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Grid/examples/Example_pvdagm_v2_3level_DenseCoarseMatrix.cc
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/*************************************************************************************
Grid physics library, www.github.com/paboyle/Grid
Source file: ./examples/Example_pvdagm_v2_3level_DenseCoarseMatrix.cc
Copyright (C) 2026
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 */
//
// PVdagM three level multigrid on the V2 coarse operator.
//
// STAGES ONE AND TWO: grids, types, subspace, and the L1 and L2 coarsenings.
// The dense bottom and the solves are not here yet.
//
// Differences from Example_pvdagm_mrhs_3level_DenseCoarseMatrix.cc:
//
// * The coarse space is UNVECTORISED (sComplexD). The fine space stays
// vectorised. MultiRHSBlockProject carries the mixed layout.
//
// * One operator, not two. V1 needed GeneralCoarsenedMatrix to coarsen and
// MultiGeneralCoarsenedMatrix to apply, bridged by CopyMatrix. V2 does
// both, and single versus multiRHS is SetGrid on the same object with the
// matrix elements built once.
//
// * Nrhs is unconstrained. V1 required nrhs % vComplex::Nsimd() == 0 because
// its multiRHS grid carried the SIMD in the rhs direction.
//
// * CoarsenOperator takes the subspace vectors, not an Aggregation. It block
// orthonormalises them IN PLACE -- the vectors are far too large to copy
// defensively -- so rawNull is taken first and the RAW vectors are what
// define the L2 null space. Do not insert an Orthogonalise() anywhere:
// projecting a block-orthonormal vector onto its own block-orthonormalised
// aggregation gives e_k, and the near null content is silently gone. The
// ||<psi|psi> - I||_F guard below is what catches that.
//
// Env: LATT LS MASS NBASIS(compile time) NRHS BLOCK BLOCK2 COARSEN_BATCH
// HOT_START CONFIG SUBSPACE_FILE V1_CHECK MRHS_COARSEN
//
#include <Grid/Grid.h>
#include <Grid/lattice/PaddedCell.h>
#include <Grid/stencil/GeneralLocalStencil.h>
#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
#include <Grid/algorithms/multigrid/DenseCoarseMatrix.h>
#include <memory>
using namespace std;
using namespace Grid;
// Compile time so it can be cut down for laptop runs: -DNBASIS=8
#ifndef NBASIS
#define NBASIS 60
#endif
RealD mass = 0.00078;
int Nrhs = 12;
int Ls = 24;
int CoarsenBatch = 9;
std::vector<int> lat_size({48,48,48,96});
// Solver tuning, values as in the V1 example
RealD FineSmootherShift = 0.1;
int FineSmootherOrder = 16;
RealD CoarseSmootherShift = 0.1;
int CoarseSmootherNstep = 4;
RealD CoarseSolverTol = 0.03;
int CoarseSolverOrder = 200;
RealD OuterTol = 1.0e-8;
int OuterMmax = 8;
int OuterNstep = 8;
void ParseEnvironment(void)
{
if(getenv("MASS")) mass = atof(getenv("MASS"));
if(getenv("NRHS")) Nrhs = atoi(getenv("NRHS"));
if(getenv("LS")) Ls = atoi(getenv("LS"));
if(getenv("COARSEN_BATCH")) CoarsenBatch= atoi(getenv("COARSEN_BATCH"));
if(getenv("FineSmootherShift")) FineSmootherShift = atof(getenv("FineSmootherShift"));
if(getenv("FineSmootherOrder")) FineSmootherOrder = atoi(getenv("FineSmootherOrder"));
if(getenv("CoarseSmootherShift"))CoarseSmootherShift= atof(getenv("CoarseSmootherShift"));
if(getenv("CoarseSmootherNstep"))CoarseSmootherNstep= atoi(getenv("CoarseSmootherNstep"));
if(getenv("CoarseSolverTol")) CoarseSolverTol = atof(getenv("CoarseSolverTol"));
if(getenv("CoarseSolverOrder")) CoarseSolverOrder = atoi(getenv("CoarseSolverOrder"));
if(getenv("OuterTol")) OuterTol = atof(getenv("OuterTol"));
if(getenv("OuterMmax")) OuterMmax = atoi(getenv("OuterMmax"));
if(getenv("OuterNstep")) OuterNstep = atoi(getenv("OuterNstep"));
if(getenv("LATT")){
Coordinate l;
GridCmdOptionIntVector(std::string(getenv("LATT")),l);
GRID_ASSERT(l.size()==4);
for(int d=0;d<4;d++) lat_size[d]=l[d];
}
std::cout << GridLogMessage << "PARAM: LATT "
<< lat_size[0]<<"."<<lat_size[1]<<"."<<lat_size[2]<<"."<<lat_size[3] << std::endl;
std::cout << GridLogMessage << "PARAM: LS " << Ls << std::endl;
std::cout << GridLogMessage << "PARAM: MASS " << mass << std::endl;
std::cout << GridLogMessage << "PARAM: NBASIS " << NBASIS << std::endl;
std::cout << GridLogMessage << "PARAM: NRHS " << Nrhs << std::endl;
std::cout << GridLogMessage << "PARAM: COARSEN_BATCH " << CoarsenBatch << std::endl;
}
template <class Field>
void saveSubspace(std::vector<Field> &subspace, std::string const fname){
#ifdef HAVE_LIME
Grid::emptyUserRecord record;
Grid::ScidacWriter SW(subspace[0].Grid()->IsBoss());
SW.open(fname);
for (int k = 0; k < (int)subspace.size(); k++) SW.writeScidacFieldRecord(subspace[k], record);
SW.close();
#endif
}
template <class Field>
void loadSubspace(std::vector<Field> &subspace, std::string const fname){
#ifdef HAVE_LIME
Grid::emptyUserRecord record;
Grid::ScidacReader SR;
SR.open(fname);
for (int k = 0; k < (int)subspace.size(); k++) SR.readScidacFieldRecord(subspace[k], record);
SR.close();
#endif
}
//////////////////////////////////////////////////////////////////////
// A = PV^dag M (non-Hermitian)
//////////////////////////////////////////////////////////////////////
template<class Matrix,class Field>
class PVdagMLinearOperator : public LinearOperatorBase<Field> {
Matrix &_Mat; Matrix &_PV;
public:
PVdagMLinearOperator(Matrix &Mat,Matrix &PV): _Mat(Mat),_PV(PV) {};
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 Op (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); }
void AdjOp (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(in,tmp); _Mat.Mdag(tmp,out); }
void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ HermOp(in,out); ComplexD d=innerProduct(in,out); n1=real(d); n2=norm2(out); }
void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
};
//////////////////////////////////////////////////////////////////////
// ||<v|v> - I||_F over a set of coarse vectors. Small means the raw near null
// content survived the projection; see GramGuard for where a leak lands.
//////////////////////////////////////////////////////////////////////
template<class CoarseField>
RealD GramDefect(std::vector<CoarseField> &v)
{
RealD s2=0.0;
for(int i=0;i<(int)v.size();i++){
for(int j=0;j<(int)v.size();j++){
ComplexD sij=TensorRemove(innerProduct(v[i],v[j]));
ComplexD d=sij-(i==j?ComplexD(1.0):ComplexD(0.0));
s2+=real(d)*real(d)+imag(d)*imag(d);
}
}
return std::sqrt(s2);
}
// On a leak every image collapses to the block unit e_k, the Gram becomes
// N*I, and the defect lands at (N-1)*sqrt(nbasis) -- orders above the ~0.2
// of a content preserving projection. Trip well below that so a mis-set
// threshold costs a log line rather than the run.
template<class CoarseField>
void GramGuard(const std::string &name,std::vector<CoarseField> &v,GridBase *grid)
{
RealD defect = GramDefect(v);
RealD N = (RealD)grid->gSites();
RealD leak = (N-1.0)*std::sqrt((RealD)v.size());
RealD trip = std::sqrt(N);
std::cout << GridLogMessage << "GUARD: ||<"<<name<<"|"<<name<<"> - I||_F = " << defect
<< " (e_k leak would be " << leak << ", trip at " << trip << ")" << std::endl;
GRID_ASSERT( defect < trip );
}
//////////////////////////////////////////////////////////////////////
// Shifted variants for the smoothers
//////////////////////////////////////////////////////////////////////
template<class Matrix,class Field>
class ShiftedPVdagMLinearOperator : public LinearOperatorBase<Field> {
Matrix &_Mat; Matrix &_PV;
public:
RealD shift;
ShiftedPVdagMLinearOperator(RealD _shift,Matrix &Mat,Matrix &PV): shift(_shift),_Mat(Mat),_PV(PV){};
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 Op (const Field &in, Field &out){ Field tmp(in.Grid()); _Mat.M(in,tmp); _PV.Mdag(tmp,out); out = out + shift*in; }
void AdjOp (const Field &in, Field &out){ Field tmp(in.Grid()); _PV.M(tmp,out); _Mat.Mdag(in,tmp); out = out + shift*in; }
void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
void HermOp(const Field &in, Field &out){ Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
};
template<class Field>
class ShiftedLinearOperator : public LinearOperatorBase<Field> {
LinearOperatorBase<Field> &_Op; RealD shift;
public:
ShiftedLinearOperator(RealD _shift, LinearOperatorBase<Field> &Op) : _Op(Op), shift(_shift) {}
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 Op (const Field &in, Field &out) { _Op.Op(in,out); out = out + shift*in; }
void AdjOp (const Field &in, Field &out) { _Op.AdjOp(in,out); out = out + shift*in; }
void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){ assert(0); }
void HermOp (const Field &in, Field &out) { Field tmp(in.Grid()); Op(in,tmp); AdjOp(tmp,out); }
};
//////////////////////////////////////////////////////////////////////
// Dense L3 solve on the packed D+1 coarse-coarse field
//////////////////////////////////////////////////////////////////////
template<class DenseType, class CoarseCoarseField>
class MrhsDenseCCSolve : public LinearFunction<CoarseCoarseField> {
public:
DenseType &_Dense;
int _nrhs;
MrhsDenseCCSolve(DenseType &D, int nrhs) : _Dense(D), _nrhs(nrhs) {}
using LinearFunction<CoarseCoarseField>::operator();
virtual void operator()(const CoarseCoarseField &in, CoarseCoarseField &out){
_Dense.ApplyBatch6D(in, out, _nrhs);
}
};
//////////////////////////////////////////////////////////////////////
// mrhs interfaces + single-polynomial mrhs PGCR
//////////////////////////////////////////////////////////////////////
template<class Field>
class MrhsLinearFunction {
public:
virtual void operator()(std::vector<Field> &in, std::vector<Field> &out) = 0;
};
template<class Field>
class MrhsPGCRNonHermitian {
public:
RealD Tolerance; Integer MaxIterations; int mmax,nstep,steps,level;
int ZeroGuess = 0; int FirstCycle = 0;
std::string name = "Level 1";
LinearOperatorBase<Field> &Linop;
MrhsLinearFunction<Field> &Preconditioner;
void Level(int lv){ name = "Level " + std::to_string(lv); level=lv; }
void Name(std::string n){ name = n; }
void SetZeroGuess(int z){ ZeroGuess=z; }
MrhsPGCRNonHermitian(RealD tol,Integer maxit,LinearOperatorBase<Field> &_Linop,MrhsLinearFunction<Field> &Prec,int _mmax,int _nstep)
: Tolerance(tol),MaxIterations(maxit),Linop(_Linop),Preconditioner(Prec),mmax(_mmax),nstep(_nstep){ level=1; }
static RealD vnorm2(std::vector<Field> &x){ RealD s=0; for(auto &f:x) s+=norm2(f); return s; }
static ComplexD vinnerProduct(std::vector<Field> &x,std::vector<Field> &y){ ComplexD s(0); for(int r=0;r<(int)x.size();r++) s+=innerProduct(x[r],y[r]); return s; }
static void vaxpy(std::vector<Field> &z,ComplexD a,std::vector<Field> &x,std::vector<Field> &y){ for(int r=0;r<(int)z.size();r++) axpy(z[r],a,x[r],y[r]); }
void vOp(std::vector<Field> &in,std::vector<Field> &out){ for(int r=0;r<(int)in.size();r++) Linop.Op(in[r],out[r]); }
void operator()(std::vector<Field> &src,std::vector<Field> &psi){
RealD cp,ssq,rsq; int nrhs=src.size(); GridBase *grid=src[0].Grid();
ssq=vnorm2(src); rsq=Tolerance*Tolerance*ssq;
std::vector<Field> r(nrhs,grid);
GridStopWatch T; T.Start(); steps=0; FirstCycle=1;
for(int k=0;k<MaxIterations;k++){
cp=GCRnStep(src,psi,rsq);
std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR("<<mmax<<","<<nstep<<") "<<steps<<" steps cp = "<<cp<<" target "<<rsq<<std::endl;
if(cp<rsq){
T.Stop(); vOp(psi,r); for(int rr=0;rr<nrhs;rr++) axpy(r[rr],-1.0,src[rr],r[rr]);
RealD tr=vnorm2(r);
std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR: Converged on iteration "<<steps
<<" computed residual "<<std::sqrt(cp/ssq)<<" true residual "<<std::sqrt(tr/ssq)<<" target "<<Tolerance<<std::endl;
std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR Time elapsed: Total "<<T.Elapsed()<<std::endl;
return;
}
}
std::cout<<GridLogMessage<<"MrhsPGCR: did not converge"<<std::endl;
}
RealD GCRnStep(std::vector<Field> &src,std::vector<Field> &psi,RealD rsq){
RealD cp; ComplexD a,b,rq; RealD zAAz; int nrhs=src.size(); GridBase *grid=src[0].Grid();
std::vector<Field> r(nrhs,grid),z(nrhs,grid),Az(nrhs,grid);
std::vector< std::vector<Field> > q(mmax,std::vector<Field>(nrhs,grid));
std::vector< std::vector<Field> > p(mmax,std::vector<Field>(nrhs,grid));
std::vector<RealD> qq(mmax);
if (ZeroGuess && FirstCycle) { for(int rr=0;rr<nrhs;rr++){ psi[rr]=Zero(); r[rr]=src[rr]; } }
else { vOp(psi,Az); for(int rr=0;rr<nrhs;rr++) r[rr]=src[rr]-Az[rr]; }
FirstCycle=0;
Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
p[0]=z; q[0]=Az; qq[0]=zAAz; cp=vnorm2(r);
for(int k=0;k<nstep;k++){
steps++; int kp=k+1, peri_k=k%mmax, peri_kp=kp%mmax;
rq=vinnerProduct(q[peri_k],r); a=rq/qq[peri_k];
vaxpy(psi,a,p[peri_k],psi); vaxpy(r,-a,q[peri_k],r); cp=vnorm2(r);
std::cout<<GridLogMessage<<std::string(level,'\t')<<" "<<name<<" MrhsPGCR step["<<steps<<"] resid "<<cp<<" target "<<rsq<<std::endl;
if((k==nstep-1)||(cp<rsq)) return cp;
Preconditioner(r,z); vOp(z,Az); zAAz=vnorm2(Az);
q[peri_kp]=Az; p[peri_kp]=z;
int northog=((kp)>(mmax-1))?(mmax-1):(kp);
for(int back=0;back<northog;back++){ int peri_back=(k-back)%mmax; GRID_ASSERT((k-back)>=0);
b=-real(vinnerProduct(q[peri_back],Az))/qq[peri_back];
vaxpy(p[peri_kp],b,p[peri_back],p[peri_kp]); vaxpy(q[peri_kp],b,q[peri_back],q[peri_kp]); }
qq[peri_kp]=vnorm2(q[peri_kp]);
}
GRID_ASSERT(0); return cp;
}
};
//////////////////////////////////////////////////////////////////////
// L2->L3 mrhs V-cycle on the D+1 coarse field
//////////////////////////////////////////////////////////////////////
template<class CoarseField, class CoarseCoarseField>
class MrhsCoarseThreeLevelPrec : public LinearFunction<CoarseField> {
public:
LinearOperatorBase<CoarseField> &_CoarseOp;
LinearFunction<CoarseField> &_CoarseSmoother;
MultiRHSBlockProject<CoarseField> &_Projector;
LinearFunction<CoarseCoarseField> &_CoarseCoarseSolve;
GridBase *_Coarse5d, *_CoarseCoarse5d, *_CoarseCoarseMrhs;
int _nrhs;
MrhsCoarseThreeLevelPrec(LinearOperatorBase<CoarseField> &CoarseOp,
LinearFunction<CoarseField> &CoarseSmoother,
MultiRHSBlockProject<CoarseField> &Projector,
LinearFunction<CoarseCoarseField> &CoarseCoarseSolve,
GridBase *Coarse5d, GridBase *CoarseCoarse5d, GridBase *CoarseCoarseMrhs, int nrhs)
: _CoarseOp(CoarseOp), _CoarseSmoother(CoarseSmoother), _Projector(Projector),
_CoarseCoarseSolve(CoarseCoarseSolve),
_Coarse5d(Coarse5d), _CoarseCoarse5d(CoarseCoarse5d), _CoarseCoarseMrhs(CoarseCoarseMrhs), _nrhs(nrhs) {}
using LinearFunction<CoarseField>::operator();
virtual void operator()(const CoarseField &in, CoarseField &out) {
int nrhs=_nrhs;
CoarseField vec1(in.Grid());
CoarseField vec2(in.Grid());
out = in;
_CoarseOp.Op(out,vec1); sub(vec1,in,vec1);
// restrict, through the mixed blockProject: D+1 coarse in, D+1 cc out
CoarseCoarseField CCsrc(_CoarseCoarseMrhs);
CoarseCoarseField CCsol(_CoarseCoarseMrhs);
_Projector.blockProject(vec1,CCsrc);
CCsol=Zero();
_CoarseCoarseSolve(CCsrc,CCsol);
_Projector.blockPromote(vec1,CCsol);
add(out,out,vec1);
_CoarseOp.Op(out,vec1); sub(vec1,in,vec1);
vec2=Zero();
_CoarseSmoother(vec1,vec2);
add(out,out,vec2);
}
};
//////////////////////////////////////////////////////////////////////
// L1->L2 mrhs V-cycle
//////////////////////////////////////////////////////////////////////
template<class FineField, class MrhsCoarseVector, class FineSmoother>
class MrhsTwoLevelMG : public MrhsLinearFunction<FineField> {
public:
typedef MrhsCoarseVector CoarseVector;
LinearOperatorBase<FineField> &_FineOperator;
FineSmoother &_PostSmoother;
MultiRHSBlockProject<FineField> &_Projector;
LinearFunction<CoarseVector> &_CoarseSolve;
GridBase *_CoarseGrid, *_CoarseGridMrhs;
MrhsTwoLevelMG(LinearOperatorBase<FineField> &FineOp, FineSmoother &Post,
MultiRHSBlockProject<FineField> &Projector, LinearFunction<CoarseVector> &CoarseSolve,
GridBase *CoarseGrid, GridBase *CoarseGridMrhs)
: _FineOperator(FineOp),_PostSmoother(Post),_Projector(Projector),_CoarseSolve(CoarseSolve),
_CoarseGrid(CoarseGrid),_CoarseGridMrhs(CoarseGridMrhs){}
virtual void operator()(std::vector<FineField> &in, std::vector<FineField> &out){
int nrhs=in.size(); GridBase *fgrid=in[0].Grid();
std::vector<FineField> vec1(nrhs,fgrid),vec2(nrhs,fgrid);
for(int r=0;r<nrhs;r++) out[r]=in[r];
for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
// fine vector -> D+1 coarse, via the mixed blockProject
CoarseVector CsrcMrhs(_CoarseGridMrhs), CsolMrhs(_CoarseGridMrhs);
_Projector.blockProject(vec1,CsrcMrhs);
CsolMrhs=Zero();
_CoarseSolve(CsrcMrhs,CsolMrhs);
_Projector.blockPromote(vec1,CsolMrhs);
for(int r=0;r<nrhs;r++) add(out[r],out[r],vec1[r]);
for(int r=0;r<nrhs;r++){ _FineOperator.Op(out[r],vec1[r]); sub(vec1[r],in[r],vec1[r]); }
for(int r=0;r<nrhs;r++){ vec2[r]=Zero(); _PostSmoother(vec1[r],vec2[r]); add(out[r],out[r],vec2[r]); }
}
};
int main (int argc, char ** argv)
{
Grid_init(&argc,&argv);
ParseEnvironment();
RealD M5=1.8, b=1.5, c=0.5;
const int nbasis=NBASIS;
const int nrhs=Nrhs;
const int batch=CoarsenBatch;
Coordinate mpi = GridDefaultMpi();
Coordinate fsimd= GridDefaultSimd(Nd,vComplex::Nsimd());
GridCartesian * UGrid = SpaceTimeGrid::makeFourDimGrid(lat_size,fsimd,mpi);
GridRedBlackCartesian * UrbGrid = SpaceTimeGrid::makeFourDimRedBlackGrid(UGrid);
GridCartesian * FGrid = SpaceTimeGrid::makeFiveDimGrid(Ls,UGrid);
GridRedBlackCartesian * FrbGrid = SpaceTimeGrid::makeFiveDimRedBlackGrid(Ls,UGrid);
// Level 1 blocking (default 2^4)
Coordinate clatt = lat_size;
Coordinate Block({2,2,2,2});
if ( getenv("BLOCK") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK")),Block); GRID_ASSERT(Block.size()==4); }
for(int d=0;d<4;d++){ GRID_ASSERT(lat_size[d]%Block[d]==0); clatt[d]=lat_size[d]/Block[d]; }
std::cout << GridLogMessage << "Block " << Block << " coarse lattice " << clatt << std::endl;
//////////////////////////////////////////////////////////////////////
// The coarse space is unvectorised. The 5D coarse grid is built here
// rather than through SpaceTimeGrid so the SIMD layout is ours.
//////////////////////////////////////////////////////////////////////
Coordinate c5latt({1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate c5simd({1,1,1,1,1});
Coordinate c5mpi ({1,mpi[0],mpi[1],mpi[2],mpi[3]});
GridCartesian *Coarse5d = new GridCartesian(c5latt,c5simd,c5mpi);
// 6D coarse multiRHS grid: rhs is dim 0, undistributed and unvectorised.
// No divisibility constraint on nrhs, unlike V1.
Coordinate cmlatt({nrhs,1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate cmsimd({1,1,1,1,1,1});
Coordinate cmmpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
GridCartesian *CoarseMrhs = new GridCartesian(cmlatt,cmsimd,cmmpi);
// 6D coarse grid at the coarsening batch, used only while CoarsenOperator
// runs. The matrix elements survive the change back to nrhs.
Coordinate cblatt({batch,1,clatt[0],clatt[1],clatt[2],clatt[3]});
GridCartesian *CoarseBatch = new GridCartesian(cblatt,cmsimd,cmmpi);
// 6D fine grid carrying the coarsening batch: fine SIMD layout preserved
Coordinate fmlatt({batch,Ls,lat_size[0],lat_size[1],lat_size[2],lat_size[3]});
Coordinate fmsimd({1,1,fsimd[0],fsimd[1],fsimd[2],fsimd[3]});
Coordinate fmmpi ({1,1,mpi[0],mpi[1],mpi[2],mpi[3]});
GridCartesian *FineMrhs = new GridCartesian(fmlatt,fmsimd,fmmpi);
std::cout << GridLogMessage << "Nsimd fine " << FGrid->Nsimd()
<< " coarse " << Coarse5d->Nsimd() << std::endl;
GridParallelRNG RNG4(UGrid); RNG4.SeedFixedIntegers({1,2,3,4});
GridParallelRNG RNG5(FGrid); RNG5.SeedFixedIntegers({5,6,7,8});
//////////////////////////////////////////////////////////////////////
// Gauge field
//////////////////////////////////////////////////////////////////////
LatticeGaugeField Umu(UGrid);
if ( getenv("HOT_START") ) {
std::cout << GridLogMessage << "Hot start gauge field" << std::endl;
SU<Nc>::HotConfiguration(RNG4,Umu);
} else {
std::string file("/ccs/home/poare/ckpoint_lat.1000");
if ( getenv("CONFIG") ) file = std::string(getenv("CONFIG"));
std::cout << GridLogMessage << "Reading gauge field " << file << std::endl;
FieldMetaData header;
NerscIO::readConfiguration(Umu,header,file);
}
MobiusFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5,b,c);
MobiusFermionD Dpv (Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0, M5,b,c);
typedef PVdagMLinearOperator<MobiusFermionD,LatticeFermionD> PVdagM_t;
typedef ShiftedPVdagMLinearOperator<MobiusFermionD,LatticeFermionD> ShiftedPVdagM_t;
PVdagM_t PVdagM(Ddwf,Dpv);
//////////////////////////////////////////////////////////////////////
// Level 1 types: unvectorised coarse scalar
//////////////////////////////////////////////////////////////////////
typedef sTComplexD CComplexS;
typedef MultiGeneralCoarsenedOperatorV2<vSpinColourVector,CComplexS,nbasis> CoarseOperator;
typedef CoarseOperator::CoarseVector CoarseVector;
typedef Aggregation<vSpinColourVector,CComplexS,nbasis> Subspace;
NextToNearestStencilGeometry5D geom(Coarse5d);
//////////////////////////////////////////////////////////////////////
// Subspace: load RAW (no Orthogonalise!), or generate.
//
// The Aggregation is scaffolding for CreateSubspaceGCR only. That runs
// entirely on the fine grid and ends in GlobalOrthonormalise, which is a
// whole-lattice Gram-Schmidt, so the coarse grid it holds is never
// dereferenced and may be the unvectorised one.
//////////////////////////////////////////////////////////////////////
std::string subspace_file = "subspace_nb" + std::to_string(nbasis) + ".scidac";
if ( getenv("SUBSPACE_FILE") ) subspace_file = std::string(getenv("SUBSPACE_FILE"));
uint64_t file_exists=0;
if ( UGrid->IsBoss() ){ std::ifstream f(subspace_file); file_exists=f.good()?1:0; }
UGrid->GlobalSum(file_exists);
const int cb=0;
Subspace AggregatesGCR(Coarse5d,FGrid,cb);
if ( file_exists ){
std::cout << GridLogMessage << "*** Loading subspace from disk (kept RAW) ***" << std::endl;
loadSubspace(AggregatesGCR.subspace, subspace_file);
} else {
std::cout << GridLogMessage << "*** GCR subspace generation ***" << std::endl;
AggregatesGCR.CreateSubspaceGCR(RNG5,PVdagM,nbasis);
saveSubspace(AggregatesGCR.subspace, subspace_file);
}
// RAW copy BEFORE CoarsenOperator block-orthonormalises in place.
std::vector<LatticeFermionD> rawNull(nbasis,FGrid);
for(int k=0;k<nbasis;k++) rawNull[k]=AggregatesGCR.subspace[k];
//////////////////////////////////////////////////////////////////////
// L1 coarsening. The fine operator is single RHS, so it is promoted to
// the 6D batch grid; a natively multiRHS fine operator would substitute
// here with no other change.
//////////////////////////////////////////////////////////////////////
CoarseOperator CoarseOpPV(geom,Coarse5d);
CoarseOpPV.SetGrid(CoarseBatch);
std::cout << GridLogMessage << "*** L1 CoarsenOperator, batch "<<batch<<" ***" << std::endl;
if ( getenv("MRHS_COARSEN") ) {
// Promote the single RHS operator and pack the batch: costs an
// ExtractSlice/InsertSlice pair per rhs. Here for the A/B only; this is
// the path a natively multiRHS fine operator would take.
MrhsPromotedOperator<LatticeFermionD> MrhsPVdagM(PVdagM,FGrid,batch);
CoarseOpPV.CoarsenOperator(MrhsPVdagM,FineMrhs,AggregatesGCR.subspace,Coarse5d);
} else {
// PVdagM is single RHS: apply it directly, batch on the coarse side.
CoarseOpPV.CoarsenOperator(PVdagM,AggregatesGCR.subspace,Coarse5d,batch);
}
// Stay on the batch grid: the L2 coarsening drives this operator at the
// batch. It is switched to the solve Nrhs once L2 is built.
//////////////////////////////////////////////////////////////////////
// psi_coarse = P^dag (RAW fine null) -> Galerkin images that carry the
// near null content, and are free: A_c (P psi) = P A psi.
//////////////////////////////////////////////////////////////////////
MultiRHSBlockProject<LatticeFermionD> MrhsProjector;
MrhsProjector.Allocate(nbasis,FGrid,Coarse5d);
MrhsProjector.ImportBasis(AggregatesGCR.subspace); // block orthonormal basis
std::vector<CoarseVector> psi_coarse(nbasis,Coarse5d);
MrhsProjector.blockProject(rawNull,psi_coarse); // RAW vectors in
rawNull.clear(); rawNull.shrink_to_fit();
GramGuard("psi_coarse",psi_coarse,Coarse5d);
//////////////////////////////////////////////////////////////////////
// Optional cross check of the coarse matrix elements against the V1
// path, which needs a vectorised coarse space. Block Gram-Schmidt is
// idempotent, so V1 may re-orthonormalise the same vectors in place
// without a second copy of the subspace.
//////////////////////////////////////////////////////////////////////
if ( getenv("V1_CHECK") ) {
typedef GeneralCoarsenedMatrix <vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
typedef MultiGeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> MrhsLittleDiracOperator;
typedef Aggregation <vSpinColourVector,vTComplex,nbasis> SubspaceV;
Coordinate v5latt({1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate v5simd({1,fsimd[0],fsimd[1],fsimd[2],fsimd[3]});
GridCartesian *Coarse5dV = new GridCartesian(v5latt,v5simd,c5mpi);
int nrhs_v1 = vComplex::Nsimd();
Coordinate vmlatt({nrhs_v1,1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate vmsimd({vComplex::Nsimd(),1,1,1,1,1});
GridCartesian *CoarseMrhsV = new GridCartesian(vmlatt,vmsimd,cmmpi);
NextToNearestStencilGeometry5D geomV(Coarse5dV);
SubspaceV AggV(Coarse5dV,FGrid,cb);
for(int k=0;k<nbasis;k++) AggV.subspace[k]=AggregatesGCR.subspace[k];
LittleDiracOperator LittleDiracOpPV(geomV,FGrid,Coarse5dV);
std::cout << GridLogMessage << "*** V1 CoarsenOperator (cross check) ***" << std::endl;
LittleDiracOpPV.CoarsenOperator(PVdagM,AggV);
MrhsLittleDiracOperator mrhsV1(geomV,CoarseMrhsV);
mrhsV1.CopyMatrix(LittleDiracOpPV);
// BLAS_A is written by GridtoBLAS in lSite order and both sides carry
// the same scalar_object, so the two are directly comparable.
typedef MrhsLittleDiracOperator::calcMatrix calcMatrix;
int npoint = geom.npoint;
RealD num=0.0, den=0.0;
for(int p=0;p<npoint;p++){
int64_t sites = mrhsV1.BLAS_A[p].size();
GRID_ASSERT(sites == (int64_t)CoarseOpPV.BLAS_A[p].size());
std::vector<calcMatrix> h1(sites),h2(sites);
acceleratorCopyFromDevice(&mrhsV1.BLAS_A[p][0], &h1[0],sites*sizeof(calcMatrix));
acceleratorCopyFromDevice(&CoarseOpPV.BLAS_A[p][0],&h2[0],sites*sizeof(calcMatrix));
ComplexD *w1=(ComplexD *)&h1[0];
ComplexD *w2=(ComplexD *)&h2[0];
int64_t words = sites*sizeof(calcMatrix)/sizeof(ComplexD);
for(int64_t i=0;i<words;i++){
ComplexD d=w1[i]-w2[i];
num += real(d)*real(d)+imag(d)*imag(d);
den += real(w1[i])*real(w1[i])+imag(w1[i])*imag(w1[i]);
}
}
std::cout << GridLogMessage << "V1_CHECK: |A_V1|^2 = " << den << std::endl;
std::cout << GridLogMessage << "V1_CHECK: |A_V1 - A_V2|^2 / |A_V1|^2 = " << num/den << std::endl;
GRID_ASSERT( den > 0.0 );
GRID_ASSERT( num/den < 1.0e-18 );
}
//////////////////////////////////////////////////////////////////////
// STAGE TWO: L2 -> L3.
//
// The fine operator here is V2 at L1, which is natively multiRHS, so the
// multiRHS driver applies with no promotion adapter: its D+1 grid IS the
// batch grid the L1 operator is currently set to.
//////////////////////////////////////////////////////////////////////
Coordinate cclatt = clatt;
Coordinate Block2({8,4,3,6});
if ( getenv("BLOCK2") ){ GridCmdOptionIntVector(std::string(getenv("BLOCK2")),Block2); GRID_ASSERT(Block2.size()==4); }
for(int d=0;d<4;d++){ GRID_ASSERT(clatt[d]%Block2[d]==0); cclatt[d]=clatt[d]/Block2[d]; }
std::cout << GridLogMessage << "Block2 " << Block2 << " coarse-coarse lattice " << cclatt << std::endl;
Coordinate cc5latt({1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
GridCartesian *CoarseCoarse5d = new GridCartesian(cc5latt,c5simd,c5mpi);
Coordinate ccmlatt({nrhs,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
GridCartesian *CoarseCoarseMrhs = new GridCartesian(ccmlatt,cmsimd,cmmpi);
Coordinate ccblatt({batch,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
GridCartesian *CoarseCoarseBatch = new GridCartesian(ccblatt,cmsimd,cmmpi);
// Coarsening deepens the tensor nest by one iScalar
typedef CoarseVector::vector_object CoarseSiteObj;
typedef iScalar<CComplexS> CComplexS2;
typedef MultiGeneralCoarsenedOperatorV2<CoarseSiteObj,CComplexS2,nbasis> CoarseCoarseOperator;
typedef CoarseCoarseOperator::CoarseVector CoarseCoarseVector;
NextToNearestStencilGeometry5D geom2(CoarseCoarse5d);
// RAW copy of the coarse null vectors, for the same reason as rawNull:
// the L2 CoarsenOperator block-orthonormalises its subspace in place, and
// the L3 basis must be defined by the vectors that still carry content.
std::vector<CoarseVector> rawPsi(nbasis,Coarse5d);
for(int k=0;k<nbasis;k++) rawPsi[k]=psi_coarse[k];
CoarseCoarseOperator CoarseOpL2(geom2,CoarseCoarse5d);
CoarseOpL2.SetGrid(CoarseCoarseBatch);
NonHermitianLinearOperator<CoarseOperator,CoarseVector> LinOpCoarse(CoarseOpPV);
std::cout << GridLogMessage << "*** L2 CoarsenOperator, batch "<<batch<<" ***" << std::endl;
CoarseOpL2.CoarsenOperator(LinOpCoarse,CoarseBatch,psi_coarse,CoarseCoarse5d);
//////////////////////////////////////////////////////////////////////
// Both operators to the solve Nrhs. The matrix elements are Nrhs
// independent and survive the change.
//////////////////////////////////////////////////////////////////////
CoarseOpPV.SetGrid(CoarseMrhs);
CoarseOpL2.SetGrid(CoarseCoarseMrhs);
std::cout << GridLogMessage << "L1 operator at Nrhs " << CoarseOpPV.Nrhs()
<< ", L2 operator at Nrhs " << CoarseOpL2.Nrhs() << std::endl;
//////////////////////////////////////////////////////////////////////
// psi_cc from the RAW coarse null vectors, and the same guard
//////////////////////////////////////////////////////////////////////
MultiRHSBlockProject<CoarseVector> MrhsProjectorL2;
MrhsProjectorL2.Allocate(nbasis,Coarse5d,CoarseCoarse5d);
MrhsProjectorL2.ImportBasis(psi_coarse); // block orthonormal basis
{
std::vector<CoarseCoarseVector> psi_cc(nbasis,CoarseCoarse5d);
MrhsProjectorL2.blockProject(rawPsi,psi_cc); // RAW vectors in
GramGuard("psi_cc",psi_cc,CoarseCoarse5d);
}
rawPsi.clear(); rawPsi.shrink_to_fit();
//////////////////////////////////////////////////////////////////////
// Both coarse operators apply on their solve grids
//////////////////////////////////////////////////////////////////////
{
GridParallelRNG cRNG(Coarse5d); cRNG.SeedFixedIntegers({3,4,5,6});
CoarseVector cin(CoarseMrhs), cout_(CoarseMrhs);
random(cRNG,cin);
CoarseOpPV.M(cin,cout_);
std::cout << GridLogMessage << "L1 apply |in|^2 = " << norm2(cin)
<< " |M in|^2 = " << norm2(cout_) << std::endl;
GRID_ASSERT( norm2(cout_) > 0.0 );
GridParallelRNG ccRNG(CoarseCoarse5d); ccRNG.SeedFixedIntegers({7,8,9,10});
CoarseCoarseVector ccin(CoarseCoarseMrhs), ccout(CoarseCoarseMrhs);
random(ccRNG,ccin);
CoarseOpL2.M(ccin,ccout);
std::cout << GridLogMessage << "L2 apply |in|^2 = " << norm2(ccin)
<< " |M in|^2 = " << norm2(ccout) << std::endl;
GRID_ASSERT( norm2(ccout) > 0.0 );
}
//////////////////////////////////////////////////////////////////////
// STAGE THREE (part one): the dense bottom on L2.
//
// DenseCoarseMatrix is bilingual: it takes the elements through
// Geometry()/ExtractMatrix(), so the V2 operator serves directly. It does
// detect that a multiRHS op cannot apply on the D dimensional grid and
// skips its own certificate and VERIFY, so the equivalent check is done
// here instead, driving the L2 operator at Nrhs 1 through a slice.
//////////////////////////////////////////////////////////////////////
typedef DenseCoarseMatrix<CComplexS2,nbasis> DenseCC_t;
std::unique_ptr<DenseCC_t> DenseCC;
if ( getenv("DENSE_CC")==nullptr || atoi(getenv("DENSE_CC")) ) {
std::cout << GridLogMessage << "*** L3 dense bottom: import from the V2 L2 operator ***" << std::endl;
DenseCC.reset(new DenseCC_t(CoarseCoarse5d));
DenseCC->Import(CoarseOpL2);
////////////////////////////////////////////////////////////////////
// ||A Ainv x - x|| / ||x||, the check Import could not run itself
////////////////////////////////////////////////////////////////////
Coordinate cc1latt({1,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
GridCartesian *CoarseCoarseOne = new GridCartesian(cc1latt,cmsimd,cmmpi);
CoarseOpL2.SetGrid(CoarseCoarseOne);
CoarseCoarseVector x(CoarseCoarse5d),y(CoarseCoarse5d),z(CoarseCoarse5d);
GridParallelRNG dRNG(CoarseCoarse5d); dRNG.SeedFixedIntegers({11,12,13,14});
random(dRNG,x);
(*DenseCC)(x,y); // y = Ainv x
CoarseCoarseVector y1(CoarseCoarseOne),z1(CoarseCoarseOne);
InsertSliceFast(y,y1,0,0);
CoarseOpL2.M(y1,z1); // z = A y
ExtractSliceFast(z,z1,0,0);
z = z - x;
RealD rel = std::sqrt(norm2(z)/norm2(x));
std::cout << GridLogMessage << "L3 dense: ||A Ainv x - x||/||x|| = " << rel << std::endl;
GRID_ASSERT( rel < 1.0e-2 );
CoarseOpL2.SetGrid(CoarseCoarseMrhs);
delete CoarseCoarseOne;
}
//////////////////////////////////////////////////////////////////////
// STAGE THREE (part two): the solves.
//
// Both operators are driven from the SAME objects at whatever Nrhs is
// asked for -- the matrix elements were built once and survive SetGrid --
// so single RHS and multiRHS are the same code path with a different grid.
//////////////////////////////////////////////////////////////////////
GRID_ASSERT(DenseCC != nullptr); // the PGCR bottom is not ported yet
typedef PrecGeneralisedConjugateResidualNonHermitian<LatticeFermionD> FineSmoother_t;
ShiftedPVdagM_t ShiftedPVdagM(FineSmootherShift,Ddwf,Dpv);
TrivialPrecon<LatticeFermionD> simple_fine;
TrivialPrecon<CoarseVector> simpleC;
auto RunSolve = [&](int nr)
{
std::cout << GridLogMessage << "**********************************************" << std::endl;
std::cout << GridLogMessage << " V2 THREE-level solve, Nrhs = " << nr << std::endl;
std::cout << GridLogMessage << "**********************************************" << std::endl;
Coordinate cml({nr,1,clatt[0],clatt[1],clatt[2],clatt[3]});
Coordinate ccml({nr,1,cclatt[0],cclatt[1],cclatt[2],cclatt[3]});
GridCartesian *CMrhs = new GridCartesian(cml, cmsimd,cmmpi);
GridCartesian *CCMrhs = new GridCartesian(ccml,cmsimd,cmmpi);
CoarseOpPV.SetGrid(CMrhs);
CoarseOpL2.SetGrid(CCMrhs);
NonHermitianLinearOperator<CoarseOperator,CoarseVector> LinOpC (CoarseOpPV);
NonHermitianLinearOperator<CoarseCoarseOperator,CoarseCoarseVector> LinOpCC(CoarseOpL2);
MrhsDenseCCSolve<DenseCC_t,CoarseCoarseVector> ccSolve(*DenseCC,nr);
ShiftedLinearOperator<CoarseVector> ShiftedC(CoarseSmootherShift, LinOpC);
PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
CoarseSmootherGCR(0.01,1,ShiftedC,simpleC,CoarseSmootherNstep,CoarseSmootherNstep);
CoarseSmootherGCR.Level(2); CoarseSmootherGCR.Name("Csmoother"); CoarseSmootherGCR.SetZeroGuess(1);
MrhsCoarseThreeLevelPrec<CoarseVector,CoarseCoarseVector>
L2to3Precon(LinOpC, CoarseSmootherGCR, MrhsProjectorL2, ccSolve,
Coarse5d, CoarseCoarse5d, CCMrhs, nr);
PrecGeneralisedConjugateResidualNonHermitian<CoarseVector>
L2PGCR(CoarseSolverTol, CoarseSolverOrder/16, LinOpC, L2to3Precon, 16, 16);
L2PGCR.Level(2); L2PGCR.Name("Couter"); L2PGCR.SetZeroGuess(1);
FineSmoother_t SmootherGCR(0.0,1,ShiftedPVdagM,simple_fine,FineSmootherOrder,FineSmootherOrder);
SmootherGCR.Level(1); SmootherGCR.Name("Fsmoother"); SmootherGCR.SetZeroGuess(1);
MrhsTwoLevelMG<LatticeFermionD,CoarseVector,FineSmoother_t>
ThreeLevelPrecon(PVdagM, SmootherGCR, MrhsProjector, L2PGCR, Coarse5d, CMrhs);
MrhsPGCRNonHermitian<LatticeFermionD>
L1PGCR(OuterTol,1000,PVdagM,ThreeLevelPrecon,OuterMmax,OuterNstep);
L1PGCR.Level(1); L1PGCR.Name("Fouter"); L1PGCR.SetZeroGuess(1);
std::vector<LatticeFermionD> src(nr,FGrid), sol(nr,FGrid);
for(int r=0;r<nr;r++){ gaussian(RNG5,src[r]); sol[r]=Zero(); }
GridStopWatch w; w.Start();
L1PGCR(src,sol);
w.Stop();
std::cout << GridLogMessage << "V2 3-level solve Nrhs "<<nr<<" total " << w.Elapsed()
<< " (per RHS: " << w.useconds()/1.0e6/nr << " s)" << std::endl;
{ LatticeFermionD Ax(FGrid); RealD worst=0.0;
for(int r=0;r<nr;r++){ PVdagM.Op(sol[r],Ax); Ax=Ax-src[r];
RealD rn=std::sqrt(norm2(Ax)/norm2(src[r]));
std::cout << GridLogMessage << "FINAL Nrhs "<<nr<<": rhs["<<r<<"] true residual = " << rn << std::endl;
worst=std::max(worst,rn); }
std::cout << GridLogMessage << "FINAL Nrhs "<<nr<<": worst-case residual = " << worst << std::endl;
}
// The operators borrow these grids and build a PaddedCell on them, so
// they must let go before the grids are destroyed.
CoarseOpPV.ReleaseGrid();
CoarseOpL2.ReleaseGrid();
delete CMrhs; delete CCMrhs;
};
RunSolve(nrhs);
if ( getenv("SOLVE_SRHS")==nullptr || atoi(getenv("SOLVE_SRHS")) ) RunSolve(1);
std::cout << GridLogMessage << "*** stage three complete: solves done ***" << std::endl;
Grid_finalize();
}
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