GeneralCoarsenedMatrix.h

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/*************************************************************************************
 
    Grid physics library, www.github.com/paboyle/Grid 
 
    Source file: ./lib/algorithms/GeneralCoarsenedMatrix.h
 
    Copyright (C) 2015
 
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 */
#pragma once
 
#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
 
#include <Grid/lattice/PaddedCell.h>
#include <Grid/stencil/GeneralLocalStencil.h>
 
NAMESPACE_BEGIN(Grid);
 
// Fine Object == (per site) type of fine field
// nbasis      == number of deflation vectors
template<class Fobj,class CComplex,int nbasis>
class GeneralCoarsenedMatrix : public SparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
public:
 
  typedef GeneralCoarsenedMatrix<Fobj,CComplex,nbasis> GeneralCoarseOp;
  typedef iVector<CComplex,nbasis >           siteVector;
  typedef iMatrix<CComplex,nbasis >           siteMatrix;
  typedef Lattice<iScalar<CComplex> >         CoarseComplexField;
  typedef Lattice<siteVector>                 CoarseVector;
  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
  typedef iMatrix<CComplex,nbasis >  Cobj;
  typedef iVector<CComplex,nbasis >  Cvec;
  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
  typedef Lattice<Fobj >        FineField;
  typedef Lattice<CComplex >    FineComplexField;
  typedef CoarseVector Field;
  // Data members
  int hermitian;
  GridBase      *       _FineGrid; 
  GridCartesian *       _CoarseGrid; 
  NonLocalStencilGeometry &geom;
  PaddedCell Cell;
  GeneralLocalStencil Stencil;
  
  std::vector<CoarseMatrix> _A;
  std::vector<CoarseMatrix> _Adag;
  std::vector<CoarseVector> MultTemporaries;

  // Interface
  GridBase      * Grid(void)           { return _CoarseGrid; };   // this is all the linalg routines need to know
  GridBase      * FineGrid(void)       { return _FineGrid; };   // this is all the linalg routines need to know
  GridCartesian * CoarseGrid(void)     { return _CoarseGrid; };   // this is all the linalg routines need to know
 
  /*  void ShiftMatrix(RealD shift)
  {
    int Nd=_FineGrid->Nd(); 
    Coordinate zero_shift(Nd,0);
    for(int p=0;p<geom.npoint;p++){
      if ( zero_shift==geom.shifts[p] ) {
    _A[p] = _A[p]+shift;
    //  _Adag[p] = _Adag[p]+shift;
      }
    }    
  }
  void ProjectNearestNeighbour(RealD shift, GeneralCoarseOp &CopyMe)
  {
    int nfound=0;
    std::cout << GridLogMessage <<"GeneralCoarsenedMatrix::ProjectNearestNeighbour "<< CopyMe._A[0].Grid()<<std::endl;
    for(int p=0;p<geom.npoint;p++){
      for(int pp=0;pp<CopyMe.geom.npoint;pp++){
    // Search for the same relative shift
    // Avoids brutal handling of Grid pointers
    if ( CopyMe.geom.shifts[pp]==geom.shifts[p] ) {
      _A[p] = CopyMe.Cell.Extract(CopyMe._A[pp]);
      //      _Adag[p] = CopyMe.Cell.Extract(CopyMe._Adag[pp]);
      nfound++;
    }
      }
    }
    assert(nfound==geom.npoint);
    ExchangeCoarseLinks();
  }
  */
  
  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridBase *FineGrid, GridCartesian * CoarseGrid)
    : geom(_geom),
      _FineGrid(FineGrid),
      _CoarseGrid(CoarseGrid),
      hermitian(1),
      Cell(_geom.Depth(),_CoarseGrid),
      Stencil(Cell.grids.back(),geom.shifts)
  {
    {
      int npoint = _geom.npoint;
    }
    _A.resize(geom.npoint,CoarseGrid);
    //    _Adag.resize(geom.npoint,CoarseGrid);
  }
  void M (const CoarseVector &in, CoarseVector &out)
  {
    Mult(_A,in,out);
  }
  void Mdag (const CoarseVector &in, CoarseVector &out)
  {
    assert(hermitian);
    Mult(_A,in,out);
    //    if ( hermitian ) M(in,out);
    //    else Mult(_Adag,in,out);
  }
  void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
  {
    RealD tviews=0;    RealD ttot=0;    RealD tmult=0;   RealD texch=0;    RealD text=0; RealD ttemps=0; RealD tcopy=0;
    RealD tmult2=0;
 
    ttot=-usecond();
    conformable(CoarseGrid(),in.Grid());
    conformable(in.Grid(),out.Grid());
    out.Checkerboard() = in.Checkerboard();
    CoarseVector tin=in;
 
    texch-=usecond();
    CoarseVector pin = Cell.ExchangePeriodic(tin);
    texch+=usecond();
 
    CoarseVector pout(pin.Grid());
 
    int npoint = geom.npoint;
    typedef LatticeView<Cobj> Aview;
    typedef LatticeView<Cvec> Vview;
      
    const int Nsimd = CComplex::Nsimd();
    
    int64_t osites=pin.Grid()->oSites();
 
    RealD flops = 1.0* npoint * nbasis * nbasis * 8.0 * osites * CComplex::Nsimd();
    RealD bytes = 1.0*osites*sizeof(siteMatrix)*npoint
                + 2.0*osites*sizeof(siteVector)*npoint;
      
    {
      tviews-=usecond();
      autoView( in_v , pin, AcceleratorRead);
      autoView( out_v , pout, AcceleratorWriteDiscard);
      autoView( Stencil_v  , Stencil, AcceleratorRead);
      tviews+=usecond();
 
      // Static and prereserve to keep UVM region live and not resized across multiple calls
      ttemps-=usecond();
      MultTemporaries.resize(npoint,pin.Grid());       
      ttemps+=usecond();
      std::vector<Aview> AcceleratorViewContainer_h;
      std::vector<Vview> AcceleratorVecViewContainer_h; 
 
      tviews-=usecond();
      for(int p=0;p<npoint;p++) {
    AcceleratorViewContainer_h.push_back(      A[p].View(AcceleratorRead));
    AcceleratorVecViewContainer_h.push_back(MultTemporaries[p].View(AcceleratorWrite));
      }
      tviews+=usecond();
 
      static deviceVector<Aview> AcceleratorViewContainer; AcceleratorViewContainer.resize(npoint);
      static deviceVector<Vview> AcceleratorVecViewContainer; AcceleratorVecViewContainer.resize(npoint); 
      
      auto Aview_p = &AcceleratorViewContainer[0];
      auto Vview_p = &AcceleratorVecViewContainer[0];
      tcopy-=usecond();
      acceleratorCopyToDevice(&AcceleratorViewContainer_h[0],&AcceleratorViewContainer[0],npoint *sizeof(Aview));
      acceleratorCopyToDevice(&AcceleratorVecViewContainer_h[0],&AcceleratorVecViewContainer[0],npoint *sizeof(Vview));
      tcopy+=usecond();
 
      tmult-=usecond();
      accelerator_for(spb, osites*nbasis*npoint, Nsimd, {
      typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
      int32_t ss   = spb/(nbasis*npoint);
      int32_t bp   = spb%(nbasis*npoint);
      int32_t point= bp/nbasis;
      int32_t b    = bp%nbasis;
      auto SE  = Stencil_v.GetEntry(point,ss);
      auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
      auto res = coalescedRead(Aview_p[point][ss](0,b))*nbr(0);
      for(int bb=1;bb<nbasis;bb++) {
        res = res + coalescedRead(Aview_p[point][ss](bb,b))*nbr(bb);
      }
      coalescedWrite(Vview_p[point][ss](b),res);
      });
      tmult2-=usecond();
      accelerator_for(sb, osites*nbasis, Nsimd, {
      int ss = sb/nbasis;
      int b  = sb%nbasis;
      auto res = coalescedRead(Vview_p[0][ss](b));
      for(int point=1;point<npoint;point++){
        res = res + coalescedRead(Vview_p[point][ss](b));
      }
      coalescedWrite(out_v[ss](b),res);
      });
      tmult2+=usecond();
      tmult+=usecond();
      for(int p=0;p<npoint;p++) {
    AcceleratorViewContainer_h[p].ViewClose();
    AcceleratorVecViewContainer_h[p].ViewClose();
      }
    }
 
    text-=usecond();
    out = Cell.Extract(pout);
    text+=usecond();
    ttot+=usecond();
    
    std::cout << GridLogPerformance<<"Coarse 1rhs Mult Aviews "<<tviews<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult exch "<<texch<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult mult "<<tmult<<" us"<<std::endl;
    std::cout << GridLogPerformance<<" of which mult2  "<<tmult2<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult temps "<<ttemps<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult copy  "<<tcopy<<" us"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<std::endl;
    //    std::cout << GridLogPerformance<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Kernel flops "<< flops<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Kernel flop/s "<< flops/tmult<<" mflop/s"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse Kernel bytes/s "<< bytes/tmult<<" MB/s"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse overall flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
    std::cout << GridLogPerformance<<"Coarse total bytes   "<< bytes/1e6<<" MB"<<std::endl;
 
  };
  
  void PopulateAdag(void)
  {
    for(int64_t bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
      Coordinate bcoor;
      CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
      
      for(int p=0;p<geom.npoint;p++){
    Coordinate scoor = bcoor;
    for(int mu=0;mu<bcoor.size();mu++){
      int L = CoarseGrid()->GlobalDimensions()[mu];
      scoor[mu] = (bcoor[mu] - geom.shifts[p][mu] + L) % L; // Modulo arithmetic
    }
    // Flip to poke/peekLocalSite and not too bad
    auto link = peekSite(_A[p],scoor);
    int pp = geom.Reverse(p);
    pokeSite(adj(link),_Adag[pp],bcoor);
      }
    }
  }

  // 
  // A) Only reduced flops option is to use a padded cell of depth 4
  // and apply MpcDagMpc in the padded cell.
  //
  // Makes for ONE application of MpcDagMpc per vector instead of 30 or 80.
  // With the effective cell size around (B+8)^4 perhaps 12^4/4^4 ratio
  // Cost is 81x more, same as stencil size.
  //
  // But: can eliminate comms and do as local dirichlet.
  //
  // Local exchange gauge field once.
  // Apply to all vectors, local only computation.
  // Must exchange ghost subcells in reverse process of PaddedCell to take inner products
  //
  // B) Can reduce cost: pad by 1, apply Deo      (4^4+6^4+8^4+8^4 )/ (4x 4^4)
  //                     pad by 2, apply Doe
  //                     pad by 3, apply Deo
  //                     then break out 8x directions; cost is ~10x MpcDagMpc per vector
  //
  // => almost factor of 10 in setup cost, excluding data rearrangement
  //
  // Intermediates -- ignore the corner terms, leave approximate and force Hermitian
  // Intermediates -- pad by 2 and apply 1+8+24 = 33 times.

    // BFM HDCG style approach: Solve a system of equations to get Aij
    /*
     *     Here, k,l index which possible shift within the 3^Nd "ball" connected by MdagM.
     *
     *     conj(phases[block]) proj[k][ block*Nvec+j ] =  \sum_ball  e^{i q_k . delta} < phi_{block,j} | MdagM | phi_{(block+delta),i} > 
     *                                                 =  \sum_ball e^{iqk.delta} A_ji
     *
     *     Must invert matrix M_k,l = e^[i q_k . delta_l]
     *
     *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
     */
#if 0
  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
               Aggregation<Fobj,CComplex,nbasis> & Subspace)
  {
    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
    GridBase *grid = FineGrid();
 
    RealD tproj=0.0;
    RealD teigen=0.0;
    RealD tmat=0.0;
    RealD tphase=0.0;
    RealD tinv=0.0;

    // Orthogonalise the subblocks over the basis
    CoarseScalar InnerProd(CoarseGrid()); 
    blockOrthogonalise(InnerProd,Subspace.subspace);
 
    const int npoint = geom.npoint;
      
    Coordinate clatt = CoarseGrid()->GlobalDimensions();
    int Nd = CoarseGrid()->Nd();
 
      /*
       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
       *     Matrix index i is mapped to this shift via 
       *               geom.shifts[i]
       *
       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
       *       = M_{kl} A_ji^{b.b+l}
       *
       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
       *  
       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
       *
       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
       */
    teigen-=usecond();
    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
    ComplexD ci(0.0,1.0);
    for(int k=0;k<npoint;k++){ // Loop over momenta
 
      for(int l=0;l<npoint;l++){ // Loop over nbr relative
    ComplexD phase(0.0,0.0);
    for(int mu=0;mu<Nd;mu++){
      RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
      phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
    }
    phase=exp(phase*ci);
    Mkl(k,l) = phase;
      }
    }
    invMkl = Mkl.inverse();
    teigen+=usecond();

    // Now compute the matrix elements of linop between the orthonormal
    // set of vectors.
    FineField phaV(grid); // Phased block basis vector
    FineField MphaV(grid);// Matrix applied
    CoarseVector coarseInner(CoarseGrid());
 
    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
    for(int i=0;i<nbasis;i++){// Loop over basis vectors
      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
    // Stick a phase on every block
    tphase-=usecond();
    CoarseComplexField coor(CoarseGrid());
    CoarseComplexField pha(CoarseGrid());   pha=Zero();
    for(int mu=0;mu<Nd;mu++){
      LatticeCoordinate(coor,mu);
      RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
      pha = pha + (TwoPiL * geom.shifts[p][mu]) * coor;
    }
    pha  =exp(pha*ci);
    phaV=Zero();
    blockZAXPY(phaV,pha,Subspace.subspace[i],phaV);
    tphase+=usecond();

    // Multiple phased subspace vector by matrix and project to subspace
    // Remove local bulk phase to leave relative phases
    tmat-=usecond();
    linop.Op(phaV,MphaV);
    tmat+=usecond();
 
    tproj-=usecond();
    blockProject(coarseInner,MphaV,Subspace.subspace);
    coarseInner = conjugate(pha) * coarseInner;
 
    ComputeProj[p] = coarseInner;
    tproj+=usecond();
 
      }
 
      tinv-=usecond();
      for(int k=0;k<npoint;k++){
    FT[k] = Zero();
    for(int l=0;l<npoint;l++){
      FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
    }
      
    int osites=CoarseGrid()->oSites();
    autoView( A_v  , _A[k], AcceleratorWrite);
    autoView( FT_v  , FT[k], AcceleratorRead);
    accelerator_for(sss, osites, 1, {
        for(int j=0;j<nbasis;j++){
          A_v[sss](i,j) = FT_v[sss](j);
        }
        });
      }
      tinv+=usecond();
    }
 
    // Only needed if nonhermitian
    if ( ! hermitian ) {
      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
      //      PopulateAdag();
    }
 
    // Need to write something to populate Adag from A
    ExchangeCoarseLinks();
    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
  }
#else
  // Galerkin projection of matrix
  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
               Aggregation<Fobj,CComplex,nbasis> & Subspace)
  {
    CoarsenOperator(linop,Subspace,Subspace);
  }

  // Petrov - Galerkin projection of matrix
  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
               Aggregation<Fobj,CComplex,nbasis> & U,
               Aggregation<Fobj,CComplex,nbasis> & V)
  {
    std::cout << GridLogMessage<< "GeneralCoarsenMatrix "<< std::endl;
    GridBase *grid = FineGrid();
 
    RealD tproj=0.0;
    RealD teigen=0.0;
    RealD tmat=0.0;
    RealD tphase=0.0;
    RealD tphaseBZ=0.0;
    RealD tinv=0.0;

    // Orthogonalise the subblocks over the basis
    CoarseScalar InnerProd(CoarseGrid()); 
    blockOrthogonalise(InnerProd,V.subspace);
    blockOrthogonalise(InnerProd,U.subspace);
 
    const int npoint = geom.npoint;
      
    Coordinate clatt = CoarseGrid()->GlobalDimensions();
    int Nd = CoarseGrid()->Nd();
 
      /*
       *     Here, k,l index which possible momentum/shift within the N-points connected by MdagM.
       *     Matrix index i is mapped to this shift via 
       *               geom.shifts[i]
       *
       *     conj(pha[block]) proj[k (which mom)][j (basis vec cpt)][block] 
       *       =  \sum_{l in ball}  e^{i q_k . delta_l} < phi_{block,j} | MdagM | phi_{(block+delta_l),i} > 
       *       =  \sum_{l in ball} e^{iqk.delta_l} A_ji^{b.b+l}
       *       = M_{kl} A_ji^{b.b+l}
       *
       *     Must assemble and invert matrix M_k,l = e^[i q_k . delta_l]
       *  
       *     Where q_k = delta_k . (2*M_PI/global_nb[mu])
       *
       *     Then A{ji}^{b,b+l} = M^{-1}_{lm} ComputeProj_{m,b,i,j}
       */
    teigen-=usecond();
    Eigen::MatrixXcd Mkl    = Eigen::MatrixXcd::Zero(npoint,npoint);
    Eigen::MatrixXcd invMkl = Eigen::MatrixXcd::Zero(npoint,npoint);
    ComplexD ci(0.0,1.0);
    for(int k=0;k<npoint;k++){ // Loop over momenta
 
      for(int l=0;l<npoint;l++){ // Loop over nbr relative
    ComplexD phase(0.0,0.0);
    for(int mu=0;mu<Nd;mu++){
      RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
      phase=phase+TwoPiL*geom.shifts[k][mu]*geom.shifts[l][mu];
    }
    phase=exp(phase*ci);
    Mkl(k,l) = phase;
      }
    }
    invMkl = Mkl.inverse();
    teigen+=usecond();

    // Now compute the matrix elements of linop between the orthonormal
    // set of vectors.
    FineField phaV(grid); // Phased block basis vector
    FineField MphaV(grid);// Matrix applied
    std::vector<FineComplexField> phaF(npoint,grid);
    std::vector<CoarseComplexField> pha(npoint,CoarseGrid());
    
    CoarseVector coarseInner(CoarseGrid());
    
    typedef typename CComplex::scalar_type SComplex;
    FineComplexField one(grid); one=SComplex(1.0);
    FineComplexField zz(grid); zz = Zero();
    tphase=-usecond();
    for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
      // Stick a phase on every block
      CoarseComplexField coor(CoarseGrid());
      pha[p]=Zero();
      for(int mu=0;mu<Nd;mu++){
    LatticeCoordinate(coor,mu);
    RealD TwoPiL =  M_PI * 2.0/ clatt[mu];
    pha[p] = pha[p] + (TwoPiL * geom.shifts[p][mu]) * coor;
      }
      pha[p]  =exp(pha[p]*ci);
 
      blockZAXPY(phaF[p],pha[p],one,zz);
      
    }
    tphase+=usecond();
    
    std::vector<CoarseVector> ComputeProj(npoint,CoarseGrid());
    std::vector<CoarseVector>          FT(npoint,CoarseGrid());
    for(int i=0;i<nbasis;i++){// Loop over basis vectors
      std::cout << GridLogMessage<< "CoarsenMatrixColoured vec "<<i<<"/"<<nbasis<< std::endl;
      for(int p=0;p<npoint;p++){ // Loop over momenta in npoint
    tphaseBZ-=usecond();
    phaV = phaF[p]*V.subspace[i];
    tphaseBZ+=usecond();

    // Multiple phased subspace vector by matrix and project to subspace
    // Remove local bulk phase to leave relative phases
    tmat-=usecond();
    linop.Op(phaV,MphaV);
    tmat+=usecond();
    //  std::cout << i << " " <<p << " MphaV "<<norm2(MphaV)<<" "<<norm2(phaV)<<std::endl;
 
    tproj-=usecond();
    blockProject(coarseInner,MphaV,U.subspace);
    coarseInner = conjugate(pha[p]) * coarseInner;
 
    ComputeProj[p] = coarseInner;
    tproj+=usecond();
    //  std::cout << i << " " <<p << " ComputeProj "<<norm2(ComputeProj[p])<<std::endl;
 
      }
 
      tinv-=usecond();
      for(int k=0;k<npoint;k++){
    FT[k] = Zero();
    for(int l=0;l<npoint;l++){
      FT[k]= FT[k]+ invMkl(l,k)*ComputeProj[l];
    }
      
    int osites=CoarseGrid()->oSites();
    autoView( A_v  , _A[k], AcceleratorWrite);
    autoView( FT_v  , FT[k], AcceleratorRead);
    accelerator_for(sss, osites, 1, {
        for(int j=0;j<nbasis;j++){
          A_v[sss](i,j) = FT_v[sss](j);
        }
        });
      }
      tinv+=usecond();
    }
 
    // Only needed if nonhermitian
    if ( ! hermitian ) {
      //      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
      //      PopulateAdag();
    }
 
    for(int p=0;p<geom.npoint;p++){
      std::cout << " _A["<<p<<"] "<<norm2(_A[p])<<std::endl;
    }
 
    // Need to write something to populate Adag from A
    ExchangeCoarseLinks();
    std::cout << GridLogMessage<<"CoarsenOperator eigen  "<<teigen<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator phase  "<<tphase<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator phaseBZ "<<tphaseBZ<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator mat    "<<tmat <<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator proj   "<<tproj<<" us"<<std::endl;
    std::cout << GridLogMessage<<"CoarsenOperator inv    "<<tinv<<" us"<<std::endl;
  }
#endif  
  void ExchangeCoarseLinks(void){
    for(int p=0;p<geom.npoint;p++){
      _A[p] = Cell.ExchangePeriodic(_A[p]);
      //      _Adag[p]= Cell.ExchangePeriodic(_Adag[p]);
    }
  }
  virtual  void Mdiag    (const Field &in, Field &out){ assert(0);};
  virtual  void Mdir     (const Field &in, Field &out,int dir, int disp){assert(0);};
  virtual  void MdirAll  (const Field &in, std::vector<Field> &out){assert(0);};
};
 
 
  
NAMESPACE_END(Grid);