#include <Grid.h>
#include <algorithms/iterative/PrecGeneralisedConjugateResidual.h>
//#include <algorithms/iterative/PrecConjugateResidual.h>
using namespace std;
using namespace Grid;
using namespace Grid::QCD;
RealD InverseApproximation(RealD x){
return 1.0/x;
}
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 & _Matrix;
FineOperator & _FineOperator;
// Constructor
MultiGridPreconditioner(Aggregates &Agg, CoarseOperator &Coarse, FineOperator &Fine,Matrix &FineMatrix)
: _Aggregates(Agg),
_CoarseOperator(Coarse),
_FineOperator(Fine),
_Matrix(FineMatrix)
{
}
void PowerMethod(const FineField &in) {
FineField p1(in._grid);
FineField p2(in._grid);
MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
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 << "Power method on mdagm "<<i<<" " << absp2/absp1<<std::endl;
p1=p2*(1.0/std::sqrt(absp2));
}
}
#if 0
void operator()(const FineField &in, FineField & out) {
FineField Min(in._grid);
FineField tmp(in._grid);
CoarseVector Csrc(_CoarseOperator.Grid());
CoarseVector Ctmp(_CoarseOperator.Grid());
CoarseVector Csol(_CoarseOperator.Grid());
// Monitor completeness of low mode space
_Aggregates.ProjectToSubspace (Csrc,in);
_Aggregates.PromoteFromSubspace(Csrc,out);
std::cout<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
// Build some solvers
ConjugateGradient<FineField> fCG(1.0e-3,1000);
ConjugateGradient<CoarseVector> CG(1.0e-8,100000);
////////////////////////////////////////////////////////////////////////
// ADEF2: [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
////////////////////////////////////////////////////////////////////////
// Smoothing step, followed by coarse grid correction
MdagMLinearOperator<Matrix,FineField> MdagMOp(_Matrix);
Min=in;
std::cout<< " Preconditioner in " << norm2(in)<<std::endl;
_FineOperator.AdjOp(Min,tmp);
std::cout<< " Preconditioner tmp " << norm2(in)<<std::endl;
fCG(MdagMOp,tmp,out);
_FineOperator.Op(out,tmp);
std::cout<< " Preconditioner in " << norm2(in)<<std::endl;
std::cout<< " Preconditioner out " << norm2(out)<<std::endl;
std::cout<< " Preconditioner Aout" << norm2(tmp)<<std::endl;
tmp = tmp - in;
std::cout<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;
/*
// _FineOperator.Op(Min,out);
// out = in -out; // out = in - A Min
out = in;
MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
Csol=zero;
_Aggregates.ProjectToSubspace (Csrc,out);
HermOp.AdjOp(Csrc,Ctmp);// Normal equations
CG(MdagMOp ,Ctmp,Csol);
_Aggregates.PromoteFromSubspace(Csol,out);
out = Min + out;;
*/
}
#endif
////////////////////////////////////////////////////////////////////////
// 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 0
void operator()(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(_Matrix);
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<<"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<<"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<<"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<<"promoted sol residual "<<std::sqrt(norm2(res)/norm2(tmp))<<std::endl;
_Aggregates.ProjectToSubspace (Csrc,res);
std::cout<<"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<< " Preconditioner in " << norm2(in)<<std::endl;
std::cout<< " Preconditioner out " << norm2(out)<<std::endl;
std::cout<<"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 0
void operator()(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(_Matrix,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<<"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<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;
}
#endif
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(_Matrix);
ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix,0.5);
RealD Ni,r;
Ni = norm2(in);
for(int ilo=0;ilo<4;ilo++){
for(int ord=10;ord<60;ord+=10){
_FineOperator.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 << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;
}
}
}
void operator()(const FineField &in, FineField & out) {
CoarseVector Csrc(_CoarseOperator.Grid());
CoarseVector Ctmp(_CoarseOperator.Grid());
CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;
ConjugateGradient<CoarseVector> CG(1.0e-5,100000);
ConjugateGradient<FineField> fCG(3.0e-2,1000);
HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
// MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix,1.0);
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 (2.0,70.0,10,InverseApproximation);
Chebyshev<FineField> ChebyAccu(2.0,70.0,10,InverseApproximation);
_Aggregates.ProjectToSubspace (Csrc,in);
_Aggregates.PromoteFromSubspace(Csrc,out);
std::cout<<"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);
_FineOperator.AdjOp(in,vec1);// this is the G5 herm bit
ChebyAccu(fMdagMOp,vec1,out); // solves MdagM = g5 M g5M
std::cout << "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 << "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 << "Coarse resid "<<std::sqrt(r/Ni)<<std::endl;
// Reapply smoother
_FineOperator.Op(vec1,vec2); // this is the G5 herm bit
ChebyAccu(fMdagMOp,vec2,vec1); // solves MdagM = g5 M g5M
out =out+vec1;
_FineOperator.Op(out,vec1);// this is the G5 herm bit
vec1 = in - vec1; // tmp = in - A Min
r=norm2(vec1);
std::cout << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;
}
};
int main (int argc, char ** argv)
{
Grid_init(&argc,&argv);
const int Ls=8;
GridCartesian * UGrid = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
GridCartesian * FGrid = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
///////////////////////////////////////////////////
// Construct a coarsened grid; utility for this?
///////////////////////////////////////////////////
const int block=2;
std::vector<int> clatt = GridDefaultLatt();
for(int d=0;d<clatt.size();d++){
clatt[d] = clatt[d]/block;
}
GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());;
GridCartesian *Coarse5d = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
std::vector<int> seeds4({1,2,3,4});
std::vector<int> seeds5({5,6,7,8});
std::vector<int> cseeds({5,6,7,8});
GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers(seeds5);
GridParallelRNG RNG4(UGrid); RNG4.SeedFixedIntegers(seeds4);
GridParallelRNG CRNG(Coarse5d);CRNG.SeedFixedIntegers(cseeds);
Gamma g5(Gamma::Gamma5);
LatticeFermion src(FGrid); gaussian(RNG5,src);// src=src+g5*src;
LatticeFermion result(FGrid); result=zero;
LatticeFermion ref(FGrid); ref=zero;
LatticeFermion tmp(FGrid);
LatticeFermion err(FGrid);
LatticeGaugeField Umu(UGrid);
NerscField header;
std::string file("./ckpoint_lat.4000");
readNerscConfiguration(Umu,header,file);
// SU3::ColdConfiguration(RNG4,Umu);
// SU3::TepidConfiguration(RNG4,Umu);
// SU3::HotConfiguration(RNG4,Umu);
// Umu=zero;
RealD mass=0.01;
RealD M5=1.8;
std::cout << "**************************************************"<< std::endl;
std::cout << "Building g5R5 hermitian DWF operator" <<std::endl;
std::cout << "**************************************************"<< std::endl;
DomainWallFermion Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
const int nbasis = 32;
// const int nbasis = 4;
typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> CoarseOperator;
typedef CoarseOperator::CoarseVector CoarseVector;
std::cout << "**************************************************"<< std::endl;
std::cout << "Calling Aggregation class to build subspace" <<std::endl;
std::cout << "**************************************************"<< std::endl;
MdagMLinearOperator<DomainWallFermion,LatticeFermion> HermDefOp(Ddwf);
Subspace Aggregates(Coarse5d,FGrid);
// Aggregates.CreateSubspace(RNG5,HermDefOp,nbasis);
assert ( (nbasis & 0x1)==0);
int nb=nbasis/2;
std::cout << " nbasis/2 = "<<nb<<std::endl;
Aggregates.CreateSubspace(RNG5,HermDefOp,nb);
for(int n=0;n<nb;n++){
G5R5(Aggregates.subspace[n+nb],Aggregates.subspace[n]);
std::cout<<n<<" subspace "<<norm2(Aggregates.subspace[n+nb])<<" "<<norm2(Aggregates.subspace[n]) <<std::endl;
}
for(int n=0;n<nbasis;n++){
std::cout << "vec["<<n<<"] = "<<norm2(Aggregates.subspace[n]) <<std::endl;
}
// for(int i=0;i<nbasis;i++){
// result = Aggregates.subspace[i];
// Aggregates.subspace[i]=result+g5*result;
// }
result=zero;
std::cout << "**************************************************"<< std::endl;
std::cout << "Building coarse representation of Indef operator" <<std::endl;
std::cout << "**************************************************"<< std::endl;
Gamma5R5HermitianLinearOperator<DomainWallFermion,LatticeFermion> HermIndefOp(Ddwf);
CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LDOp(*Coarse5d);
LDOp.CoarsenOperator(FGrid,HermIndefOp,Aggregates);
std::cout << "**************************************************"<< std::endl;
std::cout << "Testing some coarse space solvers " <<std::endl;
std::cout << "**************************************************"<< std::endl;
CoarseVector c_src (Coarse5d);
CoarseVector c_res (Coarse5d);
gaussian(CRNG,c_src);
c_res=zero;
std::cout << "**************************************************"<< std::endl;
std::cout << "Solving posdef-CG on coarse space "<< std::endl;
std::cout << "**************************************************"<< std::endl;
MdagMLinearOperator<CoarseOperator,CoarseVector> PosdefLdop(LDOp);
ConjugateGradient<CoarseVector> CG(1.0e-6,100000);
CG(PosdefLdop,c_src,c_res);
// std::cout << "**************************************************"<< std::endl;
// std::cout << "Solving indef-MCR on coarse space "<< std::endl;
// std::cout << "**************************************************"<< std::endl;
// HermitianLinearOperator<CoarseOperator,CoarseVector> HermIndefLdop(LDOp);
// ConjugateResidual<CoarseVector> MCR(1.0e-6,100000);
//MCR(HermIndefLdop,c_src,c_res);
std::cout << "**************************************************"<< std::endl;
std::cout << "Building deflation preconditioner "<< std::endl;
std::cout << "**************************************************"<< std::endl;
MultiGridPreconditioner <vSpinColourVector,vTComplex,nbasis,DomainWallFermion> Precon(Aggregates, LDOp,HermIndefOp,Ddwf);
TrivialPrecon<LatticeFermion> simple;
std::cout << "**************************************************"<< std::endl;
std::cout << "Testing smoother efficacy"<< std::endl;
std::cout << "**************************************************"<< std::endl;
Precon.SmootherTest(src);
std::cout << "**************************************************"<< std::endl;
std::cout << "Unprec CG "<< std::endl;
std::cout << "**************************************************"<< std::endl;
// TrivialPrecon<LatticeFermion> simple;
// ConjugateGradient<LatticeFermion> fCG(1.0e-8,100000);
// fCG(HermDefOp,src,result);
// exit(0);
std::cout << "**************************************************"<< std::endl;
std::cout << "Testing GCR on indef matrix "<< std::endl;
std::cout << "**************************************************"<< std::endl;
// PrecGeneralisedConjugateResidual<LatticeFermion> UPGCR(1.0e-8,100000,simple,8,128);
// UPGCR(HermIndefOp,src,result);
/// Get themax eval
std::cout << "**************************************************"<< std::endl;
std::cout <<" Applying power method to find spectral range "<<std::endl;
std::cout << "**************************************************"<< std::endl;
Precon.PowerMethod(src);
std::cout << "**************************************************"<< std::endl;
std::cout << "Building a two level PGCR "<< std::endl;
std::cout << "**************************************************"<< std::endl;
PrecGeneralisedConjugateResidual<LatticeFermion> PGCR(1.0e-8,100000,Precon,8,128);
std::cout<<"checking norm src "<<norm2(src)<<std::endl;
PGCR(HermIndefOp,src,result);
std::cout << "**************************************************"<< std::endl;
std::cout << "Done "<< std::endl;
std::cout << "**************************************************"<< std::endl;
Grid_finalize();
}