BelosBlockGCRODRIter.hpp

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// @HEADER
// *****************************************************************************
//                 Belos: Block Linear Solvers Package
//
// Copyright 2004-2016 NTESS and the Belos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#ifndef BELOS_BLOCK_GCRODR_ITER_HPP
#define BELOS_BLOCK_GCRODR_ITER_HPP


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

// MLP
#include <unistd.h>

namespace Belos{



  template <class ScalarType, class MV>
  struct BlockGCRODRIterState {
    int curDim;

    Teuchos::RCP<MV> V; 

    Teuchos::RCP<MV> U, C;  

     Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > H;
        
     Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B;

     BlockGCRODRIterState() : curDim(0), V(Teuchos::null),
      U(Teuchos::null), C(Teuchos::null),
      H(Teuchos::null), B(Teuchos::null)
     {}

  };






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

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



    template<class ScalarType, class MV, class OP>
    class BlockGCRODRIter : virtual public Iteration<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;
  typedef Teuchos::SerialDenseMatrix<int,ScalarType> SDM;
      typedef Teuchos::SerialDenseVector<int,ScalarType> SDV;



       BlockGCRODRIter( 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 ~BlockGCRODRIter() {};
 


       void iterate();

       void initialize() {
          BlockGCRODRIterState<ScalarType,MV> empty;
        initialize(empty);
       }  

       void initialize(BlockGCRODRIterState<ScalarType,MV>& newstate);
       
       BlockGCRODRIterState<ScalarType,MV> getState() const{
    BlockGCRODRIterState<ScalarType,MV> state;
    state.curDim = curDim_;
          state.V = V_;
          state.U = U_;
          state.C = C_;
          state.H = H_;
          state.B = B_;
          return state;
       }



       bool isInitialized(){ return initialized_;};

       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;







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

       int getNumBlocks() const { return numBlocks_; }

       int getBlockSize() const { return blockSize_; };

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

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

       int getRecycledBlocks() const { return recycledBlocks_; };





       void updateLSQR( int dim = -1);

       void setBlockSize(int blockSize){ blockSize_ = blockSize; }

       void setRecycledBlocks(int recycledBlocks) { setSize( recycledBlocks, numBlocks_ ); };

       void setNumBlocks(int numBlocks) { setSize( recycledBlocks_, numBlocks ); };

       void setSize( int recycledBlocks, int numBlocks ) {
       // only call resize if size changed
       if ( (recycledBlocks_ != recycledBlocks) || (numBlocks_ != numBlocks) ) {
        recycledBlocks_ = recycledBlocks;
        numBlocks_ = numBlocks;
        cs_.sizeUninitialized( numBlocks_ );
        sn_.sizeUninitialized( numBlocks_ );
        Z_.shapeUninitialized( numBlocks_*blockSize_, blockSize_ );
      }
    }


      private:

  //
  // Internal methods
  //



      //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
      //

      //numBlocks_ is the size of the allocated space for the Krylov basis, in blocks.
      //blockSize_ is the number of columns in each block Krylov vector.
      int numBlocks_, blockSize_;

      //boolean vector indicating which right-hand sides we care about
      //when we are testing residual norms.  THIS IS NOT IMPLEMENTED.  RIGHT NOW JUST
      //SELECTS ALL RIGHT HANDS SIDES FOR NORM COMPUTATION.
      std::vector<bool> trueRHSIndices_;

      // recycledBlocks_ is the size of the allocated space for the recycled subspace, in vectors.
      int recycledBlocks_;    

      //Storage for QR factorization of the least squares system if using plane rotations.
      SDV sn_;
      Teuchos::SerialDenseVector<int,MagnitudeType> cs_;

      //Storage for QR factorization of the least squares system if using Householder reflections
      //Per block Krylov vector, we actually construct a 2*blockSize_ by 2*blockSize_ matrix which
      //is the product of all Householder transformations for that block.  This has been shown to yield
      //speed ups without losing accuracy because we can apply previous Householder transformations
      //with BLAS3 operations.
      std::vector< SDM >House_;
      SDV beta_;

      //
      //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_;    
    
      // Current subspace dimension, number of iterations performed, and number of iterations performed in this cycle.
      int curDim_, iter_, lclIter_;
  
      //
      // Recycled Krylov Method Storage
      //


      Teuchos::RCP<MV> V_;

      Teuchos::RCP<MV> U_, C_;




      Teuchos::RCP<SDM > H_;

      Teuchos::RCP<SDM > B_;

      Teuchos::RCP<SDM> R_;

      SDM Z_;


      // File stream variables to use Mike Parks' Matlab output codes.
      std::ofstream ofs;
      char filename[30];

   };//End BlockGCRODRIter Class Definition

   //Constructor.
   template<class ScalarType, class MV, class OP>
   BlockGCRODRIter<ScalarType,MV,OP>::BlockGCRODRIter(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) {
      numBlocks_      = 0;
  blockSize_  = 0;
      recycledBlocks_ = 0;
      initialized_    = false;
      curDim_         = 0;
      iter_           = 0;
  lclIter_        = 0;
      V_              = Teuchos::null;
      U_              = Teuchos::null;
    C_              = Teuchos::null;
      H_              = Teuchos::null;
      B_              = Teuchos::null;
  R_              = Teuchos::null;
  // Get the maximum number of blocks allowed for this Krylov subspace
  TEUCHOS_TEST_FOR_EXCEPTION(!params.isParameter("Num Blocks"), std::invalid_argument, "Belos::BlockGCRODRIter::constructor: mandatory parameter \"Num Blocks\" is not specified.");
  int nb = Teuchos::getParameter<int>(params, "Num Blocks");

  TEUCHOS_TEST_FOR_EXCEPTION(!params.isParameter("Recycled Blocks"), std::invalid_argument,"Belos::BlockGCRODRIter::constructor: mandatory parameter \"Recycled Blocks\" is not specified.");
  int rb = Teuchos::getParameter<int>(params, "Recycled Blocks");

  TEUCHOS_TEST_FOR_EXCEPTION(nb <= 0, std::invalid_argument, "Belos::BlockGCRODRIter() was passed a non-positive argument for \"Num Blocks\".");
  TEUCHOS_TEST_FOR_EXCEPTION(rb >= nb, std::invalid_argument, "Belos::BlockGCRODRIter() the number of recycled blocks is larger than the allowable subspace.");


  int bs = Teuchos::getParameter<int>(params, "Block Size");

  TEUCHOS_TEST_FOR_EXCEPTION(bs <= 0, std::invalid_argument, "Belos::BlockGCRODRIter() the block size was passed a non-postitive argument.");


  numBlocks_ = nb;
  recycledBlocks_ = rb;
  blockSize_ = bs;

  //INITIALIZE ENTRIES OF trueRHSIndices_ TO CHECK EVERY NORM FOR NOW.  LATER, THE USER
  //SHOULD SPECIFY WHICH RIGHT HAND SIDES ARE IMPORTANT FOR CONVERGENCE TESTING
  trueRHSIndices_.resize(blockSize_);
  int i;
  for(i=0; i<blockSize_; i++){
    trueRHSIndices_[i] = true;
  }

        //THIS MAKES SPACE FOR GIVENS ROTATIONS BUT IN REALITY WE NEED TO DO TESTING ON BLOCK SIZE
        //AND CHOOSE BETWEEN GIVENS ROTATIONS AND HOUSEHOLDER TRANSFORMATIONS.        
        cs_.sizeUninitialized( numBlocks_+1 );
      sn_.sizeUninitialized( numBlocks_+1 );
      Z_.shapeUninitialized( (numBlocks_+1)*blockSize_,blockSize_ );

  House_.resize(numBlocks_);

  for(i=0; i<numBlocks_;i++){
    House_[i].shapeUninitialized(2*blockSize_, 2*blockSize_);
  }
   }//End Constructor Definition

   // Iterate until the status test informs us we should stop.
   template <class ScalarType, class MV, class OP>
   void BlockGCRODRIter<ScalarType,MV,OP>::iterate() {
  TEUCHOS_TEST_FOR_EXCEPTION( initialized_ == false, BlockGCRODRIterInitFailure,"Belos::BlockGCRODRIter::iterate(): GCRODRIter class not initialized." );

// MLP
//sleep(1);
//std::cout << "Calling setSize" << std::endl;
  // Force call to setsize to ensure internal storage is correct dimension
  setSize( recycledBlocks_, numBlocks_ );

  Teuchos::RCP<MV> Vnext;
  Teuchos::RCP<const MV> Vprev;
  std::vector<int> curind(blockSize_);

  // z_ must be zeroed out in order to compute Givens rotations correctly
  Z_.putScalar(0.0);

  // Orthonormalize the new V_0
  for(int i = 0; i<blockSize_; i++){curind[i] = i;};
  
// MLP
//sleep(1);
//std::cout << "Calling normalize" << std::endl;
  Vnext = MVT::CloneViewNonConst(*V_,curind);
  //Orthonormalize Initial Columns
  //Store orthogonalization coefficients in Z0
  Teuchos::RCP<SDM > Z0 =
               Teuchos::rcp( new SDM(blockSize_,blockSize_) );
  int rank = ortho_->normalize(*Vnext,Z0);

// MLP
//sleep(1);
//std::cout << "Assigning Z" << std::endl;
  TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_,BlockGCRODRIterOrthoFailure, "Belos::BlockGCRODRIter::iterate(): couldn't generate basis of full rank at the initial step.");
  // Copy Z0 into the leading blockSize_ by blockSize_ block of Z_
  Teuchos::RCP<SDM > Z_block = Teuchos::rcp( new SDM(Teuchos::View, Z_, blockSize_,blockSize_) );
  Z_block->assign(*Z0);

  std::vector<int> prevind(blockSize_*(numBlocks_ + 1));

  // iterate until the status test tells us to stop.
  //
  // also break if the basis is full
  //
  while( (stest_->checkStatus(this) != Passed) && (curDim_+blockSize_-1) < (numBlocks_*blockSize_)) {
    lclIter_++;
    iter_++;
//KMS
//std::cout << "Iter=" << iter_ << std::endl << "lclIter=" << lclIter_ <<  std::endl;

    int HFirstCol = curDim_-blockSize_;//First column of H we need view of
    int HLastCol = HFirstCol + blockSize_-1 ;//last column of H we need a view of
    int HLastOrthRow = HLastCol;//Last row of H we will put orthog coefficients in
    int HFirstNormRow = HLastOrthRow + 1;//First row of H where normalization matrix goes
//KMS
//std::cout << "curDim_ = " << curDim_ << ", HFirstCol = " << HFirstCol << ", HLastCol =  " << HLastCol <<", HLastOrthRow =  " << HLastOrthRow << ", HFirstNormRow =  " << HFirstNormRow << std::endl;    
    // Get next basis indices
    for(int i = 0; i< blockSize_; i++){
      curind[i] = curDim_ + i;
    }
    Vnext = MVT::CloneViewNonConst(*V_,curind);

    //Get a view of the previous block Krylov vector.
    //This is used for orthogonalization and for computing V^H K H
    // Get next basis indices
    for(int i = 0; i< blockSize_; i++){
                        curind[blockSize_ - 1 - i] = curDim_ -  i - 1;
                }
    Vprev = MVT::CloneView(*V_,curind);
    // Compute the next vector in the Krylov basis:  Vnext = Op*Vprev
    lp_->apply(*Vprev,*Vnext);
    Vprev = Teuchos::null;

    //First, remove the recycled subspace (C) from Vnext and put coefficients in B.

    //Get a view of the matrix B and put the pointer into an array
    //Put a pointer to C in another array
    Teuchos::Array<Teuchos::RCP<const MV> > C(1, C_);

    Teuchos::RCP<SDM >
            subB = Teuchos::rcp( new SDM ( Teuchos::View,*B_,recycledBlocks_,blockSize_,0, HFirstCol ) );

    Teuchos::Array<Teuchos::RCP<SDM > > AsubB;
    AsubB.append( subB );
    // Project out the recycled subspace.
                ortho_->project( *Vnext, AsubB, C );
    //Now, remove block Krylov Subspace from Vnext and store coefficients in H_ and R_
    
    // Get a view of all the previous vectors
    prevind.resize(curDim_);
    for (int i=0; i<curDim_; 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<SDM> subH = Teuchos::rcp( new SDM  ( Teuchos::View,*H_,curDim_,blockSize_,0,HFirstCol ) );
    Teuchos::Array<Teuchos::RCP<SDM > > AsubH;
    AsubH.append( subH );
    // Get a view of the part of the Hessenberg matrix needed to hold the norm coeffs.
    Teuchos::RCP<SDM >  subR = Teuchos::rcp( new SDM ( Teuchos::View,*H_,blockSize_,blockSize_,HFirstNormRow,HFirstCol ) );
    // Project out the previous Krylov vectors and normalize the next vector.
    int rank = ortho_->projectAndNormalize(*Vnext,AsubH,subR,AVprev);

    // Copy over the coefficients to R just in case we run into an error.
    SDM subR2( Teuchos::View,*R_,(lclIter_+1)*blockSize_,blockSize_,0,HFirstCol);
    SDM subH2( Teuchos::View,*H_,(lclIter_+1)*blockSize_,blockSize_,0,HFirstCol);
    subR2.assign(subH2);

    TEUCHOS_TEST_FOR_EXCEPTION(rank != blockSize_,BlockGCRODRIterOrthoFailure, "Belos::BlockGCRODRIter::iterate(): couldn't generate basis of full rank.");

    // Update the QR factorization of the upper Hessenberg matrix
    updateLSQR();

          // Update basis dim
                curDim_ = curDim_ + blockSize_;



  }//end while(stest_->checkStatus(this) ~= Passed && curDim_+1 <= numBlocks_*blockSize_)
  
   }//end iterate() defintition

   //Initialize this iteration object.
   template <class ScalarType, class MV, class OP>
   void BlockGCRODRIter<ScalarType,MV,OP>::initialize(BlockGCRODRIterState<ScalarType,MV>& newstate) {
  if (newstate.V != Teuchos::null &&  newstate.H != Teuchos::null) {
          curDim_ = newstate.curDim;
          V_      = newstate.V;
          U_      = newstate.U;
          C_      = newstate.C;
          H_      = newstate.H;
          B_      = newstate.B;
    lclIter_ = 0;//resets the count of local iterations for the new cycle
    R_      = Teuchos::rcp(new SDM(H_->numRows(), H_->numCols() )); //R_ should look like H but point to separate memory

    //All Householder product matrices start out as identity matrices.
    //We construct an identity from which to copy.
    SDM Identity(2*blockSize_, 2*blockSize_);
    for(int i=0;i<2*blockSize_; i++){
      Identity[i][i] = 1;
    } 
    for(int i=0; i<numBlocks_;i++){
      House_[i].assign(Identity);
    }
      }
      else {
          TEUCHOS_TEST_FOR_EXCEPTION(newstate.V == Teuchos::null,std::invalid_argument,"Belos::GCRODRIter::initialize(): BlockGCRODRIterState does not have V initialized.");
          TEUCHOS_TEST_FOR_EXCEPTION(newstate.H == Teuchos::null,std::invalid_argument,"Belos::GCRODRIter::initialize(): BlockGCRODRIterState does not have H initialized.");
      }
      // the solver is initialized
        initialized_ = true;
   }//end initialize() defintition

   //Get the native residuals stored in this iteration.
   //This function will only compute the native residuals for 
   //right-hand sides we are interested in, as dictated by 
   //std::vector<int> trueRHSIndices_ (THIS IS NOT YET IMPLEMENTED.  JUST GETS ALL RESIDUALS)
   //A norm of -1 is entered for all residuals about which we do not care.
   template <class ScalarType, class MV, class OP>
   Teuchos::RCP<const MV> 
   BlockGCRODRIter<ScalarType,MV,OP>::getNativeResiduals( std::vector<MagnitudeType> *norms ) const
   {
  //
  // NOTE: Make sure the incoming std::vector is the correct size!
  //
  if (norms != NULL) {
    if (static_cast<int> (norms->size()) < blockSize_) {
          norms->resize( blockSize_ );
    }
          Teuchos::BLAS<int,ScalarType> blas;
          for (int j=0; j<blockSize_; j++) {
      if(trueRHSIndices_[j]){
              (*norms)[j] = blas.NRM2( blockSize_, &Z_(curDim_-blockSize_+j, j), 1);
      }
      else{
        (*norms)[j] = -1;
      }
          }
      return Teuchos::null;
      } else { // norms is NULL
    // FIXME If norms is NULL, return residual vectors.
      return Teuchos::null;
  }
   }//end getNativeResiduals() definition

   //Get the current update from this subspace.
   template <class ScalarType, class MV, class OP>
   Teuchos::RCP<MV> BlockGCRODRIter<ScalarType,MV,OP>::getCurrentUpdate() const {
  //
  // If this is the first iteration of the Arnoldi factorization,
  // there is no update, so return Teuchos::null.
  //
  Teuchos::RCP<MV> currentUpdate = Teuchos::null;
//KMS if(curDim_==0) {
  if(curDim_<=blockSize_) {
    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!
    //
    SDM Y( Teuchos::Copy, Z_, curDim_-blockSize_, blockSize_ );
    Teuchos::RCP<SDM> Rtmp = Teuchos::rcp(new SDM(Teuchos::View, *R_, curDim_, curDim_-blockSize_));
//KMS
//sleep(1);
//std::cout << "Before TRSM" << std::endl;
//sleep(1);
//std::cout << "The size of Rtmp is " << Rtmp -> numRows() << " by " << Rtmp -> numCols() << std::endl;
//std::cout << "The size of Y is " << Y.numRows() << " by " << Y.numCols() << std::endl;
//std::cout << "blockSize_ = " << blockSize_ << std::endl;
//std::cout << "curDim_ =  " << curDim_ << std::endl;
//std::cout << "curDim_ - blockSize_ =  " << curDim_ - blockSize_ << std::endl;
    //
    // Solve the least squares problem.
    // Observe that in calling TRSM, we use the value
    // curDim_ -blockSize_. This is because curDim_ has
    // already been incremented but the proper size of R is still 
    // based on the previous value.
    //
    blas.TRSM( Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::NO_TRANS,
                Teuchos::NON_UNIT_DIAG, curDim_-blockSize_, blockSize_, one,
                Rtmp->values(), Rtmp->stride(), Y.values(), Y.stride() );
//KMS
//sleep(1);
//std::cout << "After TRSM" << std::endl;
          //
                //  Compute the current update from the Krylov basis; V(:,1:curDim_)*y.
                //
                std::vector<int> index(curDim_-blockSize_);
          for ( int i=0; i<curDim_-blockSize_; i++ ) index[i] = i;
          Teuchos::RCP<const MV> Vjp1 = MVT::CloneView( *V_, index );
          MVT::MvTimesMatAddMv( one, *Vjp1, Y, zero, *currentUpdate );



          //
                //  Add in portion of update from recycled subspace U; U(:,1:recycledBlocks_)*B*y.
                //
                if (U_ != Teuchos::null) {
            SDM z(recycledBlocks_,blockSize_);
            SDM subB( Teuchos::View, *B_, recycledBlocks_, curDim_-blockSize_ );
            z.multiply( Teuchos::NO_TRANS, Teuchos::NO_TRANS, one, subB, Y, zero );

            //std::cout << (*U_).MyLength() << " " << (*U_).NumVectors() << " " << subB.numRows() << " " << subB.numCols() << " " << Y.numRows() << " " << Y.numCols()<< " " << curDim_ << " " << recycledBlocks_;  
            MVT::MvTimesMatAddMv( -one, *U_, z, one, *currentUpdate );
          }
      }



      return currentUpdate;
    }//end getCurrentUpdate() definition

    template<class ScalarType, class MV, class OP>
    void BlockGCRODRIter<ScalarType,MV,OP>::updateLSQR( int dim ) {
  
  int i;
  const ScalarType zero = Teuchos::ScalarTraits<ScalarType>::zero();
  const ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();

    using Teuchos::rcp;

  // 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;

  if(blockSize_ == 1){//if only one right-hand side then use Givens rotations
    //
    // Apply previous rotations and compute new rotations to reduce upper-Hessenberg
    // system to upper-triangular form.
    //
    // QR factorization of Least-Squares system with Givens rotations
    //
    for (i=0; i<curDim-1; i++) {
            //
            // Apply previous Givens rotations to new column of Hessenberg matrix
            //
            blas.ROT( 1, &(*R_)(i,curDim-1), 1, &(*R_)(i+1, curDim-1), 1, &cs_[i], &sn_[i] );
        }
        //
          // Calculate new Givens rotation
          //
          blas.ROTG( &(*R_)(curDim-1,curDim-1), &(*R_)(curDim,curDim-1), &cs_[curDim-1], &sn_[curDim-1] );
        (*R_)(curDim,curDim-1) = zero;
        //
          // Update RHS w/ new transformation
          //
          blas.ROT( 1, &Z_(curDim-1,0), 1, &Z_(curDim,0), 1, &cs_[curDim-1], &sn_[curDim-1] );
  }
  else{//if multiple right-hand sides then use Householder transormations
    //
    //apply previous reflections and compute new reflections to reduce upper-Hessenberg
    //system to upper-triagular form.

    //In Matlab, applying the reflection to a matrix M would look like
    // M_refl = M - 2*v_refl*(v_refl'*M)/(norm(v_refl)^2)

    //In order to take advantage of BLAS while applying reflections to a matrix, we
    //perform it in a two step process
    //1. workvec = M'*v_refl    {using BLAS.GEMV()}
    //2. M_refl = M_refl - 2*v_refl*workvec'/(norm(v_refl)^2)    {using BLAS.GER()}

    Teuchos::RCP< SDM > workmatrix = Teuchos::null;//matrix of column vectors onto which we apply the reflection
    Teuchos::RCP< SDV > workvec = Teuchos::null;//where we store the result of the first step of the 2-step reflection process
    Teuchos::RCP<SDV> v_refl = Teuchos::null;//the reflection vector
    int R_colStart = curDim_-blockSize_;
    Teuchos::RCP< SDM >Rblock = Teuchos::null;

    //
    //Apply previous reflections
    //
    for(i=0; i<lclIter_-1; i++){
      int R_rowStart = i*blockSize_;
      //get a view of the part of R_ effected by these reflections. 
      Teuchos::RCP< SDM > RblockCopy = rcp(new SDM (Teuchos::Copy, *R_, 2*blockSize_,blockSize_, R_rowStart, R_colStart));
      Teuchos::RCP< SDM > RblockView = rcp(new SDM (Teuchos::View, *R_, 2*blockSize_,blockSize_, R_rowStart, R_colStart));
      blas.GEMM(Teuchos::NO_TRANS,Teuchos::NO_TRANS, 2*blockSize_,blockSize_,2*blockSize_,one,House_[i].values(),House_[i].stride(), RblockCopy->values(),RblockCopy -> stride(), zero, RblockView->values(),RblockView -> stride());

    }


    //Get a view of last 2*blockSize entries of entire block to 
    //generate new reflections.
    Rblock = rcp(new SDM (Teuchos::View, *R_, 2*blockSize_,blockSize_, curDim_-blockSize_, curDim_-blockSize_));

    //Calculate and apply the new reflections
    for(i=0; i<blockSize_; i++){
      //
      //Calculating Reflection
      //
      int curcol = (lclIter_ - 1)*blockSize_ + i;//current column of R_
      int lclCurcol = i;//current column of Rblock
      ScalarType signDiag = (*R_)(curcol,curcol) / Teuchos::ScalarTraits<ScalarType>::magnitude((*R_)(curcol,curcol));

                        // Norm of the vector to be reflected.
                        // BLAS returns a ScalarType, but it really should be a magnitude.
      ScalarType nvs = blas.NRM2(blockSize_+1,&((*R_)[curcol][curcol]),1);
      ScalarType alpha = -signDiag*nvs;

      //norm of reflection vector which is just the vector being reflected
      //i.e. v = R_(curcol:curcol+blockSize_,curcol))
      //v_refl = v - alpha*e1
      //norm(v_refl) = norm(v) + alpha^2 - 2*v*alpha
      //store in v_refl

                        // Beware, nvs should have a zero imaginary part (since
                        // it is a norm of a vector), but it may not due to rounding 
                        // error.
      //nvs = nvs + alpha*alpha - 2*(*R_)(curcol,curcol)*alpha;
      //(*R_)(curcol,curcol) -= alpha;

      //Copy relevant values of the current column of R_ into the reflection vector
      //Modify first entry
      //Take norm of reflection vector
      //Square the norm
      v_refl = rcp(new SDV(Teuchos::Copy, &((*R_)(curcol,curcol)), blockSize_ + 1 ));
      (*v_refl)[0] -= alpha;
      nvs = blas.NRM2(blockSize_+1,v_refl -> values(),1);
      nvs *= nvs;

      //
      //Apply new reflector to:
      //1. To subsequent columns of R_ in the current block
      //2. To House[iter_] to store product of reflections for this column
      //3. To the least-squares right-hand side.
      //4. The current column 
      //      
      //


      //
      //1.
      //
      if(i < blockSize_ - 1){//only do this when there are subsquent columns in the block to apply to
        workvec = Teuchos::rcp(new SDV(blockSize_ - i -1));
        //workvec = Teuchos::rcp(new SDV(2*blockSize_));
        workmatrix = Teuchos::rcp(new SDM (Teuchos::View, *Rblock, blockSize_+1, blockSize_ - i -1, lclCurcol, lclCurcol +1 ) );
        blas.GEMV(Teuchos::TRANS, workmatrix->numRows(), workmatrix->numCols(), one, workmatrix->values(), workmatrix->stride(), v_refl->values(), 1, zero, workvec->values(), 1);
        blas.GER(workmatrix->numRows(),workmatrix->numCols(), -2.0*one/nvs, v_refl->values(),1,workvec->values(),1,workmatrix->values(),workmatrix->stride());
      }


      //
      //2.
      //
      workvec = Teuchos::rcp(new SDV(2*blockSize_));
      workmatrix = Teuchos::rcp(new SDM (Teuchos::View, House_[lclIter_ -1], blockSize_+1, 2*blockSize_, i, 0 ) );
      blas.GEMV(Teuchos::TRANS,workmatrix->numRows(),workmatrix->numCols(),one,workmatrix->values(),workmatrix->stride(), v_refl->values(), 1,zero,workvec->values(),1);
      blas.GER(workmatrix->numRows(),workmatrix->numCols(), -2.0*one/nvs, v_refl -> values(),1,workvec->values(),1,workmatrix->values(),(*workmatrix).stride());

                        //
                        //3.
                        //
      workvec = Teuchos::rcp(new SDV(blockSize_));
      workmatrix = Teuchos::rcp(new SDM (Teuchos::View, Z_, blockSize_+1, blockSize_, curcol, 0 ) );
      blas.GEMV(Teuchos::TRANS, workmatrix->numRows(), workmatrix->numCols(), one, workmatrix-> values(), workmatrix->stride(), v_refl -> values(), 1, zero, workvec->values(), 1);
                        blas.GER((*workmatrix).numRows(),(*workmatrix).numCols(), -2.0*one/nvs,v_refl -> values(), 1,&((*workvec)[0]),1,(*workmatrix)[0],(*workmatrix).stride());

      //
      //4.
      //
      (*R_)[curcol][curcol] = alpha;
      for(int ii=1; ii<= blockSize_; ii++){
        (*R_)[curcol][curcol+ii] = 0;
      }
    }

  }

    } // end updateLSQR()


}//End Belos Namespace

#endif /* BELOS_BLOCK_GCRODR_ITER_HPP */