I/O for coarse op and reorganise multigrid headers

Need to work on the PaddedCell now to make much faster

Grid/algorithms/Algorithms.h

@@ -69,7 +69,8 @@ NAMESPACE_CHECK(BiCGSTAB);
 #include <Grid/algorithms/iterative/PowerMethod.h>
 
 NAMESPACE_CHECK(PowerMethod);
-#include <Grid/algorithms/CoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/MultiGrid.h>
+
 NAMESPACE_CHECK(CoarsendMatrix);
 #include <Grid/algorithms/FFT.h>
 

Grid/algorithms/CoarsenedMatrix.h

@@ -123,7 +123,7 @@ public:
 };
   
 template<class Fobj,class CComplex,int nbasis>
-class Aggregation   {
+class Aggregation {
 public:
   typedef iVector<CComplex,nbasis >             siteVector;
   typedef Lattice<siteVector>                 CoarseVector;
@@ -158,7 +158,20 @@ public:
     blockPromote(CoarseVec,FineVec,subspace);
   }
 
-  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) {
+  virtual void CreateSubspaceRandom(GridParallelRNG  &RNG) {
+    int nn=nbasis;
+    RealD scale;
+    FineField noise(FineGrid);
+    for(int b=0;b<nn;b++){
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      subspace[b] = noise;
+    }
+  }
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis)
+  {
 
     RealD scale;
 
@@ -217,6 +230,11 @@ public:
     scale = std::pow(norm2(noise),-0.5); 
     noise=noise*scale;
 
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-1 : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-2 : nbasis"<<nn<<" min "
+	      <<ordermin<<" step "<<orderstep
+	      <<" lo"<<filterlo<<std::endl;
+
     // Initial matrix element
     hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
 
@@ -290,6 +308,44 @@ public:
     }
     assert(b==nn);
   }
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+
+  }
 
 };
 

Grid/algorithms/GeneralCoarsenedMatrix.h

@@ -0,0 +1,573 @@
+/*************************************************************************************
+
+    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);
+
+// Fixme need coalesced read gpermute
+template<class vobj> void gpermute(vobj & inout,int perm){
+  vobj tmp=inout;
+  if (perm & 0x1 ) { permute(inout,tmp,0); tmp=inout;}
+  if (perm & 0x2 ) { permute(inout,tmp,1); tmp=inout;}
+  if (perm & 0x4 ) { permute(inout,tmp,2); tmp=inout;}
+  if (perm & 0x8 ) { permute(inout,tmp,3); tmp=inout;}
+}
+
+/////////////////////////////////////////////////////////////////
+// Reuse Aggregation class from CoarsenedMatrix for now
+// Might think about *smoothed* Aggregation
+// Equivalent of Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+class NonLocalStencilGeometry {
+public:
+  int depth;
+  int hops;
+  int npoint;
+  std::vector<Coordinate> shifts;
+  Coordinate stencil_size;
+  Coordinate stencil_lo;
+  Coordinate stencil_hi;
+  GridCartesian *grid;
+  GridCartesian *Grid() {return grid;};
+  int Depth(void){return 1;};   // Ghost zone depth
+  int Hops(void){return hops;}; // # of hops=> level of corner fill in in stencil
+
+  virtual int DimSkip(void) =0;
+
+  virtual ~NonLocalStencilGeometry() {};
+
+  int  Reverse(int point)
+  {
+    int Nd = Grid()->Nd();
+    Coordinate shft = shifts[point];
+    Coordinate rev(Nd);
+    for(int mu=0;mu<Nd;mu++) rev[mu]= -shft[mu];
+    for(int p=0;p<npoint;p++){
+      if(rev==shifts[p]){
+	return p;
+      }
+    }
+    assert(0);
+    return -1;
+  }
+  void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    int Nd = this->grid->Nd();
+
+    int dd = this->DimSkip();
+    for(int s0=this->stencil_lo[dd+0];s0<=this->stencil_hi[dd+0];s0++){
+    for(int s1=this->stencil_lo[dd+1];s1<=this->stencil_hi[dd+1];s1++){
+    for(int s2=this->stencil_lo[dd+2];s2<=this->stencil_hi[dd+2];s2++){
+    for(int s3=this->stencil_lo[dd+3];s3<=this->stencil_hi[dd+3];s3++){
+      Coordinate sft(Nd,0);
+      sft[dd+0] = s0;
+      sft[dd+1] = s1;
+      sft[dd+2] = s2;
+      sft[dd+3] = s3;
+      int nhops = abs(s0)+abs(s1)+abs(s2)+abs(s3);
+      if(nhops<=this->hops) this->shifts.push_back(sft);
+    }}}}
+    this->npoint = this->shifts.size();
+    std::cout << GridLogMessage << "NonLocalStencilGeometry has "<< this->npoint << " terms in stencil "<<std::endl;
+  }
+  
+  NonLocalStencilGeometry(GridCartesian *_coarse_grid,int _hops) : grid(_coarse_grid), hops(_hops)
+  {
+    Coordinate latt = grid->GlobalDimensions();
+    stencil_size.resize(grid->Nd());
+    stencil_lo.resize(grid->Nd());
+    stencil_hi.resize(grid->Nd());
+    for(int d=0;d<grid->Nd();d++){
+     if ( latt[d] == 1 ) {
+      stencil_lo[d] = 0;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 1;
+     } else if ( latt[d] == 2 ) {
+      stencil_lo[d] = -1;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 2;
+     } else if ( latt[d] > 2 ) {
+       stencil_lo[d] = -1;
+       stencil_hi[d] =  1;
+       stencil_size[d]= 3;
+     }
+    }
+  };
+
+};
+
+// Need to worry about red-black now
+class NonLocalStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  virtual int DimSkip(void) { return 0;};
+  NonLocalStencilGeometry4D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops) { };
+  virtual ~NonLocalStencilGeometry4D() {};
+};
+class NonLocalStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  virtual int DimSkip(void) { return 1; }; 
+  NonLocalStencilGeometry5D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops)  { };
+  virtual ~NonLocalStencilGeometry5D() {};
+};
+/*
+ * Bunch of different options classes
+ */
+class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
+public:
+  NextToNextToNextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,4)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNextToNextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNextToNextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,4)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,2)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,2)
+  {
+    this->BuildShifts();
+  };
+};
+class NearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,1)
+  {
+    this->BuildShifts();
+  };
+};
+class NearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,1)
+  {
+    this->BuildShifts();
+  };
+};
+
+// 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 Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  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;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _FineGrid; };   // 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 ProjectNearestNeighbour(RealD shift, GeneralCoarseOp &CopyMe)
+  {
+    int nfound=0;
+    std::cout << " 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;
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      int osites=Stencil.Grid()->oSites();
+      for(int ss=0;ss<osites;ss++){
+	for(int point=0;point<npoint;point++){
+	  auto SE = Stencil_v.GetEntry(point,ss);
+	  int o = SE->_offset;
+	  assert( o< osites);
+	}
+      }    
+    }
+
+    _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)
+  {
+    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;
+    ttot=-usecond();
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+    CoarseVector tin=in;
+
+    texch-=usecond();
+    CoarseVector pin  = Cell.Exchange(tin);
+    texch+=usecond();
+
+    CoarseVector pout(pin.Grid()); pout=Zero();
+
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+      
+    const int Nsimd = CComplex::Nsimd();
+    
+    int osites=pin.Grid()->oSites();
+    //    int gsites=pin.Grid()->gSites();
+
+    RealD flops = 1.0* npoint * nbasis * nbasis * 8 * osites;
+    RealD bytes = (1.0*osites*sizeof(siteMatrix)*npoint+2.0*osites*sizeof(siteVector))*npoint;
+      
+    //    for(int point=0;point<npoint;point++){
+    //      conformable(A[point],pin);
+    //    }
+
+    {
+      tviews-=usecond();
+      autoView( in_v , pin, AcceleratorRead);
+      autoView( out_v , pout, AcceleratorWrite);
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      tviews+=usecond();
+      
+      for(int point=0;point<npoint;point++){
+	tviews-=usecond();
+	autoView( A_v, A[point],AcceleratorRead);
+	tviews+=usecond();
+	tmult-=usecond();
+	accelerator_for(sss, osites*nbasis, Nsimd, {
+
+	    typedef decltype(coalescedRead(in_v[0]))    calcVector;
+
+	    int ss = sss/nbasis;
+	    int b  = sss%nbasis;
+
+	    auto SE  = Stencil_v.GetEntry(point,ss);
+	    auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
+	    auto res = out_v(ss)(b);
+	    for(int bb=0;bb<nbasis;bb++) {
+	      res = res + coalescedRead(A_v[ss](b,bb))*nbr(bb);
+	    }
+	    coalescedWrite(out_v[ss](b),res);
+	});
+
+	tmult+=usecond();
+      }
+    }
+    text-=usecond();
+    out = Cell.Extract(pout);
+    text+=usecond();
+    ttot+=usecond();
+
+    std::cout << GridLogPerformance<<"Coarse 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<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel "<< flops/tmult<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Kernel "<< bytes/tmult<<" MB/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse flops/s "<< flops/ttot<<" mflop/s"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse 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])
+     */
+  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](j,i) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    for(int p=0;p<geom.npoint;p++){
+      Coordinate coor({0,0,0,0,0});
+      auto sval = peekSite(_A[p],coor);
+    }
+
+    // Only needed if nonhermitian
+    if ( ! hermitian ) {
+      std::cout << GridLogMessage<<"PopulateAdag  "<<std::endl;
+      PopulateAdag();
+    }
+
+    // Need to write something to populate Adag from A
+    std::cout << GridLogMessage<<"ExchangeCoarseLinks  "<<std::endl;
+    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;
+  }
+  void ExchangeCoarseLinks(void){
+    for(int p=0;p<geom.npoint;p++){
+      std::cout << "Exchange "<<p<<std::endl;
+      _A[p] = Cell.Exchange(_A[p]);
+      _Adag[p]= Cell.Exchange(_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);

Grid/algorithms/approx/Chebyshev.h

@@ -90,9 +90,8 @@ public:
     order=_order;
       
     if(order < 2) exit(-1);
-    Coeffs.resize(order);
+    Coeffs.resize(order,0.0);
-    Coeffs.assign(0.,order);
+    Coeffs[order-1] = 1.0;
-    Coeffs[order-1] = 1.;
   };
   
   // PB - more efficient low pass drops high modes above the low as 1/x uses all Chebyshev's.

Grid/algorithms/iterative/AdefGeneric.h

@@ -33,15 +33,6 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
    * Script A = SolverMatrix 
    * Script P = Preconditioner
    *
-   * Deflation methods considered
-   *      -- Solve P A x = P b        [ like Luscher ]
-   * DEF-1        M P A x = M P b     [i.e. left precon]
-   * DEF-2        P^T M A x = P^T M b
-   * ADEF-1       Preconditioner = M P + Q      [ Q + M + M A Q]
-   * ADEF-2       Preconditioner = P^T M + Q
-   * BNN          Preconditioner = P^T M P + Q
-   * BNN2         Preconditioner = M P + P^TM +Q - M P A M 
-   * 
    * Implement ADEF-2
    *
    * Vstart = P^Tx + Qb
@@ -49,202 +40,245 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
    * M2=M3=1
    * Vout = x
    */
+NAMESPACE_BEGIN(Grid);
 
-// abstract base
+template<class Field>
-template<class Field, class CoarseField>
+class TwoLevelCG : public LinearFunction<Field>
-class TwoLevelFlexiblePcg : public LinearFunction<Field>
 {
  public:
-  int verbose;
   RealD   Tolerance;
   Integer MaxIterations;
-  const int mmax = 5;
   GridBase *grid;
-  GridBase *coarsegrid;
 
-  LinearOperatorBase<Field>   *_Linop
+  // Fine operator, Smoother, CoarseSolver
-  OperatorFunction<Field>     *_Smoother,
+  LinearOperatorBase<Field>   &_FineLinop;
-  LinearFunction<CoarseField> *_CoarseSolver;
+  LinearFunction<Field>   &_Smoother;
-
-  // Need somthing that knows how to get from Coarse to fine and back again
   
   // more most opertor functions
-  TwoLevelFlexiblePcg(RealD tol,
+  TwoLevelCG(RealD tol,
-		     Integer maxit,
+	     Integer maxit,
-		     LinearOperatorBase<Field> *Linop,
+	     LinearOperatorBase<Field>   &FineLinop,
-		     LinearOperatorBase<Field> *SmootherLinop,
+	     LinearFunction<Field>       &Smoother,
-		     OperatorFunction<Field>   *Smoother,
+	     GridBase *fine) : 
-		     OperatorFunction<CoarseField>  CoarseLinop
-		     ) : 
       Tolerance(tol), 
       MaxIterations(maxit),
-      _Linop(Linop),
+      _FineLinop(FineLinop),
-      _PreconditionerLinop(PrecLinop),
+      _Smoother(Smoother)
-      _Preconditioner(Preconditioner)
   {
-    verbose=0;
+    grid       = fine;
   };
   
-  // The Pcg routine is common to all, but the various matrices differ from derived 
+  virtual void operator() (const Field &src, Field &psi)
-  // implementation to derived implmentation
+  {
-  void operator() (const Field &src, Field &psi){
+    Field resid(grid);
-  void operator() (const Field &src, Field &psi){
-
-    psi.Checkerboard() = src.Checkerboard();
-    grid             = src.Grid();
-
     RealD f;
     RealD rtzp,rtz,a,d,b;
     RealD rptzp;
-    RealD tn;
-    RealD guess = norm2(psi);
-    RealD ssq   = norm2(src);
-    RealD rsq   = ssq*Tolerance*Tolerance;
     
-    /////////////////////////////
+    Field x(grid); 
-    // Set up history vectors
+    Field p(grid);
-    /////////////////////////////
+    Field z(grid);
-    std::vector<Field> p  (mmax,grid);
-    std::vector<Field> mmp(mmax,grid);
-    std::vector<RealD> pAp(mmax);
-
-    Field x  (grid); x = psi;
-    Field z  (grid);
     Field tmp(grid);
+    Field mmp(grid);
     Field r  (grid);
     Field mu (grid);
+    Field rp (grid);
     
+    //Initial residual computation & set up
+    RealD guess = norm2(psi);
+    double tn;
+
+    GridStopWatch HDCGTimer;
+    HDCGTimer.Start();
     //////////////////////////
     // x0 = Vstart -- possibly modify guess
     //////////////////////////
-    x=src;
+    x=Zero();
     Vstart(x,src);
 
     // r0 = b -A x0
-    HermOp(x,mmp); // Shouldn't this be something else?
+    _FineLinop.HermOp(x,mmp);
-    axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
+
+    axpy(r, -1.0, mmp, src);    // Recomputes r=src-x0
+    rp=r;
 
     //////////////////////////////////
     // Compute z = M1 x
     //////////////////////////////////
-    M1(r,z,tmp,mp,SmootherMirs);
+    PcgM1(r,z);
     rtzp =real(innerProduct(r,z));
 
     ///////////////////////////////////////
-    // Solve for Mss mu = P A z and set p = z-mu
+    // Except Def2, M2 is trivial
-    // Def2: p = 1 - Q Az = Pright z 
-    // Other algos M2 is trivial
     ///////////////////////////////////////
-    M2(z,p[0]);
+    p=z;
 
-    for (int k=0;k<=MaxIterations;k++){
+    RealD ssq =  norm2(src);
+    RealD rsq =  ssq*Tolerance*Tolerance;
 
-      int peri_k  = k % mmax;
+    std::cout<<GridLogMessage<<"HDCG: k=0 residual "<<rtzp<<" target rsq "<<rsq<<" ssq "<<ssq<<std::endl;
-      int peri_kp = (k+1) % mmax;
+    
+    for (int k=1;k<=MaxIterations;k++){
 
       rtz=rtzp;
-      d= M3(p[peri_k],mp,mmp[peri_k],tmp);
+      d= PcgM3(p,mmp);
       a = rtz/d;
 
-      // Memorise this
+      axpy(x,a,p,x);
-      pAp[peri_k] = d;
+      RealD rn = axpy_norm(r,-a,mmp,r);
 
-      axpy(x,a,p[peri_k],x);
+      PcgM1(r,z);
-      RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
-
-      // Compute z = M x
-      M1(r,z,tmp,mp);
 
       rtzp =real(innerProduct(r,z));
 
-      M2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+      int ipcg=1; // almost free inexact preconditioned CG
-
+      if (ipcg) {
-      p[peri_kp]=p[peri_k];
+	rptzp =real(innerProduct(rp,z));
-
+      } else {
-      // Standard search direction  p -> z + b p    ; b = 
+	rptzp =0;
-      b = (rtzp)/rtz;
-
-      int northog;
-      //    northog     = (peri_kp==0)?1:peri_kp; // This is the fCG(mmax) algorithm
-      northog     = (k>mmax-1)?(mmax-1):k;        // This is the fCG-Tr(mmax-1) algorithm
-    
-      for(int back=0; back < northog; back++){
-	int peri_back = (k-back)%mmax;
-	RealD pbApk= real(innerProduct(mmp[peri_back],p[peri_kp]));
-	RealD beta = -pbApk/pAp[peri_back];
-	axpy(p[peri_kp],beta,p[peri_back],p[peri_kp]);
       }
+      b = (rtzp-rptzp)/rtz;
+
+      PcgM2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+
+      axpy(p,b,p,mu);  // mu = A r
 
       RealD rrn=sqrt(rn/ssq);
-      std::cout<<GridLogMessage<<"TwoLevelfPcg: k= "<<k<<" residual = "<<rrn<<std::endl;
+      RealD rtn=sqrt(rtz/ssq);
+      std::cout<<GridLogMessage<<"HDCG: Pcg k= "<<k<<" residual = "<<rrn<<std::endl;
+
+      if ( ipcg ) {
+	axpy(rp,0.0,r,r);
+      }
 
       // Stopping condition
       if ( rn <= rsq ) { 
 
-	HermOp(x,mmp); // Shouldn't this be something else?
+	HDCGTimer.Stop();
-	axpy(tmp,-1.0,src,mmp[0]);
+	std::cout<<GridLogMessage<<"HDCG: Pcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
 
-	RealD psinorm = sqrt(norm2(x));
+	_FineLinop.HermOp(x,mmp);			  
-	RealD srcnorm = sqrt(norm2(src));
+	axpy(tmp,-1.0,src,mmp);
-	RealD tmpnorm = sqrt(norm2(tmp));
+
-	RealD true_residual = tmpnorm/srcnorm;
+	RealD  mmpnorm = sqrt(norm2(mmp));
-	std::cout<<GridLogMessage<<"TwoLevelfPcg:   true residual is "<<true_residual<<std::endl;
+	RealD  xnorm   = sqrt(norm2(x));
-	std::cout<<GridLogMessage<<"TwoLevelfPcg: target residual was"<<Tolerance<<std::endl;
+	RealD  srcnorm = sqrt(norm2(src));
-	return k;
+	RealD  tmpnorm = sqrt(norm2(tmp));
+	RealD  true_residual = tmpnorm/srcnorm;
+	std::cout<<GridLogMessage<<"HDCG: true residual is "<<true_residual
+		 <<" solution "<<xnorm<<" source "<<srcnorm<<std::endl;
+
+	return;
       }
+
     }
-    // Non-convergence
+    std::cout << "HDCG: Pcg not converged"<<std::endl;
-    assert(0);
+    return ;
   }
   
+
  public:
 
-  virtual void M(Field & in,Field & out,Field & tmp) {
+  virtual void PcgM1(Field & in, Field & out)     =0;
+  virtual void Vstart(Field & x,const Field & src)=0;
 
+  virtual void PcgM2(const Field & in, Field & out) {
+    out=in;
   }
 
-  virtual void M1(Field & in, Field & out) {// the smoother
+  virtual RealD PcgM3(const Field & p, Field & mmp){
+    RealD dd;
+    _FineLinop.HermOp(p,mmp);
+    ComplexD dot = innerProduct(p,mmp);
+    dd=real(dot);
+    return dd;
+  }
 
+  /////////////////////////////////////////////////////////////////////
+  // Only Def1 has non-trivial Vout.
+  /////////////////////////////////////////////////////////////////////
+  virtual void   Vout  (Field & in, Field & out,Field & src){
+    out = in;
+  }
+
+};
+  
+template<class Field, class CoarseField, class Aggregation>
+class TwoLevelADEF2 : public TwoLevelCG<Field>
+{
+ public:
+  ///////////////////////////////////////////////////////////////////////////////////
+  // Need something that knows how to get from Coarse to fine and back again
+  //  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+  //  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+  ///////////////////////////////////////////////////////////////////////////////////
+  GridBase *coarsegrid;
+  Aggregation &_Aggregates;                    
+  LinearFunction<CoarseField> &_CoarseSolver;
+  LinearFunction<CoarseField> &_CoarseSolverPrecise;
+  ///////////////////////////////////////////////////////////////////////////////////
+  
+  // more most opertor functions
+  TwoLevelADEF2(RealD tol,
+		Integer maxit,
+		LinearOperatorBase<Field>   &FineLinop,
+		LinearFunction<Field>   &Smoother,
+		LinearFunction<CoarseField>  &CoarseSolver,
+		LinearFunction<CoarseField>  &CoarseSolverPrecise,
+		Aggregation &Aggregates
+		) :
+    TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,Aggregates.FineGrid),
+      _CoarseSolver(CoarseSolver),
+      _CoarseSolverPrecise(CoarseSolverPrecise),
+      _Aggregates(Aggregates)
+  {
+    coarsegrid = Aggregates.CoarseGrid;
+  };
+
+  virtual void PcgM1(Field & in, Field & out)
+  {
     // [PTM+Q] in = [1 - Q A] M in + Q in = Min + Q [ in -A Min]
-    Field tmp(grid);
-    Field Min(grid);
 
-    PcgM(in,Min); // Smoother call
+    Field tmp(this->grid);
+    Field Min(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
 
-    HermOp(Min,out);
+    GridStopWatch SmootherTimer;
+    GridStopWatch MatrixTimer;
+    SmootherTimer.Start();
+    this->_Smoother(in,Min);
+    SmootherTimer.Stop();
+
+    MatrixTimer.Start();
+    this->_FineLinop.HermOp(Min,out);
+    MatrixTimer.Stop();
     axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
 
-    ProjectToSubspace(tmp,PleftProj);     
+    GridStopWatch ProjTimer;
-    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    GridStopWatch CoarseTimer;
-    PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    GridStopWatch PromTimer;
+    ProjTimer.Start();
+    this->_Aggregates.ProjectToSubspace(PleftProj,tmp);     
+    ProjTimer.Stop();
+    CoarseTimer.Start();
+    this->_CoarseSolver(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    CoarseTimer.Stop();
+    PromTimer.Start();
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
+    PromTimer.Stop();
+    std::cout << GridLogPerformance << "PcgM1 breakdown "<<std::endl;
+    std::cout << GridLogPerformance << "\tSmoother   " << SmootherTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProj       " << ProjTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tCoarse     " << CoarseTimer.Elapsed() <<std::endl;
+    std::cout << GridLogPerformance << "\tProm       " << PromTimer.Elapsed() <<std::endl;
+
     axpy(out,1.0,Min,tmp); // Min+tmp
   }
 
-  virtual void M2(const Field & in, Field & out) {
+  virtual void Vstart(Field & x,const Field & src)
-    out=in;
+  {
-    // Must override for Def2 only
-    //  case PcgDef2:
-    //    Pright(in,out);
-    //    break;
-  }
-
-  virtual RealD M3(const Field & p, Field & mmp){
-    double d,dd;
-    HermOpAndNorm(p,mmp,d,dd);
-    return dd;
-    // Must override for Def1 only
-    //  case PcgDef1:
-    //    d=linop_d->Mprec(p,mmp,tmp,0,1);// Dag no
-    //      linop_d->Mprec(mmp,mp,tmp,1);// Dag yes
-    //    Pleft(mp,mmp);
-    //    d=real(linop_d->inner(p,mmp));
-  }
-
-  virtual void VstartDef2(Field & xconst Field & src){
-    //case PcgDef2:
-    //case PcgAdef2: 
-    //case PcgAdef2f:
-    //case PcgV11f:
     ///////////////////////////////////
     // Choose x_0 such that 
     // x_0 = guess +  (A_ss^inv) r_s = guess + Ass_inv [src -Aguess]
@@ -256,142 +290,72 @@ class TwoLevelFlexiblePcg : public LinearFunction<Field>
     //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
     //                   = 0 
     ///////////////////////////////////
-    Field r(grid);
+    Field r(this->grid);
-    Field mmp(grid);
+    Field mmp(this->grid);
+    CoarseField PleftProj(this->coarsegrid);
+    CoarseField PleftMss_proj(this->coarsegrid);
 
-    HermOp(x,mmp);
+    this->_Aggregates.ProjectToSubspace(PleftProj,src);     
-    axpy (r, -1.0, mmp, src);        // r_{-1} = src - A x
+    this->_CoarseSolverPrecise(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    ProjectToSubspace(r,PleftProj);     
+    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,x);  
-    ApplyInverseCG(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    PromoteFromSubspace(PleftMss_proj,mmp);  
-    x=x+mmp;
 
   }
 
-  virtual void Vstart(Field & x,const Field & src){
+};
-    return;
-  }
-
-  /////////////////////////////////////////////////////////////////////
-  // Only Def1 has non-trivial Vout. Override in Def1
-  /////////////////////////////////////////////////////////////////////
-  virtual void   Vout  (Field & in, Field & out,Field & src){
-    out = in;
-    //case PcgDef1:
-    //    //Qb + PT x
-    //    ProjectToSubspace(src,PleftProj);     
-    //    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    //    PromoteFromSubspace(PleftMss_proj,tmp);  
-    //    
-    //    Pright(in,out);
-    //    
-    //    linop_d->axpy(out,tmp,out,1.0);
-    //    break;
-  }
-
-  ////////////////////////////////////////////////////////////////////////////////////////////////
-  // Pright and Pleft are common to all implementations
-  ////////////////////////////////////////////////////////////////////////////////////////////////
-  virtual void Pright(Field & in,Field & out){
-    // P_R  = [ 1              0 ] 
-    //        [ -Mss^-1 Msb    0 ] 
-    Field in_sbar(grid);
-
-    ProjectToSubspace(in,PleftProj);     
-    PromoteFromSubspace(PleftProj,out);  
-    axpy(in_sbar,-1.0,out,in);       // in_sbar = in - in_s 
-
-    HermOp(in_sbar,out);
-    ProjectToSubspace(out,PleftProj);           // Mssbar in_sbar  (project)
-
-    ApplyInverse     (PleftProj,PleftMss_proj); // Mss^{-1} Mssbar 
-    PromoteFromSubspace(PleftMss_proj,out);     // 
-
-    axpy(out,-1.0,out,in_sbar);     // in_sbar - Mss^{-1} Mssbar in_sbar
-  }
-  virtual void Pleft (Field & in,Field & out){
-    // P_L  = [ 1  -Mbs Mss^-1] 
-    //        [ 0   0         ] 
-    Field in_sbar(grid);
-    Field    tmp2(grid);
-    Field    Mtmp(grid);
-
-    ProjectToSubspace(in,PleftProj);     
-    PromoteFromSubspace(PleftProj,out);  
-    axpy(in_sbar,-1.0,out,in);      // in_sbar = in - in_s
-
-    ApplyInverse(PleftProj,PleftMss_proj); // Mss^{-1} in_s
-    PromoteFromSubspace(PleftMss_proj,out);
-
-    HermOp(out,Mtmp);
-
-    ProjectToSubspace(Mtmp,PleftProj);      // Msbar s Mss^{-1}
-    PromoteFromSubspace(PleftProj,tmp2);
-
-    axpy(out,-1.0,tmp2,Mtmp);
-    axpy(out,-1.0,out,in_sbar);     // in_sbar - Msbars Mss^{-1} in_s
-  }
-}
 
 template<class Field>
-class TwoLevelFlexiblePcgADef2 : public TwoLevelFlexiblePcg<Field> {
+class TwoLevelADEF1defl : public TwoLevelCG<Field>
- public:
+{
-  virtual void M(Field & in,Field & out,Field & tmp){
+public:
+  const std::vector<Field> &evec;
+  const std::vector<RealD> &eval;
   
+  TwoLevelADEF1defl(RealD tol,
+		   Integer maxit,
+		   LinearOperatorBase<Field>   &FineLinop,
+		   LinearFunction<Field>   &Smoother,
+		   std::vector<Field> &_evec,
+		   std::vector<RealD> &_eval) : 
+    TwoLevelCG<Field>(tol,maxit,FineLinop,Smoother,_evec[0].Grid()),
+    evec(_evec),
+    eval(_eval)
+  {};
+
+  // Can just inherit existing Vout
+  // Can just inherit existing M2
+  // Can just inherit existing M3
+
+  // Simple vstart - do nothing
+  virtual void Vstart(Field & x,const Field & src){ x=src; };
+
+  // Override PcgM1
+  virtual void PcgM1(Field & in, Field & out)
+  {
+    int N=evec.size();
+    Field Pin(this->grid);
+    Field Qin(this->grid);
+
+    //MP  + Q = M(1-AQ) + Q = M
+    // // If we are eigenvector deflating in coarse space
+    // // Q   = Sum_i |phi_i> 1/lambda_i <phi_i|
+    // // A Q = Sum_i |phi_i> <phi_i|
+    // // M(1-AQ) = M(1-proj) + Q
+    Qin.Checkerboard()=in.Checkerboard();
+    Qin = Zero();
+    Pin = in;
+    for (int i=0;i<N;i++) {
+      const Field& tmp = evec[i];
+      auto ip = TensorRemove(innerProduct(tmp,in));
+      axpy(Qin, ip / eval[i],tmp,Qin);
+      axpy(Pin, -ip ,tmp,Pin);
+    }
+
+    this->_Smoother(Pin,out);
+
+    out = out + Qin;
   }
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp){
+};
 
-  }
+NAMESPACE_END(Grid);
-  virtual void M2(Field & in, Field & out){
 
-  }
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp){
-
-  }
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp){
-
-  }
-}
-/*
-template<class Field>
-class TwoLevelFlexiblePcgAD : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgDef1 : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-  virtual void   Vout  (Field & in, Field & out,Field & src,Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgDef2 : public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-
-template<class Field>
-class TwoLevelFlexiblePcgV11: public TwoLevelFlexiblePcg<Field> {
- public:
-  virtual void M(Field & in,Field & out,Field & tmp); 
-  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp);
-  virtual void M2(Field & in, Field & out);
-  virtual RealD M3(Field & p, Field & mp,Field & mmp, Field & tmp);
-  virtual void Vstart(Field & in, Field & src, Field & r, Field & mp, Field & mmp, Field & tmp);
-}
-*/
 #endif

Grid/algorithms/iterative/ConjugateGradient.h

@@ -183,13 +183,13 @@ public:
 		  << "\tTrue residual " << true_residual
 		  << "\tTarget " << Tolerance << std::endl;
 
-        std::cout << GridLogMessage << "Time breakdown "<<std::endl;
 	std::cout << GridLogMessage << "\tElapsed    " << SolverTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+        std::cout << GridLogPerformance << "Time breakdown "<<std::endl;
-	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
-	std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogPerformance << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
 	std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
 

Grid/algorithms/iterative/ImplicitlyRestartedLanczos.h

@@ -465,7 +465,7 @@ until convergence
 
     Field& evec_k = evec[k];
 
-    _PolyOp(evec_k,w);    std::cout<<GridLogIRL << "PolyOp" <<std::endl;
+    _PolyOp(evec_k,w);    std::cout<<GridLogDebug << "PolyOp" <<std::endl;
 
     if(k>0) w -= lme[k-1] * evec[k-1];
 
@@ -480,9 +480,9 @@ until convergence
     lme[k] = beta;
 
     if ( (k>0) && ( (k % orth_period) == 0 )) {
-      std::cout<<GridLogIRL << "Orthogonalising " <<k<<std::endl;
+      std::cout<<GridLogDebug << "Orthogonalising " <<k<<std::endl;
       orthogonalize(w,evec,k); // orthonormalise
-      std::cout<<GridLogIRL << "Orthogonalised " <<k<<std::endl;
+      std::cout<<GridLogDebug << "Orthogonalised " <<k<<std::endl;
     }
 
     if(k < Nm-1) evec[k+1] = w;
@@ -491,7 +491,7 @@ until convergence
     if ( beta < tiny ) 
       std::cout<<GridLogIRL << " beta is tiny "<<beta<<std::endl;
 
-    std::cout<<GridLogIRL << "Lanczos step complete " <<k<<std::endl;
+    std::cout<<GridLogDebug << "Lanczos step complete " <<k<<std::endl;
   }
 
   void diagonalize_Eigen(std::vector<RealD>& lmd, std::vector<RealD>& lme, 

Grid/algorithms/iterative/NormalEquations.h

@@ -33,7 +33,7 @@ NAMESPACE_BEGIN(Grid);
 ///////////////////////////////////////////////////////////////////////////////////////////////////////
 // Take a matrix and form an NE solver calling a Herm solver
 ///////////////////////////////////////////////////////////////////////////////////////////////////////
-template<class Field> class NormalEquations {
+template<class Field> class NormalEquations : public LinearFunction<Field>{
 private:
   SparseMatrixBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -60,7 +60,7 @@ public:
   }     
 };
 
-template<class Field> class HPDSolver {
+template<class Field> class HPDSolver : public LinearFunction<Field> {
 private:
   LinearOperatorBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -84,7 +84,7 @@ public:
 };
 
 
-template<class Field> class MdagMSolver {
+template<class Field> class MdagMSolver : public LinearFunction<Field> {
 private:
   SparseMatrixBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;

Grid/algorithms/iterative/PowerMethod.h

@@ -20,7 +20,7 @@ template<class Field> class PowerMethod
     RealD evalMaxApprox = 0.0; 
     auto src_n = src; 
     auto tmp = src; 
-    const int _MAX_ITER_EST_ = 50; 
+    const int _MAX_ITER_EST_ = 100; 
 
     for (int i=0;i<_MAX_ITER_EST_;i++) { 
       

Grid/algorithms/multigrid/Aggregates.h

@@ -0,0 +1,262 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/Aggregates.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    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
+
+NAMESPACE_BEGIN(Grid);
+
+template<class Fobj,class CComplex,int nbasis>
+class Aggregation {
+public:
+  typedef iVector<CComplex,nbasis >             siteVector;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+
+  GridBase *CoarseGrid;
+  GridBase *FineGrid;
+  std::vector<Lattice<Fobj> > subspace;
+  int checkerboard;
+  int Checkerboard(void){return checkerboard;}
+  Aggregation(GridBase *_CoarseGrid,GridBase *_FineGrid,int _checkerboard) : 
+    CoarseGrid(_CoarseGrid),
+    FineGrid(_FineGrid),
+    subspace(nbasis,_FineGrid),
+    checkerboard(_checkerboard)
+  {
+  };
+  
+  
+  void Orthogonalise(void){
+    CoarseScalar InnerProd(CoarseGrid); 
+    //    std::cout << GridLogMessage <<" Block Gramm-Schmidt pass 1"<<std::endl;
+    blockOrthogonalise(InnerProd,subspace);
+  } 
+  void ProjectToSubspace(CoarseVector &CoarseVec,const FineField &FineVec){
+    blockProject(CoarseVec,FineVec,subspace);
+  }
+  void PromoteFromSubspace(const CoarseVector &CoarseVec,FineField &FineVec){
+    FineVec.Checkerboard() = subspace[0].Checkerboard();
+    blockPromote(CoarseVec,FineVec,subspace);
+  }
+
+  virtual void CreateSubspaceRandom(GridParallelRNG  &RNG) {
+    int nn=nbasis;
+    RealD scale;
+    FineField noise(FineGrid);
+    for(int b=0;b<nn;b++){
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      subspace[b] = noise;
+    }
+  }
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis)
+  {
+
+    RealD scale;
+
+    ConjugateGradient<FineField> CG(1.0e-2,100,false);
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+
+    for(int b=0;b<nn;b++){
+      
+      subspace[b] = Zero();
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+      
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise   ["<<b<<"] <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+      for(int i=0;i<1;i++){
+
+	CG(hermop,noise,subspace[b]);
+
+	noise = subspace[b];
+	scale = std::pow(norm2(noise),-0.5); 
+	noise=noise*scale;
+
+      }
+
+      hermop.Op(noise,Mn); std::cout<<GridLogMessage << "filtered["<<b<<"] <f|MdagM|f> "<<norm2(Mn)<<std::endl;
+      subspace[b]   = noise;
+
+    }
+  }
+
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+  // World of possibilities here. But have tried quite a lot of experiments (250+ jobs run on Summit)
+  // and this is the best I found
+  ////////////////////////////////////////////////////////////////////////////////////////////////
+
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter,
+				       int ordermin,
+				       int orderstep,
+				       double filterlo
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    gaussian(RNG,noise);
+    scale = std::pow(norm2(noise),-0.5); 
+    noise=noise*scale;
+
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-1 : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pass-2 : nbasis"<<nn<<" min "
+	      <<ordermin<<" step "<<orderstep
+	      <<" lo"<<filterlo<<std::endl;
+
+    // Initial matrix element
+    hermop.Op(noise,Mn); std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+
+    int b =0;
+    {
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+      b++;
+    }
+
+    // Generate a full sequence of Chebyshevs
+    {
+      lo=filterlo;
+      noise=Mn;
+
+      FineField T0(FineGrid); T0 = noise;  
+      FineField T1(FineGrid); 
+      FineField T2(FineGrid);
+      FineField y(FineGrid);
+      
+      FineField *Tnm = &T0;
+      FineField *Tn  = &T1;
+      FineField *Tnp = &T2;
+
+      // Tn=T1 = (xscale M + mscale)in
+      RealD xscale = 2.0/(hi-lo);
+      RealD mscale = -(hi+lo)/(hi-lo);
+      hermop.HermOp(T0,y);
+      T1=y*xscale+noise*mscale;
+
+      for(int n=2;n<=ordermin+orderstep*(nn-2);n++){
+	
+	hermop.HermOp(*Tn,y);
+
+	autoView( y_v , y, AcceleratorWrite);
+	autoView( Tn_v , (*Tn), AcceleratorWrite);
+	autoView( Tnp_v , (*Tnp), AcceleratorWrite);
+	autoView( Tnm_v , (*Tnm), AcceleratorWrite);
+	const int Nsimd = CComplex::Nsimd();
+	accelerator_for(ss, FineGrid->oSites(), Nsimd, {
+	  coalescedWrite(y_v[ss],xscale*y_v(ss)+mscale*Tn_v(ss));
+	  coalescedWrite(Tnp_v[ss],2.0*y_v(ss)-Tnm_v(ss));
+        });
+
+	// Possible more fine grained control is needed than a linear sweep,
+	// but huge productivity gain if this is simple algorithm and not a tunable
+	int m =1;
+	if ( n>=ordermin ) m=n-ordermin;
+	if ( (m%orderstep)==0 ) { 
+	  Mn=*Tnp;
+	  scale = std::pow(norm2(Mn),-0.5);         Mn=Mn*scale;
+	  subspace[b] = Mn;
+	  hermop.Op(Mn,tmp); 
+	  std::cout<<GridLogMessage << n<<" filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+	  b++;
+	}
+
+	// Cycle pointers to avoid copies
+	FineField *swizzle = Tnm;
+	Tnm    =Tn;
+	Tn     =Tnp;
+	Tnp    =swizzle;
+	  
+      }
+    }
+    assert(b==nn);
+  }
+  virtual void CreateSubspaceChebyshev(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,
+				       int nn,
+				       double hi,
+				       double lo,
+				       int orderfilter
+				       ) {
+
+    RealD scale;
+
+    FineField noise(FineGrid);
+    FineField Mn(FineGrid);
+    FineField tmp(FineGrid);
+
+    // New normalised noise
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise : ord "<<orderfilter<<" ["<<lo<<","<<hi<<"]"<<std::endl;
+    std::cout << GridLogMessage<<" Chebyshev subspace pure noise  : nbasis "<<nn<<std::endl;
+
+
+    for(int b =0;b<nbasis;b++)
+    {
+      gaussian(RNG,noise);
+      scale = std::pow(norm2(noise),-0.5); 
+      noise=noise*scale;
+
+      // Initial matrix element
+      hermop.Op(noise,Mn);
+      if(b==0) std::cout<<GridLogMessage << "noise <n|MdagM|n> "<<norm2(Mn)<<std::endl;
+      // Filter
+      Chebyshev<FineField> Cheb(lo,hi,orderfilter);
+      Cheb(hermop,noise,Mn);
+      // normalise
+      scale = std::pow(norm2(Mn),-0.5); 	Mn=Mn*scale;
+      subspace[b]   = Mn;
+      hermop.Op(Mn,tmp); 
+      std::cout<<GridLogMessage << "filt ["<<b<<"] <n|MdagM|n> "<<norm2(tmp)<<std::endl;
+    }
+
+  }
+
+};
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/CoarsenedMatrix.h

@@ -0,0 +1,814 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./lib/algorithms/CoarsenedMatrix.h
+
+    Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
+Author: paboyle <paboyle@ph.ed.ac.uk>
+
+    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 */
+#ifndef  GRID_ALGORITHM_COARSENED_MATRIX_H
+#define  GRID_ALGORITHM_COARSENED_MATRIX_H
+
+#include <Grid/qcd/QCD.h> // needed for Dagger(Yes|No), Inverse(Yes|No)
+
+NAMESPACE_BEGIN(Grid);
+
+template<class vobj,class CComplex>
+inline void blockMaskedInnerProduct(Lattice<CComplex> &CoarseInner,
+				    const Lattice<decltype(innerProduct(vobj(),vobj()))> &FineMask,
+				    const Lattice<vobj> &fineX,
+				    const Lattice<vobj> &fineY)
+{
+  typedef decltype(innerProduct(vobj(),vobj())) dotp;
+
+  GridBase *coarse(CoarseInner.Grid());
+  GridBase *fine  (fineX.Grid());
+
+  Lattice<dotp> fine_inner(fine); fine_inner.Checkerboard() = fineX.Checkerboard();
+  Lattice<dotp> fine_inner_msk(fine);
+
+  // Multiply could be fused with innerProduct
+  // Single block sum kernel could do both masks.
+  fine_inner = localInnerProduct(fineX,fineY);
+  mult(fine_inner_msk, fine_inner,FineMask);
+  blockSum(CoarseInner,fine_inner_msk);
+}
+
+// Fine Object == (per site) type of fine field
+// nbasis      == number of deflation vectors
+template<class Fobj,class CComplex,int nbasis>
+class CoarsenedMatrix : public CheckerBoardedSparseMatrixBase<Lattice<iVector<CComplex,nbasis > > >  {
+public:
+    
+  typedef iVector<CComplex,nbasis >           siteVector;
+  typedef Lattice<CComplex >                  CoarseComplexField;
+  typedef Lattice<siteVector>                 CoarseVector;
+  typedef Lattice<iMatrix<CComplex,nbasis > > CoarseMatrix;
+  typedef iMatrix<CComplex,nbasis >  Cobj;
+  typedef Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  typedef CoarseVector FermionField;
+
+  // enrich interface, use default implementation as in FermionOperator ///////
+  void Dminus(CoarseVector const& in, CoarseVector& out) { out = in; }
+  void DminusDag(CoarseVector const& in, CoarseVector& out) { out = in; }
+  void ImportPhysicalFermionSource(CoarseVector const& input, CoarseVector& imported) { imported = input; }
+  void ImportUnphysicalFermion(CoarseVector const& input, CoarseVector& imported) { imported = input; }
+  void ExportPhysicalFermionSolution(CoarseVector const& solution, CoarseVector& exported) { exported = solution; };
+  void ExportPhysicalFermionSource(CoarseVector const& solution, CoarseVector& exported) { exported = solution; };
+
+  ////////////////////
+  // Data members
+  ////////////////////
+  Geometry         geom;
+  GridBase *       _grid; 
+  GridBase*        _cbgrid;
+  int hermitian;
+
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> Stencil; 
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> StencilEven;
+  CartesianStencil<siteVector,siteVector,DefaultImplParams> StencilOdd;
+
+  std::vector<CoarseMatrix> A;
+  std::vector<CoarseMatrix> Aeven;
+  std::vector<CoarseMatrix> Aodd;
+
+  CoarseMatrix AselfInv;
+  CoarseMatrix AselfInvEven;
+  CoarseMatrix AselfInvOdd;
+
+  Vector<RealD> dag_factor;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase * Grid(void)         { return _grid; };   // this is all the linalg routines need to know
+  GridBase * RedBlackGrid()     { return _cbgrid; };
+
+  int ConstEE() { return 0; }
+
+  void M (const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    SimpleCompressor<siteVector> compressor;
+
+    Stencil.HaloExchange(in,compressor);
+    autoView( in_v , in, AcceleratorRead);
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+      
+    Vector<Aview> AcceleratorViewContainer;
+  
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer.push_back(A[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    int osites=Grid()->oSites();
+
+    accelerator_for(sss, Grid()->oSites()*nbasis, Nsimd, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      calcComplex res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      for(int point=0;point<npoint;point++){
+
+	SE=Stencil_v.GetEntry(ptype,point,ss);
+	  
+	if(SE->_is_local) { 
+	  nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+	} else {
+	  nbr = coalescedRead(Stencil_v.CommBuf()[SE->_offset]);
+	}
+	acceleratorSynchronise();
+
+	for(int bb=0;bb<nbasis;bb++) {
+	  res = res + coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+	}
+      }
+      coalescedWrite(out_v[ss](b),res);
+      });
+
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  };
+
+  void Mdag (const CoarseVector &in, CoarseVector &out)
+  {
+    if(hermitian) {
+      // corresponds to Petrov-Galerkin coarsening
+      return M(in,out);
+    } else {
+      // corresponds to Galerkin coarsening
+      return MdagNonHermitian(in, out);
+    }
+  };
+
+  void MdagNonHermitian(const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(_grid,in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    SimpleCompressor<siteVector> compressor;
+
+    Stencil.HaloExchange(in,compressor);
+    autoView( in_v , in, AcceleratorRead);
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+
+    Vector<Aview> AcceleratorViewContainer;
+
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer.push_back(A[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    int osites=Grid()->oSites();
+
+    Vector<int> points(geom.npoint, 0);
+    for(int p=0; p<geom.npoint; p++)
+      points[p] = geom.points_dagger[p];
+
+    auto points_p = &points[0];
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    accelerator_for(sss, Grid()->oSites()*nbasis, Nsimd, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      calcComplex res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      for(int p=0;p<npoint;p++){
+        int point = points_p[p];
+
+	SE=Stencil_v.GetEntry(ptype,point,ss);
+
+	if(SE->_is_local) {
+	  nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+	} else {
+	  nbr = coalescedRead(Stencil_v.CommBuf()[SE->_offset]);
+	}
+	acceleratorSynchronise();
+
+	for(int bb=0;bb<nbasis;bb++) {
+	  res = res + dag_factor_p[b*nbasis+bb]*coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+	}
+      }
+      coalescedWrite(out_v[ss](b),res);
+      });
+
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  }
+
+  void MdirComms(const CoarseVector &in)
+  {
+    SimpleCompressor<siteVector> compressor;
+    Stencil.HaloExchange(in,compressor);
+  }
+  void MdirCalc(const CoarseVector &in, CoarseVector &out, int point)
+  {
+    conformable(_grid,in.Grid());
+    conformable(_grid,out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+
+    typedef LatticeView<Cobj> Aview;
+    Vector<Aview> AcceleratorViewContainer;
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer.push_back(A[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    autoView( out_v , out, AcceleratorWrite);
+    autoView( in_v  , in, AcceleratorRead);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    accelerator_for(sss, Grid()->oSites()*nbasis, Nsimd, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      calcComplex res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      SE=Stencil_v.GetEntry(ptype,point,ss);
+	  
+      if(SE->_is_local) { 
+	nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+      } else {
+	nbr = coalescedRead(Stencil_v.CommBuf()[SE->_offset]);
+      }
+      acceleratorSynchronise();
+
+      for(int bb=0;bb<nbasis;bb++) {
+	res = res + coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+      }
+      coalescedWrite(out_v[ss](b),res);
+    });
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  }
+  void MdirAll(const CoarseVector &in,std::vector<CoarseVector> &out)
+  {
+    this->MdirComms(in);
+    int ndir=geom.npoint-1;
+    if ((out.size()!=ndir)&&(out.size()!=ndir+1)) { 
+      std::cout <<"MdirAll out size "<< out.size()<<std::endl;
+      std::cout <<"MdirAll ndir "<< ndir<<std::endl;
+      assert(0);
+    }
+    for(int p=0;p<ndir;p++){
+      MdirCalc(in,out[p],p);
+    }
+  };
+  void Mdir(const CoarseVector &in, CoarseVector &out, int dir, int disp){
+
+    this->MdirComms(in);
+
+    MdirCalc(in,out,geom.point(dir,disp));
+  };
+
+  void Mdiag(const CoarseVector &in, CoarseVector &out)
+  {
+    int point=geom.npoint-1;
+    MdirCalc(in, out, point); // No comms
+  };
+
+  void Mooee(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerNo, InverseNo);
+  }
+
+  void MooeeInv(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerNo, InverseYes);
+  }
+
+  void MooeeDag(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerYes, InverseNo);
+  }
+
+  void MooeeInvDag(const CoarseVector &in, CoarseVector &out) {
+    MooeeInternal(in, out, DaggerYes, InverseYes);
+  }
+
+  void Meooe(const CoarseVector &in, CoarseVector &out) {
+    if(in.Checkerboard() == Odd) {
+      DhopEO(in, out, DaggerNo);
+    } else {
+      DhopOE(in, out, DaggerNo);
+    }
+  }
+
+  void MeooeDag(const CoarseVector &in, CoarseVector &out) {
+    if(in.Checkerboard() == Odd) {
+      DhopEO(in, out, DaggerYes);
+    } else {
+      DhopOE(in, out, DaggerYes);
+    }
+  }
+
+  void Dhop(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _grid); // verifies full grid
+    conformable(in.Grid(), out.Grid());
+
+    out.Checkerboard() = in.Checkerboard();
+
+    DhopInternal(Stencil, A, in, out, dag);
+  }
+
+  void DhopOE(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _cbgrid);    // verifies half grid
+    conformable(in.Grid(), out.Grid()); // drops the cb check
+
+    assert(in.Checkerboard() == Even);
+    out.Checkerboard() = Odd;
+
+    DhopInternal(StencilEven, Aodd, in, out, dag);
+  }
+
+  void DhopEO(const CoarseVector &in, CoarseVector &out, int dag) {
+    conformable(in.Grid(), _cbgrid);    // verifies half grid
+    conformable(in.Grid(), out.Grid()); // drops the cb check
+
+    assert(in.Checkerboard() == Odd);
+    out.Checkerboard() = Even;
+
+    DhopInternal(StencilOdd, Aeven, in, out, dag);
+  }
+
+  void MooeeInternal(const CoarseVector &in, CoarseVector &out, int dag, int inv) {
+    out.Checkerboard() = in.Checkerboard();
+    assert(in.Checkerboard() == Odd || in.Checkerboard() == Even);
+
+    CoarseMatrix *Aself = nullptr;
+    if(in.Grid()->_isCheckerBoarded) {
+      if(in.Checkerboard() == Odd) {
+        Aself = (inv) ? &AselfInvOdd : &Aodd[geom.npoint-1];
+        DselfInternal(StencilOdd, *Aself, in, out, dag);
+      } else {
+        Aself = (inv) ? &AselfInvEven : &Aeven[geom.npoint-1];
+        DselfInternal(StencilEven, *Aself, in, out, dag);
+      }
+    } else {
+      Aself = (inv) ? &AselfInv : &A[geom.npoint-1];
+      DselfInternal(Stencil, *Aself, in, out, dag);
+    }
+    assert(Aself != nullptr);
+  }
+
+  void DselfInternal(CartesianStencil<siteVector,siteVector,DefaultImplParams> &st, CoarseMatrix &a,
+                       const CoarseVector &in, CoarseVector &out, int dag) {
+    int point = geom.npoint-1;
+    autoView( out_v, out, AcceleratorWrite);
+    autoView( in_v,  in,  AcceleratorRead);
+    autoView( st_v,  st,  AcceleratorRead);
+    autoView( a_v,   a,   AcceleratorRead);
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    if(dag) {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        SE=st_v.GetEntry(ptype,point,ss);
+
+        if(SE->_is_local) {
+          nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+        } else {
+          nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+        }
+        acceleratorSynchronise();
+
+        for(int bb=0;bb<nbasis;bb++) {
+          res = res + dag_factor_p[b*nbasis+bb]*coalescedRead(a_v[ss](b,bb))*nbr(bb);
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    } else {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        SE=st_v.GetEntry(ptype,point,ss);
+
+        if(SE->_is_local) {
+          nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+        } else {
+          nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+        }
+        acceleratorSynchronise();
+
+        for(int bb=0;bb<nbasis;bb++) {
+          res = res + coalescedRead(a_v[ss](b,bb))*nbr(bb);
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    }
+  }
+
+  void DhopInternal(CartesianStencil<siteVector,siteVector,DefaultImplParams> &st, std::vector<CoarseMatrix> &a,
+                    const CoarseVector &in, CoarseVector &out, int dag) {
+    SimpleCompressor<siteVector> compressor;
+
+    st.HaloExchange(in,compressor);
+    autoView( in_v,  in,  AcceleratorRead);
+    autoView( out_v, out, AcceleratorWrite);
+    autoView( st_v , st,  AcceleratorRead);
+    typedef LatticeView<Cobj> Aview;
+
+    // determine in what order we need the points
+    int npoint = geom.npoint-1;
+    Vector<int> points(npoint, 0);
+    for(int p=0; p<npoint; p++)
+      points[p] = (dag && !hermitian) ? geom.points_dagger[p] : p;
+
+    auto points_p = &points[0];
+
+    Vector<Aview> AcceleratorViewContainer;
+    for(int p=0;p<npoint;p++) AcceleratorViewContainer.push_back(a[p].View(AcceleratorRead));
+    Aview *Aview_p = & AcceleratorViewContainer[0];
+
+    const int Nsimd = CComplex::Nsimd();
+    typedef decltype(coalescedRead(in_v[0])) calcVector;
+    typedef decltype(coalescedRead(in_v[0](0))) calcComplex;
+
+    RealD* dag_factor_p = &dag_factor[0];
+
+    if(dag) {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        for(int p=0;p<npoint;p++){
+          int point = points_p[p];
+          SE=st_v.GetEntry(ptype,point,ss);
+
+          if(SE->_is_local) {
+            nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+          } else {
+            nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+          }
+          acceleratorSynchronise();
+
+          for(int bb=0;bb<nbasis;bb++) {
+            res = res + dag_factor_p[b*nbasis+bb]*coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+          }
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    } else {
+      accelerator_for(sss, in.Grid()->oSites()*nbasis, Nsimd, {
+        int ss = sss/nbasis;
+        int b  = sss%nbasis;
+        calcComplex res = Zero();
+        calcVector nbr;
+        int ptype;
+        StencilEntry *SE;
+
+        for(int p=0;p<npoint;p++){
+          int point = points_p[p];
+          SE=st_v.GetEntry(ptype,point,ss);
+
+          if(SE->_is_local) {
+            nbr = coalescedReadPermute(in_v[SE->_offset],ptype,SE->_permute);
+          } else {
+            nbr = coalescedRead(st_v.CommBuf()[SE->_offset]);
+          }
+          acceleratorSynchronise();
+
+          for(int bb=0;bb<nbasis;bb++) {
+            res = res + coalescedRead(Aview_p[point][ss](b,bb))*nbr(bb);
+          }
+        }
+        coalescedWrite(out_v[ss](b),res);
+      });
+    }
+
+    for(int p=0;p<npoint;p++) AcceleratorViewContainer[p].ViewClose();
+  }
+  
+  CoarsenedMatrix(GridCartesian &CoarseGrid, int hermitian_=0) 	:
+    _grid(&CoarseGrid),
+    _cbgrid(new GridRedBlackCartesian(&CoarseGrid)),
+    geom(CoarseGrid._ndimension),
+    hermitian(hermitian_),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilEven(_cbgrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilOdd(_cbgrid,geom.npoint,Odd,geom.directions,geom.displacements),
+    A(geom.npoint,&CoarseGrid),
+    Aeven(geom.npoint,_cbgrid),
+    Aodd(geom.npoint,_cbgrid),
+    AselfInv(&CoarseGrid),
+    AselfInvEven(_cbgrid),
+    AselfInvOdd(_cbgrid),
+    dag_factor(nbasis*nbasis)
+  {
+    fillFactor();
+  };
+
+  CoarsenedMatrix(GridCartesian &CoarseGrid, GridRedBlackCartesian &CoarseRBGrid, int hermitian_=0) 	:
+
+    _grid(&CoarseGrid),
+    _cbgrid(&CoarseRBGrid),
+    geom(CoarseGrid._ndimension),
+    hermitian(hermitian_),
+    Stencil(&CoarseGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilEven(&CoarseRBGrid,geom.npoint,Even,geom.directions,geom.displacements),
+    StencilOdd(&CoarseRBGrid,geom.npoint,Odd,geom.directions,geom.displacements),
+    A(geom.npoint,&CoarseGrid),
+    Aeven(geom.npoint,&CoarseRBGrid),
+    Aodd(geom.npoint,&CoarseRBGrid),
+    AselfInv(&CoarseGrid),
+    AselfInvEven(&CoarseRBGrid),
+    AselfInvOdd(&CoarseRBGrid),
+    dag_factor(nbasis*nbasis)
+  {
+    fillFactor();
+  };
+
+  void fillFactor() {
+    Eigen::MatrixXd dag_factor_eigen = Eigen::MatrixXd::Ones(nbasis, nbasis);
+    if(!hermitian) {
+      const int nb = nbasis/2;
+      dag_factor_eigen.block(0,nb,nb,nb) *= -1.0;
+      dag_factor_eigen.block(nb,0,nb,nb) *= -1.0;
+    }
+
+    // GPU readable prefactor
+    thread_for(i, nbasis*nbasis, {
+      int j = i/nbasis;
+      int k = i%nbasis;
+      dag_factor[i] = dag_factor_eigen(j, k);
+    });
+  }
+
+  void CoarsenOperator(GridBase *FineGrid,LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    typedef Lattice<typename Fobj::tensor_reduced> FineComplexField;
+    typedef typename Fobj::scalar_type scalar_type;
+
+    std::cout << GridLogMessage<< "CoarsenMatrix "<< std::endl;
+
+    FineComplexField one(FineGrid); one=scalar_type(1.0,0.0);
+    FineComplexField zero(FineGrid); zero=scalar_type(0.0,0.0);
+
+    std::vector<FineComplexField> masks(geom.npoint,FineGrid);
+    FineComplexField imask(FineGrid); // contributions from within this block
+    FineComplexField omask(FineGrid); // contributions from outwith this block
+
+    FineComplexField evenmask(FineGrid);
+    FineComplexField oddmask(FineGrid); 
+
+    FineField     phi(FineGrid);
+    FineField     tmp(FineGrid);
+    FineField     zz(FineGrid); zz=Zero();
+    FineField    Mphi(FineGrid);
+    FineField    Mphie(FineGrid);
+    FineField    Mphio(FineGrid);
+    std::vector<FineField>     Mphi_p(geom.npoint,FineGrid);
+
+    Lattice<iScalar<vInteger> > coor (FineGrid);
+    Lattice<iScalar<vInteger> > bcoor(FineGrid);
+    Lattice<iScalar<vInteger> > bcb  (FineGrid); bcb = Zero();
+
+    CoarseVector iProj(Grid()); 
+    CoarseVector oProj(Grid()); 
+    CoarseVector SelfProj(Grid()); 
+    CoarseComplexField iZProj(Grid()); 
+    CoarseComplexField oZProj(Grid()); 
+
+    CoarseScalar InnerProd(Grid()); 
+
+    std::cout << GridLogMessage<< "CoarsenMatrix Orthog "<< std::endl;
+    // Orthogonalise the subblocks over the basis
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    // Compute the matrix elements of linop between this orthonormal
+    // set of vectors.
+    std::cout << GridLogMessage<< "CoarsenMatrix masks "<< std::endl;
+    int self_stencil=-1;
+    for(int p=0;p<geom.npoint;p++)
+    { 
+      int dir   = geom.directions[p];
+      int disp  = geom.displacements[p];
+      A[p]=Zero();
+      if( geom.displacements[p]==0){
+	self_stencil=p;
+      }
+
+      Integer block=(FineGrid->_rdimensions[dir])/(Grid()->_rdimensions[dir]);
+
+      LatticeCoordinate(coor,dir);
+
+      ///////////////////////////////////////////////////////
+      // Work out even and odd block checkerboarding for fast diagonal term
+      ///////////////////////////////////////////////////////
+      if ( disp==1 ) {
+	bcb   = bcb + div(coor,block);
+      }
+	
+      if ( disp==0 ) {
+	  masks[p]= Zero();
+      } else if ( disp==1 ) {
+	masks[p] = where(mod(coor,block)==(block-1),one,zero);
+      } else if ( disp==-1 ) {
+	masks[p] = where(mod(coor,block)==(Integer)0,one,zero);
+      }
+    }
+    evenmask = where(mod(bcb,2)==(Integer)0,one,zero);
+    oddmask  = one-evenmask;
+
+    assert(self_stencil!=-1);
+
+    for(int i=0;i<nbasis;i++){
+
+      phi=Subspace.subspace[i];
+
+      std::cout << GridLogMessage<< "CoarsenMatrix vector "<<i << std::endl;
+      linop.OpDirAll(phi,Mphi_p);
+      linop.OpDiag  (phi,Mphi_p[geom.npoint-1]);
+
+      for(int p=0;p<geom.npoint;p++){ 
+
+	Mphi = Mphi_p[p];
+
+	int dir   = geom.directions[p];
+	int disp  = geom.displacements[p];
+
+	if ( (disp==-1) || (!hermitian ) ) {
+
+	  ////////////////////////////////////////////////////////////////////////
+	  // Pick out contributions coming from this cell and neighbour cell
+	  ////////////////////////////////////////////////////////////////////////
+	  omask = masks[p];
+	  imask = one-omask;
+	
+	  for(int j=0;j<nbasis;j++){
+	    
+	    blockMaskedInnerProduct(oZProj,omask,Subspace.subspace[j],Mphi);
+	    
+	    autoView( iZProj_v , iZProj, AcceleratorRead) ;
+	    autoView( oZProj_v , oZProj, AcceleratorRead) ;
+	    autoView( A_p     ,  A[p], AcceleratorWrite);
+	    autoView( A_self  , A[self_stencil], AcceleratorWrite);
+
+	    accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{ coalescedWrite(A_p[ss](j,i),oZProj_v(ss)); });
+	    if ( hermitian && (disp==-1) ) {
+	      for(int pp=0;pp<geom.npoint;pp++){// Find the opposite link and set <j|A|i> = <i|A|j>*
+		int dirp   = geom.directions[pp];
+		int dispp  = geom.displacements[pp];
+		if ( (dirp==dir) && (dispp==1) ){
+		  auto sft = conjugate(Cshift(oZProj,dir,1));
+		  autoView( sft_v    ,  sft  , AcceleratorWrite);
+		  autoView( A_pp     ,  A[pp], AcceleratorWrite);
+		  accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{ coalescedWrite(A_pp[ss](i,j),sft_v(ss)); });
+		}
+	      }
+	    }
+
+	  }
+	}
+      }
+
+      ///////////////////////////////////////////
+      // Faster alternate self coupling.. use hermiticity to save 2x
+      ///////////////////////////////////////////
+      {
+	mult(tmp,phi,evenmask);  linop.Op(tmp,Mphie);
+	mult(tmp,phi,oddmask );  linop.Op(tmp,Mphio);
+
+	{
+	  autoView( tmp_      , tmp, AcceleratorWrite);
+	  autoView( evenmask_ , evenmask, AcceleratorRead);
+	  autoView( oddmask_  ,  oddmask, AcceleratorRead);
+	  autoView( Mphie_    ,  Mphie, AcceleratorRead);
+	  autoView( Mphio_    ,  Mphio, AcceleratorRead);
+	  accelerator_for(ss, FineGrid->oSites(), Fobj::Nsimd(),{ 
+	      coalescedWrite(tmp_[ss],evenmask_(ss)*Mphie_(ss) + oddmask_(ss)*Mphio_(ss));
+	    });
+	}
+
+	blockProject(SelfProj,tmp,Subspace.subspace);
+
+	autoView( SelfProj_ , SelfProj, AcceleratorRead);
+	autoView( A_self  , A[self_stencil], AcceleratorWrite);
+
+	accelerator_for(ss, Grid()->oSites(), Fobj::Nsimd(),{
+	  for(int j=0;j<nbasis;j++){
+	    coalescedWrite(A_self[ss](j,i), SelfProj_(ss)(j));
+	  }
+	});
+
+      }
+    }
+    if(hermitian) {
+      std::cout << GridLogMessage << " ForceHermitian, new code "<<std::endl;
+    }
+
+    InvertSelfStencilLink(); std::cout << GridLogMessage << "Coarse self link inverted" << std::endl;
+    FillHalfCbs(); std::cout << GridLogMessage << "Coarse half checkerboards filled" << std::endl;
+  }
+
+  void InvertSelfStencilLink() {
+    std::cout << GridLogDebug << "CoarsenedMatrix::InvertSelfStencilLink" << std::endl;
+    int localVolume = Grid()->lSites();
+
+    typedef typename Cobj::scalar_object scalar_object;
+
+    autoView(Aself_v,    A[geom.npoint-1], CpuRead);
+    autoView(AselfInv_v, AselfInv,         CpuWrite);
+    thread_for(site, localVolume, { // NOTE: Not able to bring this to GPU because of Eigen + peek/poke
+      Eigen::MatrixXcd selfLinkEigen    = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+      Eigen::MatrixXcd selfLinkInvEigen = Eigen::MatrixXcd::Zero(nbasis, nbasis);
+
+      scalar_object selfLink    = Zero();
+      scalar_object selfLinkInv = Zero();
+
+      Coordinate lcoor;
+
+      Grid()->LocalIndexToLocalCoor(site, lcoor);
+      peekLocalSite(selfLink, Aself_v, lcoor);
+
+      for (int i = 0; i < nbasis; ++i)
+        for (int j = 0; j < nbasis; ++j)
+          selfLinkEigen(i, j) = static_cast<ComplexD>(TensorRemove(selfLink(i, j)));
+
+      selfLinkInvEigen = selfLinkEigen.inverse();
+
+      for(int i = 0; i < nbasis; ++i)
+        for(int j = 0; j < nbasis; ++j)
+          selfLinkInv(i, j) = selfLinkInvEigen(i, j);
+
+      pokeLocalSite(selfLinkInv, AselfInv_v, lcoor);
+    });
+  }
+
+  void FillHalfCbs() {
+    std::cout << GridLogDebug << "CoarsenedMatrix::FillHalfCbs" << std::endl;
+    for(int p = 0; p < geom.npoint; ++p) {
+      pickCheckerboard(Even, Aeven[p], A[p]);
+      pickCheckerboard(Odd, Aodd[p], A[p]);
+    }
+    pickCheckerboard(Even, AselfInvEven, AselfInv);
+    pickCheckerboard(Odd, AselfInvOdd, AselfInv);
+  }
+};
+
+NAMESPACE_END(Grid);
+#endif

Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h

@@ -0,0 +1,418 @@
+/*************************************************************************************
+
+    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 Lattice< CComplex >   CoarseScalar; // used for inner products on fine field
+  typedef Lattice<Fobj >        FineField;
+  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;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridBase      * Grid(void)           { return _FineGrid; };   // 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 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;
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      int osites=Stencil.Grid()->oSites();
+      for(int ss=0;ss<osites;ss++){
+	for(int point=0;point<npoint;point++){
+	  auto SE = Stencil_v.GetEntry(point,ss);
+	  int o = SE->_offset;
+	  assert( o< osites);
+	}
+      }    
+    }
+
+    _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)
+  {
+    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;
+    ttot=-usecond();
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+    CoarseVector tin=in;
+
+    texch-=usecond();
+    CoarseVector pin  = Cell.Exchange(tin);
+    texch+=usecond();
+
+    CoarseVector pout(pin.Grid()); pout=Zero();
+
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+      
+    const int Nsimd = CComplex::Nsimd();
+    
+    int osites=pin.Grid()->oSites();
+    //    int gsites=pin.Grid()->gSites();
+
+    RealD flops = 1.0* npoint * nbasis * nbasis * 8 * osites;
+    RealD bytes = (1.0*osites*sizeof(siteMatrix)*npoint+2.0*osites*sizeof(siteVector))*npoint;
+      
+    //    for(int point=0;point<npoint;point++){
+    //      conformable(A[point],pin);
+    //    }
+
+    {
+      tviews-=usecond();
+      autoView( in_v , pin, AcceleratorRead);
+      autoView( out_v , pout, AcceleratorWrite);
+      autoView( Stencil_v  , Stencil, AcceleratorRead);
+      tviews+=usecond();
+      
+      for(int point=0;point<npoint;point++){
+	tviews-=usecond();
+	autoView( A_v, A[point],AcceleratorRead);
+	tviews+=usecond();
+	tmult-=usecond();
+	accelerator_for(sss, osites*nbasis, Nsimd, {
+
+	    typedef decltype(coalescedRead(in_v[0]))    calcVector;
+
+	    int ss = sss/nbasis;
+	    int b  = sss%nbasis;
+
+	    auto SE  = Stencil_v.GetEntry(point,ss);
+	    auto nbr = coalescedReadGeneralPermute(in_v[SE->_offset],SE->_permute,Nd);
+	    auto res = out_v(ss)(b);
+	    for(int bb=0;bb<nbasis;bb++) {
+	      res = res + coalescedRead(A_v[ss](b,bb))*nbr(bb);
+	    }
+	    coalescedWrite(out_v[ss](b),res);
+	});
+
+	tmult+=usecond();
+      }
+    }
+    text-=usecond();
+    out = Cell.Extract(pout);
+    text+=usecond();
+    ttot+=usecond();
+
+    std::cout << GridLogPerformance<<"Coarse 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<<"Coarse Mult ext  "<<text<<" us"<<std::endl;
+    std::cout << GridLogPerformance<<"Coarse Mult tot  "<<ttot<<" us"<<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])
+     */
+  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](j,i) = FT_v[sss](j);
+	    }
+        });
+      }
+      tinv+=usecond();
+    }
+
+    for(int p=0;p<geom.npoint;p++){
+      Coordinate coor({0,0,0,0,0});
+      auto sval = peekSite(_A[p],coor);
+    }
+
+    // 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;
+  }
+  void ExchangeCoarseLinks(void){
+    for(int p=0;p<geom.npoint;p++){
+      _A[p] = Cell.Exchange(_A[p]);
+      _Adag[p]= Cell.Exchange(_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);

Grid/algorithms/multigrid/Geometry.h

@@ -0,0 +1,243 @@
+/*************************************************************************************
+
+    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
+
+NAMESPACE_BEGIN(Grid);
+
+
+/////////////////////////////////////////////////////////////////
+// Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+
+class Geometry {
+public:
+  int npoint;
+  int base;
+  std::vector<int> directions   ;
+  std::vector<int> displacements;
+  std::vector<int> points_dagger;
+
+  Geometry(int _d)  {
+    
+    base = (_d==5) ? 1:0;
+
+    // make coarse grid stencil for 4d , not 5d
+    if ( _d==5 ) _d=4;
+
+    npoint = 2*_d+1;
+    directions.resize(npoint);
+    displacements.resize(npoint);
+    points_dagger.resize(npoint);
+    for(int d=0;d<_d;d++){
+      directions[d   ] = d+base;
+      directions[d+_d] = d+base;
+      displacements[d  ] = +1;
+      displacements[d+_d]= -1;
+      points_dagger[d   ] = d+_d;
+      points_dagger[d+_d] = d;
+    }
+    directions   [2*_d]=0;
+    displacements[2*_d]=0;
+    points_dagger[2*_d]=2*_d;
+  }
+
+  int point(int dir, int disp) {
+    assert(disp == -1 || disp == 0 || disp == 1);
+    assert(base+0 <= dir && dir < base+4);
+
+    // directions faster index = new indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  1  2  3  0  1  2  3  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  2  3  4  1  2  3  4  0
+    // disp +1 +1 +1 +1 -1 -1 -1 -1  0
+
+    // displacements faster index = old indexing
+    // 4d (base = 0):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   0  0  1  1  2  2  3  3  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+    // 5d (base = 1):
+    // point 0  1  2  3  4  5  6  7  8
+    // dir   1  1  2  2  3  3  4  4  0
+    // disp +1 -1 +1 -1 +1 -1 +1 -1  0
+
+    if(dir == 0 and disp == 0)
+      return 8;
+    else // New indexing
+      return (1 - disp) / 2 * 4 + dir - base;
+    // else // Old indexing
+    //   return (4 * (dir - base) + 1 - disp) / 2;
+  }
+};
+
+/////////////////////////////////////////////////////////////////
+// Less local equivalent of Geometry class in cartesian case
+/////////////////////////////////////////////////////////////////
+class NonLocalStencilGeometry {
+public:
+  int depth;
+  int hops;
+  int npoint;
+  std::vector<Coordinate> shifts;
+  Coordinate stencil_size;
+  Coordinate stencil_lo;
+  Coordinate stencil_hi;
+  GridCartesian *grid;
+  GridCartesian *Grid() {return grid;};
+  int Depth(void){return 1;};   // Ghost zone depth
+  int Hops(void){return hops;}; // # of hops=> level of corner fill in in stencil
+
+  virtual int DimSkip(void) =0;
+
+  virtual ~NonLocalStencilGeometry() {};
+
+  int  Reverse(int point)
+  {
+    int Nd = Grid()->Nd();
+    Coordinate shft = shifts[point];
+    Coordinate rev(Nd);
+    for(int mu=0;mu<Nd;mu++) rev[mu]= -shft[mu];
+    for(int p=0;p<npoint;p++){
+      if(rev==shifts[p]){
+	return p;
+      }
+    }
+    assert(0);
+    return -1;
+  }
+  void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    int Nd = this->grid->Nd();
+
+    int dd = this->DimSkip();
+    for(int s0=this->stencil_lo[dd+0];s0<=this->stencil_hi[dd+0];s0++){
+    for(int s1=this->stencil_lo[dd+1];s1<=this->stencil_hi[dd+1];s1++){
+    for(int s2=this->stencil_lo[dd+2];s2<=this->stencil_hi[dd+2];s2++){
+    for(int s3=this->stencil_lo[dd+3];s3<=this->stencil_hi[dd+3];s3++){
+      Coordinate sft(Nd,0);
+      sft[dd+0] = s0;
+      sft[dd+1] = s1;
+      sft[dd+2] = s2;
+      sft[dd+3] = s3;
+      int nhops = abs(s0)+abs(s1)+abs(s2)+abs(s3);
+      if(nhops<=this->hops) this->shifts.push_back(sft);
+    }}}}
+    this->npoint = this->shifts.size();
+    std::cout << GridLogMessage << "NonLocalStencilGeometry has "<< this->npoint << " terms in stencil "<<std::endl;
+  }
+  
+  NonLocalStencilGeometry(GridCartesian *_coarse_grid,int _hops) : grid(_coarse_grid), hops(_hops)
+  {
+    Coordinate latt = grid->GlobalDimensions();
+    stencil_size.resize(grid->Nd());
+    stencil_lo.resize(grid->Nd());
+    stencil_hi.resize(grid->Nd());
+    for(int d=0;d<grid->Nd();d++){
+     if ( latt[d] == 1 ) {
+      stencil_lo[d] = 0;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 1;
+     } else if ( latt[d] == 2 ) {
+      stencil_lo[d] = -1;
+      stencil_hi[d] = 0;
+      stencil_size[d]= 2;
+     } else if ( latt[d] > 2 ) {
+       stencil_lo[d] = -1;
+       stencil_hi[d] =  1;
+       stencil_size[d]= 3;
+     }
+    }
+  };
+
+};
+
+// Need to worry about red-black now
+class NonLocalStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  virtual int DimSkip(void) { return 0;};
+  NonLocalStencilGeometry4D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops) { };
+  virtual ~NonLocalStencilGeometry4D() {};
+};
+class NonLocalStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  virtual int DimSkip(void) { return 1; }; 
+  NonLocalStencilGeometry5D(GridCartesian *Coarse,int _hops) : NonLocalStencilGeometry(Coarse,_hops)  { };
+  virtual ~NonLocalStencilGeometry5D() {};
+};
+/*
+ * Bunch of different options classes
+ */
+class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry4D {
+public:
+  NextToNextToNextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,4)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNextToNextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNextToNextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,4)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NextToNearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,2)
+  {
+    this->BuildShifts();
+  };
+};
+class NextToNearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NextToNearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,2)
+  {
+    this->BuildShifts();
+  };
+};
+class NearestStencilGeometry4D : public  NonLocalStencilGeometry4D {
+public:
+  NearestStencilGeometry4D(GridCartesian *Coarse) :  NonLocalStencilGeometry4D(Coarse,1)
+  {
+    this->BuildShifts();
+  };
+};
+class NearestStencilGeometry5D : public  NonLocalStencilGeometry5D {
+public:
+  NearestStencilGeometry5D(GridCartesian *Coarse) :  NonLocalStencilGeometry5D(Coarse,1)
+  {
+    this->BuildShifts();
+  };
+};
+
+NAMESPACE_END(Grid);

Grid/algorithms/multigrid/Multigrid.h

@@ -0,0 +1,33 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid
+
+    Source file: Grid/algorithms/multigrid/MultiGrid.h
+
+    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 */
+#pragma once
+
+#include <Grid/algorithms/multigrid/Aggregates.h>
+#include <Grid/algorithms/multigrid/Geometry.h>
+#include <Grid/algorithms/multigrid/CoarsenedMatrix.h>
+#include <Grid/algorithms/multigrid/GeneralCoarsenedMatrix.h>

Grid/cartesian/Cartesian_base.h

@@ -70,8 +70,8 @@ public:
   Coordinate _istride;    // Inner stride i.e. within simd lane
   int _osites;                  // _isites*_osites = product(dimensions).
   int _isites;
-  int _fsites;                  // _isites*_osites = product(dimensions).
+  int64_t _fsites;                  // _isites*_osites = product(dimensions).
-  int _gsites;
+  int64_t _gsites;
   Coordinate _slice_block;// subslice information
   Coordinate _slice_stride;
   Coordinate _slice_nblock;
@@ -183,7 +183,7 @@ public:
   inline int Nsimd(void)  const { return _isites; };// Synonymous with iSites
   inline int oSites(void) const { return _osites; };
   inline int lSites(void) const { return _isites*_osites; }; 
-  inline int gSites(void) const { return _isites*_osites*_Nprocessors; }; 
+  inline int64_t gSites(void) const { return (int64_t)_isites*(int64_t)_osites*(int64_t)_Nprocessors; }; 
   inline int Nd    (void) const { return _ndimension;};
 
   inline const Coordinate LocalStarts(void)             { return _lstart;    };
@@ -214,7 +214,7 @@ public:
   ////////////////////////////////////////////////////////////////
   // Global addressing
   ////////////////////////////////////////////////////////////////
-  void GlobalIndexToGlobalCoor(int gidx,Coordinate &gcoor){
+  void GlobalIndexToGlobalCoor(int64_t gidx,Coordinate &gcoor){
     assert(gidx< gSites());
     Lexicographic::CoorFromIndex(gcoor,gidx,_gdimensions);
   }
@@ -222,7 +222,7 @@ public:
     assert(lidx<lSites());
     Lexicographic::CoorFromIndex(lcoor,lidx,_ldimensions);
   }
-  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int & gidx){
+  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int64_t & gidx){
     gidx=0;
     int mult=1;
     for(int mu=0;mu<_ndimension;mu++) {

Grid/lattice/Lattice_base.h

@@ -360,7 +360,7 @@ public:
 
 template<class vobj> std::ostream& operator<< (std::ostream& stream, const Lattice<vobj> &o){
   typedef typename vobj::scalar_object sobj;
-  for(int g=0;g<o.Grid()->_gsites;g++){
+  for(int64_t g=0;g<o.Grid()->_gsites;g++){
 
     Coordinate gcoor;
     o.Grid()->GlobalIndexToGlobalCoor(g,gcoor);

Grid/lattice/Lattice_rng.h

@@ -361,9 +361,14 @@ public:
     _bernoulli.resize(_vol,std::discrete_distribution<int32_t>{1,1});
     _uid.resize(_vol,std::uniform_int_distribution<uint32_t>() );
   }
-
+  template <class vobj,class distribution> inline void fill(Lattice<vobj> &l,std::vector<distribution> &dist)
-  template <class vobj,class distribution> inline void fill(Lattice<vobj> &l,std::vector<distribution> &dist){
+  {
-
+    if ( l.Grid()->_isCheckerBoarded ) {
+      Lattice<vobj> tmp(_grid);
+      fill(tmp,dist);
+      pickCheckerboard(l.Checkerboard(),l,tmp);
+      return;
+    }
     typedef typename vobj::scalar_object scalar_object;
     typedef typename vobj::scalar_type scalar_type;
     typedef typename vobj::vector_type vector_type;
@@ -427,7 +432,7 @@ public:
 #if 1
     thread_for( lidx, _grid->lSites(), {
 
-	int gidx;
+	int64_t gidx;
 	int o_idx;
 	int i_idx;
 	int rank;

Grid/lattice/Lattice_transfer.h

@@ -471,13 +471,13 @@ inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData)
 
   vobj zz = Zero();
   
-  accelerator_for(sc,coarse->oSites(),1,{
+  accelerator_for(sc,coarse->oSites(),vobj::Nsimd(),{
 
       // One thread per sub block
       Coordinate coor_c(_ndimension);
       Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);  // Block coordinate
 
-      vobj cd = zz;
+      auto cd = coalescedRead(zz);
       
       for(int sb=0;sb<blockVol;sb++){
 
@@ -488,10 +488,10 @@ inline void blockSum(Lattice<vobj> &coarseData,const Lattice<vobj> &fineData)
 	for(int d=0;d<_ndimension;d++) coor_f[d]=coor_c[d]*block_r[d] + coor_b[d];
 	Lexicographic::IndexFromCoor(coor_f,sf,fine_rdimensions);
 
-	cd=cd+fineData_p[sf];
+	cd=cd+coalescedRead(fineData_p[sf]);
       }
 
-      coarseData_p[sc] = cd;
+      coalescedWrite(coarseData_p[sc],cd);
 
     });
   return;
@@ -1054,7 +1054,7 @@ void Replicate(const Lattice<vobj> &coarse,Lattice<vobj> & fine)
 
   Coordinate fcoor(nd);
   Coordinate ccoor(nd);
-  for(int g=0;g<fg->gSites();g++){
+  for(int64_t g=0;g<fg->gSites();g++){
 
     fg->GlobalIndexToGlobalCoor(g,fcoor);
     for(int d=0;d<nd;d++){

Grid/lattice/PaddedCell.h

@@ -63,8 +63,9 @@ public:
     dims=_grid->Nd();
     AllocateGrids();
     Coordinate local     =unpadded_grid->LocalDimensions();
+    Coordinate procs     =unpadded_grid->ProcessorGrid();
     for(int d=0;d<dims;d++){
-      assert(local[d]>=depth);
+      if ( procs[d] > 1 ) assert(local[d]>=depth);
     }
   }
   void DeleteGrids(void)
@@ -85,7 +86,9 @@ public:
     // expand up one dim at a time
     for(int d=0;d<dims;d++){
 
-      plocal[d] += 2*depth; 
+      if ( processors[d] > 1 ) { 
+	plocal[d] += 2*depth; 
+      }
       
       for(int d=0;d<dims;d++){
 	global[d] = plocal[d]*processors[d];
@@ -97,11 +100,17 @@ public:
   template<class vobj>
   inline Lattice<vobj> Extract(const Lattice<vobj> &in) const
   {
+    Coordinate processors=unpadded_grid->_processors;
+
     Lattice<vobj> out(unpadded_grid);
 
     Coordinate local     =unpadded_grid->LocalDimensions();
-    Coordinate fll(dims,depth); // depends on the MPI spread
+    // depends on the MPI spread      
+    Coordinate fll(dims,depth);
     Coordinate tll(dims,0); // depends on the MPI spread
+    for(int d=0;d<dims;d++){
+      if( processors[d]==1 ) fll[d]=0;
+    }
     localCopyRegion(in,out,fll,tll,local);
     return out;
   }
@@ -120,6 +129,7 @@ public:
   template<class vobj>
   inline Lattice<vobj> Expand(int dim, const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
+    Coordinate processors=unpadded_grid->_processors;
     GridBase *old_grid = in.Grid();
     GridCartesian *new_grid = grids[dim];//These are new grids
     Lattice<vobj>  padded(new_grid);
@@ -133,35 +143,47 @@ public:
 
     double tins=0, tshift=0;
 
-    // Middle bit
+    int islocal = 0 ;
-    double t = usecond();
+    if ( processors[dim] == 1 ) islocal = 1;
-    for(int x=0;x<local[dim];x++){
+
-      InsertSliceLocal(in,padded,x,depth+x,dim);
+    if ( islocal ) {
+      
+      double t = usecond();
+      for(int x=0;x<local[dim];x++){
+	InsertSliceLocal(in,padded,x,x,dim);
+      }
+      tins += usecond() - t;
+      
+    } else { 
+      // Middle bit
+      double t = usecond();
+      for(int x=0;x<local[dim];x++){
+	InsertSliceLocal(in,padded,x,depth+x,dim);
+      }
+      tins += usecond() - t;
+    
+      // High bit
+      t = usecond();
+      shifted = cshift.Cshift(in,dim,depth);
+      tshift += usecond() - t;
+
+      t=usecond();
+      for(int x=0;x<depth;x++){
+	InsertSliceLocal(shifted,padded,local[dim]-depth+x,depth+local[dim]+x,dim);
+      }
+      tins += usecond() - t;
+    
+      // Low bit
+      t = usecond();
+      shifted = cshift.Cshift(in,dim,-depth);
+      tshift += usecond() - t;
+    
+      t = usecond();
+      for(int x=0;x<depth;x++){
+	InsertSliceLocal(shifted,padded,x,x,dim);
+      }
+      tins += usecond() - t;
     }
-    tins += usecond() - t;
-    
-    // High bit
-    t = usecond();
-    shifted = cshift.Cshift(in,dim,depth);
-    tshift += usecond() - t;
-
-    t=usecond();
-    for(int x=0;x<depth;x++){
-      InsertSliceLocal(shifted,padded,local[dim]-depth+x,depth+local[dim]+x,dim);
-    }
-    tins += usecond() - t;
-    
-    // Low bit
-    t = usecond();
-    shifted = cshift.Cshift(in,dim,-depth);
-    tshift += usecond() - t;
-    
-    t = usecond();
-    for(int x=0;x<depth;x++){
-      InsertSliceLocal(shifted,padded,x,x,dim);
-    }
-    tins += usecond() - t;
-
     std::cout << GridLogPerformance << "PaddedCell::Expand timings: cshift:" << tshift/1000 << "ms, insert-slice:" << tins/1000 << "ms" << std::endl;
     
     return padded;

Grid/qcd/utils/WilsonLoops.h

@@ -487,7 +487,7 @@ public:
     for(int mu=0;mu<Nd;mu++){
       { //view scope
 	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View();
+	auto gStencil_v = gStencil.View(AcceleratorRead);
 	
 	accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
 	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
@@ -1199,7 +1199,7 @@ public:
 
       { //view scope
 	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View();
+	auto gStencil_v = gStencil.View(AcceleratorRead);
 
 	accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
 	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;

Grid/simd/Grid_vector_types.h

@@ -1130,6 +1130,14 @@ static_assert(sizeof(SIMD_Ftype) == sizeof(SIMD_Itype), "SIMD vector lengths inc
 #endif
 #endif
 
+// Fixme need coalesced read gpermute
+template<class vobj> void gpermute(vobj & inout,int perm){
+  vobj tmp=inout;
+  if (perm & 0x1 ) { permute(inout,tmp,0); tmp=inout;}
+  if (perm & 0x2 ) { permute(inout,tmp,1); tmp=inout;}
+  if (perm & 0x4 ) { permute(inout,tmp,2); tmp=inout;}
+  if (perm & 0x8 ) { permute(inout,tmp,3); tmp=inout;}
+}
 
 NAMESPACE_END(Grid);
 

Grid/stencil/GeneralLocalStencil.h

@@ -46,7 +46,7 @@ class GeneralLocalStencilView {
   accelerator_inline GeneralStencilEntry * GetEntry(int point,int osite) { 
     return & this->_entries_p[point+this->_npoints*osite]; 
   }
-
+  void ViewClose(void){};
 };
 ////////////////////////////////////////
 // The Stencil Class itself
@@ -61,7 +61,7 @@ protected:
 public: 
   GridBase *Grid(void) const { return _grid; }
 
-  View_type View(void) const {
+  View_type View(int mode) const {
     View_type accessor(*( (View_type *) this));
     return accessor;
   }

Grid/threads/Accelerator.h

@@ -137,6 +137,18 @@ inline void cuda_mem(void)
     dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
     LambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda);	\
   }
+#define prof_accelerator_for2dNB( iter1, num1, iter2, num2, nsimd, ... )	\
+  {									\
+    int nt=acceleratorThreads();					\
+    typedef uint64_t Iterator;						\
+    auto lambda = [=] accelerator					\
+      (Iterator iter1,Iterator iter2,Iterator lane) mutable {		\
+      __VA_ARGS__;							\
+    };									\
+    dim3 cu_threads(nsimd,acceleratorThreads(),1);			\
+    dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
+    ProfileLambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda); \
+  }
 
 #define accelerator_for6dNB(iter1, num1,				\
                             iter2, num2,				\
@@ -157,6 +169,20 @@ inline void cuda_mem(void)
     Lambda6Apply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,num3,num4,num5,num6,lambda); \
   }
 
+
+#define accelerator_for2dNB( iter1, num1, iter2, num2, nsimd, ... )	\
+  {									\
+    int nt=acceleratorThreads();					\
+    typedef uint64_t Iterator;						\
+    auto lambda = [=] accelerator					\
+      (Iterator iter1,Iterator iter2,Iterator lane) mutable {		\
+      __VA_ARGS__;							\
+    };									\
+    dim3 cu_threads(nsimd,acceleratorThreads(),1);			\
+    dim3 cu_blocks ((num1+nt-1)/nt,num2,1);				\
+    LambdaApply<<<cu_blocks,cu_threads,0,computeStream>>>(num1,num2,nsimd,lambda);	\
+  }
+
 template<typename lambda>  __global__
 void LambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
 {
@@ -168,6 +194,17 @@ void LambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
     Lambda(x,y,z);
   }
 }
+template<typename lambda>  __global__
+void ProfileLambdaApply(uint64_t num1, uint64_t num2, uint64_t num3, lambda Lambda)
+{
+  // Weird permute is to make lane coalesce for large blocks
+  uint64_t x = threadIdx.y + blockDim.y*blockIdx.x;
+  uint64_t y = threadIdx.z + blockDim.z*blockIdx.y;
+  uint64_t z = threadIdx.x;
+  if ( (x < num1) && (y<num2) && (z<num3) ) {
+    Lambda(x,y,z);
+  }
+}
 
 template<typename lambda>  __global__
 void Lambda6Apply(uint64_t num1, uint64_t num2, uint64_t num3,
@@ -208,6 +245,7 @@ inline void *acceleratorAllocShared(size_t bytes)
   if( err != cudaSuccess ) {
     ptr = (void *) NULL;
     printf(" cudaMallocManaged failed for %d %s \n",bytes,cudaGetErrorString(err));
+    assert(0);
   }
   return ptr;
 };
@@ -460,6 +498,9 @@ inline void acceleratorCopySynchronise(void) { hipStreamSynchronize(copyStream);
 #if defined(GRID_SYCL) || defined(GRID_CUDA) || defined(GRID_HIP)
 // FIXME -- the non-blocking nature got broken March 30 2023 by PAB
 #define accelerator_forNB( iter1, num1, nsimd, ... ) accelerator_for2dNB( iter1, num1, iter2, 1, nsimd, {__VA_ARGS__} );  
+#define prof_accelerator_for( iter1, num1, nsimd, ... ) \
+  prof_accelerator_for2dNB( iter1, num1, iter2, 1, nsimd, {__VA_ARGS__} );\
+  accelerator_barrier(dummy);
 
 #define accelerator_for( iter, num, nsimd, ... )		\
   accelerator_forNB(iter, num, nsimd, { __VA_ARGS__ } );	\

Grid/util/Coordinate.h

@@ -94,6 +94,13 @@ static constexpr int MaxDims = GRID_MAX_LATTICE_DIMENSION;
 
 typedef AcceleratorVector<int,MaxDims> Coordinate;
 
+template<class T,int _ndim>
+inline bool operator==(const AcceleratorVector<T,_ndim> &v,const AcceleratorVector<T,_ndim> &w)
+{
+  if (v.size()!=w.size()) return false;
+  for(int i=0;i<v.size();i++) if ( v[i]!=w[i] ) return false;
+  return true;
+}
 template<class T,int _ndim>
 inline std::ostream & operator<<(std::ostream &os, const AcceleratorVector<T,_ndim> &v)
 {

Grid/util/Lexicographic.h

@@ -8,7 +8,7 @@ namespace Grid{
   public:
 
     template<class coor_t>
-    static accelerator_inline void CoorFromIndex (coor_t& coor,int index,const coor_t &dims){
+    static accelerator_inline void CoorFromIndex (coor_t& coor,int64_t index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=0;d<nd;d++){
@@ -18,28 +18,45 @@ namespace Grid{
     }
 
     template<class coor_t>
-    static accelerator_inline void IndexFromCoor (const coor_t& coor,int &index,const coor_t &dims){
+    static accelerator_inline void IndexFromCoor (const coor_t& coor,int64_t &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=0;d<nd;d++){
-	index = index+stride*coor[d];
+	index = index+(int64_t)stride*coor[d];
 	stride=stride*dims[d];
       }
     }
+    template<class coor_t>
+    static accelerator_inline void IndexFromCoor (const coor_t& coor,int &index,const coor_t &dims){
+      int64_t index64;
+      IndexFromCoor(coor,index64,dims);
+      assert(index64<2*1024*1024*1024LL);
+      index = (int) index64;
+    }
 
     template<class coor_t>
-    static inline void IndexFromCoorReversed (const coor_t& coor,int &index,const coor_t &dims){
+    static inline void IndexFromCoorReversed (const coor_t& coor,int64_t &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=nd-1;d>=0;d--){
-	index = index+stride*coor[d];
+	index = index+(int64_t)stride*coor[d];
 	stride=stride*dims[d];
       }
     }
     template<class coor_t>
-    static inline void CoorFromIndexReversed (coor_t& coor,int index,const coor_t &dims){
+    static inline void IndexFromCoorReversed (const coor_t& coor,int &index,const coor_t &dims){
+      int64_t index64;
+      IndexFromCoorReversed(coor,index64,dims);
+      if ( index64>=2*1024*1024*1024LL ){
+	std::cout << " IndexFromCoorReversed " << coor<<" index " << index64<< " dims "<<dims<<std::endl;
+      }
+      assert(index64<2*1024*1024*1024LL);
+      index = (int) index64;
+    }
+    template<class coor_t>
+    static inline void CoorFromIndexReversed (coor_t& coor,int64_t index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=nd-1;d>=0;d--){

systems/Frontier/benchmarks/bench2.slurm

@@ -0,0 +1,43 @@
+#!/bin/bash -l
+#SBATCH --job-name=bench
+##SBATCH --partition=small-g
+#SBATCH --nodes=2
+#SBATCH --ntasks-per-node=8
+#SBATCH --cpus-per-task=7
+#SBATCH --gpus-per-node=8
+#SBATCH --time=00:10:00
+#SBATCH --account=phy157_dwf
+#SBATCH --gpu-bind=none
+#SBATCH --exclusive
+#SBATCH --mem=0
+
+cat << EOF > select_gpu
+#!/bin/bash
+export GPU_MAP=(0 1 2 3 7 6 5 4)
+export NUMA_MAP=(3 3 1 1 2 2 0 0)
+export GPU=\${GPU_MAP[\$SLURM_LOCALID]}
+export NUMA=\${NUMA_MAP[\$SLURM_LOCALID]}
+export HIP_VISIBLE_DEVICES=\$GPU
+unset ROCR_VISIBLE_DEVICES
+echo RANK \$SLURM_LOCALID using GPU \$GPU    
+exec numactl -m \$NUMA -N \$NUMA \$*
+EOF
+
+chmod +x ./select_gpu
+
+root=$HOME/Frontier/Grid/systems/Frontier/
+source ${root}/sourceme.sh
+
+export OMP_NUM_THREADS=7
+export MPICH_GPU_SUPPORT_ENABLED=1
+export MPICH_SMP_SINGLE_COPY_MODE=XPMEM
+
+for vol in 32.32.32.64
+do
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-overlap --shm 2048 --shm-mpi 0 --grid $vol  > log.shm0.ov.$vol
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-overlap --shm 2048 --shm-mpi 1 --grid $vol  > log.shm1.ov.$vol
+
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-sequential --shm 2048 --shm-mpi 0 --grid $vol  > log.shm0.seq.$vol
+srun ./select_gpu ./Benchmark_dwf_fp32 --mpi 2.2.2.2 --accelerator-threads 8 --comms-sequential --shm 2048 --shm-mpi 1 --grid $vol > log.shm1.seq.$vol
+done
+

systems/Frontier/config-command

@@ -0,0 +1,23 @@
+CLIME=`spack find --paths c-lime@2-3-9 | grep c-lime| cut -c 15-`
+../../configure --enable-comms=mpi-auto \
+--with-lime=$CLIME \
+--enable-unified=no \
+--enable-shm=nvlink \
+--enable-tracing=timer \
+--enable-accelerator=hip \
+--enable-gen-simd-width=64 \
+--disable-gparity \
+--disable-fermion-reps \
+--enable-simd=GPU \
+--enable-accelerator-cshift \
+--with-gmp=$OLCF_GMP_ROOT \
+--with-fftw=$FFTW_DIR/.. \
+--with-mpfr=/opt/cray/pe/gcc/mpfr/3.1.4/ \
+--disable-fermion-reps \
+CXX=hipcc MPICXX=mpicxx \
+CXXFLAGS="-fPIC -I{$ROCM_PATH}/include/ -std=c++14 -I${MPICH_DIR}/include -L/lib64 " \
+ LDFLAGS="-L/lib64 -L${MPICH_DIR}/lib -lmpi -L${CRAY_MPICH_ROOTDIR}/gtl/lib -lmpi_gtl_hsa -lamdhip64 "
+
+
+
+

systems/Frontier/mpiwrapper.sh

@@ -0,0 +1,13 @@
+#!/bin/bash
+
+lrank=$SLURM_LOCALID
+lgpu=(0 1 2 3 7 6 5 4)
+
+export ROCR_VISIBLE_DEVICES=${lgpu[$lrank]}
+
+echo "`hostname` - $lrank device=$ROCR_VISIBLE_DEVICES "
+
+$*
+
+
+

systems/Frontier/sourceme.sh

@@ -0,0 +1,13 @@
+. /autofs/nccs-svm1_home1/paboyle/Crusher/Grid/spack/share/spack/setup-env.sh
+spack load c-lime
+#export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/sw/crusher/spack-envs/base/opt/cray-sles15-zen3/gcc-11.2.0/gperftools-2.9.1-72ubwtuc5wcz2meqltbfdb76epufgzo2/lib
+module load emacs 
+module load PrgEnv-gnu
+module load rocm
+module load cray-mpich/8.1.23
+module load gmp
+module load cray-fftw
+module load craype-accel-amd-gfx90a
+export LD_LIBRARY_PATH=/opt/gcc/mpfr/3.1.4/lib:$LD_LIBRARY_PATH
+#Hack for lib
+#export LD_LIBRARY_PATH=`pwd`:$LD_LIBRARY_PATH

systems/Frontier/wrap.sh

@@ -0,0 +1,9 @@
+#!/bin/sh
+
+export HIP_VISIBLE_DEVICES=$ROCR_VISIBLE_DEVICES
+unset ROCR_VISIBLE_DEVICES
+
+#rank=$SLURM_PROCID
+#rocprof -d rocprof.$rank -o rocprof.$rank/results.rank$SLURM_PROCID.csv --sys-trace $@
+
+$@

systems/mac-arm/config-command-mpi

@@ -1,4 +1,3 @@
 BREW=/opt/local/
 MPICXX=mpicxx ../../configure --enable-simd=GEN --enable-comms=mpi-auto --enable-unified=yes --prefix $HOME/QCD/GridInstall --with-lime=/Users/peterboyle/QCD/SciDAC/install/ --with-openssl=$BREW --disable-fermion-reps --disable-gparity --disable-debug
 
-

tests/debug/Test_general_coarse.cc

@@ -0,0 +1,235 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+///////////////////////
+// Tells little dirac op to use MdagM as the .Op()
+///////////////////////
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  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){
+    wrapped.HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=4;
+
+  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
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/2;
+  }
+
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt,
+							    GridDefaultSimd(Nd,vComplex::Nsimd()),
+							    GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  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);
+
+  LatticeFermion    src(FGrid); random(RNG5,src);
+  LatticeFermion result(FGrid); result=Zero();
+  LatticeFermion    ref(FGrid); ref=Zero();
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid);
+  SU<Nc>::HotConfiguration(RNG4,Umu);
+  //  Umu=Zero();
+  
+  RealD mass=0.1;
+  RealD M5=1.8;
+
+  DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+
+  const int nbasis = 16;
+  const int cb = 0 ;
+  LatticeFermion prom(FGrid);
+
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+
+  std::cout<<GridLogMessage<<"Calling Aggregation class" <<std::endl;
+
+  ///////////////////////////////////////////////////////////
+  // Squared operator is in HermOp
+  ///////////////////////////////////////////////////////////
+  MdagMLinearOperator<DomainWallFermionD,LatticeFermion> HermDefOp(Ddwf);
+
+  ///////////////////////////////////////////////////
+  // Random aggregation space
+  ///////////////////////////////////////////////////
+  std::cout<<GridLogMessage << "Building random aggregation class"<< std::endl;
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace Aggregates(Coarse5d,FGrid,cb);
+  Aggregates.CreateSubspaceRandom(RNG5);
+
+  ///////////////////////////////////////////////////
+  // Build little dirac op
+  ///////////////////////////////////////////////////
+  std::cout<<GridLogMessage << "Building little Dirac operator"<< std::endl;
+
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+  LittleDiracOperator LittleDiracOp(geom,FGrid,Coarse5d);
+  LittleDiracOperator LittleDiracOpCol(geom,FGrid,Coarse5d);
+
+  HermOpAdaptor<LatticeFermionD> HOA(HermDefOp);
+
+  int pp=16;
+  LittleDiracOp.CoarsenOperator(HOA,Aggregates);
+  
+  ///////////////////////////////////////////////////
+  // Test the operator
+  ///////////////////////////////////////////////////
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_res_dag(Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+
+  subspace=Aggregates.subspace;
+
+  //  random(CRNG,c_src);
+  c_src = 1.0;
+
+  blockPromote(c_src,err,subspace);
+
+  prom=Zero();
+  for(int b=0;b<nbasis;b++){
+    prom=prom+subspace[b];
+  }
+  err=err-prom; 
+  std::cout<<GridLogMessage<<"Promoted back from subspace: err "<<norm2(err)<<std::endl;
+  std::cout<<GridLogMessage<<"c_src "<<norm2(c_src)<<std::endl;
+  std::cout<<GridLogMessage<<"prom  "<<norm2(prom)<<std::endl;
+
+  HermDefOp.HermOp(prom,tmp);
+
+  blockProject(c_proj,tmp,subspace);
+  std::cout<<GridLogMessage<<" Called Big Dirac Op "<<norm2(tmp)<<std::endl;
+
+  std::cout<<GridLogMessage<<" Calling little Dirac Op "<<std::endl;
+  LittleDiracOp.M(c_src,c_res);
+  LittleDiracOp.Mdag(c_src,c_res_dag);
+
+  std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
+  std::cout<<GridLogMessage<<"Little dop dag : "<<norm2(c_res_dag)<<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;
+
+  c_res_dag = c_res_dag - c_res;
+  std::cout<<GridLogMessage<<"Little dopDag - dop: "<<norm2(c_res_dag)<<std::endl;
+
+  std::cout<<GridLogMessage << "Testing Hermiticity stochastically "<< std::endl;
+  CoarseVector phi(Coarse5d);
+  CoarseVector chi(Coarse5d);
+  CoarseVector Aphi(Coarse5d);
+  CoarseVector Achi(Coarse5d);
+
+  random(CRNG,phi);
+  random(CRNG,chi);
+
+  std::cout<<GridLogMessage<<"Made randoms "<<norm2(phi)<<" " << norm2(chi)<<std::endl;
+
+  LittleDiracOp.M(phi,Aphi);
+
+  LittleDiracOp.Mdag(chi,Achi);
+
+  std::cout<<GridLogMessage<<"Aphi "<<norm2(Aphi)<<" A chi" << norm2(Achi)<<std::endl;
+
+  ComplexD pAc = innerProduct(chi,Aphi);
+  ComplexD cAp = innerProduct(phi,Achi);
+  ComplexD cAc = innerProduct(chi,Achi);
+  ComplexD pAp = innerProduct(phi,Aphi);
+
+  std::cout<<GridLogMessage<< "pAc "<<pAc<<" cAp "<< cAp<< " diff "<<pAc-adj(cAp)<<std::endl;
+  std::cout<<GridLogMessage<< "pAp "<<pAp<<" cAc "<< cAc<<"Should be real"<< std::endl;
+
+  std::cout<<GridLogMessage<<"Testing linearity"<<std::endl;
+  CoarseVector PhiPlusChi(Coarse5d);
+  CoarseVector APhiPlusChi(Coarse5d);
+  CoarseVector linerr(Coarse5d);
+  PhiPlusChi = phi+chi;
+  LittleDiracOp.M(PhiPlusChi,APhiPlusChi);
+
+  linerr= APhiPlusChi-Aphi;
+  linerr= linerr-Achi;
+  std::cout<<GridLogMessage<<"**Diff "<<norm2(linerr)<<std::endl;
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_hdcg.cc

@@ -0,0 +1,408 @@
+    /*************************************************************************************
+
+    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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+//#include <Grid/algorithms/GeneralCoarsenedMatrix.h>
+#include <Grid/algorithms/iterative/AdefGeneric.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);
+  }
+  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);
+  }    
+  RD.close();
+  Operator.ExchangeCoarseLinks();
+#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);
+  }
+  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);
+  }    
+  RD.close();
+#endif
+}
+
+
+template<class Field> class TestSolver : public LinearFunction<Field> {
+public:
+  TestSolver() {};
+  void operator() (const Field &in, Field &out){    out = Zero();  }     
+};
+
+
+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 Matrix> 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);
+  }
+};
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=16;
+  const int nbasis = 40;
+  const int cb = 0 ;
+  RealD mass=0.01;
+  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 clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/4;
+  }
+  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);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.4000");
+  NerscIO::readConfiguration(Umu,header,file);
+
+  //////////////////////// 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);
+  
+  LatticeFermion result(FrbGrid); result=Zero();
+
+  LatticeFermion    src(FrbGrid); random(RNG5,src);
+
+  // 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);
+  NearestStencilGeometry5D geom_nn(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);
+
+  bool load=false;
+  if ( load ) {
+    LoadBasis(Aggregates,"Subspace.scidac");
+    LoadOperator(LittleDiracOp,"LittleDiracOp.scidac");
+  } else {
+    Aggregates.CreateSubspaceChebyshev(RNG5,HermOpEO,nbasis,
+				       95.0,0.1,
+				       //				     400,200,200 -- 48 iters
+				       //				     600,200,200 -- 38 iters, 162s
+				       //				     600,200,100 -- 38 iters, 169s
+				       //				     600,200,50  -- 88 iters. 370s 
+				       600,
+				       200,
+				       100,
+				       0.0);
+    LittleDiracOp.CoarsenOperator(FineHermOp,Aggregates);
+    SaveBasis(Aggregates,"Subspace.scidac");
+    SaveOperator(LittleDiracOp,"LittleDiracOp.scidac");
+  }
+  
+  // Try projecting to one hop only
+  LittleDiracOperator LittleDiracOpProj(geom_nn,FrbGrid,Coarse5d);
+  LittleDiracOpProj.ProjectNearestNeighbour(0.2,LittleDiracOp);
+
+  typedef HermitianLinearOperator<LittleDiracOperator,CoarseVector> HermMatrix;
+  HermMatrix CoarseOp (LittleDiracOp);
+  HermMatrix CoarseOpProj (LittleDiracOpProj);
+  
+  //////////////////////////////////////////
+  // Build a coarse lanczos
+  //////////////////////////////////////////
+  Chebyshev<CoarseVector>      IRLCheby(0.5,60.0,71);  // 1 iter
+  FunctionHermOp<CoarseVector> IRLOpCheby(IRLCheby,CoarseOp);
+  PlainHermOp<CoarseVector>    IRLOp    (CoarseOp);
+  int Nk=48;
+  int Nm=64;
+  int Nstop=Nk;
+  ImplicitlyRestartedLanczos<CoarseVector> IRL(IRLOpCheby,IRLOp,Nstop,Nk,Nm,1.0e-5,20);
+
+  int Nconv;
+  std::vector<RealD>            eval(Nm);
+  std::vector<CoarseVector>     evec(Nm,Coarse5d);
+  CoarseVector c_src(Coarse5d); c_src=1.0;
+  CoarseVector c_res(Coarse5d); 
+  CoarseVector c_ref(Coarse5d); 
+
+  PowerMethod<CoarseVector>       cPM;   cPM(CoarseOp,c_src);
+
+  IRL.calc(eval,evec,c_src,Nconv);
+  DeflatedGuesser<CoarseVector> DeflCoarseGuesser(evec,eval);
+
+  
+  //////////////////////////////////////////
+  // Build a coarse space solver
+  //////////////////////////////////////////
+  int maxit=20000;
+  ConjugateGradient<CoarseVector>  CG(1.0e-8,maxit,false);
+  ConjugateGradient<LatticeFermionD>  CGfine(1.0e-8,10000,false);
+  ZeroGuesser<CoarseVector> CoarseZeroGuesser;
+
+  //  HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,CoarseZeroGuesser);
+  HPDSolver<CoarseVector> HPDSolve(CoarseOp,CG,DeflCoarseGuesser);
+  c_res=Zero();
+  HPDSolve(c_src,c_res); c_ref = c_res;
+
+  //////////////////////////////////////////////////////////////////////////
+  // Deflated (with real op EV's) solve for the projected coarse op
+  // Work towards ADEF1 in the coarse space
+  //////////////////////////////////////////////////////////////////////////
+  HPDSolver<CoarseVector> HPDSolveProj(CoarseOpProj,CG,DeflCoarseGuesser);
+  c_res=Zero();
+  HPDSolveProj(c_src,c_res);
+  c_res = c_res - c_ref;
+  std::cout << "Projected solver error "<<norm2(c_res)<<std::endl;
+
+  //////////////////////////////////////////////////////////////////////
+  // Coarse ADEF1 with deflation space
+  //////////////////////////////////////////////////////////////////////
+  ChebyshevSmoother<CoarseVector,HermMatrix > CoarseSmoother(4.0,45.,16,CoarseOpProj);  // 311
+  //  ChebyshevSmoother<CoarseVector,HermMatrix > CoarseSmoother(0.5,36.,10,CoarseOpProj);  // 311
+
+  ////////////////////////////////////////////////////////
+  // CG, Cheby mode spacing 200,200
+  // Unprojected Coarse CG solve to 1e-8 : 190 iters, 4.9s
+  // Unprojected Coarse CG solve to 4e-2 :  33 iters, 0.8s
+  // Projected Coarse CG solve to 1e-8 : 100 iters, 0.36s
+  ////////////////////////////////////////////////////////
+  // CoarseSmoother(1.0,48.,8,CoarseOpProj); 48 evecs 
+  ////////////////////////////////////////////////////////
+  // ADEF1 Coarse solve to 1e-8 : 44 iters, 2.34s  2.1x gain
+  // ADEF1 Coarse solve to 4e-2 : 7 iters, 0.4s
+  // HDCG 38 iters 162s
+  //
+  // CoarseSmoother(1.0,40.,8,CoarseOpProj); 48 evecs 
+  // ADEF1 Coarse solve to 1e-8 : 37 iters, 2.0s  2.1x gain
+  // ADEF1 Coarse solve to 4e-2 : 6 iters, 0.36s
+  // HDCG 38 iters 169s
+
+  TwoLevelADEF1defl<CoarseVector>
+    cADEF1(1.0e-8, 100,
+	   CoarseOp,
+	   CoarseSmoother,
+	   evec,eval);
+
+  c_res=Zero();
+  cADEF1(c_src,c_res);
+  c_res = c_res - c_ref;
+  std::cout << "cADEF1 solver error "<<norm2(c_res)<<std::endl;
+  
+  cADEF1.Tolerance = 1.0e-9;
+  c_res=Zero();
+  cADEF1(c_src,c_res);
+  c_res = c_res - c_ref;
+  std::cout << "cADEF1 solver error "<<norm2(c_res)<<std::endl;
+  
+  //////////////////////////////////////////
+  // Build a smoother
+  //////////////////////////////////////////
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(10.0,100.0,10,FineHermOp); //499
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(3.0,100.0,10,FineHermOp);  //383
+  //  ChebyshevSmoother<LatticeFermionD,HermFineMatrix > Smoother(1.0,100.0,10,FineHermOp);  //328
+  //  std::vector<RealD> los({0.5,1.0,3.0}); // 147/142/146 nbasis 1
+  //  std::vector<RealD> los({1.0,2.0}); // Nbasis 24: 88,86 iterations
+  //  std::vector<RealD> los({2.0,4.0}); // Nbasis 32 == 52, iters
+  //  std::vector<RealD> los({2.0,4.0}); // Nbasis 40 == 36,36 iters
+
+  //
+  // Turns approx 2700 iterations into 340 fine multiplies with Nbasis 40
+  // Need to measure cost of coarse space.
+  //
+  // -- i) Reduce coarse residual   -- 0.04
+  // -- ii) Lanczos on coarse space -- done
+  // -- iii) Possible 1 hop project and/or preconditioning it - easy - PrecCG it and
+  //         use a limited stencil. Reread BFM code to check on evecs / deflation strategy with prec
+  //
+  std::vector<RealD> los({3.0}); // Nbasis 40 == 36,36 iters
+
+  //  std::vector<int> ords({7,8,10}); // Nbasis 40 == 40,38,36 iters (320,342,396 mults)
+  std::vector<int> ords({7}); // Nbasis 40 == 40 iters (320 mults)  
+
+  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,HermFineMatrix > Smoother(lo,92,ords[o],FineHermOp);  // 311
+
+      //////////////////////////////////////////
+      // Build a HDCG solver
+      //////////////////////////////////////////
+      TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
+	HDCG(1.0e-8, 3000,
+	     FineHermOp,
+	     Smoother,
+	     HPDSolveSloppy,
+	     HPDSolve,
+	     Aggregates);
+
+      result=Zero();
+      HDCG(src,result);
+
+      TwoLevelADEF2<LatticeFermion,CoarseVector,Subspace>
+	HDCGdefl(1.0e-8, 100,
+		 FineHermOp,
+		 Smoother,
+		 cADEF1,
+		 HPDSolve,
+		 Aggregates);
+      
+      result=Zero();
+      HDCGdefl(src,result);
+      
+    }
+  }
+
+  // Standard CG
+  result=Zero();
+  CGfine(HermOpEO, src, result);
+  
+  Grid_finalize();
+  return 0;
+}

tests/debug/Test_general_coarse_pvdagm.cc

@@ -0,0 +1,267 @@
+/*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell.cc
+
+    Copyright (C) 2023
+
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    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>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidual.h>
+#include <Grid/algorithms/iterative/PrecGeneralisedConjugateResidualNonHermitian.h>
+#include <Grid/algorithms/iterative/BiCGSTAB.h>
+
+using namespace std;
+using namespace Grid;
+
+template<class Field>
+class HermOpAdaptor : public LinearOperatorBase<Field>
+{
+  LinearOperatorBase<Field> & wrapped;
+public:
+  HermOpAdaptor(LinearOperatorBase<Field> &wrapme) : wrapped(wrapme)  {};
+  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){
+    wrapped.HermOp(in,out);
+  }
+  void AdjOp     (const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    wrapped.HermOp(in,out);
+  }
+  
+};
+
+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(tmp,out);
+    _Mat.Mdag(in,tmp);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,RealD &n1,RealD &n2){    assert(0);  }
+  void HermOp(const Field &in, Field &out){
+    std::cout << "HermOp"<<std::endl;
+    Field tmp(in.Grid());
+    _Mat.M(in,tmp);
+    _PV.Mdag(tmp,out);
+    _PV.M(out,tmp);
+    _Mat.Mdag(tmp,out);
+    std::cout << "HermOp done "<<norm2(out)<<std::endl;
+    
+  }
+};
+
+template<class Field> class DumbOperator  : public LinearOperatorBase<Field> {
+public:
+  LatticeComplex scale;
+  DumbOperator(GridBase *grid) : scale(grid)
+  {
+    scale = 0.0;
+    LatticeComplex scalesft(grid);
+    LatticeComplex scaletmp(grid);
+    for(int d=0;d<4;d++){
+      Lattice<iScalar<vInteger> > x(grid); LatticeCoordinate(x,d+1);
+      LatticeCoordinate(scaletmp,d+1);
+      scalesft = Cshift(scaletmp,d+1,1);
+      scale = 100.0*scale + where( mod(x    ,2)==(Integer)0, scalesft,scaletmp);
+    }
+    std::cout << " scale\n" << scale << std::endl;
+  }
+  // Support for coarsening to a multigrid
+  void OpDiag (const Field &in, Field &out) {};
+  void OpDir  (const Field &in, Field &out,int dir,int disp){};
+  void OpDirAll  (const Field &in, std::vector<Field> &out) {};
+
+  void Op     (const Field &in, Field &out){
+    out = scale * in;
+  }
+  void AdjOp  (const Field &in, Field &out){
+    out = scale * in;
+  }
+  void HermOp(const Field &in, Field &out){
+    double n1, n2;
+    HermOpAndNorm(in,out,n1,n2);
+  }
+  void HermOpAndNorm(const Field &in, Field &out,double &n1,double &n2){
+    ComplexD dot;
+
+    out = scale * in;
+
+    dot= innerProduct(in,out);
+    n1=real(dot);
+
+    dot = innerProduct(out,out);
+    n2=real(dot);
+  }
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  const int Ls=2;
+
+  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
+  Coordinate clatt = GridDefaultLatt();
+  for(int d=0;d<clatt.size();d++){
+    clatt[d] = clatt[d]/4;
+  }
+  GridCartesian *Coarse4d =  SpaceTimeGrid::makeFourDimGrid(clatt, GridDefaultSimd(Nd,vComplex::Nsimd()),GridDefaultMpi());;
+  GridCartesian *Coarse5d =  SpaceTimeGrid::makeFiveDimGrid(1,Coarse4d);
+
+  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);
+
+  LatticeFermion    src(FGrid); random(RNG5,src);
+  LatticeFermion result(FGrid); result=Zero();
+  LatticeFermion    ref(FGrid); ref=Zero();
+  LatticeFermion    tmp(FGrid);
+  LatticeFermion    err(FGrid);
+  LatticeGaugeField Umu(UGrid);
+
+  FieldMetaData header;
+  std::string file("ckpoint_lat.4000");
+  NerscIO::readConfiguration(Umu,header,file);
+  //Umu = 1.0;
+  
+  RealD mass=0.5;
+  RealD M5=1.8;
+
+  DomainWallFermionD Ddwf(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,mass,M5);
+  DomainWallFermionD Dpv(Umu,*FGrid,*FrbGrid,*UGrid,*UrbGrid,1.0,M5);
+
+  const int nbasis = 1;
+  const int cb = 0 ;
+  LatticeFermion prom(FGrid);
+
+  typedef GeneralCoarsenedMatrix<vSpinColourVector,vTComplex,nbasis> LittleDiracOperator;
+  typedef LittleDiracOperator::CoarseVector CoarseVector;
+
+  NextToNearestStencilGeometry5D geom(Coarse5d);
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  
+  PVdagMLinearOperator<DomainWallFermionD,LatticeFermionD> PVdagM(Ddwf,Dpv);
+  HermOpAdaptor<LatticeFermionD> HOA(PVdagM);
+
+  // Run power method on HOA??
+  PowerMethod<LatticeFermion>       PM;   PM(HOA,src);
+ 
+  // Warning: This routine calls PVdagM.Op, not PVdagM.HermOp
+  typedef Aggregation<vSpinColourVector,vTComplex,nbasis> Subspace;
+  Subspace AggregatesPD(Coarse5d,FGrid,cb);
+  AggregatesPD.CreateSubspaceChebyshev(RNG5,
+				       HOA,
+				       nbasis,
+				       5000.0,
+				       0.02,
+				       100,
+				       50,
+				       50,
+				       0.0);
+  
+  LittleDiracOperator LittleDiracOpPV(geom,FGrid,Coarse5d);
+  LittleDiracOpPV.CoarsenOperator(PVdagM,AggregatesPD);
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"Testing coarsened operator "<<std::endl;
+  
+  CoarseVector c_src (Coarse5d);
+  CoarseVector c_res (Coarse5d);
+  CoarseVector c_proj(Coarse5d);
+
+  std::vector<LatticeFermion> subspace(nbasis,FGrid);
+  subspace=AggregatesPD.subspace;
+
+  Complex one(1.0);
+  c_src = one;  // 1 in every element for vector 1.
+  blockPromote(c_src,err,subspace);
+
+  prom=Zero();
+  for(int b=0;b<nbasis;b++){
+    prom=prom+subspace[b];
+  }
+  err=err-prom; 
+  std::cout<<GridLogMessage<<"Promoted back from subspace: err "<<norm2(err)<<std::endl;
+  std::cout<<GridLogMessage<<"c_src "<<norm2(c_src)<<std::endl;
+  std::cout<<GridLogMessage<<"prom  "<<norm2(prom)<<std::endl;
+
+  PVdagM.Op(prom,tmp);
+  blockProject(c_proj,tmp,subspace);
+  std::cout<<GridLogMessage<<" Called Big Dirac Op "<<norm2(tmp)<<std::endl;
+
+  LittleDiracOpPV.M(c_src,c_res);
+  std::cout<<GridLogMessage<<" Called Little Dirac Op c_src "<< norm2(c_src) << "  c_res "<< norm2(c_res) <<std::endl;
+
+  std::cout<<GridLogMessage<<"Little dop : "<<norm2(c_res)<<std::endl;
+  //  std::cout<<GridLogMessage<<" Little "<< c_res<<std::endl;
+
+  std::cout<<GridLogMessage<<"Big dop in subspace : "<<norm2(c_proj)<<std::endl;
+  //  std::cout<<GridLogMessage<<" Big "<< c_proj<<std::endl;
+  c_proj = c_proj - c_res;
+  std::cout<<GridLogMessage<<" ldop error: "<<norm2(c_proj)<<std::endl;
+  //  std::cout<<GridLogMessage<<" error "<< c_proj<<std::endl;
+
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage<<"*******************************************"<<std::endl;
+  std::cout<<GridLogMessage<<std::endl;
+  std::cout<<GridLogMessage << "Done "<< std::endl;
+
+  Grid_finalize();
+  return 0;
+}