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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.
//
// STAGE ONE: grids, types, subspace, and the L1 coarsening only. The L2
// chain, 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 COARSEN_BATCH
// HOT_START CONFIG SUBSPACE_FILE V1_CHECK
//
#include <Grid/Grid.h>
#include <Grid/lattice/PaddedCell.h>
#include <Grid/stencil/GeneralLocalStencil.h>
#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.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});
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("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. ~0.23 means the raw near
// null content survived the projection; ~sqrt(N_sites) means block
// orthonormal vectors leaked in and every image collapsed to e_k.
//////////////////////////////////////////////////////////////////////
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);
}
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;
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();
{
RealD defect = GramDefect(psi_coarse);
RealD leak = std::sqrt((double)Coarse5d->gSites());
std::cout << GridLogMessage << "GUARD: ||<psi_coarse|psi_coarse> - I||_F = " << defect
<< " (~0.23 good; ~sqrt(N_coarse)=" << leak << " = e_k leak)" << std::endl;
GRID_ASSERT( defect < leak );
}
//////////////////////////////////////////////////////////////////////
// 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
RealD defect = GramDefect(psi_cc);
RealD leak = std::sqrt((double)CoarseCoarse5d->gSites());
std::cout << GridLogMessage << "GUARD: ||<psi_cc|psi_cc> - I||_F = " << defect
<< " (~0.23 good; ~sqrt(N_cc)=" << leak << " = e_k leak)" << std::endl;
GRID_ASSERT( defect < leak );
}
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 );
}
std::cout << GridLogMessage << "*** stage two complete: L1 and L2 coarse operators built ***" << std::endl;
Grid_finalize();
}
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