BelosCGSingleRedIter.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_CG_SINGLE_RED_ITER_HPP
#define BELOS_CG_SINGLE_RED_ITER_HPP

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

#include "BelosLinearProblem.hpp"
#include "BelosOutputManager.hpp"
#include "BelosStatusTest.hpp"
#include "BelosStatusTestGenResNorm.hpp"
#include "BelosOperatorTraits.hpp"
#include "BelosMultiVecTraits.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 CGSingleRedIter : virtual public CGIteration<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;



  CGSingleRedIter( 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<StatusTestGenResNorm<ScalarType,MV,OP> > &convTester,
                   Teuchos::ParameterList &params );

  virtual ~CGSingleRedIter() {};



  
  void iterate();

  void initializeCG(CGIterationState<ScalarType,MV>& newstate);

  void initialize()
  {
    CGIterationState<ScalarType,MV> empty;
    initializeCG(empty);
  }
  
  CGIterationState<ScalarType,MV> getState() const {
    CGIterationState<ScalarType,MV> state;
    state.R = R_;
    state.P = P_;
    state.AP = AP_;
    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 { return Teuchos::null; }

  


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

  int getBlockSize() const { return 1; }

  void setBlockSize(int blockSize) {
    TEUCHOS_TEST_FOR_EXCEPTION(blockSize!=1,std::invalid_argument,
           "Belos::CGSingleRedIter::setBlockSize(): Cannot use a block size that is not one.");
  }

  bool isInitialized() { return initialized_; }

  void setDoCondEst(bool /* val */){/*ignored*/}

  Teuchos::ArrayView<MagnitudeType> getDiag() { 
    Teuchos::ArrayView<MagnitudeType> temp;
    return temp;
  }

  Teuchos::ArrayView<MagnitudeType> getOffDiag() {
    Teuchos::ArrayView<MagnitudeType> temp;
    return temp;
  }


  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<StatusTestGenResNorm<ScalarType,MV,OP> >       convTest_;

  //  
  // 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 been initialized.
  // This initialization may be postponed if the linear problem was generated without 
  // the right-hand side or solution vectors.
  bool stateStorageInitialized_;

  // Current number of iterations performed.
  int iter_;

  // Should the allreduce for convergence detection be merged with the inner products?
  bool foldConvergenceDetectionIntoAllreduce_;

  // <r,z>
  ScalarType rHz_;
  // <r,r>
  ScalarType rHr_;
  
  // 
  // State Storage
  //
  // Residual
  Teuchos::RCP<MV> R_;
  // Preconditioned residual
  Teuchos::RCP<MV> Z_;
  // Operator applied to preconditioned residual
  Teuchos::RCP<MV> AZ_;
  // Direction vector
  Teuchos::RCP<MV> P_;
  // Operator applied to direction vector
  Teuchos::RCP<MV> AP_;
  //
  // W_ = (R_, AZ_, Z_)
  Teuchos::RCP<MV> W_;
  // S_ = (R_, AZ_)
  Teuchos::RCP<MV> S_;
  // T_ = (Z_, R_)
  Teuchos::RCP<MV> T_;
  // U_ = (AZ_, Z_)
  Teuchos::RCP<MV> U_;
  // V_ = (AP_, P_)
  Teuchos::RCP<MV> V_;

};

  // Constructor.
  template<class ScalarType, class MV, class OP>
  CGSingleRedIter<ScalarType,MV,OP>::CGSingleRedIter(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<StatusTestGenResNorm<ScalarType,MV,OP> > &convTester,
                 Teuchos::ParameterList &params ):
    lp_(problem),
    om_(printer),
    stest_(tester),
    convTest_(convTester),
    initialized_(false),
    stateStorageInitialized_(false),
    iter_(0)
  {
    foldConvergenceDetectionIntoAllreduce_ = params.get<bool>("Fold Convergence Detection Into Allreduce",false);
  }

  // Setup the state storage.
  template <class ScalarType, class MV, class OP>
  void CGSingleRedIter<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 {
  
  // Initialize the state storage
  // If the subspace has not be initialized before, generate it using the LHS or RHS from lp_.
  if (R_ == Teuchos::null) {
    // Get the multivector that is not null.
    Teuchos::RCP<const MV> tmp = ( (rhsMV!=Teuchos::null)? rhsMV: lhsMV );
    TEUCHOS_TEST_FOR_EXCEPTION(tmp == Teuchos::null,std::invalid_argument,
           "Belos::CGSingleRedIter::setStateSize(): linear problem does not specify multivectors to clone from.");

          // W_ = (AZ_, R_, Z_)
          W_ = MVT::Clone( *tmp, 3 );
          std::vector<int> index2(2,0);
          std::vector<int> index(1,0);

          // S_ = (AZ_, R_)
          index2[0] = 0;
          index2[1] = 1;
          S_ = MVT::CloneViewNonConst( *W_, index2 );

          // U_ = (AZ_, Z_)
          index2[0] = 0;
          index2[1] = 2;
          U_ = MVT::CloneViewNonConst( *W_, index2 );

          index[0] = 1;
          R_ = MVT::CloneViewNonConst( *W_, index );
          index[0] = 0;
          AZ_ = MVT::CloneViewNonConst( *W_, index );
          index[0] = 2;
          Z_ = MVT::CloneViewNonConst( *W_, index );

          // T_ = (R_, Z_)
          index2[0] = 1;
          index2[1] = 2;
          T_ = MVT::CloneViewNonConst( *W_, index2 );

          // V_ = (AP_, P_)
          V_ = MVT::Clone( *tmp, 2 );
          index[0] = 0;
          AP_ = MVT::CloneViewNonConst( *V_, index );
          index[0] = 1;
    P_ = MVT::CloneViewNonConst( *V_, index );

  }
  
  // State storage has now been initialized.
  stateStorageInitialized_ = true;
      }
    }
  }


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

    TEUCHOS_TEST_FOR_EXCEPTION(!stateStorageInitialized_,std::invalid_argument,
           "Belos::CGSingleRedIter::initialize(): Cannot initialize state storage!");
    
    // NOTE:  In CGSingleRedIter R_, the initial residual, is required!!!  
    //
    std::string errstr("Belos::CGSingleRedIter::initialize(): Specified multivectors must have a consistent length and width.");

    if (newstate.R != Teuchos::null) {

      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetGlobalLength(*newstate.R) != MVT::GetGlobalLength(*R_),
                          std::invalid_argument, errstr );
      TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*newstate.R) != 1,
                          std::invalid_argument, errstr );

      // Copy basis vectors from newstate into V
      if (newstate.R != R_) {
        // copy over the initial residual (unpreconditioned).
  MVT::Assign( *newstate.R, *R_ );
      }

      // Compute initial direction vectors
      // Initially, they are set to the preconditioned residuals
      //
      if ( lp_->getLeftPrec() != Teuchos::null ) {
        lp_->applyLeftPrec( *R_, *Z_ );
        if ( lp_->getRightPrec() != Teuchos::null ) {
          Teuchos::RCP<MV> tmp = MVT::Clone( *Z_, 1 );
          lp_->applyRightPrec( *Z_, *tmp );
          MVT::Assign( *tmp, *Z_ );
        }
      }
      else if ( lp_->getRightPrec() != Teuchos::null ) {
        lp_->applyRightPrec( *R_, *Z_ );
      } 
      else {
        MVT::Assign( *R_, *Z_ );
      }

      // Multiply the current preconditioned residual vector by A and store in AZ_
      lp_->applyOp( *Z_, *AZ_ );

      // P_ := Z_
      // Logically, AP_ := AZ_
      MVT::Assign( *U_, *V_);
    }
    else {

      TEUCHOS_TEST_FOR_EXCEPTION(newstate.R == Teuchos::null,std::invalid_argument,
                         "Belos::CGSingleRedIter::initialize(): CGIterationState does not have initial residual.");
    }

    // The solver is initialized
    initialized_ = true;
  }


  // Get the norms of the residuals native to the solver.
  template <class ScalarType, class MV, class OP>
  Teuchos::RCP<const MV>
  CGSingleRedIter<ScalarType,MV,OP>::getNativeResiduals( std::vector<MagnitudeType> *norms ) const {
    if (convTest_->getResNormType() == Belos::PreconditionerNorm) {
      (*norms)[0] = std::sqrt(Teuchos::ScalarTraits<ScalarType>::magnitude(rHz_));
      return Teuchos::null;
    } else if (foldConvergenceDetectionIntoAllreduce_ && convTest_->getResNormType() == Belos::TwoNorm) {
      (*norms)[0] = std::sqrt(Teuchos::ScalarTraits<ScalarType>::magnitude(rHr_));
      return Teuchos::null;
    } else
      return R_;
  }


  // Iterate until the status test informs us we should stop.
  template <class ScalarType, class MV, class OP>
  void CGSingleRedIter<ScalarType,MV,OP>::iterate()
  {
    //
    // Allocate/initialize data structures
    //
    if (initialized_ == false) {
      initialize();
    }

    // Allocate memory for scalars.
    Teuchos::SerialDenseMatrix<int,ScalarType> sHz( 2, 1 );
    Teuchos::SerialDenseMatrix<int,ScalarType> sHt( 2, 2 );
    ScalarType rHz_old, alpha, beta, delta;

    // Create convenience variables for zero and one.
    const ScalarType one = Teuchos::ScalarTraits<ScalarType>::one();
    const MagnitudeType zero = Teuchos::ScalarTraits<MagnitudeType>::zero();
    
    // Get the current solution vector.
    Teuchos::RCP<MV> cur_soln_vec = lp_->getCurrLHSVec();

    // Check that the current solution vector only has one column. 
    TEUCHOS_TEST_FOR_EXCEPTION( MVT::GetNumberVecs(*cur_soln_vec) != 1, CGIterateFailure,
                        "Belos::CGSingleRedIter::iterate(): current linear system has more than one vector!" );

    if (foldConvergenceDetectionIntoAllreduce_ && convTest_->getResNormType() == Belos::TwoNorm) {
      // Compute first <S_,T_> a.k.a. <R_,Z_>, <AZ_,Z_> and <R_,R_> combined (also computes unneeded <AZ_,R_>)
      MVT::MvTransMv( one, *S_, *T_, sHt );
      rHz_ = sHt(1,1);
      delta = sHt(0,1);
      rHr_ = sHt(1,0);
    } else {
      // Compute first <s,z> a.k.a. <r,z> and <Az,z> combined
      MVT::MvTransMv( one, *S_, *Z_, sHz );
      rHz_ = sHz(1,0);
      delta = sHz(0,0);
    }
    if ((Teuchos::ScalarTraits<ScalarType>::magnitude(delta) < Teuchos::ScalarTraits<ScalarType>::eps()) &&
        (stest_->checkStatus(this) == Passed))
      return;
    alpha = rHz_ / delta;

    // Check that alpha is a positive number!
    TEUCHOS_TEST_FOR_EXCEPTION( SCT::real(alpha) <= zero, CGPositiveDefiniteFailure,
      "Belos::CGSingleRedIter::iterate(): non-positive value for p^H*A*p encountered!" );
 
    // Iterate until the status test tells us to stop.
    //
    if (foldConvergenceDetectionIntoAllreduce_ && convTest_->getResNormType() == Belos::TwoNorm) {
      // Iterate until the status test tells us to stop.
      //
      while (1) {

        // Update the solution vector x := x + alpha * P_
        //
        MVT::MvAddMv( one, *cur_soln_vec, alpha, *P_, *cur_soln_vec );
        //
        // Compute the new residual R_ := R_ - alpha * AP_
        //
        MVT::MvAddMv( one, *R_, -alpha, *AP_, *R_ );
        //
        // Apply preconditioner to new residual to update Z_
        //
        if ( lp_->getLeftPrec() != Teuchos::null ) {
          lp_->applyLeftPrec( *R_, *Z_ );
          if ( lp_->getRightPrec() != Teuchos::null ) {
            Teuchos::RCP<MV> tmp = MVT::CloneCopy( *Z_ );
            lp_->applyRightPrec( *tmp, *Z_ );
          }
        }
        else if ( lp_->getRightPrec() != Teuchos::null ) {
          lp_->applyRightPrec( *R_, *Z_ );
        }
        else {
          MVT::Assign( *R_, *Z_ );
        }
        //
        // Multiply the current preconditioned residual vector by A and store in AZ_
        lp_->applyOp( *Z_, *AZ_ );
        //
        // Compute <S_,T_> a.k.a. <R_,Z_>, <AZ_,Z_> and <R_,R_> combined (also computes unneeded <AZ_,R_>)
        MVT::MvTransMv( one, *S_, *T_, sHt );
        //
        // Update scalars.
        rHz_old = rHz_;
        rHz_ = sHt(1,1);
        delta = sHt(0,1);
        rHr_ = sHt(1,0);

        // Increment the iteration
        iter_++;
        //
        // Check the status test, now that the solution and residual have been updated
        //
        if (stest_->checkStatus(this) == Passed) {
          break;
        }
        //
        beta = rHz_ / rHz_old;
        alpha = rHz_ / (delta - (beta*rHz_ / alpha));
        //
        // Check that alpha is a positive number!
        TEUCHOS_TEST_FOR_EXCEPTION( SCT::real(alpha) <= zero, CGPositiveDefiniteFailure,
                                    "Belos::CGSingleRedIter::iterate(): non-positive value for p^H*A*p encountered!" );

        //
        // Update the direction vector P_ := Z_ + beta * P_
        // Update AP_ through recurrence relation AP_ := AZ_ + beta * AP_
        // Hence: V_ = (AP_, P_) := (AZ_, Z_) + beta (AP_, P_) = U_ + beta * V_
        //
        MVT::MvAddMv( one, *U_, beta, *V_, *V_ );

      } // end while (1)
    } else {
      // Iterate until the status test tells us to stop.
      //
      while (1) {
      
        // Update the solution vector x := x + alpha * P_
        //
        MVT::MvAddMv( one, *cur_soln_vec, alpha, *P_, *cur_soln_vec );
        //
        // Compute the new residual R_ := R_ - alpha * AP_
        //
        MVT::MvAddMv( one, *R_, -alpha, *AP_, *R_ );

        // Increment the iteration
        iter_++;
        //
        // Check the status test, now that the solution and residual have been updated
        //
        if (stest_->checkStatus(this) == Passed) {
          break;
        }
        //
        // Apply preconditioner to new residual to update Z_
        //
        if ( lp_->getLeftPrec() != Teuchos::null ) {
          lp_->applyLeftPrec( *R_, *Z_ );
          if ( lp_->getRightPrec() != Teuchos::null ) {
            Teuchos::RCP<MV> tmp = MVT::CloneCopy( *Z_ );
            lp_->applyRightPrec( *tmp, *Z_ );
          }
        }
        else if ( lp_->getRightPrec() != Teuchos::null ) {
          lp_->applyRightPrec( *R_, *Z_ );
        }
        else {
          MVT::Assign( *R_, *Z_ );
        }
        //
        // Multiply the current preconditioned residual vector by A and store in AZ_
        lp_->applyOp( *Z_, *AZ_ );
        //
        // Compute <S_,Z_> a.k.a. <R_,Z_> and <AZ_,Z_> combined
        MVT::MvTransMv( one, *S_, *Z_, sHz );
        //
        // Update scalars.
        rHz_old = rHz_;
        rHz_ = sHz(1,0);
        delta = sHz(0,0);
        //
        beta = rHz_ / rHz_old;
        alpha = rHz_ / (delta - (beta*rHz_ / alpha));
        //
        // Check that alpha is a positive number!
        TEUCHOS_TEST_FOR_EXCEPTION( SCT::real(alpha) <= zero, CGPositiveDefiniteFailure,
                                    "Belos::CGSingleRedIter::iterate(): non-positive value for p^H*A*p encountered!" );

        //
        // Update the direction vector P_ := Z_ + beta * P_
        // Update AP_ through recurrence relation AP_ := AZ_ + beta * AP_
        // Hence: V_ = (AP_, P_) := (AZ_, Z_) + beta (AP_, P_) = U_ + beta * V_
        //
        MVT::MvAddMv( one, *U_, beta, *V_, *V_ );

      } // end while (1)
    }
  }

} // end Belos namespace

#endif /* BELOS_CG_SINGLE_RED_ITER_HPP */