diff --git a/Grid/algorithms/GeneralCoarsenedMatrix.h b/Grid/algorithms/GeneralCoarsenedMatrix.h
new file mode 100644
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--- /dev/null
+++ b/Grid/algorithms/GeneralCoarsenedMatrix.h
@@ -0,0 +1,431 @@
+/*************************************************************************************
+
+    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);
+
+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 npoint;
+  std::vector<Coordinate> shifts;
+  virtual void BuildShifts(void) { assert(0); } ;
+  int Depth(void){return depth;};
+  NonLocalStencilGeometry(int _depth) : depth(_depth)
+  {
+  };
+  virtual ~NonLocalStencilGeometry() {};
+};
+// Need to worry about red-black now
+class NextToNearestStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  NextToNearestStencilGeometry4D(void) : NonLocalStencilGeometry(2)
+  {
+      this->BuildShifts();
+  };
+  virtual ~NextToNearestStencilGeometry4D() {};
+  virtual void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    // Like HDCG:  81 point stencil including self connection
+    this->shifts.push_back(Coordinate({0,0,0,0}));
+    // +-x, +-y, +-z, +-t  : 8
+    for(int s=-1;s<=1;s+=2){
+      this->shifts.push_back(Coordinate({s,0,0,0}));
+      this->shifts.push_back(Coordinate({0,s,0,0}));
+      this->shifts.push_back(Coordinate({0,0,s,0}));
+      this->shifts.push_back(Coordinate({0,0,0,s}));
+    }
+    // +-x+-y, +-x+-z, +-x+-t, +-y+-z, +-y+-t, +-z+-t : 24
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+      this->shifts.push_back(Coordinate({s1,s2,0,0}));
+      this->shifts.push_back(Coordinate({s1,0,s2,0}));
+      this->shifts.push_back(Coordinate({s1,0,0,s2}));
+      this->shifts.push_back(Coordinate({0,s1,s2,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,s1,s2}));
+    }}
+    this->npoint = this->shifts.size();
+  }
+};
+// Need to worry about red-black now
+class NextToNextToNextToNearestStencilGeometry4D : public NonLocalStencilGeometry {
+public:
+  NextToNextToNextToNearestStencilGeometry4D(void) : NonLocalStencilGeometry(4)
+  {
+    this->BuildShifts();
+  };
+  virtual ~NextToNextToNextToNearestStencilGeometry4D() {}
+  virtual void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    // Like HDCG:  81 point stencil including self connection
+    this->shifts.push_back(Coordinate({0,0,0,0}));
+    // +-x, +-y, +-z, +-t  : 8
+    for(int s=-1;s<=1;s+=2){
+      this->shifts.push_back(Coordinate({s,0,0,0}));
+      this->shifts.push_back(Coordinate({0,s,0,0}));
+      this->shifts.push_back(Coordinate({0,0,s,0}));
+      this->shifts.push_back(Coordinate({0,0,0,s}));
+    }
+    // +-x+-y, +-x+-z, +-x+-t, +-y+-z, +-y+-t, +-z+-t : 24
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+      this->shifts.push_back(Coordinate({s1,s2,0,0}));
+      this->shifts.push_back(Coordinate({s1,0,s2,0}));
+      this->shifts.push_back(Coordinate({s1,0,0,s2}));
+      this->shifts.push_back(Coordinate({0,s1,s2,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,s1,s2}));
+    }}
+    // +-x+-y+-z, +-x+-y+-z, +-x+-y+-z,
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+    for(int s3=-1;s3<=1;s3+=2){
+      this->shifts.push_back(Coordinate({s1,s2,s3,0})); // 8x4 = 32
+      this->shifts.push_back(Coordinate({s1,s2,0,s3}));
+      this->shifts.push_back(Coordinate({s1,0,s2,s3}));
+      this->shifts.push_back(Coordinate({0,s1,s2,s3}));
+    }}}
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+    for(int s3=-1;s3<=1;s3+=2){
+    for(int s4=-1;s4<=1;s4+=2){
+      this->shifts.push_back(Coordinate({s1,s2,s3,s4})); // 16 
+    }}}}
+    this->npoint = this->shifts.size();
+  }
+};
+class NextToNearestStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  NextToNearestStencilGeometry5D(void) : NonLocalStencilGeometry(2)
+  {
+      this->BuildShifts();
+  };
+  virtual ~NextToNearestStencilGeometry5D() {};
+  virtual void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    // Like HDCG:  81 point stencil including self connection
+    this->shifts.push_back(Coordinate({0,0,0,0,0}));
+    // +-x, +-y, +-z, +-t  : 8
+    for(int s=-1;s<=1;s+=2){
+      this->shifts.push_back(Coordinate({0,s,0,0,0}));
+      this->shifts.push_back(Coordinate({0,0,s,0,0}));
+      this->shifts.push_back(Coordinate({0,0,0,s,0}));
+      this->shifts.push_back(Coordinate({0,0,0,0,s}));
+    }
+    // +-x+-y, +-x+-z, +-x+-t, +-y+-z, +-y+-t, +-z+-t : 24
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+      this->shifts.push_back(Coordinate({0,s1,s2,0,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,s2,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,s1,s2,0}));
+      this->shifts.push_back(Coordinate({0,0,s1,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,0,s1,s2}));
+    }}
+    this->npoint = this->shifts.size();
+  }
+};
+// Need to worry about red-black now
+class NextToNextToNextToNearestStencilGeometry5D : public NonLocalStencilGeometry {
+public:
+  NextToNextToNextToNearestStencilGeometry5D(void) : NonLocalStencilGeometry(4)
+  {
+    this->BuildShifts();
+  };
+  virtual ~NextToNextToNextToNearestStencilGeometry5D() {}
+  virtual void BuildShifts(void)
+  {
+    this->shifts.resize(0);
+    // Like HDCG:  81 point stencil including self connection
+    this->shifts.push_back(Coordinate({0,0,0,0,0}));
+    // +-x, +-y, +-z, +-t  : 8
+    for(int s=-1;s<=1;s+=2){
+      this->shifts.push_back(Coordinate({0,s,0,0,0}));
+      this->shifts.push_back(Coordinate({0,0,s,0,0}));
+      this->shifts.push_back(Coordinate({0,0,0,s,0}));
+      this->shifts.push_back(Coordinate({0,0,0,0,s}));
+    }
+    // +-x+-y, +-x+-z, +-x+-t, +-y+-z, +-y+-t, +-z+-t : 24
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+      this->shifts.push_back(Coordinate({0,s1,s2,0,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,s2,0}));
+      this->shifts.push_back(Coordinate({0,s1,0,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,s1,s2,0}));
+      this->shifts.push_back(Coordinate({0,0,s1,0,s2}));
+      this->shifts.push_back(Coordinate({0,0,0,s1,s2}));
+    }}
+    // +-x+-y+-z, +-x+-y+-z, +-x+-y+-z,
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+    for(int s3=-1;s3<=1;s3+=2){
+      this->shifts.push_back(Coordinate({0,s1,s2,s3,0})); // 8x4 = 32
+      this->shifts.push_back(Coordinate({0,s1,s2,0,s3}));
+      this->shifts.push_back(Coordinate({0,s1,0,s2,s3}));
+      this->shifts.push_back(Coordinate({0,0,s1,s2,s3}));
+    }}}
+    for(int s1=-1;s1<=1;s1+=2){
+    for(int s2=-1;s2<=1;s2+=2){
+    for(int s3=-1;s3<=1;s3+=2){
+    for(int s4=-1;s4<=1;s4+=2){
+      this->shifts.push_back(Coordinate({0,s1,s2,s3,s4})); // 16 
+    }}}}
+    this->npoint = this->shifts.size();
+  }
+};
+
+// 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 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 Field;
+  ////////////////////
+  // Data members
+  ////////////////////
+  int hermitian;
+  GridCartesian *       _FineGrid; 
+  GridCartesian *       _CoarseGrid; 
+  NonLocalStencilGeometry &geom;
+  PaddedCell Cell;
+  GeneralLocalStencil Stencil;
+  
+  std::vector<CoarseMatrix> _A;
+  std::vector<CoarseMatrix> _Adag;
+
+  ///////////////////////
+  // Interface
+  ///////////////////////
+  GridCartesian * Grid(void)           { return _FineGrid; };   // this is all the linalg routines need to know
+  GridCartesian * 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
+
+  GeneralCoarsenedMatrix(NonLocalStencilGeometry &_geom,GridCartesian *FineGrid, GridCartesian * CoarseGrid)
+    : geom(_geom),
+      _FineGrid(FineGrid),
+      _CoarseGrid(CoarseGrid),
+      hermitian(1),
+      Cell(_geom.Depth(),_CoarseGrid),
+      Stencil(Cell.grids.back(),geom.shifts)
+  {
+    _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)
+  {
+    Mult(_Adag,in,out);
+  }
+  void Mult (std::vector<CoarseMatrix> &A,const CoarseVector &in, CoarseVector &out)
+  {
+    conformable(CoarseGrid(),in.Grid());
+    conformable(in.Grid(),out.Grid());
+    out.Checkerboard() = in.Checkerboard();
+    CoarseVector tin=in;
+    std::cout << "Calling Exchange"<<std::endl;
+    CoarseVector pin  = Cell.Exchange(tin);
+    //    std::cout << "Called Exchange"<<std::endl;
+    CoarseVector pout(pin.Grid());
+    
+    autoView( in_v , pin, AcceleratorRead);
+    autoView( out_v , pout, AcceleratorWrite);
+    autoView( Stencil_v  , Stencil, AcceleratorRead);
+    int npoint = geom.npoint;
+    typedef LatticeView<Cobj> Aview;
+      
+    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 siteVector calcVector;
+    typedef CComplex   calcComplex;
+
+    int osites=pin.Grid()->oSites();
+
+    for(int point=0;point<npoint;point++){
+      conformable(_A[point],pin);
+    }
+
+    // Should also exchange "A" and "Adag"
+    accelerator_for(sss, osites*nbasis, 1, {
+      int ss = sss/nbasis;
+      int b  = sss%nbasis;
+      assert(ss<osites);
+      calcComplex res;
+      res = Zero();
+      calcVector nbr;
+      int ptype;
+      StencilEntry *SE;
+
+      // FIXME -- exchange the A and the A dag
+      
+      for(int point=0;point<npoint;point++){
+
+	auto SE = Stencil_v.GetEntry(point,ss);
+	
+	int o = SE->_offset;
+
+	// gpermute etc..
+	nbr = in_v[o];
+	assert( o< osites);
+	gpermute(nbr,SE->_permute);
+
+	for(int bb=0;bb<nbasis;bb++) {
+	  res = res + Aview_p[point][ss](b,bb)*nbr(bb);
+	}
+      }
+      out_v[ss](b)=res;
+    });
+
+    for(int p=0;p<geom.npoint;p++) AcceleratorViewContainer[p].ViewClose();
+
+    out = Cell.Extract(pout);
+  };
+
+  void Test(LinearOperatorBase<Lattice<Fobj> > &linop,
+	    Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    // Create a random
+    GridCartesian *grid = FineGrid();
+    FineField MbV(grid);
+    FineField tmp(grid);
+    FineField f_src(grid);
+    FineField f_res(grid);
+    FineField f_ref(grid);
+    CoarseVector c_src(CoarseGrid());
+    CoarseVector c_res(CoarseGrid());
+    CoarseVector coarseInner(CoarseGrid());
+    GridParallelRNG RNG(CoarseGrid());  RNG.SeedUniqueString(std::string("Coarse RNG"));
+    random(RNG,c_src);
+    blockPromote(c_src,f_src,Subspace.subspace);
+    linop.op(f_src,f_ref);
+    this->Mult (_A,c_src,c_res);
+    blockPromote(c_res,f_res,Subspace.subspace);
+    std::cout << " GeneralCoarsenedMatrix comparison res  "<<norm2(f_res)<<std::endl;
+    std::cout << " GeneralCoarsenedMatrix comparison ref  "<<norm2(f_ref)<<std::endl;
+    f_res = f_res - f_ref;
+    std::cout << " GeneralCoarsenedMatrix comparison diff "<<norm2(f_res)<<std::endl;
+  }
+  void CoarsenOperator(LinearOperatorBase<Lattice<Fobj> > &linop,
+		       Aggregation<Fobj,CComplex,nbasis> & Subspace)
+  {
+    std::cout << GridLogMessage<< "CoarsenMatrix "<< std::endl;
+    GridCartesian *grid = FineGrid();
+    // Orthogonalise the subblocks over the basis
+    CoarseScalar InnerProd(CoarseGrid()); 
+    for(int b=0;b<nbasis;b++){
+      std::cout << "subspace["<<b<<"] " <<norm2(Subspace.subspace[b])<<std::endl;
+    }
+    blockOrthogonalise(InnerProd,Subspace.subspace);
+
+    // Now compute the matrix elements of linop between this orthonormal
+    // set of vectors.
+    FineField bV(grid);
+    FineField MbV(grid);
+    FineField tmp(grid);
+    CoarseVector coarseInner(CoarseGrid());
+
+    // Very inefficient loop of order coarse volume.
+    // First pass hack
+    // Could replace with a coloring scheme our phase scheme
+    // as in BFM
+    for(int bidx=0;bidx<CoarseGrid()->gSites() ;bidx++){
+      Coordinate bcoor;
+      CoarseGrid()->GlobalIndexToGlobalCoor(bidx,bcoor);
+      std::cout << GridLogMessage<< "CoarsenMatrix block "<< bcoor << std::endl;
+      for(int b=0;b<nbasis;b++){
+	blockPick(CoarseGrid(),Subspace.subspace[b],bV,bcoor);
+	linop.HermOp(bV,MbV);
+	blockProject(coarseInner,MbV,Subspace.subspace);
+	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
+	  }
+	  auto ip    = peekSite(coarseInner,scoor);
+	  std::cout << "A["<<b<<"]["<<p<<"]"<<scoor<<" "<<" shift "<<geom.shifts[p]<<" "<< ip <<std::endl;
+	  auto Ab    = peekSite(_A[p],scoor);
+	  auto Adagb = peekSite(_Adag[p],bcoor);
+	  for(int bb=0;bb<nbasis;bb++){
+	    Ab(bb,b)    = ip(bb);
+	    Adagb(b,bb) = conjugate(ip(bb));
+	  }
+	  pokeSite(Ab,_A[p],scoor);
+	  pokeSite(Adagb,_Adag[p],bcoor);
+	}
+      }
+    }
+    std::cout << " Exchanging _A " <<std::endl;
+    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);