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Grid/tests/debug/Test_general_coarse_hdcg_phys48.cc

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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./tests/Test_general_coarse_hdcg.cc
Copyright (C) 2023
Author: Peter Boyle <pboyle@bnl.gov>
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>
using namespace std;
using namespace Grid;
template<class Coarsened>
void SaveOperator(Coarsened &Operator,std::string file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
ScidacWriter WR(Operator.Grid()->IsBoss());
assert(Operator._A.size()==Operator.geom.npoint);
WR.open(file);
for(int p=0;p<Operator._A.size();p++){
auto tmp = Operator.Cell.Extract(Operator._A[p]);
WR.writeScidacFieldRecord(tmp,record,0,0);
// WR.writeScidacFieldRecord(tmp,record,0,BINARYIO_LEXICOGRAPHIC);
}
WR.close();
#endif
}
template<class Coarsened>
void LoadOperator(Coarsened &Operator,std::string file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
Grid::ScidacReader RD ;
RD.open(file);
assert(Operator._A.size()==Operator.geom.npoint);
for(int p=0;p<Operator.geom.npoint;p++){
conformable(Operator._A[p].Grid(),Operator.CoarseGrid());
// RD.readScidacFieldRecord(Operator._A[p],record,BINARYIO_LEXICOGRAPHIC);
RD.readScidacFieldRecord(Operator._A[p],record,0);
}
RD.close();
Operator.ExchangeCoarseLinks();
#endif
}
template<class Coarsened>
void ReLoadOperator(Coarsened &Operator,std::string file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
Grid::ScidacReader RD ;
RD.open(file);
assert(Operator._A.size()==Operator.geom.npoint);
for(int p=0;p<Operator.geom.npoint;p++){
auto tmp=Operator.Cell.Extract(Operator._A[p]);
RD.readScidacFieldRecord(tmp,record,0);
Operator._A[p] = Operator.Cell.ExchangePeriodic(tmp);
}
RD.close();
#endif
}
template<class aggregation>
void SaveBasis(aggregation &Agg,std::string file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
ScidacWriter WR(Agg.FineGrid->IsBoss());
WR.open(file);
for(int b=0;b<Agg.subspace.size();b++){
//WR.writeScidacFieldRecord(Agg.subspace[b],record,0,BINARYIO_LEXICOGRAPHIC);
WR.writeScidacFieldRecord(Agg.subspace[b],record,0,0);
}
WR.close();
#endif
}
template<class aggregation>
void LoadBasis(aggregation &Agg, std::string file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
ScidacReader RD ;
RD.open(file);
for(int b=0;b<Agg.subspace.size();b++){
// RD.readScidacFieldRecord(Agg.subspace[b],record,BINARYIO_LEXICOGRAPHIC);
RD.readScidacFieldRecord(Agg.subspace[b],record,0);
}
RD.close();
#endif
}
template<class CoarseVector>
void SaveEigenvectors(std::vector<RealD> &eval,
std::vector<CoarseVector> &evec,
std::string evec_file,
std::string eval_file)
{
#ifdef HAVE_LIME
emptyUserRecord record;
ScidacWriter WR(evec[0].Grid()->IsBoss());
WR.open(evec_file);
for(int b=0;b<evec.size();b++){
WR.writeScidacFieldRecord(evec[b],record,0,0);
}
WR.close();
XmlWriter WRx(eval_file);
write(WRx,"evals",eval);
#endif
}
template<class CoarseVector>
void LoadEigenvectors(std::vector<RealD> &eval,
std::vector<CoarseVector> &evec,
std::string evec_file,
std::string eval_file)
{
#ifdef HAVE_LIME
XmlReader RDx(eval_file);
read(RDx,"evals",eval);
emptyUserRecord record;
Grid::ScidacReader RD ;
RD.open(evec_file);
assert(evec.size()==eval.size());
for(int k=0;k<eval.size();k++) {
RD.readScidacFieldRecord(evec[k],record);
}
RD.close();
#endif
}
RealD InverseApproximation(RealD x){
return 1.0/x;
}
// Want Op in CoarsenOp to call MatPcDagMatPc
template<class Field>
class HermOpAdaptor : public LinearOperatorBase<Field>
{
LinearOperatorBase<Field> & wrapped;
public:
HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme) {};
void Op (const Field &in, Field &out) { wrapped.HermOp(in,out); }
void HermOp(const Field &in, Field &out) { wrapped.HermOp(in,out); }
void AdjOp (const Field &in, Field &out){ wrapped.HermOp(in,out); }
void OpDiag (const Field &in, Field &out) { assert(0); }
void OpDir (const Field &in, Field &out,int dir,int disp) { assert(0); }
void OpDirAll (const Field &in, std::vector<Field> &out) { assert(0); };
void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
};
template<class Field> class ChebyshevSmoother : public LinearFunction<Field>
{
public:
using LinearFunction<Field>::operator();
typedef LinearOperatorBase<Field> FineOperator;
FineOperator & _SmootherOperator;
Chebyshev<Field> Cheby;
ChebyshevSmoother(RealD _lo,RealD _hi,int _ord, FineOperator &SmootherOperator) :
_SmootherOperator(SmootherOperator),
Cheby(_lo,_hi,_ord,InverseApproximation)
{
std::cout << GridLogMessage<<" Chebyshev smoother order "<<_ord<<" ["<<_lo<<","<<_hi<<"]"<<std::endl;
};
void operator() (const Field &in, Field &out)
{
Field tmp(in.Grid());
tmp = in;
Cheby(_SmootherOperator,tmp,out);
}
};
template<class Field> class CGSmoother : public LinearFunction<Field>
{
public:
using LinearFunction<Field>::operator();
typedef LinearOperatorBase<Field> FineOperator;
FineOperator & _SmootherOperator;
int iters;
CGSmoother(int _iters, FineOperator &SmootherOperator) :
_SmootherOperator(SmootherOperator),
iters(_iters)
{
std::cout << GridLogMessage<<" Mirs smoother order "<<iters<<std::endl;
};
void operator() (const Field &in, Field &out)
{
ConjugateGradient<Field> CG(0.0,iters,false); // non-converge is just fine in a smoother
out=Zero();
CG(_SmootherOperator,in,out);
}
};
int main (int argc, char ** argv)
{
Grid_init(&argc,&argv);
const int Ls=24;
const int nbasis = 62;
// const int nbasis = 56;
// const int nbasis = 44;
// const int nbasis = 36;
const int cb = 0 ;
RealD mass=0.00078;
RealD M5=1.8;
RealD b=1.5;
RealD c=0.5;
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 with 4^4 cell
Coordinate Block({4,4,6,4});
Coordinate clatt = GridDefaultLatt();
for(int d=0;d<clatt.size();d++){
clatt[d] = clatt[d]/Block[d];
}
GridCartesian *Coarse4d = SpaceTimeGrid::makeFourDimGrid(clatt,
GridDefaultSimd(Nd,vComplex::Nsimd()),
GridDefaultMpi());;
GridCartesian *Coarse5d = SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
///////////////////////// RNGs /////////////////////////////////
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);
///////////////////////// Configuration /////////////////////////////////
LatticeGaugeField Umu(UGrid);
MemoryManager::Print();
FieldMetaData header;
std::string file("ckpoint_lat.1000");
NerscIO::readConfiguration(Umu,header,file);
MemoryManager::Print();
//////////////////////// Fermion action //////////////////////////////////
MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
SchurDiagMooeeOperator<MobiusFermionD, LatticeFermion> HermOpEO(Ddwf);
typedef HermOpAdaptor<LatticeFermionD> HermFineMatrix;
HermFineMatrix FineHermOp(HermOpEO);
// Run power method on FineHermOp
// PowerMethod<LatticeFermion> PM; PM(HermOpEO,src);
////////////////////////////////////////////////////////////
///////////// Coarse basis and Little Dirac Operator ///////
////////////////////////////////////////////////////////////
typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
typedef LittleDiracOperator::CoarseVector CoarseVector;
NextToNextToNextToNearestStencilGeometry5D geom(Coarse5d);
// Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
Subspace Aggregates(Coarse5d,FrbGrid,cb);
////////////////////////////////////////////////////////////
// Need to check about red-black grid coarsening
////////////////////////////////////////////////////////////
LittleDiracOperator LittleDiracOp(geom,FrbGrid,Coarse5d);
std::string subspace_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Subspace.phys48.rat.18node.62");
std::string refine_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/Refine.phys48.rat.18node.62");
std::string ldop_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/LittleDiracOp.phys48.rat.18node.62");
std::string evec_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/evecs.scidac");
std::string eval_file("/lustre/orion/phy157/proj-shared/phy157_dwf/paboyle/eval.xml");
bool load_agg=true;
bool load_refine=true;
bool load_mat=true;
bool load_evec=false;
MemoryManager::Print();
int refine=1;
if ( load_agg ) {
if ( !(refine) || (!load_refine) ) {
LoadBasis(Aggregates,subspace_file);
}
} else {
Aggregates.CreateSubspaceMultishift(RNG5,HermOpEO,
0.0003,1.0e-5,2000); // Lo, tol, maxit
// Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,95.,0.01,1500); <== last run
SaveBasis(Aggregates,subspace_file);
}
if(refine){
if ( load_refine ) {
LoadBasis(Aggregates,refine_file);
} else {
// HDCG used Pcg to refine
Aggregates.RefineSubspace(HermOpEO,0.001,1.0e-3,3000);
SaveBasis(Aggregates,refine_file);
}
}
Aggregates.Orthogonalise();
if ( load_mat ) {
LoadOperator(LittleDiracOp,ldop_file);
} else {
LittleDiracOp.CoarsenOperator(FineHermOp,Aggregates);
// SaveOperator(LittleDiracOp,ldop_file);
}
// I/O test:
CoarseVector c_src(Coarse5d); random(CRNG,c_src);
CoarseVector c_res(Coarse5d);
CoarseVector c_ref(Coarse5d);
if (0){
///////////////////////////////////////////////////
// Test the operator
///////////////////////////////////////////////////
CoarseVector c_proj(Coarse5d);
LatticeFermionD tmp(FrbGrid);
LatticeFermionD prom(FrbGrid);
blockPromote(c_src,prom,Aggregates.subspace);
FineHermOp.HermOp(prom,tmp);
std::cout<<GridLogMessage<<" Calling big dirac op "<<norm2(tmp)<<std::endl;
blockProject(c_proj,tmp,Aggregates.subspace);
std::cout<<GridLogMessage<<" Calling little Dirac Op "<<std::endl;
LittleDiracOp.M(c_src,c_res);
std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
std::cout<<GridLogMessage<<"Big dop in subspace : "<<norm2(c_proj)<<std::endl;
c_proj = c_proj - c_res;
std::cout<<GridLogMessage<<" ldop error: "<<norm2(c_proj)<<std::endl;
}
//////////////////////////////////////
// mrhs coarse operator
// Create a higher dim coarse grid
//////////////////////////////////////////////////////////////////////////////////////
std::cout << "**************************************"<<std::endl;
std::cout << "Building MultiRHS Coarse operator"<<std::endl;
std::cout << "**************************************"<<std::endl;
ConjugateGradient<CoarseVector> coarseCG(4.0e-2,20000,true);
const int nrhs=vComplex::Nsimd()*3;
Coordinate mpi=GridDefaultMpi();
Coordinate rhMpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
Coordinate rhLatt({nrhs,1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate rhSimd({vComplex::Nsimd(),1, 1,1,1,1});
GridCartesian *CoarseMrhs = new GridCartesian(rhLatt,rhSimd,rhMpi);
// MultiGeneralCoarsenedMatrix mrhs(LittleDiracOp,CoarseMrhs);
typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> MultiGeneralCoarsenedMatrix_t;
MultiGeneralCoarsenedMatrix_t mrhs(geom,CoarseMrhs);
// mrhs.CopyMatrix(LittleDiracOp);
// mrhs.SetMatrix(LittleDiracOp.);
mrhs.CoarsenOperator(FineHermOp,Aggregates,Coarse5d);
// mrhs.CheckMatrix(LittleDiracOp);
//////////////////////////////////////////
// Build a coarse lanczos
//////////////////////////////////////////
std::cout << "**************************************"<<std::endl;
std::cout << "Building Coarse Lanczos "<<std::endl;
std::cout << "**************************************"<<std::endl;
typedef HermitianLinearOperator<LittleDiracOperator,CoarseVector> HermMatrix;
HermMatrix CoarseOp (LittleDiracOp);
int Nk=192;
int Nm=256;
int Nstop=Nk;
Chebyshev<CoarseVector> IRLCheby(0.005,40.0,201); // 1 iter
FunctionHermOp<CoarseVector> IRLOpCheby(IRLCheby,CoarseOp);
PlainHermOp<CoarseVector> IRLOp (CoarseOp);
ImplicitlyRestartedLanczos<CoarseVector> IRL(IRLOpCheby,IRLOp,Nstop,Nk,Nm,1e-5,10);
int Nconv;
std::vector<RealD> eval(Nm);
std::vector<CoarseVector> evec(Nm,Coarse5d);
PowerMethod<CoarseVector> cPM; cPM(CoarseOp,c_src);
if ( load_evec ) {
eval.resize(Nstop);
evec.resize(Nstop,Coarse5d);
LoadEigenvectors(eval,evec,evec_file,eval_file);
} else {
IRL.calc(eval,evec,c_src,Nconv);
assert(Nstop==eval.size());
SaveEigenvectors(eval,evec,evec_file,eval_file);
}
DeflatedGuesser<CoarseVector> DeflCoarseGuesser(evec,eval);
MultiRHSDeflation<CoarseVector> MrhsGuesser;
//////////////////////////////////////////
// Build a coarse space solver
//////////////////////////////////////////
int maxit=30000;
ConjugateGradient<CoarseVector> CG(1.0e-10,maxit,false);
ConjugateGradient<LatticeFermionD> CGfine(1.0e-8,30000,false);
ZeroGuesser<CoarseVector> CoarseZeroGuesser;
HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,DeflCoarseGuesser);
c_res=Zero();
/////////// MRHS test .////////////
typedef HermitianLinearOperator<MultiGeneralCoarsenedMatrix_t,CoarseVector> MrhsHermMatrix;
MrhsHermMatrix MrhsCoarseOp (mrhs);
#if 1
{
CoarseVector rh_res(CoarseMrhs);
CoarseVector rh_guess(CoarseMrhs);
CoarseVector rh_src(CoarseMrhs);
rh_res= Zero();
rh_guess= Zero();
std::cout << "*************************"<<std::endl;
std::cout << " MrhsGuesser importing"<<std::endl;
std::cout << "*************************"<<std::endl;
MrhsGuesser.ImportEigenBasis(evec,eval);
std::vector<CoarseVector> BlasGuess(nrhs,Coarse5d);
std::vector<CoarseVector> BlasSource(nrhs,Coarse5d);
for(int r=0;r<nrhs;r++){
random(CRNG,BlasSource[r]);
}
MrhsGuesser.DeflateSources(BlasSource,BlasGuess);
for(int r=0;r<nrhs;r++){
std::cout << "*************************"<<std::endl;
std::cout << "**** DeflCoarseGuesser &&&&& "<<std::endl;
std::cout << "*************************"<<std::endl;
c_src=BlasSource[r];
DeflCoarseGuesser(c_src,c_res);
std::cout << "Deflated guess "<< norm2(c_res)<<std::endl;
std::cout << "Blas deflated guess "<< norm2(BlasGuess[r])<<std::endl;
std::cout << "*************************"<<std::endl;
BlasGuess[r] = BlasGuess[r] - c_res;
std::cout << "Diff " <<norm2(BlasGuess[r])<<std::endl;
std::cout << "*************************"<<std::endl;
InsertSlice(c_res,rh_res,r,0);
InsertSlice(c_res,rh_guess,r,0);
InsertSlice(c_src,rh_src,r,0);
}
std::cout << " Calling the multiRHS coarse CG"<<std::endl;
coarseCG(MrhsCoarseOp,rh_src,rh_res);
//redo with block CG ?
for(int r=0;r<nrhs;r++){
std::cout << " compare to single RHS "<<r<<"/"<<nrhs<<std::endl;
ExtractSlice(c_src,rh_src,r,0);
ExtractSlice(c_res,rh_res,r,0);
ExtractSlice(c_ref,rh_guess,r,0);
coarseCG(CoarseOp,c_src,c_ref);
std::cout << " mrhs [" <<r <<"] "<< norm2(c_res)<<std::endl;
std::cout << " srhs [" <<r <<"] "<< norm2(c_ref)<<std::endl;
c_ref=c_ref-c_res;
RealD diff =norm2(c_ref)/norm2(c_src);
std::cout << r << " diff " << diff<<std::endl;
assert(diff < 1.0e-1);
}
}
#endif
//////////////////////////////////////
// fine solve
//////////////////////////////////////
std::vector<RealD> los({2.0});
std::vector<int> ords({7});
/*
Powerlaw setup 62 vecs
slurm-1494943.out:Grid : Message : 4874.186617 s : HDCG: Pcg converged in 171 iterations and 1706.548006 s 1.0 32
slurm-1494943.out:Grid : Message : 6490.121648 s : HDCG: Pcg converged in 194 iterations and 1616.219654 s 1.0 16
Cheby setup: 56vecs
-- CG smoother O(16): 487
Power law setup, 56 vecs -- lambda^-5
slurm-1494383.out:Grid : Message : 4377.173265 s : HDCG: Pcg converged in 204 iterations and 1153.548935 s 1.0 32
Power law setup, 56 vecs -- lambda^-3
slurm-1494242.out:Grid : Message : 4370.464814 s : HDCG: Pcg converged in 204 iterations and 1143.494776 s 1.0 32
slurm-1494242.out:Grid : Message : 5432.414820 s : HDCG: Pcg converged in 237 iterations and 1061.455882 s 1.0 16
slurm-1494242.out:Grid : Message : 6588.727977 s : HDCG: Pcg converged in 205 iterations and 1156.565210 s 0.5 32
Power law setup, 56 vecs -- lambda^-4
-- CG smoother O(16): 290
-- Cheby smoother O(16): 218 -- getting close to the deflation level I expect 169 from BFM paper @O(7) smoother and 64 nbasis
Conclusion: higher order smoother is doing better. Much better. Use a Krylov smoother instead Mirs as in BFM version.
*/
//
MemoryManager::Print();
for(int l=0;l<los.size();l++){
RealD lo = los[l];
for(int o=0;o<ords.size();o++){
ConjugateGradient<CoarseVector> CGsloppy(4.0e-2,maxit,false);
HPDSolver<CoarseVector> HPDSolveSloppy(CoarseOp,CGsloppy,DeflCoarseGuesser);
// ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(lo,92,10,FineHermOp); // 36 best case
ChebyshevSmoother<LatticeFermionD > ChebySmooth(lo,95,ords[o],FineHermOp); // 311
RealD MirsShift = lo;
ShiftedHermOpLinearOperator<LatticeFermionD> ShiftedFineHermOp(HermOpEO,MirsShift);
CGSmoother<LatticeFermionD> CGsmooth(ords[o],ShiftedFineHermOp) ;
//////////////////////////////////////////
// Build a HDCG solver
//////////////////////////////////////////
TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
HDCG(1.0e-8, 700,
FineHermOp,
CGsmooth,
HPDSolveSloppy,
HPDSolve,
Aggregates);
// result=Zero();
// std::cout << "Calling HDCG single RHS"<<std::endl;
// HDCG(src,result);
//////////////////////////////////////////
// Build a HDCG mrhs solver
//////////////////////////////////////////
#if 1
MemoryManager::Print();
DoNothingGuesser<CoarseVector> DoNothing;
HPDSolver<CoarseVector> HPDSolveMrhs(MrhsCoarseOp,CG,DoNothing);
HPDSolver<CoarseVector> HPDSolveMrhsSloppy(MrhsCoarseOp,CGsloppy,DoNothing);
TwoLevelADEF2mrhs<LatticeFermion,CoarseVector,Subspace>
HDCGmrhs(1.0e-8, 500,
FineHermOp,
CGsmooth,
// HPDSolveSloppy, // Never used
// HPDSolve, // Used in Vstart
HPDSolveMrhsSloppy, // Used in M1
HPDSolveMrhs, // Used in Vstart
DeflCoarseGuesser, // single RHS guess used in M1
CoarseMrhs, // Grid needed to Mrhs grid
Aggregates);
std::cout << "Calling mRHS HDCG"<<std::endl;
FrbGrid->Barrier();
std::vector<LatticeFermionD> src_mrhs(nrhs,FrbGrid);
std::cout << " mRHS source"<<std::endl;
std::vector<LatticeFermionD> res_mrhs(nrhs,FrbGrid);
std::cout << " mRHS result"<<std::endl;
random(RNG5,src_mrhs[0]);
for(int r=0;r<nrhs;r++){
if(r>0)src_mrhs[r]=src_mrhs[0];
res_mrhs[r]=Zero();
std::cout << "Setup mrhs source "<<r<<std::endl;
}
std::cout << "Calling the mRHS HDCG"<<std::endl;
MemoryManager::Print();
HDCGmrhs(src_mrhs,res_mrhs);
MemoryManager::Print();
#endif
}
}
// Standard CG
#if 1
{
LatticeFermion result(FrbGrid); result=Zero();
LatticeFermion src(FrbGrid); random(RNG5,src);
result=Zero();
CGfine(HermOpEO, src, result);
}
#endif
Grid_finalize();
return 0;
}
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