BelosGCRODRIter.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_GCRODR_ITER_HPP
#define BELOS_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"

namespace Belos {
  

  
  template <class ScalarType, class MV>
  struct GCRODRIterState {
    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;

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

  
  class GCRODRIterInitFailure : public BelosError {
    public:
      GCRODRIterInitFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };
  
  class GCRODRIterOrthoFailure : public BelosError {
    public:
      GCRODRIterOrthoFailure(const std::string& what_arg) : BelosError(what_arg) {}
  };
  
  
  
  template<class ScalarType, class MV, class OP>
  class GCRODRIter : 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;
    

    
    GCRODRIter( 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 ~GCRODRIter() {};
    
    

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

    
    const LinearProblem<ScalarType,MV,OP>& getProblem() const { return *lp_; }
    
    int getNumBlocks() const { return numBlocks_; }
    
    void setNumBlocks(int numBlocks) { setSize( recycledBlocks_, numBlocks ); };
    
    int getRecycledBlocks() const { return recycledBlocks_; }

    void setRecycledBlocks(int recycledBlocks) { setSize( recycledBlocks, numBlocks_ ); };
    
    int getBlockSize() const { return 1; }
    
    void setBlockSize(int blockSize) {
      TEUCHOS_TEST_FOR_EXCEPTION(blockSize!=1,std::invalid_argument,"Belos::GCRODRIter::setBlockSize(): Cannot use a block size that is not one.");
    }

    void setSize( int recycledBlocks, int numBlocks ) {
      // only call resize if size changed
      if ( (recycledBlocks_ != recycledBlocks) || (numBlocks_ != numBlocks) ) {
        recycledBlocks_ = recycledBlocks;
        numBlocks_ = numBlocks;
        cs_.sizeUninitialized( numBlocks_+1 );
        sn_.sizeUninitialized( numBlocks_+1 );
        z_.sizeUninitialized( numBlocks_+1 );
        R_.shapeUninitialized( numBlocks_+1,numBlocks );
      }
    }

    bool isInitialized() { return initialized_; }
    
    
  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.
    int numBlocks_; 

    // recycledBlocks_ is the size of the allocated space for the recycled subspace, in blocks.
    int recycledBlocks_; 
    
    // Storage for QR factorization of the least squares system.
    Teuchos::SerialDenseVector<int,ScalarType> 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_;
    
    // Current subspace dimension, and number of iterations performed.
    int curDim_, iter_;
    
    // 
    // State Storage
    //
    // Krylov vectors.
    Teuchos::RCP<MV> V_;
    //
    // Recycled subspace vectors.
    Teuchos::RCP<MV> U_, C_;
    //
    // Projected matrices
    // H_ : Projected matrix from the Krylov factorization AV = VH + FE^T
    Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > H_;
    //
    // B_ : Projected matrix from the recycled subspace B = C^H*A*V
    Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > B_;
    //
    // 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::SerialDenseMatrix<int,ScalarType> R_;
    Teuchos::SerialDenseVector<int,ScalarType> z_;  
  };
  
  // Constructor.
  template<class ScalarType, class MV, class OP>
  GCRODRIter<ScalarType,MV,OP>::GCRODRIter(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;
    recycledBlocks_ = 0;
    initialized_    = false;
    curDim_         = 0;
    iter_           = 0;
    V_              = Teuchos::null;
    U_              = Teuchos::null;
    C_              = Teuchos::null;
    H_              = Teuchos::null;
    B_              = 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::GCRODRIter::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::GCRODRIter::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::GCRODRIter() was passed a non-positive argument for \"Num Blocks\".");
    TEUCHOS_TEST_FOR_EXCEPTION(rb >= nb, std::invalid_argument, "Belos::GCRODRIter() the number of recycled blocks is larger than the allowable subspace.");

    numBlocks_ = nb;
    recycledBlocks_ = rb;

    cs_.sizeUninitialized( numBlocks_+1 );
    sn_.sizeUninitialized( numBlocks_+1 );
    z_.sizeUninitialized( numBlocks_+1 );
    R_.shapeUninitialized( numBlocks_+1,numBlocks_ );

  }
  
  // Get the current update from this subspace.
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<MV> GCRODRIter<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;
    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_, 1 );
      //
      //  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_, 1 );
      //
      //  Solve the least squares problem.
      //
      blas.TRSM( Teuchos::LEFT_SIDE, Teuchos::UPPER_TRI, Teuchos::NO_TRANS,
     Teuchos::NON_UNIT_DIAG, curDim_, 1, one,  
     R_.values(), R_.stride(), y.values(), y.stride() );
      //
      //  Compute the current update from the Krylov basis; V(:,1:curDim_)*y.
      //
      std::vector<int> index(curDim_);
      for ( int i=0; i<curDim_; 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) {
        Teuchos::SerialDenseMatrix<int,ScalarType> z(recycledBlocks_,1);
        Teuchos::SerialDenseMatrix<int,ScalarType> subB( Teuchos::View, *B_, recycledBlocks_, curDim_ );
        z.multiply( Teuchos::NO_TRANS, Teuchos::NO_TRANS, one, subB, y, zero );
        MVT::MvTimesMatAddMv( -one, *U_, z, one, *currentUpdate );
      }
    }
    return currentUpdate;
  }


  // Get the native residuals stored in this iteration.  
  // Note: This method does not return a MultiVector of the residual vectors, only return Teuchos::null
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<const MV> GCRODRIter<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()==0 )                         
      norms->resize( 1 );                                          
    
    if (norms) {
      Teuchos::BLAS<int,ScalarType> blas;
      (*norms)[0] = blas.NRM2( 1, &z_(curDim_), 1);
    }
    return Teuchos::null;
  }
  
  

  // Initialize this iteration object
  template <class ScalarType, class MV, class OP>
  void GCRODRIter<ScalarType,MV,OP>::initialize(GCRODRIterState<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;
    }
    else {
      TEUCHOS_TEST_FOR_EXCEPTION(newstate.V == Teuchos::null,std::invalid_argument,"Belos::GCRODRIter::initialize(): GCRODRIterState does not have V initialized.");
      TEUCHOS_TEST_FOR_EXCEPTION(newstate.H == Teuchos::null,std::invalid_argument,"Belos::GCRODRIter::initialize(): GCRODRIterState does not have H initialized.");
    }

    // the solver is initialized
    initialized_ = true;

  }


  // Iterate until the status test informs us we should stop.
  template <class ScalarType, class MV, class OP>
  void GCRODRIter<ScalarType,MV,OP>::iterate() {

    TEUCHOS_TEST_FOR_EXCEPTION( initialized_ == false, GCRODRIterInitFailure,"Belos::GCRODRIter::iterate(): GCRODRIter class not initialized." );

    // 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(1);

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

    // Orthonormalize the new V_0
    curind[0] = 0;
    Vnext = MVT::CloneViewNonConst(*V_,curind);
    // Orthonormalize first column
    // First, get a monoelemental matrix to hold the orthonormalization coefficients
    Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > z0 =
      Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType>(1,1) );
    int rank = ortho_->normalize( *Vnext, z0 );
    TEUCHOS_TEST_FOR_EXCEPTION(rank != 1,GCRODRIterOrthoFailure, "Belos::GCRODRIter::iterate(): couldn't generate basis of full rank.");
    // Copy the scalar coefficient back into the z_ vector
    z_(0) = (*z0)(0,0);

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

    // iterate until the status test tells us to stop.
    //
    // also break if our basis is full
    //
    if (U_ == Teuchos::null) { // iterate without recycle space (because none is available yet)
      while (stest_->checkStatus(this) != Passed && curDim_+1 <= numBlocks_) {
        iter_++;
        int lclDim = curDim_ + 1;

        // Get next index in basis
        curind[0] = lclDim;
        Vnext = MVT::CloneViewNonConst(*V_,curind);

        // Get previous index in basis
        curind[0] = curDim_;
        Vprev = MVT::CloneView(*V_,curind);

        // Compute the next vector in the Krylov basis:  Vnext = Op*Vprev
        lp_->apply(*Vprev,*Vnext);

        // Remove all previous Krylov basis vectors from Vnext and put coefficients in H and R.

        // Get a view of all the previous vectors
        prevind.resize(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,1,0,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> >
          subR = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType> ( Teuchos::View,*H_,1,1,lclDim,curDim_ ) );

        // Project out the previous Krylov vectors and normalize the next vector.
        rank = ortho_->projectAndNormalize(*Vnext,AsubH,subR,AVprev);

        // Copy over the coefficients to R just in case we run into an error.
        Teuchos::SerialDenseMatrix<int,ScalarType> subR2( Teuchos::View,R_,lclDim+1,1,0,curDim_ );
        Teuchos::SerialDenseMatrix<int,ScalarType> subH2( Teuchos::View,*H_,lclDim+1,1,0,curDim_ );
        subR2.assign(subH2);

        TEUCHOS_TEST_FOR_EXCEPTION(rank != 1,GCRODRIterOrthoFailure, "Belos::GCRODRIter::iterate(): couldn't generate basis of full rank.");

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

        // Update basis dim
        curDim_++;
      } // end while (statusTest == false)
    }
    else { // iterate with recycle space
      while (stest_->checkStatus(this) != Passed && curDim_+1 <= numBlocks_) {
        iter_++;
        int lclDim = curDim_ + 1; 

        // Get the current part of the basis.
        curind[0] = lclDim;
        Vnext = MVT::CloneViewNonConst(*V_,curind);

        // Get a view of the previous vectors.
        // This is used for orthogonalization and for computing V^H K H
        curind[0] = curDim_;
        Vprev = MVT::CloneView(*V_,curind);

        // Compute the next std::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.
        Teuchos::Array<Teuchos::RCP<const MV> > C(1, C_);
        Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> >
      subB = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType> ( Teuchos::View,*B_,recycledBlocks_,1,0,curDim_ ) );
        Teuchos::Array<Teuchos::RCP<Teuchos::SerialDenseMatrix<int,ScalarType> > > AsubB;
        AsubB.append( subB );

        // Project out the recycled subspace.
        ortho_->project( *Vnext, AsubB, C );

        // Now, remove all previous Krylov basis vectors from Vnext and put coefficients in H and R.          
        // Get a view of all the previous vectors
        prevind.resize(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,1,0,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> >  subR = Teuchos::rcp( new Teuchos::SerialDenseMatrix<int,ScalarType> ( Teuchos::View,*H_,1,1,lclDim,curDim_ ) );

        // Project out the previous Krylov vectors and normalize the next vector.
        rank = ortho_->projectAndNormalize(*Vnext,AsubH,subR,AVprev);

        // Copy over the coefficients to R just in case we run into an error.
        Teuchos::SerialDenseMatrix<int,ScalarType> subR2( Teuchos::View,R_,lclDim+1,1,0,curDim_ );
        Teuchos::SerialDenseMatrix<int,ScalarType> subH2( Teuchos::View,*H_,lclDim+1,1,0,curDim_ );
        subR2.assign(subH2);
      
        TEUCHOS_TEST_FOR_EXCEPTION(rank != 1,GCRODRIterOrthoFailure, "Belos::GCRODRIter::iterate(): couldn't generate basis of full rank.");

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

        // Update basis dim
        curDim_++;
      
      } // end while (statusTest == false)
    } // end if (U_ == Teuchos::null)
   
  }

  
  template<class ScalarType, class MV, class OP>
  void GCRODRIter<ScalarType,MV,OP>::updateLSQR( int dim ) {

    int i;
    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.
    //
    // 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), 1, &z_(curDim+1), 1, &cs_[curDim], &sn_[curDim] );

  } // end updateLSQR()

} // end Belos namespace

#endif /* BELOS_GCRODR_ITER_HPP */