Grid/tests/solver/Test_wilson_ddalphaamg.cc

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

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

    Source file: ./tests/Test_dwf_hdcr.cc

    Copyright (C) 2015

Author: Daniel Richtmann <daniel.richtmann@ur.de>

    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 */
#include <Grid/Grid.h>
#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
//#include <algorithms/iterative/PrecConjugateResidual.h>

using namespace std;
using namespace Grid;
using namespace Grid::QCD;

template<class Field, int nbasis>
class TestVectorAnalyzer {
public:
  void operator()(LinearOperatorBase<Field> &Linop, std::vector<Field> const & vectors, int nn=nbasis)
  {
    // this function corresponds to testvector_analysis_PRECISION from the
    // DD-αAMG codebase

    auto positiveOnes = 0;

    std::vector<Field> tmp(4, vectors[0]._grid); // bit hacky?
    Gamma g5(Gamma::Algebra::Gamma5);

    std::cout << GridLogMessage << "Test vector analysis:" << std::endl;

    for (auto i = 0; i < nn; ++i) {

      Linop.Op(vectors[i], tmp[3]);

      tmp[0] = g5 * tmp[3]; // is this the same as coarse_gamma5_PRECISION?

      auto lambda = innerProduct(vectors[i], tmp[0]) / innerProduct(vectors[i], vectors[i]);

      tmp[1] = tmp[0] - lambda * vectors[i];

      auto mu = ::sqrt(norm2(tmp[1]) / norm2(vectors[i]));

      auto nrm = ::sqrt(norm2(vectors[i]));

      if(real(lambda) > 0)
        positiveOnes++;

      std::cout << GridLogMessage << std::scientific << std::setprecision(2) << std::setw(2) << std::showpos << "vector " << i << ": "
                << "singular value: " << lambda
                << ", singular vector precision: " << mu << ", norm: " << nrm << std::endl;
    }
    std::cout << GridLogMessage << std::scientific << std::setprecision(2) << std::setw(2) << std::showpos << positiveOnes << " out of " << nn << " vectors were positive" << std::endl;
  }
};

class myclass: Serializable {
public:

  GRID_SERIALIZABLE_CLASS_MEMBERS(myclass,
			  int, domaindecompose,
			  int, domainsize,
                          int, coarsegrids,
                          int, order,
			  int, Ls,
			  double, mq,
			  double, lo,
			  double, hi,
			  int, steps);

  myclass(){};

};
myclass params;

RealD InverseApproximation(RealD x){
  return 1.0/x;
}

template <int nbasis>
struct CoarseGrids
{
public:
  // typedef Aggregation<vSpinColourVector,vTComplex,nbasis>     Subspace;
  // typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>
  // CoarseOperator; typedef typename CoarseOperator::CoarseVector
  // CoarseVector;

  std::vector<std::vector<int>> LattSizes;
  std::vector<std::vector<int>> Seeds;
  std::vector<GridCartesian *>  Grids;
  std::vector<GridParallelRNG>  PRNGs;

  CoarseGrids(std::vector<std::vector<int>> const &blockSizes,int coarsegrids = 1)
  {
    assert( blockSizes.size() == coarsegrids );

    std::cout << GridLogMessage << "Constructing " << coarsegrids << " CoarseGrids" << std::endl;

    for(int cl=0; cl<coarsegrids; ++cl) { // may be a bit ugly and slow but not perf critical
      LattSizes.push_back({GridDefaultLatt()});
      Seeds.push_back(std::vector<int>(LattSizes[cl].size()));

      for(int d=0; d<LattSizes[cl].size(); ++d) {
        LattSizes[cl][d] = LattSizes[cl][d] / blockSizes[cl][d];
        Seeds[cl][d] = (cl + 1) * LattSizes[cl].size() + d + 1; // unimportant, just to get. e.g., {5, // 6, 7, 8} for first coarse level and // so on
      }

      Grids.push_back(SpaceTimeGrid::makeFourDimGrid(LattSizes[cl], GridDefaultSimd(Nd, vComplex::Nsimd()), GridDefaultMpi()));
      PRNGs.push_back(GridParallelRNG(Grids[cl]));

      PRNGs[cl].SeedFixedIntegers(Seeds[cl]);

      std::cout << GridLogMessage << "cl = " << cl << ": LattSize = " << LattSizes[cl] << std::endl;
      std::cout << GridLogMessage << "cl = " << cl << ":    Seeds = " << Seeds[cl] << std::endl;
    }
  }
};

// template < class Fobj, class CComplex, int coarseSpins, int nbasis, class Matrix >
// class MultiGridPreconditioner : public LinearFunction< Lattice< Fobj > > {
template<class Fobj,class CComplex,int nbasis, class Matrix>
class MultiGridPreconditioner : public LinearFunction< Lattice<Fobj> > {
public:

  typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
  typedef CoarsenedMatrix<Fobj,CComplex,nbasis> CoarseOperator;

  typedef typename Aggregation<Fobj,CComplex,nbasis>::siteVector     siteVector;
  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseScalar CoarseScalar;
  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
  typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
  typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField    FineField;
  typedef LinearOperatorBase<FineField>                            FineOperator;

  Aggregates     & _Aggregates;
  CoarseOperator & _CoarseOperator;
  Matrix         & _FineMatrix;
  FineOperator   & _FineOperator;
  Matrix         & _SmootherMatrix;
  FineOperator   & _SmootherOperator;

  // Constructor
  MultiGridPreconditioner(Aggregates &Agg, CoarseOperator &Coarse, 
			  FineOperator &Fine,Matrix &FineMatrix,
			  FineOperator &Smooth,Matrix &SmootherMatrix) 
    : _Aggregates(Agg),
      _CoarseOperator(Coarse),
      _FineOperator(Fine),
      _FineMatrix(FineMatrix),
      _SmootherOperator(Smooth),
      _SmootherMatrix(SmootherMatrix)
  {
  }

  void PowerMethod(const FineField &in) {

    FineField p1(in._grid);
    FineField p2(in._grid);

    MdagMLinearOperator<Matrix,FineField>   fMdagMOp(_FineMatrix);

    p1=in;
    RealD absp2;
    for(int i=0;i<20;i++){
      RealD absp1=std::sqrt(norm2(p1));
      fMdagMOp.HermOp(p1,p2);// this is the G5 herm bit      
      //      _FineOperator.Op(p1,p2);// this is the G5 herm bit      
      RealD absp2=std::sqrt(norm2(p2));
      if(i%10==9)
	std::cout<<GridLogMessage << "Power method on mdagm "<<i<<" " << absp2/absp1<<std::endl;
      p1=p2*(1.0/std::sqrt(absp2));
    }
  }

  void operator()(const FineField &in, FineField & out) {
    if ( params.domaindecompose ) {
      operatorSAP(in,out);
    } else { 
      operatorCheby(in,out);
    }
  }

    ////////////////////////////////////////////////////////////////////////
    // ADEF2: [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
    // ADEF1: [MP+Q ] in =M [1 - A Q] in + Q in  
    ////////////////////////////////////////////////////////////////////////
#if 1
  void operatorADEF2(const FineField &in, FineField & out) {

    CoarseVector Csrc(_CoarseOperator.Grid());
    CoarseVector Ctmp(_CoarseOperator.Grid());
    CoarseVector Csol(_CoarseOperator.Grid());

    ConjugateGradient<CoarseVector>  CG(1.0e-10,100000);
    ConjugateGradient<FineField>    fCG(3.0e-2,1000);

    HermitianLinearOperator<CoarseOperator,CoarseVector>  HermOp(_CoarseOperator);
    MdagMLinearOperator<CoarseOperator,CoarseVector>     MdagMOp(_CoarseOperator);
    MdagMLinearOperator<Matrix,FineField>               fMdagMOp(_FineMatrix);

    FineField tmp(in._grid);
    FineField res(in._grid);
    FineField Min(in._grid);

    // Monitor completeness of low mode space
    _Aggregates.ProjectToSubspace  (Csrc,in);
    _Aggregates.PromoteFromSubspace(Csrc,out);
    std::cout<<GridLogMessage<<"Coarse Grid Preconditioner\nCompleteness in: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;

    // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
    _FineOperator.Op(in,tmp);// this is the G5 herm bit
    fCG(fMdagMOp,tmp,Min);    // solves  MdagM = g5 M g5M

    // Monitor completeness of low mode space
    _Aggregates.ProjectToSubspace  (Csrc,Min);
    _Aggregates.PromoteFromSubspace(Csrc,out);
    std::cout<<GridLogMessage<<"Completeness Min: "<<std::sqrt(norm2(out)/norm2(Min))<<std::endl;

    _FineOperator.Op(Min,tmp);
    tmp = in - tmp;   // in - A Min

    Csol=zero;
    _Aggregates.ProjectToSubspace  (Csrc,tmp);
    HermOp.AdjOp(Csrc,Ctmp);// Normal equations
    CG(MdagMOp,Ctmp,Csol);

    HermOp.Op(Csol,Ctmp);
    Ctmp=Ctmp-Csrc;
    std::cout<<GridLogMessage<<"coarse space true residual "<<std::sqrt(norm2(Ctmp)/norm2(Csrc))<<std::endl;
    _Aggregates.PromoteFromSubspace(Csol,out);

    _FineOperator.Op(out,res);
    res=res-tmp;
    std::cout<<GridLogMessage<<"promoted sol residual "<<std::sqrt(norm2(res)/norm2(tmp))<<std::endl;
    _Aggregates.ProjectToSubspace  (Csrc,res);
    std::cout<<GridLogMessage<<"coarse space proj of residual "<<norm2(Csrc)<<std::endl;

    
    out = out+Min; // additive coarse space correction
    //    out = Min; // no additive coarse space correction

    _FineOperator.Op(out,tmp);
    tmp=tmp-in;         // tmp is new residual

    std::cout<<GridLogMessage<< " Preconditioner in  " << norm2(in)<<std::endl; 
    std::cout<<GridLogMessage<< " Preconditioner out " << norm2(out)<<std::endl; 
    std::cout<<GridLogMessage<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;

  }
#endif
  // ADEF1: [MP+Q ] in =M [1 - A Q] in + Q in  
#if 1
  void operatorADEF1(const FineField &in, FineField & out) {

    CoarseVector Csrc(_CoarseOperator.Grid());
    CoarseVector Ctmp(_CoarseOperator.Grid());
    CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;

    ConjugateGradient<CoarseVector>  CG(1.0e-10,100000);
    ConjugateGradient<FineField>    fCG(3.0e-2,1000);

    HermitianLinearOperator<CoarseOperator,CoarseVector>  HermOp(_CoarseOperator);
    MdagMLinearOperator<CoarseOperator,CoarseVector>     MdagMOp(_CoarseOperator);
    ShiftedMdagMLinearOperator<Matrix,FineField>        fMdagMOp(_FineMatrix,0.1);

    FineField tmp(in._grid);
    FineField res(in._grid);
    FineField Qin(in._grid);

    // Monitor completeness of low mode space
    //    _Aggregates.ProjectToSubspace  (Csrc,in);
    //    _Aggregates.PromoteFromSubspace(Csrc,out);
    //    std::cout<<GridLogMessage<<"Coarse Grid Preconditioner\nCompleteness in: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
    
    _Aggregates.ProjectToSubspace  (Csrc,in);
    HermOp.AdjOp(Csrc,Ctmp);// Normal equations
    CG(MdagMOp,Ctmp,Csol);
    _Aggregates.PromoteFromSubspace(Csol,Qin);

    //    Qin=0;
    _FineOperator.Op(Qin,tmp);// A Q in
    tmp = in - tmp;            // in - A Q in

    _FineOperator.Op(tmp,res);// this is the G5 herm bit
    fCG(fMdagMOp,res,out);    // solves  MdagM = g5 M g5M

    out = out + Qin;

    _FineOperator.Op(out,tmp);
    tmp=tmp-in;         // tmp is new residual

    std::cout<<GridLogMessage<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;

  }
#endif

  void SAP (const FineField & src,FineField & psi){

    Lattice<iScalar<vInteger> > coor(src._grid);
    Lattice<iScalar<vInteger> > subset(src._grid);
    
    FineField r(src._grid);
    FineField zz(src._grid); zz=zero;
    FineField vec1(src._grid);
    FineField vec2(src._grid);

    const Integer block=params.domainsize;

    subset=zero;
    for(int mu=0;mu<Nd;mu++){
      LatticeCoordinate(coor,mu+1);
      coor = div(coor,block);
      subset = subset+coor;
    }
    subset = mod(subset,(Integer)2);
    
    ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_SmootherMatrix,0.0);
    Chebyshev<FineField> Cheby  (params.lo,params.hi,params.order,InverseApproximation);

    RealD resid;
    for(int i=0;i<params.steps;i++){
      
      // Even domain residual
      _FineOperator.Op(psi,vec1);// this is the G5 herm bit
      r= src - vec1 ;
      resid = norm2(r) /norm2(src); 
      std::cout << "SAP "<<i<<" resid "<<resid<<std::endl;

      // Even domain solve
      r= where(subset==(Integer)0,r,zz);
      _SmootherOperator.AdjOp(r,vec1);
      Cheby(fMdagMOp,vec1,vec2);    // solves  MdagM = g5 M g5M
      psi = psi + vec2;  

      // Odd domain residual
      _FineOperator.Op(psi,vec1);// this is the G5 herm bit
      r= src - vec1 ;
      r= where(subset==(Integer)1,r,zz);

      resid = norm2(r) /norm2(src); 
      std::cout << "SAP "<<i<<" resid "<<resid<<std::endl;
      
      // Odd domain solve
      _SmootherOperator.AdjOp(r,vec1);
      Cheby(fMdagMOp,vec1,vec2);    // solves  MdagM = g5 M g5M
      psi = psi + vec2;  

      _FineOperator.Op(psi,vec1);// this is the G5 herm bit
      r= src - vec1 ;
      resid = norm2(r) /norm2(src); 
      std::cout << "SAP "<<i<<" resid "<<resid<<std::endl;

    }

  };

  void SmootherTest (const FineField & in){
    
    FineField vec1(in._grid);
    FineField vec2(in._grid);
    RealD lo[3] = { 0.5, 1.0, 2.0};

    //    MdagMLinearOperator<Matrix,FineField>        fMdagMOp(_FineMatrix);
    ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_SmootherMatrix,0.0);

    RealD Ni,r;

    Ni = norm2(in);

    for(int ilo=0;ilo<3;ilo++){
      for(int ord=5;ord<50;ord*=2){

	_SmootherOperator.AdjOp(in,vec1);

	Chebyshev<FineField> Cheby  (lo[ilo],70.0,ord,InverseApproximation);
	Cheby(fMdagMOp,vec1,vec2);    // solves  MdagM = g5 M g5M

	_FineOperator.Op(vec2,vec1);// this is the G5 herm bit
	vec1  = in - vec1;   // tmp  = in - A Min
	r=norm2(vec1);
	std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;

      }
    }
  }

  void operatorCheby(const FineField &in, FineField & out) {

    CoarseVector Csrc(_CoarseOperator.Grid());
    CoarseVector Ctmp(_CoarseOperator.Grid());
    CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;

    ConjugateGradient<CoarseVector>  CG(3.0e-3,100000);
    //    ConjugateGradient<FineField>    fCG(3.0e-2,1000);

    HermitianLinearOperator<CoarseOperator,CoarseVector>  HermOp(_CoarseOperator);
    MdagMLinearOperator<CoarseOperator,CoarseVector>     MdagMOp(_CoarseOperator);
    //    MdagMLinearOperator<Matrix,FineField>        fMdagMOp(_FineMatrix);
    ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_SmootherMatrix,0.0);

    FineField vec1(in._grid);
    FineField vec2(in._grid);

    //    Chebyshev<FineField> Cheby    (0.5,70.0,30,InverseApproximation);
    //    Chebyshev<FineField> ChebyAccu(0.5,70.0,30,InverseApproximation);
    Chebyshev<FineField> Cheby    (params.lo,params.hi,params.order,InverseApproximation);
    Chebyshev<FineField> ChebyAccu(params.lo,params.hi,params.order,InverseApproximation);
    //    Cheby.JacksonSmooth();
    //    ChebyAccu.JacksonSmooth();

    //    _Aggregates.ProjectToSubspace  (Csrc,in);
    //    _Aggregates.PromoteFromSubspace(Csrc,out);
    //    std::cout<<GridLogMessage<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
    
    //    ofstream fout("smoother");
    //    Cheby.csv(fout);

    // V11 multigrid.
    // Use a fixed chebyshev and hope hermiticity helps.

    // To make a working smoother for indefinite operator
    // must multiply by "Mdag" (ouch loses all low mode content)
    // and apply to poly approx of (mdagm)^-1.
    // so that we end up with an odd polynomial.

    RealD Ni = norm2(in);

    _SmootherOperator.AdjOp(in,vec1);// this is the G5 herm bit
    ChebyAccu(fMdagMOp,vec1,out);    // solves  MdagM = g5 M g5M

    std::cout<<GridLogMessage << "Smoother norm "<<norm2(out)<<std::endl;

    // Update with residual for out
    _FineOperator.Op(out,vec1);// this is the G5 herm bit
    vec1  = in - vec1;   // tmp  = in - A Min

    RealD r = norm2(vec1);

    std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<< " " << r << " " << Ni <<std::endl;
    
    _Aggregates.ProjectToSubspace  (Csrc,vec1);
    HermOp.AdjOp(Csrc,Ctmp);// Normal equations
    CG(MdagMOp,Ctmp,Csol);
    _Aggregates.PromoteFromSubspace(Csol,vec1); // Ass^{-1} [in - A Min]_s
                                             // Q = Q[in - A Min]  
    out = out+vec1;

    // Three preconditioner smoothing -- hermitian if C3 = C1
    // Recompute error
    _FineOperator.Op(out,vec1);// this is the G5 herm bit
    vec1  = in - vec1;   // tmp  = in - A Min
    r=norm2(vec1);

    std::cout<<GridLogMessage << "Coarse resid "<<std::sqrt(r/Ni)<<std::endl;

    // Reapply smoother
    _SmootherOperator.Op(vec1,vec2);  // this is the G5 herm bit
    ChebyAccu(fMdagMOp,vec2,vec1);    // solves  MdagM = g5 M g5M

    out =out+vec1;
    vec1  = in - vec1;   // tmp  = in - A Min
    r=norm2(vec1);
    std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;

  }

  void operatorSAP(const FineField &in, FineField & out) {

    CoarseVector Csrc(_CoarseOperator.Grid());
    CoarseVector Ctmp(_CoarseOperator.Grid());
    CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;

    ConjugateGradient<CoarseVector>  CG(1.0e-3,100000);

    HermitianLinearOperator<CoarseOperator,CoarseVector>  HermOp(_CoarseOperator);
    MdagMLinearOperator<CoarseOperator,CoarseVector>     MdagMOp(_CoarseOperator);

    FineField vec1(in._grid);
    FineField vec2(in._grid);

    _Aggregates.ProjectToSubspace  (Csrc,in);
    _Aggregates.PromoteFromSubspace(Csrc,out);
    std::cout<<GridLogMessage<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
    

    // To make a working smoother for indefinite operator
    // must multiply by "Mdag" (ouch loses all low mode content)
    // and apply to poly approx of (mdagm)^-1.
    // so that we end up with an odd polynomial.
    SAP(in,out);

    // Update with residual for out
    _FineOperator.Op(out,vec1);// this is the G5 herm bit
    vec1  = in - vec1;   // tmp  = in - A Min

    RealD r = norm2(vec1);
    RealD Ni = norm2(in);
    std::cout<<GridLogMessage << "SAP resid "<<std::sqrt(r/Ni)<< " " << r << " " << Ni <<std::endl;
    
    _Aggregates.ProjectToSubspace  (Csrc,vec1);
    HermOp.AdjOp(Csrc,Ctmp);// Normal equations
    CG(MdagMOp,Ctmp,Csol);
    _Aggregates.PromoteFromSubspace(Csol,vec1); // Ass^{-1} [in - A Min]_s
                                             // Q = Q[in - A Min]  
    out = out+vec1;

    // Three preconditioner smoothing -- hermitian if C3 = C1
    // Recompute error
    _FineOperator.Op(out,vec1);// this is the G5 herm bit
    vec1  = in - vec1;   // tmp  = in - A Min
    r=norm2(vec1);

    std::cout<<GridLogMessage << "Coarse resid "<<std::sqrt(r/Ni)<<std::endl;

    // Reapply smoother
    SAP(vec1,vec2);
    out =out+vec2;


    // Update with residual for out
    _FineOperator.Op(out,vec1);// this is the G5 herm bit
    vec1  = in - vec1;   // tmp  = in - A Min

    r = norm2(vec1);
    Ni = norm2(in);
    std::cout<<GridLogMessage << "SAP resid(post) "<<std::sqrt(r/Ni)<< " " << r << " " << Ni <<std::endl;

  }

};

struct MGParams
{
    std::vector< std::vector< int > > blockSizes;
    const int                         nbasis;

    MGParams()
        : blockSizes( { { 1, 1, 1, 2 } } )
        // : blockSizes({ {1,1,1,2}, {1,1,1,2} })
        // : blockSizes({ {1,1,1,2}, {1,1,1,2}, {1,1,1,2} })
        , nbasis( 20 )
    {
    }
};

int main (int argc, char ** argv)
{
  Grid_init(&argc,&argv);

  params.domainsize= 1;
  params.coarsegrids= 1;
  params.domaindecompose = 0;
  params.order = 30;
  params.Ls = 1;
  // params.mq = .13;
  params.mq = .5;
  params.lo = 0.5;
  params.hi = 70.0;
  params.steps = 1;

  auto mgp = MGParams{};

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Params: " << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  std::cout << params << std::endl;

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Set up some fine level stuff: " << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  GridCartesian         * FGrid   = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(),GridDefaultSimd(Nd, vComplex::Nsimd()),GridDefaultMpi());
  GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(FGrid);

  std::vector<int> fSeeds( {1, 2, 3, 4} );
  GridParallelRNG    fPRNG( FGrid );
  fPRNG.SeedFixedIntegers( fSeeds );

  Gamma g5(Gamma::Algebra::Gamma5);

  LatticeFermion    src(FGrid); gaussian(fPRNG, src); // src=src+g5*src;
  LatticeFermion result(FGrid); result = zero;
  LatticeFermion    ref(FGrid); ref = zero;
  LatticeFermion    tmp(FGrid);
  LatticeFermion    err(FGrid);
  LatticeGaugeField Umu(FGrid); SU3::HotConfiguration(fPRNG, Umu);
  LatticeGaugeField UmuDD(FGrid);
  LatticeColourMatrix U(FGrid);
  LatticeColourMatrix zz(FGrid);

  if ( params.domaindecompose ) {
    Lattice<iScalar<vInteger> > coor(FGrid);
    zz=zero;
    for(int mu=0;mu<Nd;mu++){
      LatticeCoordinate(coor,mu);
      U = PeekIndex<LorentzIndex>(Umu,mu);
      U = where(mod(coor,params.domainsize)==(Integer)0,zz,U);
      PokeIndex<LorentzIndex>(UmuDD,U,mu);
    }
  } else { 
    UmuDD = Umu;
  }

  RealD mass=params.mq;

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Set up some coarser levels stuff: " << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  std::vector< std::vector< int > > blockSizes({ { 1, 1, 1, 2 } } ); // corresponds to two level algorithm
  // std::vector< std::vector<int> > blockSizes({ {1,1,1,2},       // // corresponds to three level algorithm
  //                                              {1,1,1,2} });

  const int nbasis = 20; // we fix the number of test vector to the same
                          // number on every level for now

  // // some stuff we need for every coarser lattice
  // std::vector<std::vector<int>> cLattSizes({GridDefaultLatt()});;
  // std::vector<GridCartesian *> cGrids(params.coarsegrids);
  // std::vector<std::vector<int>> cSeeds({ {5,6,7,8} });
  // std::vector<GridParallelRNG> cPRNGs;(params.coarsegrids);

  // assert(cLattSizes.size() == params.coarsegrids);
  // assert(    cGrids.size() == params.coarsegrids);
  // assert(    cSeeds.size() == params.coarsegrids);
  // assert(    cPRNGs.size() == params.coarsegrids);

  // for(int cl=0;cl<cLattSizes.size();cl++){
  //   for(int d=0;d<cLattSizes[cl].size();d++){
  //     // std::cout << cl << " " << d << " " << cLattSizes[cl][d] << " " <<
  //     blockSizes[cl][d] << std::endl; cLattSizes[cl][d] =
  //     cLattSizes[cl][d]/blockSizes[cl][d];
  //   }
  //   cGrids[cl] = SpaceTimeGrid::makeFourDimGrid(cLattSizes[cl],
  //   GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());;
  //   // std::cout << cLattSizes[cl] << std::endl;
  // }

    // GridParallelRNG cPRNG(CGrid); cPRNG.SeedFixedIntegers(cSeeds);

    CoarseGrids< nbasis > cGrids( blockSizes );

    // assert(0);

  std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  std::cout<<GridLogMessage << "Building the wilson operator on the fine grid" <<std::endl;
  std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  
  WilsonFermionR Dw(Umu,*FGrid,*FrbGrid,mass);
  WilsonFermionR DwDD(UmuDD,*FGrid,*FrbGrid,mass);

  std::cout<<GridLogMessage<< "**************************************************"<< std::endl;
  std::cout<<GridLogMessage<< "Some typedefs" <<std::endl;
  std::cout<<GridLogMessage<< "**************************************************"<< std::endl;

  typedef Aggregation<vSpinColourVector,vTComplex,nbasis>              Subspace;
  typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis>          CoarseOperator;
  typedef CoarseOperator::CoarseVector                                 CoarseVector;
  typedef TestVectorAnalyzer<LatticeFermion,nbasis> TVA;

  // typedef Aggregation<vSpinColourVector,vTComplex,1,nbasis> Subspace;
  // typedef CoarsenedMatrix<vSpinColourVector,vTComplex,1,nbasis> CoarseOperator;
  // typedef CoarseOperator::CoarseVector                 CoarseVector;

  // typedef CoarseOperator::CoarseG5PVector
  // CoarseG5PVector; // P = preserving typedef
  // CoarseOperator::CoarseG5PMatrix CoarseG5PMatrix;

#if 1
  std::cout << std::endl;
  std::cout << "type_name<decltype(vTComplex{})>()                      = " << type_name<decltype(vTComplex{})>()                      << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::scalar_type>()     = " << type_name<GridTypeMapper<vTComplex>::scalar_type>()     << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::vector_type>()     = " << type_name<GridTypeMapper<vTComplex>::vector_type>()     << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::vector_typeD>()    = " << type_name<GridTypeMapper<vTComplex>::vector_typeD>()    << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::tensor_reduced>()  = " << type_name<GridTypeMapper<vTComplex>::tensor_reduced>()  << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::scalar_object>()   = " << type_name<GridTypeMapper<vTComplex>::scalar_object>()   << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::Complexified>()    = " << type_name<GridTypeMapper<vTComplex>::Complexified>()    << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::Realified>()       = " << type_name<GridTypeMapper<vTComplex>::Realified>()       << std::endl;
  std::cout << "type_name<GridTypeMapper<vTComplex>::DoublePrecision>() = " << type_name<GridTypeMapper<vTComplex>::DoublePrecision>() << std::endl;
  std::cout << std::endl;

  std::cout << std::endl;
  std::cout << "type_name<decltype(TComplex{})>()                      = " << type_name<decltype(TComplex{})>()                      << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::scalar_type>()     = " << type_name<GridTypeMapper<TComplex>::scalar_type>()     << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::vector_type>()     = " << type_name<GridTypeMapper<TComplex>::vector_type>()     << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::vector_typeD>()    = " << type_name<GridTypeMapper<TComplex>::vector_typeD>()    << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::tensor_reduced>()  = " << type_name<GridTypeMapper<TComplex>::tensor_reduced>()  << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::scalar_object>()   = " << type_name<GridTypeMapper<TComplex>::scalar_object>()   << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::Complexified>()    = " << type_name<GridTypeMapper<TComplex>::Complexified>()    << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::Realified>()       = " << type_name<GridTypeMapper<TComplex>::Realified>()       << std::endl;
  std::cout << "type_name<GridTypeMapper<TComplex>::DoublePrecision>() = " << type_name<GridTypeMapper<TComplex>::DoublePrecision>() << std::endl;
  std::cout << std::endl;
#endif

  std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  std::cout<<GridLogMessage << "Calling Aggregation class to build subspaces" <<std::endl;
  std::cout<<GridLogMessage << "**************************************************"<< std::endl;

  // • TODO: need some way to run the smoother on the "test vectors" for a few
  //   times before constructing the subspace from them
  // • Maybe an application for an mrhs (true mrhs, no block) smoother?
  // • In WMG, the vectors are normalized but not orthogonalized, but here they
  //   are constructed randomly and then orthogonalized (rather orthonormalized) against each other
  MdagMLinearOperator<WilsonFermionR,LatticeFermion> HermOp(Dw);
  Subspace Aggregates(cGrids.Grids[0],FGrid,0);
  assert ((nbasis & 0x1)==0);
  int nb=nbasis/2;
  std::cout<<GridLogMessage << " nbasis/2 = "<<nb<<std::endl;

  Aggregates.CreateSubspace(fPRNG, HermOp /*, nb */); // Don't specify nb to see the orthogonalization check

  TVA testVectorAnalyzer;

  testVectorAnalyzer(HermOp, Aggregates.subspace, nb);

  for(int n=0;n<nb;n++){
    Aggregates.subspace[n+nb] = g5 * Aggregates.subspace[n]; // multiply with g5 normally instead of G5R5 since this specific to DWF
    std::cout<<GridLogMessage<<n<<" subspace "<<norm2(Aggregates.subspace[n+nb])<<" "<<norm2(Aggregates.subspace[n]) <<std::endl;
  }
  for(int n=0;n<nbasis;n++){
    std::cout<<GridLogMessage << "vec["<<n<<"] = "<<norm2(Aggregates.subspace[n])  <<std::endl;
  }

  // tva(HermOp, Aggregates.subspace);
  Aggregates.CheckOrthogonal();
  testVectorAnalyzer(HermOp, Aggregates.subspace);

  result=zero;

  std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  std::cout<<GridLogMessage << "Building coarse representation of Dirac operator" <<std::endl;
  std::cout<<GridLogMessage << "**************************************************"<< std::endl;

  Gamma5HermitianLinearOperator<WilsonFermionR,LatticeFermion> HermIndefOp(Dw); // this corresponds to working with H = g5 * D
  Gamma5HermitianLinearOperator<WilsonFermionR,LatticeFermion> HermIndefOpDD(DwDD);
  CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> CoarseOp(*cGrids.Grids[0]);
  CoarseOp.CoarsenOperator(FGrid, HermIndefOp, Aggregates); // uses only linop.OpDiag & linop.OpDir

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Building coarse vectors" << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  CoarseVector c_src (cGrids.Grids[0]);
  CoarseVector c_res (cGrids.Grids[0]);
  gaussian(cGrids.PRNGs[0],c_src);
  c_res=zero;

  std::cout << "type_name<decltype(c_src)>() = " << type_name< decltype( c_src ) >() << std::endl;

  // c_res = g5 * c_src;

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Solving posdef-MR on coarse space " << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  MdagMLinearOperator<CoarseOperator,CoarseVector> PosdefLdop(CoarseOp);
  MinimalResidual<CoarseVector>   MR(5.0e-2, 100, false);
  ConjugateGradient<CoarseVector> CG(5.0e-2, 100, false);

  MR(PosdefLdop, c_src, c_res);

  gaussian(cGrids.PRNGs[0], c_src);
  c_res = zero;
  CG(PosdefLdop, c_src, c_res);

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Dummy testing for building second coarse level" << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  // typedef Aggregation< CoarseVector, vTComplex, nbasis > SubspaceAgain;

  // SubspaceAgain AggregatesCoarsenedAgain(cGrids.Grids[1], cGrids.Grids[0], 0);
  // AggregatesCoarsenedAgain.CreateSubspace(cGrids.PRNGs[0], PosdefLdop);

  // for(int n=0;n<nb;n++){
  //   AggregatesCoarsenedAgain.subspace[n+nb] = g5 * AggregatesCoarsenedAgain.subspace[n]; // multiply with g5 normally instead of G5R5 since this specific to DWF
  //   std::cout<<GridLogMessage<<n<<" subspace "<<norm2(AggregatesCoarsenedAgain.subspace[n+nb])<<" "<<norm2(AggregatesCoarsenedAgain.subspace[n]) <<std::endl;
  // }

  // for(int n=0;n<nbasis;n++){
  //   std::cout<<GridLogMessage << "vec["<<n<<"] = "<<norm2(AggregatesCoarsenedAgain.subspace[n])  <<std::endl;
  // }

  // AggregatesCoarsenedAgain.CheckOrthogonal();

  // std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  // std::cout<<GridLogMessage << "Solving indef-MCR on coarse space "<< std::endl;
  // std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  // HermitianLinearOperator<CoarseOperator,CoarseVector> HermIndefLdop(CoarseOp);
  // ConjugateResidual<CoarseVector> MCR(1.0e-6,100000);
  // MCR(HermIndefLdop,c_src,c_res);

  std::cout<<GridLogMessage << "**************************************************"<< std::endl;
  std::cout<<GridLogMessage << "Building deflation preconditioner "<< std::endl;
  std::cout<<GridLogMessage << "**************************************************"<< std::endl;

  MultiGridPreconditioner <vSpinColourVector,vTComplex,nbasis,WilsonFermionR> Precon  (Aggregates, CoarseOp,
                                                                                       HermIndefOp,Dw,
                                                                                       HermIndefOp,Dw);

  MultiGridPreconditioner <vSpinColourVector,vTComplex,nbasis,WilsonFermionR> PreconDD(Aggregates, CoarseOp,
                                                                                       HermIndefOp,Dw,
                                                                                       HermIndefOpDD,DwDD);
  // MultiGridPreconditioner(Aggregates &Agg, CoarseOperator &Coarse,
  //                         FineOperator &Fine,Matrix &FineMatrix,
  //                         FineOperator &Smooth,Matrix &SmootherMatrix)
  TrivialPrecon<LatticeFermion> Simple;

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Building two level VPGCR and FGMRES solvers" << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  PrecGeneralisedConjugateResidual<LatticeFermion>    VPGCRMG(1.0e-12,100,Precon,8,8);
  FlexibleGeneralisedMinimalResidual<LatticeFermion> FGMRESMG(1.0e-12,100,Precon,8);

  std::cout << GridLogMessage << "checking norm src " << norm2(src) << std::endl;

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Building unpreconditioned VPGCR and FGMRES solvers" << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  PrecGeneralisedConjugateResidual<LatticeFermion>    VPGCRT(1.0e-12,4000000,Simple,8,8);
  FlexibleGeneralisedMinimalResidual<LatticeFermion> FGMREST(1.0e-12,4000000,Simple,8);

  std::cout << GridLogMessage << "**************************************************" << std::endl;
  std::cout << GridLogMessage << "Testing the four solvers" << std::endl;
  std::cout << GridLogMessage << "**************************************************" << std::endl;

  std::vector< OperatorFunction<LatticeFermion>*> solvers;
  solvers.push_back(&VPGCRMG);
  solvers.push_back(&FGMRESMG);
  solvers.push_back(&VPGCRT);
  solvers.push_back(&FGMREST);

  for(auto elem : solvers) {
    result = zero;
    (*elem)(HermIndefOp,src,result);
  }

  Grid_finalize();
}