Grid/lib/algorithms/iterative/PrecGeneralisedConjugateResidual.h

/*************************************************************************************

    Grid physics library, www.github.com/paboyle/Grid 

    Source file: ./lib/algorithms/iterative/PrecGeneralisedConjugateResidual.h

    Copyright (C) 2015

Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

    See the full license in the file "LICENSE" in the top level distribution directory
*************************************************************************************/
/*  END LEGAL */
#ifndef GRID_PREC_GCR_H
#define GRID_PREC_GCR_H

///////////////////////////////////////////////////////////////////////////////////////////////////////
//VPGCR Abe and Zhang, 2005.
//INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING
//Computing and Information Volume 2, Number 2, Pages 147-161
//NB. Likely not original reference since they are focussing on a preconditioner variant.
//    but VPGCR was nicely written up in their paper
///////////////////////////////////////////////////////////////////////////////////////////////////////
NAMESPACE_BEGIN(Grid);

template<class Field>
class PrecGeneralisedConjugateResidual : public OperatorFunction<Field> {
public:                                                
  RealD   Tolerance;
  Integer MaxIterations;
  int verbose;
  int mmax;
  int nstep;
  int steps;
  GridStopWatch PrecTimer;
  GridStopWatch MatTimer;
  GridStopWatch LinalgTimer;

  LinearFunction<Field> &Preconditioner;

  PrecGeneralisedConjugateResidual(RealD tol,Integer maxit,LinearFunction<Field> &Prec,int _mmax,int _nstep) : 
    Tolerance(tol), 
    MaxIterations(maxit),
    Preconditioner(Prec),
    mmax(_mmax),
    nstep(_nstep)
  { 
    verbose=1;
  };

  void operator() (LinearOperatorBase<Field> &Linop,const Field &src, Field &psi){

    psi=Zero();
    RealD cp, ssq,rsq;
    ssq=norm2(src);
    rsq=Tolerance*Tolerance*ssq;
      
    Field r(src.Grid());

    PrecTimer.Reset();
    MatTimer.Reset();
    LinalgTimer.Reset();

    GridStopWatch SolverTimer;
    SolverTimer.Start();

    steps=0;
    for(int k=0;k<MaxIterations;k++){

      cp=GCRnStep(Linop,src,psi,rsq);

      std::cout<<GridLogMessage<<"VPGCR("<<mmax<<","<<nstep<<") "<< steps <<" steps cp = "<<cp<<std::endl;

      if(cp<rsq) {

	SolverTimer.Stop();

	Linop.HermOp(psi,r);
	axpy(r,-1.0,src,r);
	RealD tr = norm2(r);
	std::cout<<GridLogMessage<<"PrecGeneralisedConjugateResidual: Converged on iteration " <<steps
		 << " computed residual "<<sqrt(cp/ssq)
		 << " true residual "    <<sqrt(tr/ssq)
		 << " target "           <<Tolerance <<std::endl;

	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Total  "<< SolverTimer.Elapsed() <<std::endl;
	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Precon "<<   PrecTimer.Elapsed() <<std::endl;
	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Matrix "<<    MatTimer.Elapsed() <<std::endl;
	std::cout<<GridLogMessage<<"VPGCR Time elapsed: Linalg "<< LinalgTimer.Elapsed() <<std::endl;
	return;
      }

    }
    std::cout<<GridLogMessage<<"Variable Preconditioned GCR did not converge"<<std::endl;
    assert(0);
  }

  RealD GCRnStep(LinearOperatorBase<Field> &Linop,const Field &src, Field &psi,RealD rsq){

    RealD cp;
    RealD a, b, c, d;
    RealD zAz, zAAz;
    RealD rAq, rq;

    GridBase *grid = src.Grid();

    Field r(grid);
    Field z(grid);
    Field tmp(grid);
    Field ttmp(grid);
    Field Az(grid);

    ////////////////////////////////
    // history for flexible orthog
    ////////////////////////////////
    std::vector<Field> q(mmax,grid);
    std::vector<Field> p(mmax,grid);
    std::vector<RealD> qq(mmax);
      
    //////////////////////////////////
    // initial guess x0 is taken as nonzero.
    // r0=src-A x0 = src
    //////////////////////////////////
    MatTimer.Start();
    Linop.HermOpAndNorm(psi,Az,zAz,zAAz); 
    MatTimer.Stop();
    r=src-Az;
      
    /////////////////////
    // p = Prec(r)
    /////////////////////
    PrecTimer.Start();
    Preconditioner(r,z);
    PrecTimer.Stop();

    MatTimer.Start();
    Linop.HermOp(z,tmp); 
    MatTimer.Stop();

    ttmp=tmp;
    tmp=tmp-r;

    /*
      std::cout<<GridLogMessage<<r<<std::endl;
      std::cout<<GridLogMessage<<z<<std::endl;
      std::cout<<GridLogMessage<<ttmp<<std::endl;
      std::cout<<GridLogMessage<<tmp<<std::endl;
    */

    MatTimer.Start();
    Linop.HermOpAndNorm(z,Az,zAz,zAAz); 
    MatTimer.Stop();

    //p[0],q[0],qq[0] 
    p[0]= z;
    q[0]= Az;
    qq[0]= zAAz;

    cp =norm2(r);

    for(int k=0;k<nstep;k++){

      steps++;

      int kp     = k+1;
      int peri_k = k %mmax;
      int peri_kp= kp%mmax;

      rq= real(innerProduct(r,q[peri_k])); // what if rAr not real?
      a = rq/qq[peri_k];

      axpy(psi,a,p[peri_k],psi);         

      cp = axpy_norm(r,-a,q[peri_k],r);  

      if((k==nstep-1)||(cp<rsq)){
	return cp;
      }

      std::cout<<GridLogMessage<< " VPGCR_step["<<steps<<"]  resid " <<sqrt(cp/rsq)<<std::endl; 

      PrecTimer.Start();
      Preconditioner(r,z);// solve Az = r
      PrecTimer.Stop();

      MatTimer.Start();
      Linop.HermOpAndNorm(z,Az,zAz,zAAz);
      Linop.HermOp(z,tmp);
      MatTimer.Stop();
      tmp=tmp-r;
      std::cout<<GridLogMessage<< " Preconditioner resid " <<sqrt(norm2(tmp)/norm2(r))<<std::endl; 

      q[peri_kp]=Az;
      p[peri_kp]=z;

      int northog = ((kp)>(mmax-1))?(mmax-1):(kp);  // if more than mmax done, we orthog all mmax history.
      for(int back=0;back<northog;back++){

	int peri_back=(k-back)%mmax;   	  assert((k-back)>=0);

	b=-real(innerProduct(q[peri_back],Az))/qq[peri_back];
	p[peri_kp]=p[peri_kp]+b*p[peri_back];
	q[peri_kp]=q[peri_kp]+b*q[peri_back];

      }
      qq[peri_kp]=norm2(q[peri_kp]); // could use axpy_norm


    }
    assert(0); // never reached
    return cp;
  }
};
NAMESPACE_END(Grid);
#endif