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d1afebf71e
6000 matmuls CG unprec 2000 matmuls CG prec (4000 eo muls) 1050 matmuls PGCR on 16^3 x 32 x 8 m=.01 Substantial effort on timing and logging infrastructure
522 lines
20 KiB
C++
522 lines
20 KiB
C++
#include <Grid.h>
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#include <algorithms/iterative/PrecGeneralisedConjugateResidual.h>
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//#include <algorithms/iterative/PrecConjugateResidual.h>
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using namespace std;
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using namespace Grid;
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using namespace Grid::QCD;
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RealD InverseApproximation(RealD x){
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return 1.0/x;
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}
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template<class Fobj,class CComplex,int nbasis, class Matrix>
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class MultiGridPreconditioner : public LinearFunction< Lattice<Fobj> > {
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public:
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typedef Aggregation<Fobj,CComplex,nbasis> Aggregates;
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typedef CoarsenedMatrix<Fobj,CComplex,nbasis> CoarseOperator;
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typedef typename Aggregation<Fobj,CComplex,nbasis>::siteVector siteVector;
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typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseScalar CoarseScalar;
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typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseVector CoarseVector;
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typedef typename Aggregation<Fobj,CComplex,nbasis>::CoarseMatrix CoarseMatrix;
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typedef typename Aggregation<Fobj,CComplex,nbasis>::FineField FineField;
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typedef LinearOperatorBase<FineField> FineOperator;
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Aggregates & _Aggregates;
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CoarseOperator & _CoarseOperator;
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Matrix & _Matrix;
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FineOperator & _FineOperator;
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// Constructor
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MultiGridPreconditioner(Aggregates &Agg, CoarseOperator &Coarse, FineOperator &Fine,Matrix &FineMatrix)
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: _Aggregates(Agg),
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_CoarseOperator(Coarse),
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_FineOperator(Fine),
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_Matrix(FineMatrix)
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{
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}
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void PowerMethod(const FineField &in) {
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FineField p1(in._grid);
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FineField p2(in._grid);
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MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
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p1=in;
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RealD absp2;
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for(int i=0;i<20;i++){
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RealD absp1=std::sqrt(norm2(p1));
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fMdagMOp.HermOp(p1,p2);// this is the G5 herm bit
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// _FineOperator.Op(p1,p2);// this is the G5 herm bit
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RealD absp2=std::sqrt(norm2(p2));
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if(i%10==9)
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std::cout<<GridLogMessage << "Power method on mdagm "<<i<<" " << absp2/absp1<<std::endl;
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p1=p2*(1.0/std::sqrt(absp2));
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}
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}
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#if 0
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void operator()(const FineField &in, FineField & out) {
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FineField Min(in._grid);
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FineField tmp(in._grid);
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid());
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// Monitor completeness of low mode space
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_Aggregates.ProjectToSubspace (Csrc,in);
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_Aggregates.PromoteFromSubspace(Csrc,out);
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std::cout<<GridLogMessage<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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// Build some solvers
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ConjugateGradient<FineField> fCG(1.0e-3,1000);
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ConjugateGradient<CoarseVector> CG(1.0e-8,100000);
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////////////////////////////////////////////////////////////////////////
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// ADEF2: [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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////////////////////////////////////////////////////////////////////////
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// Smoothing step, followed by coarse grid correction
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MdagMLinearOperator<Matrix,FineField> MdagMOp(_Matrix);
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Min=in;
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std::cout<<GridLogMessage<< " Preconditioner in " << norm2(in)<<std::endl;
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_FineOperator.AdjOp(Min,tmp);
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std::cout<<GridLogMessage<< " Preconditioner tmp " << norm2(in)<<std::endl;
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fCG(MdagMOp,tmp,out);
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_FineOperator.Op(out,tmp);
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std::cout<<GridLogMessage<< " Preconditioner in " << norm2(in)<<std::endl;
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std::cout<<GridLogMessage<< " Preconditioner out " << norm2(out)<<std::endl;
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std::cout<<GridLogMessage<< " Preconditioner Aout" << norm2(tmp)<<std::endl;
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tmp = tmp - in;
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std::cout<<GridLogMessage<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;
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/*
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// _FineOperator.Op(Min,out);
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// out = in -out; // out = in - A Min
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out = in;
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MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
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HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
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Csol=zero;
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_Aggregates.ProjectToSubspace (Csrc,out);
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HermOp.AdjOp(Csrc,Ctmp);// Normal equations
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CG(MdagMOp ,Ctmp,Csol);
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_Aggregates.PromoteFromSubspace(Csol,out);
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out = Min + out;;
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*/
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}
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#endif
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////////////////////////////////////////////////////////////////////////
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// ADEF2: [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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// ADEF1: [MP+Q ] in =M [1 - A Q] in + Q in
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////////////////////////////////////////////////////////////////////////
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#if 0
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void operator()(const FineField &in, FineField & out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid());
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ConjugateGradient<CoarseVector> CG(1.0e-10,100000);
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ConjugateGradient<FineField> fCG(3.0e-2,1000);
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HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
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MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
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FineField tmp(in._grid);
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FineField res(in._grid);
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FineField Min(in._grid);
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// Monitor completeness of low mode space
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_Aggregates.ProjectToSubspace (Csrc,in);
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_Aggregates.PromoteFromSubspace(Csrc,out);
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std::cout<<GridLogMessage<<"Coarse Grid Preconditioner\nCompleteness in: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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// [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
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_FineOperator.Op(in,tmp);// this is the G5 herm bit
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fCG(fMdagMOp,tmp,Min); // solves MdagM = g5 M g5M
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// Monitor completeness of low mode space
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_Aggregates.ProjectToSubspace (Csrc,Min);
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_Aggregates.PromoteFromSubspace(Csrc,out);
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std::cout<<GridLogMessage<<"Completeness Min: "<<std::sqrt(norm2(out)/norm2(Min))<<std::endl;
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_FineOperator.Op(Min,tmp);
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tmp = in - tmp; // in - A Min
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Csol=zero;
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_Aggregates.ProjectToSubspace (Csrc,tmp);
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HermOp.AdjOp(Csrc,Ctmp);// Normal equations
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CG(MdagMOp,Ctmp,Csol);
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HermOp.Op(Csol,Ctmp);
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Ctmp=Ctmp-Csrc;
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std::cout<<GridLogMessage<<"coarse space true residual "<<std::sqrt(norm2(Ctmp)/norm2(Csrc))<<std::endl;
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_Aggregates.PromoteFromSubspace(Csol,out);
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_FineOperator.Op(out,res);
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res=res-tmp;
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std::cout<<GridLogMessage<<"promoted sol residual "<<std::sqrt(norm2(res)/norm2(tmp))<<std::endl;
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_Aggregates.ProjectToSubspace (Csrc,res);
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std::cout<<GridLogMessage<<"coarse space proj of residual "<<norm2(Csrc)<<std::endl;
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out = out+Min; // additive coarse space correction
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// out = Min; // no additive coarse space correction
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_FineOperator.Op(out,tmp);
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tmp=tmp-in; // tmp is new residual
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std::cout<<GridLogMessage<< " Preconditioner in " << norm2(in)<<std::endl;
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std::cout<<GridLogMessage<< " Preconditioner out " << norm2(out)<<std::endl;
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std::cout<<GridLogMessage<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;
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}
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#endif
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// ADEF1: [MP+Q ] in =M [1 - A Q] in + Q in
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#if 0
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void operator()(const FineField &in, FineField & out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;
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ConjugateGradient<CoarseVector> CG(1.0e-10,100000);
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ConjugateGradient<FineField> fCG(3.0e-2,1000);
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HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
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ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix,0.1);
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FineField tmp(in._grid);
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FineField res(in._grid);
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FineField Qin(in._grid);
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// Monitor completeness of low mode space
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// _Aggregates.ProjectToSubspace (Csrc,in);
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// _Aggregates.PromoteFromSubspace(Csrc,out);
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// std::cout<<GridLogMessage<<"Coarse Grid Preconditioner\nCompleteness in: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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_Aggregates.ProjectToSubspace (Csrc,in);
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HermOp.AdjOp(Csrc,Ctmp);// Normal equations
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CG(MdagMOp,Ctmp,Csol);
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_Aggregates.PromoteFromSubspace(Csol,Qin);
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// Qin=0;
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_FineOperator.Op(Qin,tmp);// A Q in
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tmp = in - tmp; // in - A Q in
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_FineOperator.Op(tmp,res);// this is the G5 herm bit
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fCG(fMdagMOp,res,out); // solves MdagM = g5 M g5M
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out = out + Qin;
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_FineOperator.Op(out,tmp);
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tmp=tmp-in; // tmp is new residual
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std::cout<<GridLogMessage<<"preconditioner thinks residual is "<<std::sqrt(norm2(tmp)/norm2(in))<<std::endl;
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}
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#endif
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void SmootherTest (const FineField & in){
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FineField vec1(in._grid);
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FineField vec2(in._grid);
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RealD lo[3] = { 0.5, 1.0, 2.0};
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// MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
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ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix,0.5);
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RealD Ni,r;
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Ni = norm2(in);
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for(int ilo=0;ilo<3;ilo++){
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for(int ord=5;ord<50;ord*=2){
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_FineOperator.AdjOp(in,vec1);
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Chebyshev<FineField> Cheby (lo[ilo],70.0,ord,InverseApproximation);
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Cheby(fMdagMOp,vec1,vec2); // solves MdagM = g5 M g5M
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_FineOperator.Op(vec2,vec1);// this is the G5 herm bit
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vec1 = in - vec1; // tmp = in - A Min
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r=norm2(vec1);
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std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;
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}
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}
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}
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void operator()(const FineField &in, FineField & out) {
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CoarseVector Csrc(_CoarseOperator.Grid());
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CoarseVector Ctmp(_CoarseOperator.Grid());
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CoarseVector Csol(_CoarseOperator.Grid()); Csol=zero;
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ConjugateGradient<CoarseVector> CG(1.0e-3,100000);
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// ConjugateGradient<FineField> fCG(3.0e-2,1000);
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HermitianLinearOperator<CoarseOperator,CoarseVector> HermOp(_CoarseOperator);
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MdagMLinearOperator<CoarseOperator,CoarseVector> MdagMOp(_CoarseOperator);
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// MdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix);
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ShiftedMdagMLinearOperator<Matrix,FineField> fMdagMOp(_Matrix,0.0);
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FineField vec1(in._grid);
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FineField vec2(in._grid);
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// Chebyshev<FineField> Cheby (0.5,70.0,30,InverseApproximation);
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// Chebyshev<FineField> ChebyAccu(0.5,70.0,30,InverseApproximation);
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Chebyshev<FineField> Cheby (2.0,70.0,10,InverseApproximation);
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Chebyshev<FineField> ChebyAccu(2.0,70.0,10,InverseApproximation);
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_Aggregates.ProjectToSubspace (Csrc,in);
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_Aggregates.PromoteFromSubspace(Csrc,out);
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std::cout<<GridLogMessage<<"Completeness: "<<std::sqrt(norm2(out)/norm2(in))<<std::endl;
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// ofstream fout("smoother");
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// Cheby.csv(fout);
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// V11 multigrid.
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// Use a fixed chebyshev and hope hermiticity helps.
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// To make a working smoother for indefinite operator
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// must multiply by "Mdag" (ouch loses all low mode content)
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// and apply to poly approx of (mdagm)^-1.
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// so that we end up with an odd polynomial.
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RealD Ni = norm2(in);
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_FineOperator.AdjOp(in,vec1);// this is the G5 herm bit
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ChebyAccu(fMdagMOp,vec1,out); // solves MdagM = g5 M g5M
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std::cout<<GridLogMessage << "Smoother norm "<<norm2(out)<<std::endl;
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// Update with residual for out
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_FineOperator.Op(out,vec1);// this is the G5 herm bit
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vec1 = in - vec1; // tmp = in - A Min
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RealD r = norm2(vec1);
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std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<< " " << r << " " << Ni <<std::endl;
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_Aggregates.ProjectToSubspace (Csrc,vec1);
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HermOp.AdjOp(Csrc,Ctmp);// Normal equations
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CG(MdagMOp,Ctmp,Csol);
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_Aggregates.PromoteFromSubspace(Csol,vec1); // Ass^{-1} [in - A Min]_s
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// Q = Q[in - A Min]
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out = out+vec1;
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// Three preconditioner smoothing -- hermitian if C3 = C1
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// Recompute error
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_FineOperator.Op(out,vec1);// this is the G5 herm bit
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vec1 = in - vec1; // tmp = in - A Min
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r=norm2(vec1);
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std::cout<<GridLogMessage << "Coarse resid "<<std::sqrt(r/Ni)<<std::endl;
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// Reapply smoother
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_FineOperator.Op(vec1,vec2); // this is the G5 herm bit
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ChebyAccu(fMdagMOp,vec2,vec1); // solves MdagM = g5 M g5M
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out =out+vec1;
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_FineOperator.Op(out,vec1);// this is the G5 herm bit
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vec1 = in - vec1; // tmp = in - A Min
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r=norm2(vec1);
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std::cout<<GridLogMessage << "Smoother resid "<<std::sqrt(r/Ni)<<std::endl;
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}
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};
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int main (int argc, char ** argv)
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{
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Grid_init(&argc,&argv);
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const int Ls=8;
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GridCartesian * UGrid = SpaceTimeGrid::makeFourDimGrid(GridDefaultLatt(), GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());
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GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
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GridCartesian * FGrid = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
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GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
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///////////////////////////////////////////////////
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// Construct a coarsened grid; utility for this?
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///////////////////////////////////////////////////
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const int block=2;
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std::vector<int> clatt = GridDefaultLatt();
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for(int d=0;d<clatt.size();d++){
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clatt[d] = clatt[d]/block;
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}
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GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());;
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GridCartesian *Coarse5d = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
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std::vector<int> seeds4({1,2,3,4});
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std::vector<int> seeds5({5,6,7,8});
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std::vector<int> cseeds({5,6,7,8});
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GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers(seeds5);
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GridParallelRNG RNG4(UGrid); RNG4.SeedFixedIntegers(seeds4);
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GridParallelRNG CRNG(Coarse5d);CRNG.SeedFixedIntegers(cseeds);
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Gamma g5(Gamma::Gamma5);
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LatticeFermion src(FGrid); gaussian(RNG5,src);// src=src+g5*src;
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LatticeFermion result(FGrid); result=zero;
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LatticeFermion ref(FGrid); ref=zero;
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LatticeFermion tmp(FGrid);
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LatticeFermion err(FGrid);
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LatticeGaugeField Umu(UGrid);
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NerscField header;
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std::string file("./ckpoint_lat.400");
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readNerscConfiguration(Umu,header,file);
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// SU3::ColdConfiguration(RNG4,Umu);
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// SU3::TepidConfiguration(RNG4,Umu);
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// SU3::HotConfiguration(RNG4,Umu);
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// Umu=zero;
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RealD mass=0.01;
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RealD M5=1.8;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Building g5R5 hermitian DWF operator" <<std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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DomainWallFermion Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
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const int nbasis = 32;
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// const int nbasis = 4;
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typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
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typedef CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> CoarseOperator;
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typedef CoarseOperator::CoarseVector CoarseVector;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Calling Aggregation class to build subspace" <<std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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MdagMLinearOperator<DomainWallFermion,LatticeFermion> HermDefOp(Ddwf);
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Subspace Aggregates(Coarse5d,FGrid);
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// Aggregates.CreateSubspace(RNG5,HermDefOp,nbasis);
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assert ( (nbasis & 0x1)==0);
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int nb=nbasis/2;
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std::cout<<GridLogMessage << " nbasis/2 = "<<nb<<std::endl;
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Aggregates.CreateSubspace(RNG5,HermDefOp,nb);
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for(int n=0;n<nb;n++){
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G5R5(Aggregates.subspace[n+nb],Aggregates.subspace[n]);
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std::cout<<GridLogMessage<<n<<" subspace "<<norm2(Aggregates.subspace[n+nb])<<" "<<norm2(Aggregates.subspace[n]) <<std::endl;
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}
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for(int n=0;n<nbasis;n++){
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std::cout<<GridLogMessage << "vec["<<n<<"] = "<<norm2(Aggregates.subspace[n]) <<std::endl;
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}
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// for(int i=0;i<nbasis;i++){
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// result = Aggregates.subspace[i];
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// Aggregates.subspace[i]=result+g5*result;
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// }
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result=zero;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Building coarse representation of Indef operator" <<std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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Gamma5R5HermitianLinearOperator<DomainWallFermion,LatticeFermion> HermIndefOp(Ddwf);
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CoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LDOp(*Coarse5d);
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LDOp.CoarsenOperator(FGrid,HermIndefOp,Aggregates);
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Testing some coarse space solvers " <<std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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CoarseVector c_src (Coarse5d);
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CoarseVector c_res (Coarse5d);
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gaussian(CRNG,c_src);
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c_res=zero;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Solving posdef-CG on coarse space "<< std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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MdagMLinearOperator<CoarseOperator,CoarseVector> PosdefLdop(LDOp);
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ConjugateGradient<CoarseVector> CG(1.0e-6,100000);
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CG(PosdefLdop,c_src,c_res);
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// std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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// std::cout<<GridLogMessage << "Solving indef-MCR on coarse space "<< std::endl;
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// std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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// HermitianLinearOperator<CoarseOperator,CoarseVector> HermIndefLdop(LDOp);
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// ConjugateResidual<CoarseVector> MCR(1.0e-6,100000);
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//MCR(HermIndefLdop,c_src,c_res);
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|
|
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Building deflation preconditioner "<< std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
|
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MultiGridPreconditioner <vSpinColourVector,vTComplex,nbasis,DomainWallFermion> Precon(Aggregates, LDOp,HermIndefOp,Ddwf);
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TrivialPrecon<LatticeFermion> simple;
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|
|
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Testing smoother efficacy"<< std::endl;
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|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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Precon.SmootherTest(src);
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|
|
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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std::cout<<GridLogMessage << "Unprec CG "<< std::endl;
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
// TrivialPrecon<LatticeFermion> simple;
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|
// ConjugateGradient<LatticeFermion> fCG(1.0e-8,100000);
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// fCG(HermDefOp,src,result);
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|
// exit(0);
|
|
|
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std::cout<<GridLogMessage << "**************************************************"<< std::endl;
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|
std::cout<<GridLogMessage << "Testing GCR on indef matrix "<< std::endl;
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|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
// PrecGeneralisedConjugateResidual<LatticeFermion> UPGCR(1.0e-8,100000,simple,8,128);
|
|
// UPGCR(HermIndefOp,src,result);
|
|
|
|
|
|
/// Get themax eval
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
std::cout<<GridLogMessage <<" Applying power method to find spectral range "<<std::endl;
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
Precon.PowerMethod(src);
|
|
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
std::cout<<GridLogMessage << "Building a two level PGCR "<< std::endl;
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
PrecGeneralisedConjugateResidual<LatticeFermion> PGCR(1.0e-8,100000,Precon,8,128);
|
|
std::cout<<GridLogMessage<<"checking norm src "<<norm2(src)<<std::endl;
|
|
PGCR(HermIndefOp,src,result);
|
|
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
std::cout<<GridLogMessage << "Red Black Prec CG "<< std::endl;
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
SchurDiagMooeeOperator<DomainWallFermion,LatticeFermion> HermOpEO(Ddwf);
|
|
ConjugateGradient<LatticeFermion> pCG(1.0e-8,10000);
|
|
|
|
LatticeFermion src_o(FrbGrid);
|
|
LatticeFermion result_o(FrbGrid);
|
|
pickCheckerboard(Odd,src_o,src);
|
|
result_o=zero;
|
|
|
|
pCG(HermOpEO,src_o,result_o);
|
|
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
std::cout<<GridLogMessage << "Done "<< std::endl;
|
|
std::cout<<GridLogMessage << "**************************************************"<< std::endl;
|
|
Grid_finalize();
|
|
}
|