDim);
      for (int i=0; i<lclDim; i++) { prevind[i] = i; }
      Vprev = MVT::CloneView(*V_,prevind);
      Teuchos::Array<Teuchos::RCP<const MV> > AVprev(1, Vprev);
      
      // Get a view of the part of the Hessenberg matrix needed to hold the ortho coeffs.
      Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> >
  subH = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>
           ( Teuchos::View,*H_,lclDim,blockSize_,0,curDim_ ) );
      Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > AsubH;
      AsubH.append( subH );
      
      // Get a view of the part of the Hessenberg matrix needed to hold the norm coeffs.
      Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> >
  subH2 = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>
            ( Teuchos::View,*H_,blockSize_,blockSize_,lclDim,curDim_ ) );
      subH2->putScalar();  // Initialize subdiagonal to zero
      int rank = ortho_->projectAndNormalize(*Vnext,AsubH,subH2,AVprev);

      // Copy over the coefficients if we are saving the upper Hessenberg matrix,
      // just in case we run into an error.
      if (keepHessenberg_) {
  // Copy over the orthogonalization coefficients.
  Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> >
    subR = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>
             ( Teuchos::View,*R_,lclDim,blockSize_,0,curDim_ ) );
  subR->assign(*subH);
  
  // Copy over the lower diagonal block of the Hessenberg matrix.
  Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> >
    subR2 = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>
        ( Teuchos::View,*R_,blockSize_,blockSize_,lclDim,curDim_ ) );
  subR2->assign(*subH2);
      }

      TEST_FOR_EXCEPTION(rank != blockSize_,GmresIterationOrthoFailure,
       "Belos::BlockGmresIter::iterate(): couldn't generate basis of full rank.");
      //
      // V has been extended, and H has been extended. 
      //
      // Update the QR factorization of the upper Hessenberg matrix
      //
      updateLSQR();
      //
      // Update basis dim and release all pointers.
      //
      Vnext = Teuchos::null;
      curDim_ += blockSize_;
      //        
      /*      
      // When required, monitor some orthogonalities
      if (om_->isVerbosity( Debug ) ) {
      // Check almost everything here
      CheckList chk;
      chk.checkV = true;
      chk.checkArn = true;
      om_->print( Debug, accuracyCheck(chk, ": after local update") );
      }
      else if (om_->isVerbosity( OrthoDetails ) ) {
        CheckList chk;
        chk.checkV = true;
        om_->print( OrthoDetails, accuracyCheck(chk, ": after local update") );
      }
      */ 
      
    } // end while (statusTest == false)
   
  }

  
  template<class ScalarType, class MV, class OP>
  void BlockGmresIter<ScalarType,MV,OP>::updateLSQR( int dim )
  {
    int i, j, maxidx;
    ScalarType sigma, mu, vscale, maxelem;
    const ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
    
    // Get correct dimension based on input "dim"
    // Remember that ortho failures result in an exit before updateLSQR() is called.
    // Therefore, it is possible that dim == curDim_.
    int curDim = curDim_;
    if (dim >= curDim_ && dim < getMaxSubspaceDim()) {
      curDim = dim;
    }
    
    Teuchos::BLAS<int, ScalarType> blas;
    //
    // Apply previous transformations and compute new transformation to reduce upper-Hessenberg
    // system to upper-triangular form.
    //
    if (blockSize_ == 1) {
      //
      // QR factorization of Least-Squares system with Givens rotations
      //
      for (i=0; i<curDim; i++) {
  //
  // Apply previous Givens rotations to new column of Hessenberg matrix
  //
  blas.ROT( 1, &(*R_)(i,curDim), 1, &(*R_)(i+1, curDim), 1, &cs[i], &sn[i] );
      }
      //
      // Calculate new Givens rotation
      //
      blas.ROTG( &(*R_)(curDim,curDim), &(*R_)(curDim+1,curDim), &cs[curDim], &sn[curDim] );
      (*R_)(curDim+1,curDim) = zero;
      //
      // Update RHS w/ new transformation
      //
      blas.ROT( 1, &(*z_)(curDim,0), 1, &(*z_)(curDim+1,0), 1, &cs[curDim], &sn[curDim] );
    }
    else {
      //
      // QR factorization of Least-Squares system with Householder reflectors
      //
      for (j=0; j<blockSize_; j++) {
  //
  // Apply previous Householder reflectors to new block of Hessenberg matrix
  //
  for (i=0; i<curDim+j; i++) {
    sigma = blas.DOT( blockSize_, &(*R_)(i+1,i), 1, &(*R_)(i+1,curDim+j), 1);
    sigma += (*R_)(i,curDim+j);
    sigma *= beta[i];
    blas.AXPY(blockSize_, -sigma, &(*R_)(i+1,i), 1, &(*R_)(i+1,curDim+j), 1);
    (*R_)(i,curDim+j) -= sigma;
  }
  //
  // Compute new Householder reflector
  //
  maxidx = blas.IAMAX( blockSize_+1, &(*R_)(curDim+j,curDim+j), 1 );
  maxelem = (*R_)(curDim+j+maxidx-1,curDim+j);
  for (i=0; i<blockSize_+1; i++)
    (*R_)(curDim+j+i,curDim+j) /= maxelem;
  sigma = blas.DOT( blockSize_, &(*R_)(curDim+j+1,curDim+j), 1,
        &(*R_)(curDim+j+1,curDim+j), 1 );
  if (sigma == zero) {
    beta[curDim + j] = zero;
  } else {
    mu = std::sqrt((*R_)(curDim+j,curDim+j)*(*R_)(curDim+j,curDim+j)+sigma);
    if ( Teuchos::ScalarTraits<ScalarType>::real((*R_)(curDim+j,curDim+j)) 
         < Teuchos::ScalarTraits<MagnitudeType>::zero() ) {
      vscale = (*R_)(curDim+j,curDim+j) - mu;
    } else {
      vscale = -sigma / ((*R_)(curDim+j,curDim+j) + mu);
    }
    beta[curDim+j] = 2.0*vscale*vscale/(sigma + vscale*vscale);
    (*R_)(curDim+j,curDim+j) = maxelem*mu;
    for (i=0; i<blockSize_; i++)
      (*R_)(curDim+j+1+i,curDim+j) /= vscale;
  }
  //
  // Apply new Householder reflector to rhs
  //
  for (i=0; i<blockSize_; i++) {
    sigma = blas.DOT( blockSize_, &(*R_)(curDim+j+1,curDim+j),
          1, &(*z_)(curDim+j+1,i), 1);
    sigma += (*z_)(curDim+j,i);
    sigma *= beta[curDim+j];
    blas.AXPY(blockSize_, -sigma, &(*R_)(curDim+j+1,curDim+j),
        1, &(*z_)(curDim+j+1,i), 1);
    (*z_)(curDim+j,i) -= sigma;
  }
      }
    } // end if (blockSize_ == 1)

    // If the least-squares problem is updated wrt "dim" then update the curDim_.
    if (dim >= curDim_ && dim < getMaxSubspaceDim()) {
      curDim_ = dim + blockSize_;
    }

  } // end updateLSQR()

} // end Belos namespace

#endif /* BELOS_BLOCK_GMRES_ITER_HPP */

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