Boosted fermion attempt

Grid/Makefile.am

@@ -66,10 +66,6 @@ if BUILD_FERMION_REPS
   extra_sources+=$(ADJ_FERMION_FILES)
   extra_sources+=$(TWOIND_FERMION_FILES)
 endif
-if BUILD_SP
-    extra_sources+=$(SP_FERMION_FILES)
-    extra_sources+=$(SP_TWOIND_FERMION_FILES)
-endif
 
 lib_LIBRARIES = libGrid.a
 

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;
@@ -158,20 +158,7 @@ public:
     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)
-  {
+  virtual void CreateSubspace(GridParallelRNG  &RNG,LinearOperatorBase<FineField> &hermop,int nn=nbasis) {
 
     RealD scale;
 
@@ -230,11 +217,6 @@ 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;
 
@@ -308,44 +290,6 @@ 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

@@ -1,573 +0,0 @@
-/*************************************************************************************
-
-    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

@@ -90,8 +90,9 @@ public:
     order=_order;
       
     if(order < 2) exit(-1);
-    Coeffs.resize(order,0.0);
-    Coeffs[order-1] = 1.0;
+    Coeffs.resize(order);
+    Coeffs.assign(0.,order);
+    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

@@ -33,6 +33,15 @@ 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
@@ -40,245 +49,202 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
    * M2=M3=1
    * Vout = x
    */
-NAMESPACE_BEGIN(Grid);
 
-template<class Field>
-class TwoLevelCG : public LinearFunction<Field>
+// abstract base
+template<class Field, class CoarseField>
+class TwoLevelFlexiblePcg : public LinearFunction<Field>
 {
  public:
+  int verbose;
   RealD   Tolerance;
   Integer MaxIterations;
+  const int mmax = 5;
   GridBase *grid;
+  GridBase *coarsegrid;
 
-  // Fine operator, Smoother, CoarseSolver
-  LinearOperatorBase<Field>   &_FineLinop;
-  LinearFunction<Field>   &_Smoother;
+  LinearOperatorBase<Field>   *_Linop
+  OperatorFunction<Field>     *_Smoother,
+  LinearFunction<CoarseField> *_CoarseSolver;
+
+  // Need somthing that knows how to get from Coarse to fine and back again
   
   // more most opertor functions
-  TwoLevelCG(RealD tol,
-	     Integer maxit,
-	     LinearOperatorBase<Field>   &FineLinop,
-	     LinearFunction<Field>       &Smoother,
-	     GridBase *fine) : 
+  TwoLevelFlexiblePcg(RealD tol,
+		     Integer maxit,
+		     LinearOperatorBase<Field> *Linop,
+		     LinearOperatorBase<Field> *SmootherLinop,
+		     OperatorFunction<Field>   *Smoother,
+		     OperatorFunction<CoarseField>  CoarseLinop
+		     ) : 
       Tolerance(tol), 
       MaxIterations(maxit),
-      _FineLinop(FineLinop),
-      _Smoother(Smoother)
-  {
-    grid       = fine;
+      _Linop(Linop),
+      _PreconditionerLinop(PrecLinop),
+      _Preconditioner(Preconditioner)
+  { 
+    verbose=0;
   };
-  
-  virtual void operator() (const Field &src, Field &psi)
-  {
-    Field resid(grid);
+
+  // The Pcg routine is common to all, but the various matrices differ from derived 
+  // implementation to derived implmentation
+  void operator() (const Field &src, Field &psi){
+  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); 
-    Field p(grid);
-    Field z(grid);
+    /////////////////////////////
+    // Set up history vectors
+    /////////////////////////////
+    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=Zero();
+    x=src;
     Vstart(x,src);
 
     // r0 = b -A x0
-    _FineLinop.HermOp(x,mmp);
-
-    axpy(r, -1.0, mmp, src);    // Recomputes r=src-x0
-    rp=r;
+    HermOp(x,mmp); // Shouldn't this be something else?
+    axpy (r, -1.0,mmp[0], src);    // Recomputes r=src-Ax0
 
     //////////////////////////////////
     // Compute z = M1 x
     //////////////////////////////////
-    PcgM1(r,z);
+    M1(r,z,tmp,mp,SmootherMirs);
     rtzp =real(innerProduct(r,z));
 
     ///////////////////////////////////////
-    // Except Def2, M2 is trivial
+    // Solve for Mss mu = P A z and set p = z-mu
+    // Def2: p = 1 - Q Az = Pright z 
+    // Other algos M2 is trivial
     ///////////////////////////////////////
-    p=z;
+    M2(z,p[0]);
 
-    RealD ssq =  norm2(src);
-    RealD rsq =  ssq*Tolerance*Tolerance;
-
-    std::cout<<GridLogMessage<<"HDCG: k=0 residual "<<rtzp<<" target rsq "<<rsq<<" ssq "<<ssq<<std::endl;
+    for (int k=0;k<=MaxIterations;k++){
     
-    for (int k=1;k<=MaxIterations;k++){
+      int peri_k  = k % mmax;
+      int peri_kp = (k+1) % mmax;
 
       rtz=rtzp;
-      d= PcgM3(p,mmp);
+      d= M3(p[peri_k],mp,mmp[peri_k],tmp);
       a = rtz/d;
+    
+      // Memorise this
+      pAp[peri_k] = d;
 
-      axpy(x,a,p,x);
-      RealD rn = axpy_norm(r,-a,mmp,r);
+      axpy(x,a,p[peri_k],x);
+      RealD rn = axpy_norm(r,-a,mmp[peri_k],r);
 
-      PcgM1(r,z);
+      // Compute z = M x
+      M1(r,z,tmp,mp);
 
       rtzp =real(innerProduct(r,z));
 
-      int ipcg=1; // almost free inexact preconditioned CG
-      if (ipcg) {
-	rptzp =real(innerProduct(rp,z));
-      } else {
-	rptzp =0;
+      M2(z,mu); // ADEF-2 this is identity. Axpy possible to eliminate
+
+      p[peri_kp]=p[peri_k];
+
+      // Standard search direction  p -> z + b p    ; b = 
+      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);
-      RealD rtn=sqrt(rtz/ssq);
-      std::cout<<GridLogMessage<<"HDCG: Pcg k= "<<k<<" residual = "<<rrn<<std::endl;
-
-      if ( ipcg ) {
-	axpy(rp,0.0,r,r);
-      }
+      std::cout<<GridLogMessage<<"TwoLevelfPcg: k= "<<k<<" residual = "<<rrn<<std::endl;
 
       // Stopping condition
       if ( rn <= rsq ) { 
 
-	HDCGTimer.Stop();
-	std::cout<<GridLogMessage<<"HDCG: Pcg converged in "<<k<<" iterations and "<<HDCGTimer.Elapsed()<<std::endl;;
-
-	_FineLinop.HermOp(x,mmp);			  
-	axpy(tmp,-1.0,src,mmp);
-
-	RealD  mmpnorm = sqrt(norm2(mmp));
-	RealD  psinorm = sqrt(norm2(x));
-	RealD  srcnorm = sqrt(norm2(src));
-	RealD  tmpnorm = sqrt(norm2(tmp));
-	RealD  true_residual = tmpnorm/srcnorm;
-	std::cout<<GridLogMessage<<"HDCG: true residual is "<<true_residual
-		 <<" solution "<<psinorm<<" source "<<srcnorm<<std::endl;
-
-	return;
+	HermOp(x,mmp); // Shouldn't this be something else?
+	axpy(tmp,-1.0,src,mmp[0]);
+	
+	RealD psinorm = sqrt(norm2(x));
+	RealD srcnorm = sqrt(norm2(src));
+	RealD tmpnorm = sqrt(norm2(tmp));
+	RealD true_residual = tmpnorm/srcnorm;
+	std::cout<<GridLogMessage<<"TwoLevelfPcg:   true residual is "<<true_residual<<std::endl;
+	std::cout<<GridLogMessage<<"TwoLevelfPcg: target residual was"<<Tolerance<<std::endl;
+	return k;
       }
-
     }
-    std::cout << "HDCG: Pcg not converged"<<std::endl;
-    return ;
+    // Non-convergence
+    assert(0);
   }
-  
 
  public:
 
-  virtual void PcgM1(Field & in, Field & out)     =0;
-  virtual void Vstart(Field & x,const Field & src)=0;
+  virtual void M(Field & in,Field & out,Field & tmp) {
 
-  virtual void PcgM2(const Field & in, Field & out) {
-    out=in;
   }
 
-  virtual RealD PcgM3(const Field & p, Field & mmp){
-    RealD dd;
-    _FineLinop.HermOp(p,mmp);
-    ComplexD dot = innerProduct(p,mmp);
-    dd=real(dot);
-    return dd;
-  }
+  virtual void M1(Field & in, Field & out) {// the smoother
 
-  /////////////////////////////////////////////////////////////////////
-  // 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);
 
-    Field tmp(this->grid);
-    Field Min(this->grid);
-    CoarseField PleftProj(this->coarsegrid);
-    CoarseField PleftMss_proj(this->coarsegrid);
+    PcgM(in,Min); // Smoother call
 
-    GridStopWatch SmootherTimer;
-    GridStopWatch MatrixTimer;
-    SmootherTimer.Start();
-    this->_Smoother(in,Min);
-    SmootherTimer.Stop();
-
-    MatrixTimer.Start();
-    this->_FineLinop.HermOp(Min,out);
-    MatrixTimer.Stop();
+    HermOp(Min,out);
     axpy(tmp,-1.0,out,in);          // tmp  = in - A Min
 
-    GridStopWatch ProjTimer;
-    GridStopWatch CoarseTimer;
-    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;
-
+    ProjectToSubspace(tmp,PleftProj);     
+    ApplyInverse(PleftProj,PleftMss_proj); // Ass^{-1} [in - A Min]_s
+    PromoteFromSubspace(PleftMss_proj,tmp);// tmp = Q[in - A Min]  
     axpy(out,1.0,Min,tmp); // Min+tmp
   }
 
-  virtual void Vstart(Field & x,const Field & src)
-  {
+  virtual void M2(const Field & in, Field & out) {
+    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]
@@ -290,72 +256,142 @@ class TwoLevelADEF2 : public TwoLevelCG<Field>
     //                   = src_s - (A guess)_s - src_s  + (A guess)_s 
     //                   = 0 
     ///////////////////////////////////
-    Field r(this->grid);
-    Field mmp(this->grid);
-    CoarseField PleftProj(this->coarsegrid);
-    CoarseField PleftMss_proj(this->coarsegrid);
-
-    this->_Aggregates.ProjectToSubspace(PleftProj,src);     
-    this->_CoarseSolverPrecise(PleftProj,PleftMss_proj); // Ass^{-1} r_s
-    this->_Aggregates.PromoteFromSubspace(PleftMss_proj,x);  
+    Field r(grid);
+    Field mmp(grid);
+    
+    HermOp(x,mmp);
+    axpy (r, -1.0, mmp, src);        // r_{-1} = src - A x
+    ProjectToSubspace(r,PleftProj);     
+    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 TwoLevelADEF1defl : public TwoLevelCG<Field>
-{
-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)
-  {};
+class TwoLevelFlexiblePcgADef2 : public TwoLevelFlexiblePcg<Field> {
+ public:
+  virtual void M(Field & in,Field & out,Field & tmp){
 
-  // Can just inherit existing Vout
-  // Can just inherit existing M2
-  // Can just inherit existing M3
+  } 
+  virtual void M1(Field & in, Field & out,Field & tmp,Field & mp){
 
-  // Simple vstart - do nothing
-  virtual void Vstart(Field & x,const Field & 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 M2(Field & in, Field & out){
 
-NAMESPACE_END(Grid);
+  }
+  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 << GridLogPerformance << "Time breakdown "<<std::endl;
-	std::cout << GridLogPerformance << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
-	std::cout << GridLogPerformance << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tMatrix     " << MatrixTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinalg     " << LinalgTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tInner      " << InnerTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tAxpyNorm   " << AxpyNormTimer.Elapsed() <<std::endl;
+	std::cout << GridLogMessage << "\tLinearComb " << LinearCombTimer.Elapsed() <<std::endl;
 
 	std::cout << GridLogDebug << "\tMobius flop rate " << DwfFlops/ usecs<< " Gflops " <<std::endl;
 

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 : public LinearFunction<Field>{
+template<class Field> class NormalEquations {
 private:
   SparseMatrixBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -60,7 +60,7 @@ public:
   }     
 };
 
-template<class Field> class HPDSolver : public LinearFunction<Field> {
+template<class Field> class HPDSolver {
 private:
   LinearOperatorBase<Field> & _Matrix;
   OperatorFunction<Field> & _HermitianSolver;
@@ -84,7 +84,7 @@ public:
 };
 
 
-template<class Field> class MdagMSolver : public LinearFunction<Field> {
+template<class Field> class MdagMSolver {
 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_ = 100; 
+    const int _MAX_ITER_EST_ = 50; 
 
     for (int i=0;i<_MAX_ITER_EST_;i++) { 
       

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;
-  int64_t _fsites;                  // _isites*_osites = product(dimensions).
-  int64_t _gsites;
+  int _fsites;                  // _isites*_osites = product(dimensions).
+  int _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 int64_t gSites(void) const { return (int64_t)_isites*(int64_t)_osites*(int64_t)_Nprocessors; }; 
+  inline int gSites(void) const { return _isites*_osites*_Nprocessors; }; 
   inline int Nd    (void) const { return _ndimension;};
 
   inline const Coordinate LocalStarts(void)             { return _lstart;    };
@@ -214,7 +214,7 @@ public:
   ////////////////////////////////////////////////////////////////
   // Global addressing
   ////////////////////////////////////////////////////////////////
-  void GlobalIndexToGlobalCoor(int64_t gidx,Coordinate &gcoor){
+  void GlobalIndexToGlobalCoor(int 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,int64_t & gidx){
+  void GlobalCoorToGlobalIndex(const Coordinate & gcoor,int & gidx){
     gidx=0;
     int mult=1;
     for(int mu=0;mu<_ndimension;mu++) {

Grid/communicator/SharedMemoryMPI.cc

@@ -604,8 +604,8 @@ void GlobalSharedMemory::SharedMemoryAllocate(uint64_t bytes, int flags)
 #ifdef GRID_SYCL_LEVEL_ZERO_IPC
     typedef struct { int fd; pid_t pid ; ze_ipc_mem_handle_t ze; } clone_mem_t;
 
-    auto zeDevice    = cl::sycl::get_native<cl::sycl::backend::ext_oneapi_level_zero>(theGridAccelerator->get_device());
-    auto zeContext   = cl::sycl::get_native<cl::sycl::backend::ext_oneapi_level_zero>(theGridAccelerator->get_context());
+    auto zeDevice    = cl::sycl::get_native<cl::sycl::backend::level_zero>(theGridAccelerator->get_device());
+    auto zeContext   = cl::sycl::get_native<cl::sycl::backend::level_zero>(theGridAccelerator->get_context());
       
     ze_ipc_mem_handle_t ihandle;
     clone_mem_t handle;

Grid/lattice/Lattice.h

@@ -47,4 +47,3 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 #include <Grid/lattice/Lattice_transfer.h>
 #include <Grid/lattice/Lattice_basis.h>
 #include <Grid/lattice/Lattice_crc.h>
-#include <Grid/lattice/PaddedCell.h>

Grid/lattice/Lattice_ET.h

@@ -345,9 +345,7 @@ GridUnopClass(UnaryNot, Not(a));
 GridUnopClass(UnaryTrace, trace(a));
 GridUnopClass(UnaryTranspose, transpose(a));
 GridUnopClass(UnaryTa, Ta(a));
-GridUnopClass(UnarySpTa, SpTa(a));
 GridUnopClass(UnaryProjectOnGroup, ProjectOnGroup(a));
-GridUnopClass(UnaryProjectOnSpGroup, ProjectOnSpGroup(a));
 GridUnopClass(UnaryTimesI, timesI(a));
 GridUnopClass(UnaryTimesMinusI, timesMinusI(a));
 GridUnopClass(UnaryAbs, abs(a));
@@ -458,9 +456,7 @@ GRID_DEF_UNOP(operator!, UnaryNot);
 GRID_DEF_UNOP(trace, UnaryTrace);
 GRID_DEF_UNOP(transpose, UnaryTranspose);
 GRID_DEF_UNOP(Ta, UnaryTa);
-GRID_DEF_UNOP(SpTa, UnarySpTa);
 GRID_DEF_UNOP(ProjectOnGroup, UnaryProjectOnGroup);
-GRID_DEF_UNOP(ProjectOnSpGroup, UnaryProjectOnSpGroup);
 GRID_DEF_UNOP(timesI, UnaryTimesI);
 GRID_DEF_UNOP(timesMinusI, UnaryTimesMinusI);
 GRID_DEF_UNOP(abs, UnaryAbs);  // abs overloaded in cmath C++98; DON'T do the

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(int64_t g=0;g<o.Grid()->_gsites;g++){
+  for(int g=0;g<o.Grid()->_gsites;g++){
 
     Coordinate gcoor;
     o.Grid()->GlobalIndexToGlobalCoor(g,gcoor);

Grid/lattice/Lattice_rng.h

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

Grid/lattice/Lattice_trace.h

@@ -66,65 +66,6 @@ inline auto TraceIndex(const Lattice<vobj> &lhs) -> Lattice<decltype(traceIndex<
   return ret;
 };
 
-template<int N, class Vec>
-Lattice<iScalar<iScalar<iScalar<Vec> > > > Determinant(const Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  auto lvol = grid->lSites();
-  Lattice<iScalar<iScalar<iScalar<Vec> > > > ret(grid);
-  typedef typename Vec::scalar_type scalar;
-  autoView(Umu_v,Umu,CpuRead);
-  autoView(ret_v,ret,CpuWrite);
-  thread_for(site,lvol,{
-    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
-    Coordinate lcoor;
-    grid->LocalIndexToLocalCoor(site, lcoor);
-    iScalar<iScalar<iMatrix<scalar, N> > > Us;
-    peekLocalSite(Us, Umu_v, lcoor);
-    for(int i=0;i<N;i++){
-      for(int j=0;j<N;j++){
-	scalar tmp= Us()()(i,j);
-	ComplexD ztmp(real(tmp),imag(tmp));
-	EigenU(i,j)=ztmp;
-      }}
-    ComplexD detD  = EigenU.determinant();
-    typename Vec::scalar_type det(detD.real(),detD.imag());
-    pokeLocalSite(det,ret_v,lcoor);
-  });
-  return ret;
-}
-
-template<int N>
-Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
-{
-  GridBase *grid=Umu.Grid();
-  auto lvol = grid->lSites();
-  Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ret(grid);
-  
-  autoView(Umu_v,Umu,CpuRead);
-  autoView(ret_v,ret,CpuWrite);
-  thread_for(site,lvol,{
-    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
-    Coordinate lcoor;
-    grid->LocalIndexToLocalCoor(site, lcoor);
-    iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
-    iScalar<iScalar<iMatrix<ComplexD, N> > > Ui;
-    peekLocalSite(Us, Umu_v, lcoor);
-    for(int i=0;i<N;i++){
-      for(int j=0;j<N;j++){
-	EigenU(i,j) = Us()()(i,j);
-      }}
-    Eigen::MatrixXcd EigenUinv = EigenU.inverse();
-    for(int i=0;i<N;i++){
-      for(int j=0;j<N;j++){
-	Ui()()(i,j) = EigenUinv(i,j);
-      }}
-    pokeLocalSite(Ui,ret_v,lcoor);
-  });
-  return ret;
-}
-
-
 NAMESPACE_END(Grid);
 #endif
 

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(),vobj::Nsimd(),{
+  accelerator_for(sc,coarse->oSites(),1,{
 
       // One thread per sub block
       Coordinate coor_c(_ndimension);
       Lexicographic::CoorFromIndex(coor_c,sc,coarse_rdimensions);  // Block coordinate
 
-      auto cd = coalescedRead(zz);
+      vobj cd = 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+coalescedRead(fineData_p[sf]);
+	cd=cd+fineData_p[sf];
       }
 
-      coalescedWrite(coarseData_p[sc],cd);
+      coarseData_p[sc] = cd;
 
     });
   return;
@@ -697,68 +697,8 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
   for(int d=0;d<nd;d++){
     assert(Fg->_processors[d]  == Tg->_processors[d]);
   }
+
   // the above should guarantee that the operations are local
-  
-#if 1
-
-  size_t nsite = 1;
-  for(int i=0;i<nd;i++) nsite *= RegionSize[i];
-  
-  size_t tbytes = 4*nsite*sizeof(int);
-  int *table = (int*)malloc(tbytes);
- 
-  thread_for(idx, nsite, {
-      Coordinate from_coor, to_coor;
-      size_t rem = idx;
-      for(int i=0;i<nd;i++){
-	size_t base_i  = rem % RegionSize[i]; rem /= RegionSize[i];
-	from_coor[i] = base_i + FromLowerLeft[i];
-	to_coor[i] = base_i + ToLowerLeft[i];
-      }
-      
-      int foidx = Fg->oIndex(from_coor);
-      int fiidx = Fg->iIndex(from_coor);
-      int toidx = Tg->oIndex(to_coor);
-      int tiidx = Tg->iIndex(to_coor);
-      int* tt = table + 4*idx;
-      tt[0] = foidx;
-      tt[1] = fiidx;
-      tt[2] = toidx;
-      tt[3] = tiidx;
-    });
-  
-  int* table_d = (int*)acceleratorAllocDevice(tbytes);
-  acceleratorCopyToDevice(table,table_d,tbytes);
-
-  typedef typename vobj::vector_type vector_type;
-  typedef typename vobj::scalar_type scalar_type;
-
-  autoView(from_v,From,AcceleratorRead);
-  autoView(to_v,To,AcceleratorWrite);
-  
-  accelerator_for(idx,nsite,1,{
-      static const int words=sizeof(vobj)/sizeof(vector_type);
-      int* tt = table_d + 4*idx;
-      int from_oidx = *tt++;
-      int from_lane = *tt++;
-      int to_oidx = *tt++;
-      int to_lane = *tt;
-
-      const vector_type* from = (const vector_type *)&from_v[from_oidx];
-      vector_type* to = (vector_type *)&to_v[to_oidx];
-      
-      scalar_type stmp;
-      for(int w=0;w<words;w++){
-	stmp = getlane(from[w], from_lane);
-	putlane(to[w], stmp, to_lane);
-      }
-    });
-  
-  acceleratorFreeDevice(table_d);    
-  free(table);
-  
-
-#else  
   Coordinate ldf = Fg->_ldimensions;
   Coordinate rdf = Fg->_rdimensions;
   Coordinate isf = Fg->_istride;
@@ -798,8 +738,6 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
 #endif
     }
   });
-
-#endif
 }
 
 
@@ -892,8 +830,6 @@ void ExtractSlice(Lattice<vobj> &lowDim,const Lattice<vobj> & higherDim,int slic
 }
 
 
-//Insert subvolume orthogonal to direction 'orthog' with slice index 'slice_lo' from 'lowDim' onto slice index 'slice_hi' of higherDim
-//The local dimensions of both 'lowDim' and 'higherDim' orthogonal to 'orthog' should be the same
 template<class vobj>
 void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int slice_lo,int slice_hi, int orthog)
 {
@@ -915,65 +851,6 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
     }
   }
 
-#if 1
-  size_t nsite = lg->lSites()/lg->LocalDimensions()[orthog];
-  size_t tbytes = 4*nsite*sizeof(int);
-  int *table = (int*)malloc(tbytes);
-  
-  thread_for(idx,nsite,{
-    Coordinate lcoor(nl);
-    Coordinate hcoor(nh);
-    lcoor[orthog] = slice_lo;
-    hcoor[orthog] = slice_hi;
-    size_t rem = idx;
-    for(int mu=0;mu<nl;mu++){
-      if(mu != orthog){
-	int xmu = rem % lg->LocalDimensions()[mu];  rem /= lg->LocalDimensions()[mu];
-	lcoor[mu] = hcoor[mu] = xmu;
-      }
-    }
-    int loidx = lg->oIndex(lcoor);
-    int liidx = lg->iIndex(lcoor);
-    int hoidx = hg->oIndex(hcoor);
-    int hiidx = hg->iIndex(hcoor);
-    int* tt = table + 4*idx;
-    tt[0] = loidx;
-    tt[1] = liidx;
-    tt[2] = hoidx;
-    tt[3] = hiidx;
-    });
-   
-  int* table_d = (int*)acceleratorAllocDevice(tbytes);
-  acceleratorCopyToDevice(table,table_d,tbytes);
-
-  typedef typename vobj::vector_type vector_type;
-  typedef typename vobj::scalar_type scalar_type;
-
-  autoView(lowDim_v,lowDim,AcceleratorRead);
-  autoView(higherDim_v,higherDim,AcceleratorWrite);
-  
-  accelerator_for(idx,nsite,1,{
-      static const int words=sizeof(vobj)/sizeof(vector_type);
-      int* tt = table_d + 4*idx;
-      int from_oidx = *tt++;
-      int from_lane = *tt++;
-      int to_oidx = *tt++;
-      int to_lane = *tt;
-
-      const vector_type* from = (const vector_type *)&lowDim_v[from_oidx];
-      vector_type* to = (vector_type *)&higherDim_v[to_oidx];
-      
-      scalar_type stmp;
-      for(int w=0;w<words;w++){
-	stmp = getlane(from[w], from_lane);
-	putlane(to[w], stmp, to_lane);
-      }
-    });
-  
-  acceleratorFreeDevice(table_d);    
-  free(table);
-  
-#else
   // the above should guarantee that the operations are local
   autoView(lowDimv,lowDim,CpuRead);
   autoView(higherDimv,higherDim,CpuWrite);
@@ -989,7 +866,6 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
       pokeLocalSite(s,higherDimv,hcoor);
     }
   });
-#endif
 }
 
 
@@ -1054,7 +930,7 @@ void Replicate(const Lattice<vobj> &coarse,Lattice<vobj> & fine)
 
   Coordinate fcoor(nd);
   Coordinate ccoor(nd);
-  for(int64_t g=0;g<fg->gSites();g++){
+  for(int g=0;g<fg->gSites();g++){
 
     fg->GlobalIndexToGlobalCoor(g,fcoor);
     for(int d=0;d<nd;d++){

Grid/lattice/PaddedCell.h

@@ -26,32 +26,14 @@ Author: Peter Boyle pboyle@bnl.gov
 /*  END LEGAL */
 #pragma once
 
-#include<Grid/cshift/Cshift.h>
-
 NAMESPACE_BEGIN(Grid);
 
-//Allow the user to specify how the C-shift is performed, e.g. to respect the appropriate boundary conditions
-template<typename vobj>
-struct CshiftImplBase{
-  virtual Lattice<vobj> Cshift(const Lattice<vobj> &in, int dir, int shift) const = 0;
-  virtual ~CshiftImplBase(){}
-};
-template<typename vobj>
-struct CshiftImplDefault: public CshiftImplBase<vobj>{
-  Lattice<vobj> Cshift(const Lattice<vobj> &in, int dir, int shift) const override{ return Grid::Cshift(in,dir,shift); }
-};
-template<typename Gimpl>
-struct CshiftImplGauge: public CshiftImplBase<typename Gimpl::GaugeLinkField::vector_object>{
-  typename Gimpl::GaugeLinkField Cshift(const typename Gimpl::GaugeLinkField &in, int dir, int shift) const override{ return Gimpl::CshiftLink(in,dir,shift); }
-};  
-
 class PaddedCell {
 public:
   GridCartesian * unpadded_grid;
   int dims;
   int depth;
   std::vector<GridCartesian *> grids;
-
   ~PaddedCell()
   {
     DeleteGrids();
@@ -63,9 +45,8 @@ public:
     dims=_grid->Nd();
     AllocateGrids();
     Coordinate local     =unpadded_grid->LocalDimensions();
-    Coordinate procs     =unpadded_grid->ProcessorGrid();
     for(int d=0;d<dims;d++){
-      if ( procs[d] > 1 ) assert(local[d]>=depth);
+      assert(local[d]>=depth);
     }
   }
   void DeleteGrids(void)
@@ -86,10 +67,8 @@ public:
     // expand up one dim at a time
     for(int d=0;d<dims;d++){
 
-      if ( processors[d] > 1 ) { 
-	plocal[d] += 2*depth; 
-      }
-      
+      plocal[d] += 2*depth; 
+
       for(int d=0;d<dims;d++){
 	global[d] = plocal[d]*processors[d];
       }
@@ -98,38 +77,31 @@ public:
     }
   };
   template<class vobj>
-  inline Lattice<vobj> Extract(const Lattice<vobj> &in) const
+  inline Lattice<vobj> Extract(Lattice<vobj> &in)
   {
-    Coordinate processors=unpadded_grid->_processors;
-
     Lattice<vobj> out(unpadded_grid);
 
     Coordinate local     =unpadded_grid->LocalDimensions();
-    // depends on the MPI spread      
-    Coordinate fll(dims,depth);
+    Coordinate fll(dims,depth); // depends on the MPI spread
     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;
   }
   template<class vobj>
-  inline Lattice<vobj> Exchange(const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
+  inline Lattice<vobj> Exchange(Lattice<vobj> &in)
   {
     GridBase *old_grid = in.Grid();
     int dims = old_grid->Nd();
     Lattice<vobj> tmp = in;
     for(int d=0;d<dims;d++){
-      tmp = Expand(d,tmp,cshift); // rvalue && assignment
+      tmp = Expand(d,tmp); // rvalue && assignment
     }
     return tmp;
   }
   // expand up one dim at a time
   template<class vobj>
-  inline Lattice<vobj> Expand(int dim, const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
+  inline Lattice<vobj> Expand(int dim,Lattice<vobj> &in)
   {
-    Coordinate processors=unpadded_grid->_processors;
     GridBase *old_grid = in.Grid();
     GridCartesian *new_grid = grids[dim];//These are new grids
     Lattice<vobj>  padded(new_grid);
@@ -140,52 +112,20 @@ public:
     else       conformable(old_grid,grids[dim-1]);
 
     std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
-
-    double tins=0, tshift=0;
-
-    int islocal = 0 ;
-    if ( processors[dim] == 1 ) islocal = 1;
-
-    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;
+    // Middle bit
+    for(int x=0;x<local[dim];x++){
+      InsertSliceLocal(in,padded,x,depth+x,dim);
+    }
+    // High bit
+    shifted = Cshift(in,dim,depth);
+    for(int x=0;x<depth;x++){
+      InsertSliceLocal(shifted,padded,local[dim]-depth+x,depth+local[dim]+x,dim);
+    }
+    // Low bit
+    shifted = Cshift(in,dim,-depth);
+    for(int x=0;x<depth;x++){
+      InsertSliceLocal(shifted,padded,x,x,dim);
     }
-    std::cout << GridLogPerformance << "PaddedCell::Expand timings: cshift:" << tshift/1000 << "ms, insert-slice:" << tins/1000 << "ms" << std::endl;
-    
     return padded;
   }
 

Grid/qcd/action/fermion/CayleyFermion5D.h

@@ -124,6 +124,11 @@ public:
   RealD                _b;
   RealD                _c;
 
+  // possible boost
+  std::vector<ComplexD> qmu;
+  void set_qmu(std::vector<ComplexD> _qmu) { qmu=_qmu; assert(qmu.size()==Nd);};
+  void addQmu(const FermionField &in, FermionField &out, int dag);
+  
   // Cayley form Moebius (tanh and zolotarev)
   Vector<Coeff_t> omega;
   Vector<Coeff_t> bs;    // S dependent coeffs

Grid/qcd/action/fermion/ContinuedFractionFermion5D.h

@@ -60,6 +60,50 @@ public:
   //      virtual void   Instantiatable(void)=0;
   virtual void   Instantiatable(void) =0;
 
+  void FreePropagator(const FermionField &in,FermionField &out,RealD mass,std::vector<Complex> boundary, std::vector<double> twist)
+  {
+    std::cout << "Free Propagator for PartialFraction"<<std::endl;
+    FermionField in_k(in.Grid());
+    FermionField prop_k(in.Grid());
+    
+    FFT theFFT((GridCartesian *) in.Grid());
+
+    //phase for boundary condition
+    ComplexField coor(in.Grid());
+    ComplexField ph(in.Grid());  ph = Zero();
+    FermionField in_buf(in.Grid()); in_buf = Zero();
+    typedef typename Simd::scalar_type Scalar;
+    Scalar ci(0.0,1.0);
+    assert(twist.size() == Nd);//check that twist is Nd
+    assert(boundary.size() == Nd);//check that boundary conditions is Nd
+    int shift = 0;
+    for(unsigned int nu = 0; nu < Nd; nu++)
+      {
+	// Shift coordinate lattice index by 1 to account for 5th dimension.
+	LatticeCoordinate(coor, nu + shift);
+	double boundary_phase = ::acos(real(boundary[nu]));
+	ph = ph + boundary_phase*coor*((1./(in.Grid()->_fdimensions[nu+shift])));
+	//momenta for propagator shifted by twist+boundary
+	twist[nu] = twist[nu] + boundary_phase/((2.0*M_PI));
+      }
+    in_buf = exp(ci*ph*(-1.0))*in;
+
+    theFFT.FFT_all_dim(in_k,in,FFT::forward);
+    this->MomentumSpacePropagatorHw(prop_k,in_k,mass,twist);
+    theFFT.FFT_all_dim(out,prop_k,FFT::backward);
+    
+    //phase for boundary condition
+    out = out * exp(ci*ph);
+  };
+
+  virtual void FreePropagator(const FermionField &in,FermionField &out,RealD mass) {
+    std::vector<double> twist(Nd,0.0); //default: periodic boundarys in all directions
+    std::vector<Complex> boundary;
+    for(int i=0;i<Nd;i++) boundary.push_back(1);//default: periodic boundary conditions
+    FreePropagator(in,out,mass,boundary,twist);
+  };
+
+  
   // Efficient support for multigrid coarsening
   virtual void  Mdir (const FermionField &in, FermionField &out,int dir,int disp);
   virtual void  MdirAll(const FermionField &in, std::vector<FermionField> &out);

Grid/qcd/action/fermion/Fermion.h

@@ -126,16 +126,6 @@ typedef WilsonFermion<WilsonTwoIndexSymmetricImplD> WilsonTwoIndexSymmetricFermi
 typedef WilsonFermion<WilsonTwoIndexAntiSymmetricImplF> WilsonTwoIndexAntiSymmetricFermionF;
 typedef WilsonFermion<WilsonTwoIndexAntiSymmetricImplD> WilsonTwoIndexAntiSymmetricFermionD;
 
-// Sp(2n)
-typedef WilsonFermion<SpWilsonImplF> SpWilsonFermionF;
-typedef WilsonFermion<SpWilsonImplD> SpWilsonFermionD;
-
-typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplF> SpWilsonTwoIndexAntiSymmetricFermionF;
-typedef WilsonFermion<SpWilsonTwoIndexAntiSymmetricImplD> SpWilsonTwoIndexAntiSymmetricFermionD;
-
-typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplF> SpWilsonTwoIndexSymmetricFermionF;
-typedef WilsonFermion<SpWilsonTwoIndexSymmetricImplD> SpWilsonTwoIndexSymmetricFermionD;
-
 // Twisted mass fermion
 typedef WilsonTMFermion<WilsonImplD2> WilsonTMFermionD2;
 typedef WilsonTMFermion<WilsonImplF> WilsonTMFermionF;

Grid/qcd/action/fermion/PartialFractionFermion5D.h

@@ -39,7 +39,7 @@ class PartialFractionFermion5D : public WilsonFermion5D<Impl>
 public:
   INHERIT_IMPL_TYPES(Impl);
 
-  const int part_frac_chroma_convention=1;
+  const int part_frac_chroma_convention=0;
 
   void   Meooe_internal(const FermionField &in, FermionField &out,int dag);
   void   Mooee_internal(const FermionField &in, FermionField &out,int dag);
@@ -83,12 +83,63 @@ public:
 			   GridRedBlackCartesian &FourDimRedBlackGrid,
 			   RealD _mass,RealD M5,const ImplParams &p= ImplParams());
 
+  PartialFractionFermion5D(GaugeField &_Umu,
+			   GridCartesian         &FiveDimGrid,
+			   GridRedBlackCartesian &FiveDimRedBlackGrid,
+			   GridCartesian         &FourDimGrid,
+			   GridRedBlackCartesian &FourDimRedBlackGrid,
+			   RealD _mass,RealD M5,std::vector<RealD> &_qmu,const ImplParams &p= ImplParams());
+
+  void FreePropagator(const FermionField &in,FermionField &out,RealD mass,std::vector<Complex> boundary, std::vector<double> twist)
+  {
+    std::cout << "Free Propagator for PartialFraction"<<std::endl;
+    FermionField in_k(in.Grid());
+    FermionField prop_k(in.Grid());
+    
+    FFT theFFT((GridCartesian *) in.Grid());
+
+    //phase for boundary condition
+    ComplexField coor(in.Grid());
+    ComplexField ph(in.Grid());  ph = Zero();
+    FermionField in_buf(in.Grid()); in_buf = Zero();
+    typedef typename Simd::scalar_type Scalar;
+    Scalar ci(0.0,1.0);
+    assert(twist.size() == Nd);//check that twist is Nd
+    assert(boundary.size() == Nd);//check that boundary conditions is Nd
+    int shift = 0;
+    for(unsigned int nu = 0; nu < Nd; nu++)
+      {
+	// Shift coordinate lattice index by 1 to account for 5th dimension.
+	LatticeCoordinate(coor, nu + shift);
+	double boundary_phase = ::acos(real(boundary[nu]));
+	ph = ph + boundary_phase*coor*((1./(in.Grid()->_fdimensions[nu+shift])));
+	//momenta for propagator shifted by twist+boundary
+	twist[nu] = twist[nu] + boundary_phase/((2.0*M_PI));
+      }
+    in_buf = exp(ci*ph*(-1.0))*in;
+
+    theFFT.FFT_all_dim(in_k,in,FFT::forward);
+    this->MomentumSpacePropagatorHw(prop_k,in_k,mass,twist);
+    theFFT.FFT_all_dim(out,prop_k,FFT::backward);
+    
+    //phase for boundary condition
+    out = out * exp(ci*ph);
+  };
+
+  virtual void FreePropagator(const FermionField &in,FermionField &out,RealD mass) {
+    std::vector<double> twist(Nd,0.0); //default: periodic boundarys in all directions
+    std::vector<Complex> boundary;
+    for(int i=0;i<Nd;i++) boundary.push_back(1);//default: periodic boundary conditions
+    FreePropagator(in,out,mass,boundary,twist);
+  };
+  
 protected:
 
   virtual void SetCoefficientsTanh(Approx::zolotarev_data *zdata,RealD scale);
   virtual void SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata);
 
   // Part frac
+  std::vector<RealD> qmu;
   RealD mass;
   RealD dw_diag;
   RealD R;

Grid/qcd/action/fermion/WilsonImpl.h

@@ -261,22 +261,6 @@ typedef WilsonImpl<vComplex,  TwoIndexAntiSymmetricRepresentation, CoeffReal > W
 typedef WilsonImpl<vComplexF, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplF;  // Float
 typedef WilsonImpl<vComplexD, TwoIndexAntiSymmetricRepresentation, CoeffReal > WilsonTwoIndexAntiSymmetricImplD;  // Double
 
-//sp 2n
-
-typedef WilsonImpl<vComplex,  SpFundamentalRepresentation, CoeffReal > SpWilsonImplR;  // Real.. whichever prec
-typedef WilsonImpl<vComplexF, SpFundamentalRepresentation, CoeffReal > SpWilsonImplF;  // Float
-typedef WilsonImpl<vComplexD, SpFundamentalRepresentation, CoeffReal > SpWilsonImplD;  // Double
-
-typedef WilsonImpl<vComplex,  SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplR;  // Real.. whichever prec
-typedef WilsonImpl<vComplexF, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplF;  // Float
-typedef WilsonImpl<vComplexD, SpTwoIndexAntiSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexAntiSymmetricImplD;  // Double
-
-typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplR;  // Real.. whichever prec
-typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplF;  // Float
-typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonTwoIndexSymmetricImplD;  // Double
-
-typedef WilsonImpl<vComplex,  SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplR;  // Real.. whichever prec    // adj = 2indx symmetric for Sp(2N)
-typedef WilsonImpl<vComplexF, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplF;  // Float     // adj = 2indx symmetric for Sp(2N)
-typedef WilsonImpl<vComplexD, SpTwoIndexSymmetricRepresentation, CoeffReal > SpWilsonAdjImplD;  // Double    // adj = 2indx symmetric for Sp(2N)
 
 NAMESPACE_END(Grid);
+

Grid/qcd/action/fermion/implementation/CayleyFermion5DImplementation.h

@@ -48,7 +48,8 @@ CayleyFermion5D<Impl>::CayleyFermion5D(GaugeField &_Umu,
 			FourDimGrid,
 			FourDimRedBlackGrid,_M5,p),
   mass_plus(_mass), mass_minus(_mass)
-{ 
+{
+  // qmu defaults to zero size;
 }
 
 ///////////////////////////////////////////////////////////////
@@ -270,6 +271,34 @@ void CayleyFermion5D<Impl>::MeooeDag5D    (const FermionField &psi, FermionField
   M5Ddag(psi,psi,Din,lower,diag,upper);
 }
 
+template<class Impl>
+void CayleyFermion5D<Impl>::addQmu(const FermionField &psi,FermionField &chi, int dag)
+{
+  if ( qmu.size() ) {
+
+    Gamma::Algebra Gmu [] = {
+      Gamma::Algebra::GammaX,
+      Gamma::Algebra::GammaY,
+      Gamma::Algebra::GammaZ,
+      Gamma::Algebra::GammaT
+    };
+    std::vector<ComplexD> coeff(Nd);
+    ComplexD ci(0,1);
+
+    assert(qmu.size()==Nd);
+
+    for(int mu=0;mu<Nd;mu++){
+       coeff[mu] = ci*qmu[mu];
+       if ( dag ) coeff[mu] = conjugate(coeff[mu]);
+    }
+
+    chi = chi + Gamma(Gmu[0])*psi*coeff[0];
+    for(int mu=1;mu<Nd;mu++){
+      chi = chi + Gamma(Gmu[mu])*psi*coeff[mu];
+    }
+  }
+}
+
 template<class Impl>
 void CayleyFermion5D<Impl>::M    (const FermionField &psi, FermionField &chi)
 {
@@ -277,8 +306,12 @@ void CayleyFermion5D<Impl>::M    (const FermionField &psi, FermionField &chi)
   
   // Assemble Din
   Meooe5D(psi,Din);
-  
+
   this->DW(Din,chi,DaggerNo);
+
+  // add i q_mu gamma_mu here
+  addQmu(Din,chi,DaggerNo);
+  
   // ((b D_W + D_w hop terms +1) on s-diag
   axpby(chi,1.0,1.0,chi,psi); 
   
@@ -295,6 +328,9 @@ void CayleyFermion5D<Impl>::Mdag (const FermionField &psi, FermionField &chi)
   FermionField Din(psi.Grid());
   // Apply Dw
   this->DW(psi,Din,DaggerYes); 
+
+  // add -i conj(q_mu) gamma_mu here ... if qmu is real, gammm_5 hermitian, otherwise not.
+  addQmu(psi,Din,DaggerYes);
   
   MeooeDag5D(Din,chi);
   

Grid/qcd/action/fermion/implementation/ContinuedFractionFermion5DImplementation.h

@@ -42,13 +42,13 @@ template<class Impl>
 void ContinuedFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,Approx::zolotarev_data *zdata)
 {
   // How to check Ls matches??
-  //      std::cout<<GridLogMessage << Ls << " Ls"<<std::endl;
-  //      std::cout<<GridLogMessage << zdata->n  << " - n"<<std::endl;
-  //      std::cout<<GridLogMessage << zdata->da << " -da "<<std::endl;
-  //      std::cout<<GridLogMessage << zdata->db << " -db"<<std::endl;
-  //      std::cout<<GridLogMessage << zdata->dn << " -dn"<<std::endl;
-  //      std::cout<<GridLogMessage << zdata->dd << " -dd"<<std::endl;
+  std::cout<<GridLogMessage << zdata->n  << " - n"<<std::endl;
+  std::cout<<GridLogMessage << zdata->da << " -da "<<std::endl;
+  std::cout<<GridLogMessage << zdata->db << " -db"<<std::endl;
+  std::cout<<GridLogMessage << zdata->dn << " -dn"<<std::endl;
+  std::cout<<GridLogMessage << zdata->dd << " -dd"<<std::endl;
   int Ls = this->Ls;
+  std::cout<<GridLogMessage << Ls << " Ls"<<std::endl;
   assert(zdata->db==Ls);// Beta has Ls coeffs
 
   R=(1+this->mass)/(1-this->mass);
@@ -320,7 +320,7 @@ ContinuedFractionFermion5D<Impl>::ContinuedFractionFermion5D(
       int Ls = this->Ls;
       conformable(solution5d.Grid(),this->FermionGrid());
       conformable(exported4d.Grid(),this->GaugeGrid());
-      ExtractSlice(exported4d, solution5d, Ls-1, Ls-1);
+      ExtractSlice(exported4d, solution5d, Ls-1, 0);
     }
     template<class Impl>
     void ContinuedFractionFermion5D<Impl>::ImportPhysicalFermionSource(const FermionField &input4d,FermionField &imported5d)
@@ -330,7 +330,7 @@ ContinuedFractionFermion5D<Impl>::ContinuedFractionFermion5D(
       conformable(input4d.Grid()   ,this->GaugeGrid());
       FermionField tmp(this->FermionGrid());
       tmp=Zero();
-      InsertSlice(input4d, tmp, Ls-1, Ls-1);
+      InsertSlice(input4d, tmp, Ls-1, 0);
       tmp=Gamma(Gamma::Algebra::Gamma5)*tmp;
       this->Dminus(tmp,imported5d);
     }

Grid/qcd/action/fermion/implementation/PartialFractionFermion5DImplementation.h

@@ -255,15 +255,76 @@ void   PartialFractionFermion5D<Impl>::M_internal(const FermionField &psi, Fermi
   }
 	
   {
+    // The 'conventional' Cayley overlap operator is
+    //
+    // Dov = (1+m)/2 + (1-m)/2 g5 sgn Hw
+    //
+    //
+    // With massless limit 1/2(1+g5 sgnHw)
+    //
+    // Luscher shows quite neatly that 1+g5 sgn Hw has tree level propagator i qslash +O(a^2)
+    //
+    // However, the conventional normalisation has both a leading order factor of 2 in Zq
+    // at tree level AND a mass dependent (1-m) that are convenient to absorb.
+    //
+    // In WilsonFermion5DImplementation.h, the tree level propagator for Hw is
+    //
+    // num = -i sin kmu gmu
+    //
+    // denom ( sqrt(sk^2 + (2shk^2 - 1)^2
+    //    b_k = sk2 - M5;
+    //     
+    //    w_k = sqrt(sk + b_k*b_k);
+    //
+    //    denom= ( w_k + b_k + mass*mass) ;
+    //
+    //    denom= one/denom;
+    //    out = num*denom;
+    //
+    // Chroma, and Grid define partial fraction via 4d operator
+    //
+    //   Dpf = 2/(1-m) x Dov = (1+m)/(1-m) + g5 sgn Hw
+    //
+    // Now since:
+    //
+    //      (1+m)/(1-m) = (1-m)/(1-m) + 2m/(1-m) = 1 + 2m/(1-m)
+    //
+    // This corresponds to a modified mass parameter
+    //
+    // It has an annoying 
+    //
+    // 
     double R=(1+this->mass)/(1-this->mass);
     //R g5 psi[Ls] + p[0] H
     ag5xpbg5y_ssp(chi,R*scale,psi,p[nblock]*scale/amax,D,Ls-1,Ls-1);
-	
+    
     for(int b=0;b<nblock;b++){
       int s = 2*b+1;
       double pp = p[nblock-1-b];
       axpby_ssp(chi,1.0,chi,-sqrt(amax*pp)*scale*sign,psi,Ls-1,s);
     }
+
+    if ( qmu.size() ) {
+
+      FermionField qslash_psi(psi.Grid());
+      
+      Gamma::Algebra Gmu [] = {
+			 Gamma::Algebra::GammaX,
+			 Gamma::Algebra::GammaY,
+			 Gamma::Algebra::GammaZ,
+			 Gamma::Algebra::GammaT
+      };
+      ComplexD ci(0,1);
+      assert(qmu.size()==Nd);
+      qslash_psi = Gamma(Gmu[0])*psi;
+      for(int mu=1;mu<Nd;mu++){
+	qslash_psi = Gamma(Gmu[mu])*psi;
+      }
+      //      RealD coeff = 1.0;
+      qslash_psi = Gamma(Gamma::Algebra::Gamma5)*qslash_psi*ci ; // i g5 qslash -- 1-m factor???
+      axpby_ssp(chi,1.0,chi,1.0, qslash_psi,Ls-1,Ls-1);
+    }
+    
   }
 
 }
@@ -411,7 +472,7 @@ void  PartialFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,App
       int Ls = this->Ls;
       conformable(solution5d.Grid(),this->FermionGrid());
       conformable(exported4d.Grid(),this->GaugeGrid());
-      ExtractSlice(exported4d, solution5d, Ls-1, Ls-1);
+      ExtractSlice(exported4d, solution5d, Ls-1, 0);
     }
     template<class Impl>
     void PartialFractionFermion5D<Impl>::ImportPhysicalFermionSource(const FermionField &input4d,FermionField &imported5d)
@@ -421,7 +482,8 @@ void  PartialFractionFermion5D<Impl>::SetCoefficientsZolotarev(RealD zolo_hi,App
       conformable(input4d.Grid()   ,this->GaugeGrid());
       FermionField tmp(this->FermionGrid());
       tmp=Zero();
-      InsertSlice(input4d, tmp, Ls-1, Ls-1);
+      std::cout << " importing to slice " << Ls-1 <<std::endl;
+      InsertSlice(input4d, tmp, Ls-1, 0);
       tmp=Gamma(Gamma::Algebra::Gamma5)*tmp;
       this->Dminus(tmp,imported5d);
     }
@@ -442,7 +504,7 @@ PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
 
 {
   int Ls = this->Ls;
-
+  qmu.resize(0);
   assert((Ls&0x1)==1); // Odd Ls required
   int nrational=Ls-1;
 
@@ -460,6 +522,22 @@ PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
   Approx::zolotarev_free(zdata);
 
 }
+template<class Impl>
+PartialFractionFermion5D<Impl>::PartialFractionFermion5D(GaugeField &_Umu,
+							 GridCartesian         &FiveDimGrid,
+							 GridRedBlackCartesian &FiveDimRedBlackGrid,
+							 GridCartesian         &FourDimGrid,
+							 GridRedBlackCartesian &FourDimRedBlackGrid,
+							 RealD _mass,RealD M5,
+							 std::vector<RealD> &_qmu,
+							 const ImplParams &p)
+  : PartialFractionFermion5D<Impl>(_Umu,
+			     FiveDimGrid,FiveDimRedBlackGrid,
+			     FourDimGrid,FourDimRedBlackGrid,
+			     _mass,M5,p)
+{
+  qmu=_qmu;
+}
 
 NAMESPACE_END(Grid);
 

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonImplD

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonImplF

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplD

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplF

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonCloverFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonKernelsInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc

@@ -1 +0,0 @@
-../WilsonTMFermionInstantiation.cc.master

Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h

@@ -1 +0,0 @@
-#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF

Grid/qcd/action/fermion/instantiation/generate_instantiations.sh

@@ -10,18 +10,12 @@ WILSON_IMPL_LIST=" \
 	   WilsonImplF \
 	   WilsonImplD \
 	   WilsonImplD2 \
-	   SpWilsonImplF \
-	   SpWilsonImplD \
 	   WilsonAdjImplF \
 	   WilsonAdjImplD \
 	   WilsonTwoIndexSymmetricImplF \
 	   WilsonTwoIndexSymmetricImplD \
 	   WilsonTwoIndexAntiSymmetricImplF \
 	   WilsonTwoIndexAntiSymmetricImplD \
-	   SpWilsonTwoIndexAntiSymmetricImplF \
-	   SpWilsonTwoIndexAntiSymmetricImplD \
-	   SpWilsonTwoIndexSymmetricImplF \
-	   SpWilsonTwoIndexSymmetricImplD \
 	   GparityWilsonImplF \
 	   GparityWilsonImplD "
 

Grid/qcd/action/gauge/Gauge.h

@@ -39,9 +39,6 @@ NAMESPACE_BEGIN(Grid);
 typedef WilsonGaugeAction<PeriodicGimplR>          WilsonGaugeActionR;
 typedef WilsonGaugeAction<PeriodicGimplF>          WilsonGaugeActionF;
 typedef WilsonGaugeAction<PeriodicGimplD>          WilsonGaugeActionD;
-typedef WilsonGaugeAction<SpPeriodicGimplR>        SpWilsonGaugeActionR;
-typedef WilsonGaugeAction<SpPeriodicGimplF>        SpWilsonGaugeActionF;
-typedef WilsonGaugeAction<SpPeriodicGimplD>        SpWilsonGaugeActionD;
 typedef PlaqPlusRectangleAction<PeriodicGimplR>    PlaqPlusRectangleActionR;
 typedef PlaqPlusRectangleAction<PeriodicGimplF>    PlaqPlusRectangleActionF;
 typedef PlaqPlusRectangleAction<PeriodicGimplD>    PlaqPlusRectangleActionD;

Grid/qcd/action/gauge/GaugeImplTypes.h

@@ -61,7 +61,7 @@ NAMESPACE_BEGIN(Grid);
   typedef typename Impl::Field Field;
 
 // hardcodes the exponential approximation in the template
-template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12 > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -78,6 +78,8 @@ public:
   typedef Lattice<SiteLink>    LinkField; 
   typedef Lattice<SiteField>   Field;
 
+  typedef SU<Nrepresentation> Group;
+
   // Guido: we can probably separate the types from the HMC functions
   // this will create 2 kind of implementations
   // probably confusing the users
@@ -117,7 +119,6 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
-
     for (int mu = 0; mu < Nd; mu++) {
       Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
@@ -125,12 +126,8 @@ public:
       PokeIndex<LorentzIndex>(P, Pmu, mu);
     }
   }
-    
-  static inline Field projectForce(Field &P) {
-      Field ret(P.Grid());
-      Group::taProj(P, ret);
-      return ret;
-    }
+
+  static inline Field projectForce(Field &P) { return Ta(P); }
 
   static inline void update_field(Field& P, Field& U, double ep){
     //static std::chrono::duration<double> diff;
@@ -140,15 +137,14 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-          U_v[ss](mu) = Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu);
-          U_v[ss](mu) = Group::ProjectOnGeneralGroup(U_v[ss](mu));
+        U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](mu));
       }
     });
    //auto end = std::chrono::high_resolution_clock::now();
    // diff += end - start;
    // std::cout << "Time to exponentiate matrix " << diff.count() << " s\n";
   }
-    
+
   static inline RealD FieldSquareNorm(Field& U){
     LatticeComplex Hloc(U.Grid());
     Hloc = Zero();
@@ -161,7 +157,7 @@ public:
   }
 
   static inline void Project(Field &U) {
-    Group::ProjectOnSpecialGroup(U);
+    ProjectSUn(U);
   }
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
@@ -175,7 +171,6 @@ public:
   static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::ColdConfiguration(pRNG, U);
   }
-
 };
 
 
@@ -183,17 +178,10 @@ typedef GaugeImplTypes<vComplex, Nc> GimplTypesR;
 typedef GaugeImplTypes<vComplexF, Nc> GimplTypesF;
 typedef GaugeImplTypes<vComplexD, Nc> GimplTypesD;
 
-typedef GaugeImplTypes<vComplex, Nc, 12, Sp<Nc> > SpGimplTypesR;
-typedef GaugeImplTypes<vComplexF, Nc, 12, Sp<Nc> > SpGimplTypesF;
-typedef GaugeImplTypes<vComplexD, Nc, 12, Sp<Nc> > SpGimplTypesD;
-
 typedef GaugeImplTypes<vComplex, SU<Nc>::AdjointDimension> GimplAdjointTypesR;
 typedef GaugeImplTypes<vComplexF, SU<Nc>::AdjointDimension> GimplAdjointTypesF;
 typedef GaugeImplTypes<vComplexD, SU<Nc>::AdjointDimension> GimplAdjointTypesD;
 
-
-
-
 NAMESPACE_END(Grid);
 
 #endif // GRID_GAUGE_IMPL_TYPES_H

Grid/qcd/action/gauge/GaugeImplementations.h

@@ -176,7 +176,7 @@ public:
       return PeriodicBC::CshiftLink(Link,mu,shift);
   }
 
-  static inline void       setDirections(const std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
+  static inline void       setDirections(std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
   static inline std::vector<int> getDirections(void) { return _conjDirs; }
   static inline bool isPeriodicGaugeField(void) { return false; }
 };
@@ -193,11 +193,6 @@ typedef ConjugateGaugeImpl<GimplTypesR> ConjugateGimplR; // Real.. whichever pre
 typedef ConjugateGaugeImpl<GimplTypesF> ConjugateGimplF; // Float
 typedef ConjugateGaugeImpl<GimplTypesD> ConjugateGimplD; // Double
 
-typedef PeriodicGaugeImpl<SpGimplTypesR> SpPeriodicGimplR; // Real.. whichever prec
-typedef PeriodicGaugeImpl<SpGimplTypesF> SpPeriodicGimplF; // Float
-typedef PeriodicGaugeImpl<SpGimplTypesD> SpPeriodicGimplD; // Double
-
-
 NAMESPACE_END(Grid);
 
 #endif

Grid/qcd/action/gauge/PlaqPlusRectangleAction.h

@@ -43,7 +43,7 @@ public:
 private:
   RealD c_plaq;
   RealD c_rect;
-  typename WilsonLoops<Gimpl>::StapleAndRectStapleAllWorkspace workspace;
+
 public:
   PlaqPlusRectangleAction(RealD b,RealD c): c_plaq(b),c_rect(c){};
 
@@ -79,18 +79,27 @@ public:
     GridBase *grid = Umu.Grid();
 
     std::vector<GaugeLinkField> U (Nd,grid);
+    std::vector<GaugeLinkField> U2(Nd,grid);
+
     for(int mu=0;mu<Nd;mu++){
       U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
+      WilsonLoops<Gimpl>::RectStapleDouble(U2[mu],U[mu],mu);
     }
-    std::vector<GaugeLinkField> RectStaple(Nd,grid), Staple(Nd,grid);
-    WilsonLoops<Gimpl>::StapleAndRectStapleAll(Staple, RectStaple, U, workspace);
 
     GaugeLinkField dSdU_mu(grid);
     GaugeLinkField staple(grid);
 
     for (int mu=0; mu < Nd; mu++){
-      dSdU_mu = Ta(U[mu]*Staple[mu])*factor_p;
-      dSdU_mu = dSdU_mu + Ta(U[mu]*RectStaple[mu])*factor_r;
+
+      // Staple in direction mu
+
+      WilsonLoops<Gimpl>::Staple(staple,Umu,mu);
+
+      dSdU_mu = Ta(U[mu]*staple)*factor_p;
+
+      WilsonLoops<Gimpl>::RectStaple(Umu,staple,U2,U,mu);
+
+      dSdU_mu = dSdU_mu + Ta(U[mu]*staple)*factor_r;
 	  
       PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
     }

Grid/qcd/hmc/GenericHMCrunner.h

@@ -225,18 +225,6 @@ template <class RepresentationsPolicy,
 using GenericHMCRunnerHirep =
 				     HMCWrapperTemplate<PeriodicGimplR, Integrator, RepresentationsPolicy>;
 
-// sp2n
-
-template <template <typename, typename, typename> class Integrator>
-using GenericSpHMCRunner = HMCWrapperTemplate<SpPeriodicGimplR, Integrator>;
-
-template <class RepresentationsPolicy,
-          template <typename, typename, typename> class Integrator>
-using GenericSpHMCRunnerHirep =
-                     HMCWrapperTemplate<SpPeriodicGimplR, Integrator, RepresentationsPolicy>;
-
-
-
 template <class Implementation, class RepresentationsPolicy, 
           template <typename, typename, typename> class Integrator>
 using GenericHMCRunnerTemplate = HMCWrapperTemplate<Implementation, Integrator, RepresentationsPolicy>;

Grid/qcd/representations/fundamental.h

@@ -13,7 +13,7 @@ NAMESPACE_BEGIN(Grid);
  * Empty since HMC updates already the fundamental representation 
  */
 
-template <int ncolour, class group_name>
+template <int ncolour>
 class FundamentalRep {
 public:
   static const int Dimension = ncolour;
@@ -21,7 +21,7 @@ public:
 
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename GaugeGroup<ncolour,group_name>::LatticeMatrix LatticeMatrix;
+  typedef typename SU<ncolour>::LatticeMatrix LatticeMatrix;
   typedef LatticeGaugeField LatticeField;
   
   explicit FundamentalRep(GridBase* grid) {} //do nothing
@@ -45,8 +45,7 @@ public:
     
 
   
-typedef	 FundamentalRep<Nc,GroupName::SU> FundamentalRepresentation;
-typedef	 FundamentalRep<Nc,GroupName::Sp> SpFundamentalRepresentation;
+typedef	 FundamentalRep<Nc> FundamentalRepresentation;
 
 NAMESPACE_END(Grid);  
 

Grid/qcd/representations/two_index.h

@@ -20,14 +20,14 @@ NAMESPACE_BEGIN(Grid);
  * in the SUnTwoIndex.h file
  */
 
-template <int ncolour, TwoIndexSymmetry S, class group_name = GroupName::SU>
+template <int ncolour, TwoIndexSymmetry S>
 class TwoIndexRep {
 public:
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexMatrix LatticeMatrix;
-  typedef typename GaugeGroupTwoIndex<ncolour, S, group_name>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = GaugeGroupTwoIndex<ncolour,S,group_name>::Dimension;
+  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
+  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
+  static const int Dimension = ncolour * (ncolour + S) / 2;
   static const bool isFundamental = false;
 
   LatticeField U;
@@ -43,10 +43,10 @@ public:
     U = Zero();
     LatticeColourMatrix tmp(Uin.Grid());
 
-    Vector<typename GaugeGroup<ncolour,group_name>::Matrix> eij(Dimension);
+    Vector<typename SU<ncolour>::Matrix> eij(Dimension);
 
     for (int a = 0; a < Dimension; a++)
-      GaugeGroupTwoIndex<ncolour, S, group_name>::base(a, eij[a]);
+      SU_TwoIndex<ncolour, S>::base(a, eij[a]);
 
     for (int mu = 0; mu < Nd; mu++) {
       auto Uin_mu = peekLorentz(Uin, mu);
@@ -71,7 +71,7 @@ public:
 
       out_mu = Zero();
 
-      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector h(in.Grid());
+      typename SU<ncolour>::LatticeAlgebraVector h(in.Grid());
       projectOnAlgebra(h, in_mu, double(Nc + 2 * S));  // factor T(r)/T(fund)
       FundamentalLieAlgebraMatrix(h, out_mu);          // apply scale only once
       pokeLorentz(out, out_mu, mu);
@@ -80,23 +80,20 @@ public:
   }
 
 private:
-  void projectOnAlgebra(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
+  void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
-    GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
+    SU_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
-				   typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
-				   typename GaugeGroup<ncolour, group_name>::LatticeMatrix &out, Real scale = 1.0) const {
-    GaugeGroup<ncolour,group_name>::FundamentalLieAlgebraMatrix(h, out, scale);
+				   typename SU<ncolour>::LatticeAlgebraVector &h,
+				   typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
+    SU<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
   }
 };
 
-typedef TwoIndexRep<Nc, Symmetric, GroupName::SU> TwoIndexSymmetricRepresentation;
-typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::SU> TwoIndexAntiSymmetricRepresentation;
-
-typedef TwoIndexRep<Nc, Symmetric, GroupName::Sp> SpTwoIndexSymmetricRepresentation;
-typedef TwoIndexRep<Nc, AntiSymmetric, GroupName::Sp> SpTwoIndexAntiSymmetricRepresentation;
+typedef TwoIndexRep<Nc, Symmetric> TwoIndexSymmetricRepresentation;
+typedef TwoIndexRep<Nc, AntiSymmetric> TwoIndexAntiSymmetricRepresentation;
 
 NAMESPACE_END(Grid);
 

Grid/qcd/utils/CovariantCshift.h

@@ -37,14 +37,13 @@ NAMESPACE_BEGIN(Grid);
 // Make these members of an Impl class for BC's.
 
 namespace PeriodicBC { 
-  //Out(x) = Link(x)*field(x+mu)
+
   template<class covariant,class gauge> Lattice<covariant> CovShiftForward(const Lattice<gauge> &Link, 
 									   int mu,
 									   const Lattice<covariant> &field)
   {
     return Link*Cshift(field,mu,1);// moves towards negative mu
   }
-  //Out(x) = Link^dag(x-mu)*field(x-mu)
   template<class covariant,class gauge> Lattice<covariant> CovShiftBackward(const Lattice<gauge> &Link, 
 									    int mu,
 									    const Lattice<covariant> &field)
@@ -53,19 +52,19 @@ namespace PeriodicBC {
     tmp = adj(Link)*field;
     return Cshift(tmp,mu,-1);// moves towards positive mu
   }
-  //Out(x) = Link^dag(x-mu)
+
   template<class gauge> Lattice<gauge>
   CovShiftIdentityBackward(const Lattice<gauge> &Link, int mu) 
   {
     return Cshift(adj(Link), mu, -1);
   }
-  //Out(x) = Link(x)
+
   template<class gauge> Lattice<gauge>
   CovShiftIdentityForward(const Lattice<gauge> &Link, int mu)
   {
     return Link;
   }
-  //Link(x) = Link(x+mu)
+
   template<class gauge> Lattice<gauge>
   ShiftStaple(const Lattice<gauge> &Link, int mu)
   {

Grid/qcd/utils/GaugeGroup.h

@@ -1,470 +0,0 @@
-/*************************************************************************************
-
-Grid physics library, www.github.com/paboyle/Grid
-
-Source file: ./lib/qcd/utils/GaugeGroup.h
-
-Copyright (C) 2015
-
-Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
-Author: Peter Boyle <paboyle@ph.ed.ac.uk>
-Author: neo <cossu@post.kek.jp>
-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 QCD_UTIL_GAUGEGROUP_H
-#define QCD_UTIL_GAUGEGROUP_H
-
-// Important detail: nvcc requires all template parameters to have names.
-// This is the only reason why the second template parameter has a name.
-#define ONLY_IF_SU                                                       \
-  typename dummy_name = group_name,                                      \
-           typename named_dummy = std::enable_if_t <                                 \
-                          std::is_same<dummy_name, group_name>::value && \
-                      is_su<dummy_name>::value >
-
-#define ONLY_IF_Sp                                                       \
-  typename dummy_name = group_name,                                      \
-           typename named_dummy = std::enable_if_t <                                 \
-                          std::is_same<dummy_name, group_name>::value && \
-                      is_sp<dummy_name>::value >
-
-NAMESPACE_BEGIN(Grid);
-namespace GroupName {
-class SU {};
-class Sp {};
-}  // namespace GroupName
-
-template <typename group_name>
-struct is_su {
-  static const bool value = false;
-};
-
-template <>
-struct is_su<GroupName::SU> {
-  static const bool value = true;
-};
-
-template <typename group_name>
-struct is_sp {
-  static const bool value = false;
-};
-
-template <>
-struct is_sp<GroupName::Sp> {
-  static const bool value = true;
-};
-
-template <typename group_name>
-constexpr int compute_adjoint_dimension(int ncolour);
-
-template <>
-constexpr int compute_adjoint_dimension<GroupName::SU>(int ncolour) {
-  return ncolour * ncolour - 1;
-}
-
-template <>
-constexpr int compute_adjoint_dimension<GroupName::Sp>(int ncolour) {
-  return ncolour / 2 * (ncolour + 1);
-}
-
-template <int ncolour, class group_name>
-class GaugeGroup {
- public:
-  static const int Dimension = ncolour;
-  static const int AdjointDimension =
-      compute_adjoint_dimension<group_name>(ncolour);
-  static const int AlgebraDimension =
-      compute_adjoint_dimension<group_name>(ncolour);
-
-  template <typename vtype>
-  using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
-  template <typename vtype>
-  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-  template <typename vtype>
-  using iAlgebraVector = iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
-  static int su2subgroups(void) { return su2subgroups(group_name()); }
-
-  //////////////////////////////////////////////////////////////////////////////////////////////////
-  // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
-  // SU<2>::LatticeMatrix etc...
-  //////////////////////////////////////////////////////////////////////////////////////////////////
-  typedef iGroupMatrix<Complex> Matrix;
-  typedef iGroupMatrix<ComplexF> MatrixF;
-  typedef iGroupMatrix<ComplexD> MatrixD;
-
-  typedef iGroupMatrix<vComplex> vMatrix;
-  typedef iGroupMatrix<vComplexF> vMatrixF;
-  typedef iGroupMatrix<vComplexD> vMatrixD;
-
-  // For the projectors to the algebra
-  // these should be real...
-  // keeping complex for consistency with the SIMD vector types
-  typedef iAlgebraVector<Complex> AlgebraVector;
-  typedef iAlgebraVector<ComplexF> AlgebraVectorF;
-  typedef iAlgebraVector<ComplexD> AlgebraVectorD;
-
-  typedef iAlgebraVector<vComplex> vAlgebraVector;
-  typedef iAlgebraVector<vComplexF> vAlgebraVectorF;
-  typedef iAlgebraVector<vComplexD> vAlgebraVectorD;
-
-  typedef Lattice<vMatrix> LatticeMatrix;
-  typedef Lattice<vMatrixF> LatticeMatrixF;
-  typedef Lattice<vMatrixD> LatticeMatrixD;
-
-  typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
-  typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
-  typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
-
-  typedef iSU2Matrix<Complex> SU2Matrix;
-  typedef iSU2Matrix<ComplexF> SU2MatrixF;
-  typedef iSU2Matrix<ComplexD> SU2MatrixD;
-
-  typedef iSU2Matrix<vComplex> vSU2Matrix;
-  typedef iSU2Matrix<vComplexF> vSU2MatrixF;
-  typedef iSU2Matrix<vComplexD> vSU2MatrixD;
-
-  typedef Lattice<vSU2Matrix> LatticeSU2Matrix;
-  typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
-  typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
-
-  // Private implementation details are specified in the following files:
-  // Grid/qcd/utils/SUn.impl
-  // Grid/qcd/utils/SUn.impl
-  // The public part of the interface follows below and refers to these
-  // private member functions.
-
-#include <Grid/qcd/utils/SUn.impl.h>
-#include <Grid/qcd/utils/Sp2n.impl.h>
-
- public:
-  template <class cplx>
-  static void generator(int lieIndex, iGroupMatrix<cplx> &ta) {
-    return generator(lieIndex, ta, group_name());
-  }
-
-  static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
-    return su2SubGroupIndex(i1, i2, su2_index, group_name());
-  }
-
-  static void testGenerators(void) { testGenerators(group_name()); }
-
-  static void printGenerators(void) {
-    for (int gen = 0; gen < AlgebraDimension; gen++) {
-      Matrix ta;
-      generator(gen, ta);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << ta << std::endl;
-    }
-  }
-
-  template <typename LatticeMatrixType>
-  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out,
-                           double scale = 1.0) {
-    GridBase *grid = out.Grid();
-
-    typedef typename LatticeMatrixType::vector_type vector_type;
-
-    typedef iSinglet<vector_type> vTComplexType;
-
-    typedef Lattice<vTComplexType> LatticeComplexType;
-    typedef typename GridTypeMapper<
-        typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
-
-    LatticeComplexType ca(grid);
-    LatticeMatrixType lie(grid);
-    LatticeMatrixType la(grid);
-    ComplexD ci(0.0, scale);
-    MatrixType ta;
-
-    lie = Zero();
-
-    for (int a = 0; a < AlgebraDimension; a++) {
-      random(pRNG, ca);
-
-      ca = (ca + conjugate(ca)) * 0.5;
-      ca = ca - 0.5;
-
-      generator(a, ta);
-
-      la = ci * ca * ta;
-
-      lie = lie + la;  // e^{i la ta}
-    }
-    taExp(lie, out);
-  }
-
-  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
-                                                  LatticeMatrix &out,
-                                                  Real scale = 1.0) {
-    GridBase *grid = out.Grid();
-    LatticeReal ca(grid);
-    LatticeMatrix la(grid);
-    Complex ci(0.0, scale);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AlgebraDimension; a++) {
-      gaussian(pRNG, ca);
-      generator(a, ta);
-      la = toComplex(ca) * ta;
-      out += la;
-    }
-    out *= ci;
-  }
-
-  static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
-                                          LatticeMatrix &out,
-                                          Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeMatrix la(grid);
-    Matrix ta;
-
-    out = Zero();
-    for (int a = 0; a < AlgebraDimension; a++) {
-      generator(a, ta);
-      la = peekColour(h, a) * timesI(ta) * scale;
-      out += la;
-    }
-  }
-
-  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1
-  // ) inverse operation: FundamentalLieAlgebraMatrix
-  static void projectOnAlgebra(LatticeAlgebraVector &h_out,
-                               const LatticeMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    Matrix Ta;
-
-    for (int a = 0; a < AlgebraDimension; a++) {
-      generator(a, Ta);
-      pokeColour(h_out, -2.0 * (trace(timesI(Ta) * in)) * scale, a);
-    }
-  }
-
-   
-  template <class vtype>
-  accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r) {
-    return ProjectOnGeneralGroup(r, group_name());
-  }
-
-  template <class vtype, int N>
-  accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r) {
-    return ProjectOnGeneralGroup(r, group_name());
-  }
-
-  template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-  accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg) {
-    return ProjectOnGeneralGroup(arg, group_name());
-  }
-
-  template <int N,class vComplex_t>                  // Projects on the general groups U(N), Sp(2N)xZ2 i.e. determinant is allowed a complex phase.
-  static void ProjectOnGeneralGroup(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >, Nd> > &U) {
-    for (int mu = 0; mu < Nd; mu++) {
-      auto Umu = PeekIndex<LorentzIndex>(U, mu);
-      Umu = ProjectOnGeneralGroup(Umu);
-    }
-  }
-       
-
-  
-  template <int N,class vComplex_t>
-  static Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu) {
-    return ProjectOnGeneralGroup(Umu, group_name());
-  }
-
-  template <int N,class vComplex_t>       // Projects on SU(N), Sp(2N), with unit determinant, by first projecting on general group and then enforcing unit determinant
-  static void ProjectOnSpecialGroup(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu) {
-       Umu = ProjectOnGeneralGroup(Umu);
-       auto det = Determinant(Umu);
-
-       det = conjugate(det);
-
-       for (int i = 0; i < N; i++) {
-           auto element = PeekIndex<ColourIndex>(Umu, N - 1, i);
-           element = element * det;
-           PokeIndex<ColourIndex>(Umu, element, Nc - 1, i);
-       }
-   }
-
-  template <int N,class vComplex_t>    // reunitarise, resimplectify... previously ProjectSUn
-    static void ProjectOnSpecialGroup(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >, Nd> > &U) {
-      // Reunitarise
-      for (int mu = 0; mu < Nd; mu++) {
-        auto Umu = PeekIndex<LorentzIndex>(U, mu);
-        ProjectOnSpecialGroup(Umu);
-        PokeIndex<LorentzIndex>(U, Umu, mu);
-      }
-    }
-    
-  template <typename GaugeField>
-  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iGroupMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    LatticeMatrixType tmp(out.Grid());
-    for (int mu = 0; mu < Nd; mu++) {
-      //      LieRandomize(pRNG, Umu, 1.0);
-      //      PokeIndex<LorentzIndex>(out, Umu, mu);
-      gaussian(pRNG,Umu);
-      tmp = Ta(Umu);
-      taExp(tmp,Umu);
-      ProjectOnSpecialGroup(Umu);
-      //      ProjectSUn(Umu);
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
-  }
-  template <typename GaugeField>
-  static void TepidConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iGroupMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    for (int mu = 0; mu < Nd; mu++) {
-      LieRandomize(pRNG, Umu, 0.01);
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
-  }
-    
-  template <typename GaugeField>
-  static void ColdConfiguration(GaugeField &out) {
-    typedef typename GaugeField::vector_type vector_type;
-    typedef iGroupMatrix<vector_type> vMatrixType;
-    typedef Lattice<vMatrixType> LatticeMatrixType;
-
-    LatticeMatrixType Umu(out.Grid());
-    Umu = 1.0;
-    for (int mu = 0; mu < Nd; mu++) {
-      PokeIndex<LorentzIndex>(out, Umu, mu);
-    }
-  }
-    
-  template <typename GaugeField>
-  static void ColdConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
-    ColdConfiguration(out);
-  }
-
-  template <typename LatticeMatrixType>
-  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
-    taProj(in, out, group_name());
-  }
-    
-  template <typename LatticeMatrixType>
-  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) {
-    typedef typename LatticeMatrixType::scalar_type ComplexType;
-
-    LatticeMatrixType xn(x.Grid());
-    RealD nfac = 1.0;
-
-    xn = x;
-    ex = xn + ComplexType(1.0);  // 1+x
-
-    // Do a 12th order exponentiation
-    for (int i = 2; i <= 12; ++i) {
-      nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
-      xn = xn * x;             // x2, x3,x4....
-      ex = ex + xn * nfac;     // x2/2!, x3/3!....
-    }
-  }
-
-};
-    
-template <int ncolour>
-using SU = GaugeGroup<ncolour, GroupName::SU>;
-
-template <int ncolour>
-using Sp = GaugeGroup<ncolour, GroupName::Sp>;
-
-typedef SU<2> SU2;
-typedef SU<3> SU3;
-typedef SU<4> SU4;
-typedef SU<5> SU5;
-
-typedef SU<Nc> FundamentalMatrices;
-    
-typedef Sp<2> Sp2;
-typedef Sp<4> Sp4;
-typedef Sp<6> Sp6;
-typedef Sp<8> Sp8;
-
-template <int N,class vComplex_t>
-static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
-{
-    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(Umu);
-}
-  
-template <int N,class vComplex_t>
-static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >,Nd> > &U)
-{
-    GaugeGroup<N,GroupName::SU>::ProjectOnSpecialGroup(U);
-}
-    
-template <int N,class vComplex_t>
-static void ProjectSpn(Lattice<iScalar<iScalar<iMatrix<vComplex_t, N> > > > &Umu)
-{
-    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(Umu);
-}
-    
-template <int N,class vComplex_t>
-static void ProjectSpn(Lattice<iVector<iScalar<iMatrix<vComplex_t, N> >,Nd> > &U)
-{
-    GaugeGroup<N,GroupName::Sp>::ProjectOnSpecialGroup(U);
-}
-
-// Explicit specialisation for SU(3).
-static void ProjectSU3(Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
-{
-  GridBase *grid = Umu.Grid();
-  const int x = 0;
-  const int y = 1;
-  const int z = 2;
-  // Reunitarise
-  Umu = ProjectOnGroup(Umu);
-  autoView(Umu_v, Umu, CpuWrite);
-  thread_for(ss, grid->oSites(), {
-    auto cm = Umu_v[ss];
-    cm()()(2, x) = adj(cm()()(0, y) * cm()()(1, z) -
-                       cm()()(0, z) * cm()()(1, y));  // x= yz-zy
-    cm()()(2, y) = adj(cm()()(0, z) * cm()()(1, x) -
-                       cm()()(0, x) * cm()()(1, z));  // y= zx-xz
-    cm()()(2, z) = adj(cm()()(0, x) * cm()()(1, y) -
-                       cm()()(0, y) * cm()()(1, x));  // z= xy-yx
-    Umu_v[ss] = cm;
-  });
-}
-static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >, Nd> > &U)
-{
-  GridBase *grid = U.Grid();
-  // Reunitarise
-  for (int mu = 0; mu < Nd; mu++) {
-    auto Umu = PeekIndex<LorentzIndex>(U, mu);
-    Umu = ProjectOnGroup(Umu);
-    ProjectSU3(Umu);
-    PokeIndex<LorentzIndex>(U, Umu, mu);
-  }
-}
-
-NAMESPACE_END(Grid);
-#endif

Grid/qcd/utils/GaugeGroupTwoIndex.h

@@ -1,371 +0,0 @@
-////////////////////////////////////////////////////////////////////////
-//
-// * Two index representation generators
-//
-// * Normalisation for the fundamental generators:
-//   trace ta tb = 1/2 delta_ab = T_F delta_ab
-//   T_F = 1/2  for SU(N) groups
-//
-//
-//   base for NxN two index (anti-symmetric) matrices
-//   normalized to 1 (d_ij is the kroenecker delta)
-//
-//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
-//
-//   Then the generators are written as
-//
-//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
-//   tr[e^(lk)e^(ij)^dag T_a] )  //
-//
-//
-////////////////////////////////////////////////////////////////////////
-
-// Authors: David Preti, Guido Cossu
-
-#ifndef QCD_UTIL_GAUGEGROUPTWOINDEX_H
-#define QCD_UTIL_GAUGEGROUPTWOINDEX_H
-
-NAMESPACE_BEGIN(Grid);
-
-enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
-
-constexpr inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
-
-namespace detail {
-
-template <class cplx, int nc, TwoIndexSymmetry S>
-struct baseOffDiagonalSpHelper;
-
-template <class cplx, int nc>
-struct baseOffDiagonalSpHelper<cplx, nc, AntiSymmetric> {
-  static const int ngroup = nc / 2;
-  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
-    eij = Zero();
-    RealD tmp;
-
-    if ((i == ngroup + j) && (1 <= j) && (j < ngroup)) {
-      for (int k = 0; k < j+1; k++) {
-        if (k < j) {
-          tmp = 1 / sqrt(j * (j + 1));
-          eij()()(k, k + ngroup) = tmp;
-          eij()()(k + ngroup, k) = -tmp;
-        }
-        if (k == j) {
-          tmp = -j / sqrt(j * (j + 1));
-          eij()()(k, k + ngroup) = tmp;
-          eij()()(k + ngroup, k) = -tmp;
-        }
-      }
-
-    }
-
-    else if (i != ngroup + j) {
-      for (int k = 0; k < nc; k++)
-        for (int l = 0; l < nc; l++) {
-          eij()()(l, k) =
-              delta(i, k) * delta(j, l) - delta(j, k) * delta(i, l);
-        }
-    }
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-};
-
-template <class cplx, int nc>
-struct baseOffDiagonalSpHelper<cplx, nc, Symmetric> {
-  static void baseOffDiagonalSp(int i, int j, iScalar<iScalar<iMatrix<cplx, nc> > > &eij) {
-    eij = Zero();
-    for (int k = 0; k < nc; k++)
-      for (int l = 0; l < nc; l++)
-        eij()()(l, k) =
-            delta(i, k) * delta(j, l) + delta(j, k) * delta(i, l);
-
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-};
-
-}   // closing detail namespace
-
-template <int ncolour, TwoIndexSymmetry S, class group_name>
-class GaugeGroupTwoIndex : public GaugeGroup<ncolour, group_name> {
- public:
-  // The chosen convention is that we are taking ncolour to be N in SU<N> but 2N
-  // in Sp(2N). ngroup is equal to N for SU but 2N/2 = N for Sp(2N).
-  static_assert(std::is_same<group_name, GroupName::SU>::value or
-                    std::is_same<group_name, GroupName::Sp>::value,
-                "ngroup is only implemented for SU and Sp currently.");
-  static const int ngroup =
-      std::is_same<group_name, GroupName::SU>::value ? ncolour : ncolour / 2;
-  static const int Dimension =
-      (ncolour * (ncolour + S) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (S - 1) / 2 : 0);
-  static const int DimensionAS =
-      (ncolour * (ncolour - 1) / 2) + (std::is_same<group_name, GroupName::Sp>::value ? (- 1) : 0);
-  static const int DimensionS =
-      ncolour * (ncolour + 1) / 2;
-  static const int NumGenerators =
-      GaugeGroup<ncolour, group_name>::AlgebraDimension;
-
-  template <typename vtype>
-  using iGroupTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
-
-  typedef iGroupTwoIndexMatrix<Complex> TIMatrix;
-  typedef iGroupTwoIndexMatrix<ComplexF> TIMatrixF;
-  typedef iGroupTwoIndexMatrix<ComplexD> TIMatrixD;
-
-  typedef iGroupTwoIndexMatrix<vComplex> vTIMatrix;
-  typedef iGroupTwoIndexMatrix<vComplexF> vTIMatrixF;
-  typedef iGroupTwoIndexMatrix<vComplexD> vTIMatrixD;
-
-  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
-  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
-  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
-
-  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
-      LatticeTwoIndexField;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
-      LatticeTwoIndexFieldF;
-  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
-      LatticeTwoIndexFieldD;
-
-  template <typename vtype>
-  using iGroupMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-
-  typedef iGroupMatrix<Complex> Matrix;
-  typedef iGroupMatrix<ComplexF> MatrixF;
-  typedef iGroupMatrix<ComplexD> MatrixD;
-    
-private:
-  template <class cplx>
-  static void baseDiagonal(int Index, iGroupMatrix<cplx> &eij) {
-    eij = Zero();
-    eij()()(Index - ncolour * (ncolour - 1) / 2,
-            Index - ncolour * (ncolour - 1) / 2) = 1.0;
-  }
-    
-  template <class cplx>
-  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::SU) {
-    eij = Zero();
-    for (int k = 0; k < ncolour; k++)
-      for (int l = 0; l < ncolour; l++)
-        eij()()(l, k) =
-            delta(i, k) * delta(j, l) + S * delta(j, k) * delta(i, l);
-
-    RealD nrm = 1. / std::sqrt(2.0);
-    eij = eij * nrm;
-  }
-    
-  template <class cplx>
-  static void baseOffDiagonal(int i, int j, iGroupMatrix<cplx> &eij, GroupName::Sp) {
-    detail::baseOffDiagonalSpHelper<cplx, ncolour, S>::baseOffDiagonalSp(i, j, eij);
-  }
-
-public:
-    
-  template <class cplx>
-  static void base(int Index, iGroupMatrix<cplx> &eij) {
-  // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
-    assert(Index < Dimension);
-    eij = Zero();
-  // for the linearisation of the 2 indexes
-    static int a[ncolour * (ncolour - 1) / 2][2];  // store the a <-> i,j
-    static bool filled = false;
-    if (!filled) {
-      int counter = 0;
-      for (int i = 1; i < ncolour; i++) {
-      for (int j = 0; j < i; j++) {
-        if (std::is_same<group_name, GroupName::Sp>::value)
-          {
-            if (j==0 && i==ngroup+j && S==-1) {
-            //std::cout << "skipping" << std::endl; // for Sp2n this vanishes identically.
-              j = j+1;
-            }
-          }
-          a[counter][0] = i;
-          a[counter][1] = j;
-          counter++;
-          }
-      }
-      filled = true;
-    }
-    if (Index < ncolour*ncolour - DimensionS)
-    {
-      baseOffDiagonal(a[Index][0], a[Index][1], eij, group_name());
-    } else {
-      baseDiagonal(Index, eij);
-    }
-  }
-    
-  static void printBase(void) {
-    for (int gen = 0; gen < Dimension; gen++) {
-      Matrix tmp;
-      base(gen, tmp);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << tmp << std::endl;
-    }
-  }
-
-  template <class cplx>
-  static void generator(int Index, iGroupTwoIndexMatrix<cplx> &i2indTa) {
-    Vector<iGroupMatrix<cplx> > ta(NumGenerators);
-    Vector<iGroupMatrix<cplx> > eij(Dimension);
-    iGroupMatrix<cplx> tmp;
-
-    for (int a = 0; a < NumGenerators; a++)
-      GaugeGroup<ncolour, group_name>::generator(a, ta[a]);
-
-    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
-
-    for (int a = 0; a < Dimension; a++) {
-      tmp = transpose(eij[a]*ta[Index]) + transpose(eij[a]) * ta[Index];
-      for (int b = 0; b < Dimension; b++) {
-        Complex iTr = TensorRemove(timesI(trace(tmp * eij[b])));
-        i2indTa()()(a, b) = iTr;
-      }
-    }
-  }
-
-  static void printGenerators(void) {
-    for (int gen = 0; gen < NumGenerators; gen++) {
-      TIMatrix i2indTa;
-      generator(gen, i2indTa);
-      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
-                << std::endl;
-      std::cout << GridLogMessage << i2indTa << std::endl;
-    }
-  }
-
-  static void testGenerators(void) {
-    TIMatrix i2indTa, i2indTb;
-    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(trace(i2indTa)) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-
-    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      std::cout << GridLogMessage << a << std::endl;
-      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
-    }
-
-    std::cout << GridLogMessage << std::endl;
-    std::cout << GridLogMessage
-              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
-              << std::endl;
-    for (int a = 0; a < NumGenerators; a++) {
-      for (int b = 0; b < NumGenerators; b++) {
-        generator(a, i2indTa);
-        generator(b, i2indTb);
-
-        // generator returns iTa, so we need a minus sign here
-        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
-        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
-                  << std::endl;
-        if (a == b) {
-          assert(real(Tr) - ((ncolour + S * 2) * 0.5) < 1e-8);
-        } else {
-          assert(real(Tr) < 1e-8);
-        }
-        assert(imag(Tr) < 1e-8);
-      }
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-
-  static void TwoIndexLieAlgebraMatrix(
-      const typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h,
-      LatticeTwoIndexMatrix &out, Real scale = 1.0) {
-    conformable(h, out);
-    GridBase *grid = out.Grid();
-    LatticeTwoIndexMatrix la(grid);
-    TIMatrix i2indTa;
-
-    out = Zero();
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      la = peekColour(h, a) * i2indTa;
-      out += la;
-    }
-    out *= scale;
-  }
-
-  // Projects the algebra components
-  // of a lattice matrix ( of dimension ncol*ncol -1 )
-  static void projectOnAlgebra(
-      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
-      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    h_out = Zero();
-    TIMatrix i2indTa;
-    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
-    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
-    for (int a = 0; a < NumGenerators; a++) {
-      generator(a, i2indTa);
-      pokeColour(h_out, real(trace(i2indTa * in)) * coefficient, a);
-    }
-  }
-
-  // a projector that keeps the generators stored to avoid the overhead of
-  // recomputing them
-  static void projector(
-      typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
-      const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
-    conformable(h_out, in);
-    // to store the generators
-    static std::vector<TIMatrix> i2indTa(NumGenerators);
-    h_out = Zero();
-    static bool precalculated = false;
-    if (!precalculated) {
-      precalculated = true;
-      for (int a = 0; a < NumGenerators; a++) generator(a, i2indTa[a]);
-    }
-
-    Real coefficient =
-        -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
-    // of the trace in the two index rep
-
-    for (int a = 0; a < NumGenerators; a++) {
-      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
-    }
-  }
-};
-
-template <int ncolour, TwoIndexSymmetry S>
-using SU_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::SU>;
-
-// Some useful type names
-typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
-typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
-
-typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
-typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
-typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
-typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
-
-typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
-typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
-typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
-typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
-
-template <int ncolour, TwoIndexSymmetry S>
-using Sp_TwoIndex = GaugeGroupTwoIndex<ncolour, S, GroupName::Sp>;
-
-typedef Sp_TwoIndex<Nc, Symmetric> SpTwoIndexSymmMatrices;
-typedef Sp_TwoIndex<Nc, AntiSymmetric> SpTwoIndexAntiSymmMatrices;
-
-typedef Sp_TwoIndex<2, Symmetric> Sp2TwoIndexSymm;
-typedef Sp_TwoIndex<4, Symmetric> Sp4TwoIndexSymm;
-
-typedef Sp_TwoIndex<4, AntiSymmetric> Sp4TwoIndexAntiSymm;
-
-NAMESPACE_END(Grid);
-
-#endif

Grid/qcd/utils/SUn.h

@@ -0,0 +1,932 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./lib/qcd/utils/SUn.h
+
+Copyright (C) 2015
+
+Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+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 QCD_UTIL_SUN_H
+#define QCD_UTIL_SUN_H
+
+NAMESPACE_BEGIN(Grid);
+
+template<int N, class Vec>
+Lattice<iScalar<iScalar<iScalar<Vec> > > > Determinant(const Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iScalar<iScalar<iScalar<Vec> > > > ret(grid);
+  typedef typename Vec::scalar_type scalar;
+  autoView(Umu_v,Umu,CpuRead);
+  autoView(ret_v,ret,CpuWrite);
+  thread_for(site,lvol,{
+    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+    Coordinate lcoor;
+    grid->LocalIndexToLocalCoor(site, lcoor);
+    iScalar<iScalar<iMatrix<scalar, N> > > Us;
+    peekLocalSite(Us, Umu_v, lcoor);
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	scalar tmp= Us()()(i,j);
+	ComplexD ztmp(real(tmp),imag(tmp));
+	EigenU(i,j)=ztmp;
+      }}
+    ComplexD detD  = EigenU.determinant();
+    typename Vec::scalar_type det(detD.real(),detD.imag());
+    pokeLocalSite(det,ret_v,lcoor);
+  });
+  return ret;
+}
+
+template<int N, class Vec>
+static void ProjectSUn(Lattice<iScalar<iScalar<iMatrix<Vec, N> > > > &Umu)
+{
+  Umu      = ProjectOnGroup(Umu);
+  auto det = Determinant(Umu);
+
+  det = conjugate(det);
+
+  for(int i=0;i<N;i++){
+    auto element = PeekIndex<ColourIndex>(Umu,N-1,i);
+    element = element * det;
+    PokeIndex<ColourIndex>(Umu,element,Nc-1,i);
+  }
+}
+template<int N,class Vec>
+static void ProjectSUn(Lattice<iVector<iScalar<iMatrix<Vec, N> >,Nd> > &U)
+{
+  GridBase *grid=U.Grid();
+  // Reunitarise
+  for(int mu=0;mu<Nd;mu++){
+    auto Umu = PeekIndex<LorentzIndex>(U,mu);
+    Umu      = ProjectOnGroup(Umu);
+    ProjectSUn(Umu);
+    PokeIndex<LorentzIndex>(U,Umu,mu);
+  }
+}
+
+template <int ncolour>
+class SU {
+public:
+  static const int Dimension = ncolour;
+  static const int AdjointDimension = ncolour * ncolour - 1;
+  static int su2subgroups(void) { return (ncolour * (ncolour - 1)) / 2; }
+
+  template <typename vtype>
+  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+  template <typename vtype>
+  using iSU2Matrix = iScalar<iScalar<iMatrix<vtype, 2> > >;
+  template <typename vtype>
+  using iSUnAlgebraVector =
+    iScalar<iScalar<iVector<vtype, AdjointDimension> > >;
+
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  // Types can be accessed as SU<2>::Matrix , SU<2>::vSUnMatrix,
+  // SU<2>::LatticeMatrix etc...
+  //////////////////////////////////////////////////////////////////////////////////////////////////
+  typedef iSUnMatrix<Complex> Matrix;
+  typedef iSUnMatrix<ComplexF> MatrixF;
+  typedef iSUnMatrix<ComplexD> MatrixD;
+
+  typedef iSUnMatrix<vComplex> vMatrix;
+  typedef iSUnMatrix<vComplexF> vMatrixF;
+  typedef iSUnMatrix<vComplexD> vMatrixD;
+
+  // For the projectors to the algebra
+  // these should be real...
+  // keeping complex for consistency with the SIMD vector types
+  typedef iSUnAlgebraVector<Complex> AlgebraVector;
+  typedef iSUnAlgebraVector<ComplexF> AlgebraVectorF;
+  typedef iSUnAlgebraVector<ComplexD> AlgebraVectorD;
+
+  typedef iSUnAlgebraVector<vComplex> vAlgebraVector;
+  typedef iSUnAlgebraVector<vComplexF> vAlgebraVectorF;
+  typedef iSUnAlgebraVector<vComplexD> vAlgebraVectorD;
+
+  typedef Lattice<vMatrix> LatticeMatrix;
+  typedef Lattice<vMatrixF> LatticeMatrixF;
+  typedef Lattice<vMatrixD> LatticeMatrixD;
+
+  typedef Lattice<vAlgebraVector> LatticeAlgebraVector;
+  typedef Lattice<vAlgebraVectorF> LatticeAlgebraVectorF;
+  typedef Lattice<vAlgebraVectorD> LatticeAlgebraVectorD;
+
+  typedef iSU2Matrix<Complex> SU2Matrix;
+  typedef iSU2Matrix<ComplexF> SU2MatrixF;
+  typedef iSU2Matrix<ComplexD> SU2MatrixD;
+
+  typedef iSU2Matrix<vComplex> vSU2Matrix;
+  typedef iSU2Matrix<vComplexF> vSU2MatrixF;
+  typedef iSU2Matrix<vComplexD> vSU2MatrixD;
+
+  typedef Lattice<vSU2Matrix> LatticeSU2Matrix;
+  typedef Lattice<vSU2MatrixF> LatticeSU2MatrixF;
+  typedef Lattice<vSU2MatrixD> LatticeSU2MatrixD;
+
+  ////////////////////////////////////////////////////////////////////////
+  // There are N^2-1 generators for SU(N).
+  //
+  // We take a traceless hermitian generator basis as follows
+  //
+  // * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
+  //   T_F = 1/2  for SU(N) groups
+  //
+  // * Off diagonal
+  //    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
+  //
+  //    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
+  //      direct count off each row
+  //
+  //    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
+  //
+  //      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
+  //      1+ 2+          +   + Nc-1
+  //
+  //    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
+  //
+  //    - We enumerate the row-col pairs.
+  //    - for each row col pair there is a (sigma_x) and a (sigma_y) like
+  //    generator
+  //
+  //
+  //   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
+  //   delta_{i,i1} delta_{j,i2})
+  //   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
+  //   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
+  //
+  // * Diagonal; must be traceless and normalised
+  //   - Sequence is
+  //   N  (1,-1,0,0...)
+  //   N  (1, 1,-2,0...)
+  //   N  (1, 1, 1,-3,0...)
+  //   N  (1, 1, 1, 1,-4,0...)
+  //
+  //   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
+  //   NB this gives the famous SU3 result for su2 index 8
+  //
+  //   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
+  //
+  //   ( 1      )
+  //   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
+  //   (      -2)
+  //
+  ////////////////////////////////////////////////////////////////////////
+  template <class cplx>
+  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) {
+    // map lie index to which type of generator
+    int diagIndex;
+    int su2Index;
+    int sigxy;
+    int NNm1 = ncolour * (ncolour - 1);
+    if (lieIndex >= NNm1) {
+      diagIndex = lieIndex - NNm1;
+      generatorDiagonal(diagIndex, ta);
+      return;
+    }
+    sigxy = lieIndex & 0x1;  // even or odd
+    su2Index = lieIndex >> 1;
+    if (sigxy)
+      generatorSigmaY(su2Index, ta);
+    else
+      generatorSigmaX(su2Index, ta);
+  }
+  
+  template <class cplx>
+  static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
+    ta = Zero();
+    int i1, i2;
+    su2SubGroupIndex(i1, i2, su2Index);
+    ta()()(i1, i2) = 1.0;
+    ta()()(i2, i1) = 1.0;
+    ta = ta * 0.5;
+  }
+  
+  template <class cplx>
+  static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
+    ta = Zero();
+    cplx i(0.0, 1.0);
+    int i1, i2;
+    su2SubGroupIndex(i1, i2, su2Index);
+    ta()()(i1, i2) = i;
+    ta()()(i2, i1) = -i;
+    ta = ta * 0.5;
+  }
+
+  template <class cplx>
+  static void generatorDiagonal(int diagIndex, iSUnMatrix<cplx> &ta) {
+    // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
+    ta = Zero();
+    int k = diagIndex + 1;                  // diagIndex starts from 0
+    for (int i = 0; i <= diagIndex; i++) {  // k iterations
+      ta()()(i, i) = 1.0;
+    }
+    ta()()(k, k) = -k;  // indexing starts from 0
+    RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
+    ta = ta * nrm;
+  }
+
+
+
+  ////////////////////////////////////////////////////////////////////////
+  // Map a su2 subgroup number to the pair of rows that are non zero
+  ////////////////////////////////////////////////////////////////////////
+  static void su2SubGroupIndex(int &i1, int &i2, int su2_index) {
+    assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
+
+    int spare = su2_index;
+    for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
+      spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
+    }
+    i2 = i1 + 1 + spare;
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////
+  // Pull out a subgroup and project on to real coeffs x pauli basis
+  //////////////////////////////////////////////////////////////////////////////////////////
+  template <class vcplx>
+  static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
+                         Lattice<iSU2Matrix<vcplx> > &subgroup,
+                         const Lattice<iSUnMatrix<vcplx> > &source,
+                         int su2_index) {
+    GridBase *grid(source.Grid());
+    conformable(subgroup, source);
+    conformable(subgroup, Determinant);
+    int i0, i1;
+    su2SubGroupIndex(i0, i1, su2_index);
+
+    autoView( subgroup_v , subgroup,AcceleratorWrite);
+    autoView( source_v   , source,AcceleratorRead);
+    autoView( Determinant_v , Determinant,AcceleratorWrite);
+    accelerator_for(ss, grid->oSites(), 1, {
+
+      subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
+      subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
+      subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
+      subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
+
+      iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
+
+      Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
+
+      subgroup_v[ss] = Sigma;
+
+      // this should be purely real
+      Determinant_v[ss] =
+	Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
+    });
+  }
+
+  //////////////////////////////////////////////////////////////////////////////////////////
+  // Set matrix to one and insert a pauli subgroup
+  //////////////////////////////////////////////////////////////////////////////////////////
+  template <class vcplx>
+  static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
+                        Lattice<iSUnMatrix<vcplx> > &dest, int su2_index) {
+    GridBase *grid(dest.Grid());
+    conformable(subgroup, dest);
+    int i0, i1;
+    su2SubGroupIndex(i0, i1, su2_index);
+
+    dest = 1.0;  // start out with identity
+    autoView( dest_v , dest, AcceleratorWrite);
+    autoView( subgroup_v, subgroup, AcceleratorRead);
+    accelerator_for(ss, grid->oSites(),1,
+    {
+      dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
+      dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
+      dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
+      dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
+    });
+
+  }
+
+  ///////////////////////////////////////////////
+  // Generate e^{ Re Tr Staple Link} dlink
+  //
+  // *** Note Staple should be appropriate linear compbination between all
+  // staples.
+  // *** If already by beta pass coefficient 1.0.
+  // *** This routine applies the additional 1/Nc factor that comes after trace
+  // in action.
+  //
+  ///////////////////////////////////////////////
+  static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG,
+			       RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
+			       LatticeMatrix &link,
+			       const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
+			       int su2_subgroup, int nheatbath, LatticeInteger &wheremask) 
+  {
+    GridBase *grid = link.Grid();
+
+    const RealD twopi = 2.0 * M_PI;
+
+    LatticeMatrix staple(grid);
+
+    staple = barestaple * (beta / ncolour);
+
+    LatticeMatrix V(grid);
+    V = link * staple;
+
+    // Subgroup manipulation in the lie algebra space
+    LatticeSU2Matrix u(grid);  // Kennedy pendleton "u" real projected normalised Sigma
+    LatticeSU2Matrix uinv(grid);
+    LatticeSU2Matrix ua(grid);  // a in pauli form
+    LatticeSU2Matrix b(grid);   // rotated matrix after hb
+
+    // Some handy constant fields
+    LatticeComplex ones(grid);
+    ones = 1.0;
+    LatticeComplex zeros(grid);
+    zeros = Zero();
+    LatticeReal rones(grid);
+    rones = 1.0;
+    LatticeReal rzeros(grid);
+    rzeros = Zero();
+    LatticeComplex udet(grid);  // determinant of real(staple)
+    LatticeInteger mask_true(grid);
+    mask_true = 1;
+    LatticeInteger mask_false(grid);
+    mask_false = 0;
+
+    /*
+      PLB 156 P393 (1985) (Kennedy and Pendleton)
+
+      Note: absorb "beta" into the def of sigma compared to KP paper; staple
+      passed to this routine has "beta" already multiplied in
+
+      Action linear in links h and of form:
+
+      beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
+
+      Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
+
+      beta S = const - beta/Nc Re Tr h Sigma'
+      = const - Re Tr h Sigma
+
+      Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
+      arbitrary.
+
+      Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
+      Re Tr h Sigma = 2 h_j Re Sigma_j
+
+      Normalised re Sigma_j = xi u_j
+
+      With u_j a unit vector and U can be in SU(2);
+
+      Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
+
+      4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+      u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+      xi = sqrt(Det)/2;
+
+      Write a= u h in SU(2); a has pauli decomp a_j;
+
+      Note: Product b' xi is unvariant because scaling Sigma leaves
+      normalised vector "u" fixed; Can rescale Sigma so b' = 1.
+    */
+
+    ////////////////////////////////////////////////////////
+    // Real part of Pauli decomposition
+    // Note a subgroup can project to zero in cold start
+    ////////////////////////////////////////////////////////
+    su2Extract(udet, u, V, su2_subgroup);
+
+    //////////////////////////////////////////////////////
+    // Normalising this vector if possible; else identity
+    //////////////////////////////////////////////////////
+    LatticeComplex xi(grid);
+
+    LatticeSU2Matrix lident(grid);
+
+    SU2Matrix ident = Complex(1.0);
+    SU2Matrix pauli1;
+    SU<2>::generator(0, pauli1);
+    SU2Matrix pauli2;
+    SU<2>::generator(1, pauli2);
+    SU2Matrix pauli3;
+    SU<2>::generator(2, pauli3);
+    pauli1 = timesI(pauli1) * 2.0;
+    pauli2 = timesI(pauli2) * 2.0;
+    pauli3 = timesI(pauli3) * 2.0;
+
+    LatticeComplex cone(grid);
+    LatticeReal adet(grid);
+    adet = abs(toReal(udet));
+    lident = Complex(1.0);
+    cone = Complex(1.0);
+    Real machine_epsilon = 1.0e-7;
+    u = where(adet > machine_epsilon, u, lident);
+    udet = where(adet > machine_epsilon, udet, cone);
+
+    xi = 0.5 * sqrt(udet);  // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
+    u = 0.5 * u *
+      pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
+
+    // Debug test for sanity
+    uinv = adj(u);
+    b = u * uinv - 1.0;
+    assert(norm2(b) < 1.0e-4);
+
+    /*
+      Measure: Haar measure dh has d^4a delta(1-|a^2|)
+      In polars:
+      da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
+      = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
+      r) )
+      = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
+
+      Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta enters
+      through xi
+      =  e^{2 xi (h.u)} dh
+      =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2 xi
+      h2u2}.e^{2 xi h3u3} dh
+
+      Therefore for each site, take xi for that site
+      i) generate  |a0|<1 with dist
+      (1-a0^2)^0.5 e^{2 xi a0 } da0
+
+      Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm]; hence 2.0/Nc
+      factor in Chroma ]
+      A. Generate two uniformly distributed pseudo-random numbers R and R', R'',
+      R''' in the unit interval;
+      B. Set X = -(ln R)/alpha, X' =-(ln R')/alpha;
+      C. Set C = cos^2(2pi R"), with R" another uniform random number in [0,1] ;
+      D. Set A = XC;
+      E. Let d  = X'+A;
+      F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+      G. Set a0 = 1 - d;
+
+      Note that in step D setting B ~ X - A and using B in place of A in step E will
+      generate a second independent a 0 value.
+    */
+
+    /////////////////////////////////////////////////////////
+    // count the number of sites by picking "1"'s out of hat
+    /////////////////////////////////////////////////////////
+    Integer hit = 0;
+    LatticeReal rtmp(grid);
+    rtmp = where(wheremask, rones, rzeros);
+    RealD numSites = sum(rtmp);
+    RealD numAccepted;
+    LatticeInteger Accepted(grid);
+    Accepted = Zero();
+    LatticeInteger newlyAccepted(grid);
+
+    std::vector<LatticeReal> xr(4, grid);
+    std::vector<LatticeReal> a(4, grid);
+    LatticeReal d(grid);
+    d = Zero();
+    LatticeReal alpha(grid);
+
+    //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
+    xi = 2.0 *xi;
+    alpha = toReal(xi);
+
+    do {
+      // A. Generate two uniformly distributed pseudo-random numbers R and R',
+      // R'', R''' in the unit interval;
+      random(pRNG, xr[0]);
+      random(pRNG, xr[1]);
+      random(pRNG, xr[2]);
+      random(pRNG, xr[3]);
+
+      // B. Set X = - ln R/alpha, X' = -ln R'/alpha
+      xr[1] = -log(xr[1]) / alpha;
+      xr[2] = -log(xr[2]) / alpha;
+
+      // C. Set C = cos^2(2piR'')
+      xr[3] = cos(xr[3] * twopi);
+      xr[3] = xr[3] * xr[3];
+
+      LatticeReal xrsq(grid);
+
+      // D. Set A = XC;
+      // E. Let d  = X'+A;
+      xrsq = xr[2] + xr[1] * xr[3];
+
+      d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
+
+      // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
+      LatticeReal thresh(grid);
+      thresh = 1.0 - d * 0.5;
+      xrsq = xr[0] * xr[0];
+      LatticeInteger ione(grid);
+      ione = 1;
+      LatticeInteger izero(grid);
+      izero = Zero();
+
+      newlyAccepted = where(xrsq < thresh, ione, izero);
+      Accepted = where(newlyAccepted, newlyAccepted, Accepted);
+      Accepted = where(wheremask, Accepted, izero);
+
+      // FIXME need an iSum for integer to avoid overload on return type??
+      rtmp = where(Accepted, rones, rzeros);
+      numAccepted = sum(rtmp);
+
+      hit++;
+
+    } while ((numAccepted < numSites) && (hit < nheatbath));
+
+    // G. Set a0 = 1 - d;
+    a[0] = Zero();
+    a[0] = where(wheremask, 1.0 - d, a[0]);
+
+    //////////////////////////////////////////
+    //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
+    //////////////////////////////////////////
+
+    LatticeReal a123mag(grid);
+    a123mag = sqrt(abs(1.0 - a[0] * a[0]));
+
+    LatticeReal cos_theta(grid);
+    LatticeReal sin_theta(grid);
+    LatticeReal phi(grid);
+
+    random(pRNG, phi);
+    phi = phi * twopi;  // uniform in [0,2pi]
+    random(pRNG, cos_theta);
+    cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
+    sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
+
+    a[1] = a123mag * sin_theta * cos(phi);
+    a[2] = a123mag * sin_theta * sin(phi);
+    a[3] = a123mag * cos_theta;
+
+    ua = toComplex(a[0]) * ident  + toComplex(a[1]) * pauli1 +
+         toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
+
+    b = 1.0;
+    b = where(wheremask, uinv * ua, b);
+    su2Insert(b, V, su2_subgroup);
+
+    // mask the assignment back based on Accptance
+    link = where(Accepted, V * link, link);
+
+    //////////////////////////////
+    // Debug Checks
+    // SU2 check
+    LatticeSU2Matrix check(grid);  // rotated matrix after hb
+    u = Zero();
+    check = ua * adj(ua) - 1.0;
+    check = where(Accepted, check, u);
+    assert(norm2(check) < 1.0e-4);
+
+    check = b * adj(b) - 1.0;
+    check = where(Accepted, check, u);
+    assert(norm2(check) < 1.0e-4);
+
+    LatticeMatrix Vcheck(grid);
+    Vcheck = Zero();
+    Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
+    //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
+    assert(norm2(Vcheck) < 1.0e-4);
+
+    // Verify the link stays in SU(3)
+    //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
+    Vcheck = link * adj(link) - 1.0;
+    assert(norm2(Vcheck) < 1.0e-4);
+    /////////////////////////////////
+  }
+
+  static void printGenerators(void) {
+    for (int gen = 0; gen < AdjointDimension; gen++) {
+      Matrix ta;
+      generator(gen, ta);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << ta << std::endl;
+    }
+  }
+
+
+
+  static void testGenerators(void) {
+    Matrix ta;
+    Matrix tb;
+    std::cout << GridLogMessage
+              << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
+              << std::endl;
+    for (int a = 0; a < AdjointDimension; a++) {
+      for (int b = 0; b < AdjointDimension; b++) {
+        generator(a, ta);
+        generator(b, tb);
+        Complex tr = TensorRemove(trace(ta * tb));
+        std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
+                  << std::endl;
+        if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
+        if (a != b) assert(abs(tr) < 1.0e-6);
+      }
+      std::cout << GridLogMessage << std::endl;
+    }
+    std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
+              << std::endl;
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, ta);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(ta - adj(ta)) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+
+    std::cout << GridLogMessage << "Fundamental - Checking if traceless"
+              << std::endl;
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, ta);
+      Complex tr = TensorRemove(trace(ta));
+      std::cout << GridLogMessage << a << " " << std::endl;
+      assert(abs(tr) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+
+  // reunitarise??
+  template <typename LatticeMatrixType>
+  static void LieRandomize(GridParallelRNG &pRNG, LatticeMatrixType &out, double scale = 1.0) 
+  {
+    GridBase *grid = out.Grid();
+
+    typedef typename LatticeMatrixType::vector_type vector_type;
+
+    typedef iSinglet<vector_type> vTComplexType;
+
+    typedef Lattice<vTComplexType> LatticeComplexType;
+    typedef typename GridTypeMapper<typename LatticeMatrixType::vector_object>::scalar_object MatrixType;
+
+    LatticeComplexType ca(grid);
+    LatticeMatrixType lie(grid);
+    LatticeMatrixType la(grid);
+    ComplexD ci(0.0, scale);
+    //    ComplexD cone(1.0, 0.0);
+    MatrixType ta;
+
+    lie = Zero();
+
+    for (int a = 0; a < AdjointDimension; a++) {
+      random(pRNG, ca);
+
+      ca = (ca + conjugate(ca)) * 0.5;
+      ca = ca - 0.5;
+
+      generator(a, ta);
+
+      la = ci * ca * ta;
+
+      lie = lie + la;  // e^{i la ta}
+
+    }
+    taExp(lie, out);
+  }
+
+  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+                                                  LatticeMatrix &out,
+                                                  Real scale = 1.0) {
+    GridBase *grid = out.Grid();
+    LatticeReal ca(grid);
+    LatticeMatrix la(grid);
+    Complex ci(0.0, scale);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AdjointDimension; a++) {
+      gaussian(pRNG, ca);
+      generator(a, ta);
+      la = toComplex(ca) * ta;
+      out += la;
+    }
+    out *= ci;
+  }
+
+  static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
+                                          LatticeMatrix &out,
+                                          Real scale = 1.0) {
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeMatrix la(grid);
+    Matrix ta;
+
+    out = Zero();
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, ta);
+      la = peekColour(h, a) * timesI(ta) * scale;
+      out += la;
+    }
+  }
+/*
+ * Fundamental rep gauge xform
+ */
+  template<typename Fundamental,typename GaugeMat>
+  static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
+    GridBase *grid = ferm._grid;
+    conformable(grid,g._grid);
+    ferm = g*ferm;
+  }
+/*
+ * Adjoint rep gauge xform
+ */
+
+  template<typename Gimpl>
+  static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
+    GridBase *grid = Umu.Grid();
+    conformable(grid,g.Grid());
+
+    typename Gimpl::GaugeLinkField U(grid);
+    typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
+
+    for(int mu=0;mu<Nd;mu++){
+      U= PeekIndex<LorentzIndex>(Umu,mu);
+      U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
+      PokeIndex<LorentzIndex>(Umu,U,mu);
+    }
+  }
+  template<typename Gimpl>
+  static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
+    GridBase *grid = g.Grid();
+    typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
+    for(int mu=0;mu<Nd;mu++){
+      U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
+    }
+  }
+  template<typename Gimpl>
+  static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
+    LieRandomize(pRNG,g,1.0);
+    GaugeTransform<Gimpl>(Umu,g);
+  }
+
+  // Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
+  // inverse operation: FundamentalLieAlgebraMatrix
+  static void projectOnAlgebra(LatticeAlgebraVector &h_out, const LatticeMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    h_out = Zero();
+    Matrix Ta;
+
+    for (int a = 0; a < AdjointDimension; a++) {
+      generator(a, Ta);
+      pokeColour(h_out, - 2.0 * (trace(timesI(Ta) * in)) * scale, a);
+    }
+  }
+
+  template <typename GaugeField>
+  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) {
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    LatticeMatrixType tmp(out.Grid());
+    for (int mu = 0; mu < Nd; mu++) {
+      //      LieRandomize(pRNG, Umu, 1.0);
+      //      PokeIndex<LorentzIndex>(out, Umu, mu);
+      gaussian(pRNG,Umu);
+      tmp = Ta(Umu);
+      taExp(tmp,Umu);
+      ProjectSUn(Umu);
+      PokeIndex<LorentzIndex>(out, Umu, mu);
+    }
+  }
+  template<typename GaugeField>
+  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    for(int mu=0;mu<Nd;mu++){
+      LieRandomize(pRNG,Umu,0.01);
+      PokeIndex<LorentzIndex>(out,Umu,mu);
+    }
+  }
+  template<typename GaugeField>
+  static void ColdConfiguration(GaugeField &out){
+    typedef typename GaugeField::vector_type vector_type;
+    typedef iSUnMatrix<vector_type> vMatrixType;
+    typedef Lattice<vMatrixType> LatticeMatrixType;
+
+    LatticeMatrixType Umu(out.Grid());
+    Umu=1.0;
+    for(int mu=0;mu<Nd;mu++){
+      PokeIndex<LorentzIndex>(out,Umu,mu);
+    }
+  }
+  template<typename GaugeField>
+  static void ColdConfiguration(GridParallelRNG &pRNG,GaugeField &out){
+    ColdConfiguration(out);
+  }
+
+  template<typename LatticeMatrixType>
+  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out){
+    out = Ta(in);
+  }
+  template <typename LatticeMatrixType>
+  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) {
+    typedef typename LatticeMatrixType::scalar_type ComplexType;
+
+    LatticeMatrixType xn(x.Grid());
+    RealD nfac = 1.0;
+
+    xn = x;
+    ex = xn + ComplexType(1.0);  // 1+x
+
+    // Do a 12th order exponentiation
+    for (int i = 2; i <= 12; ++i) {
+      nfac = nfac / RealD(i);  // 1/2, 1/2.3 ...
+      xn = xn * x;             // x2, x3,x4....
+      ex = ex + xn * nfac;     // x2/2!, x3/3!....
+    }
+  }
+};
+
+template<int N>
+Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > Inverse(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  auto lvol = grid->lSites();
+  Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > ret(grid);
+  
+  autoView(Umu_v,Umu,CpuRead);
+  autoView(ret_v,ret,CpuWrite);
+  thread_for(site,lvol,{
+    Eigen::MatrixXcd EigenU = Eigen::MatrixXcd::Zero(N,N);
+    Coordinate lcoor;
+    grid->LocalIndexToLocalCoor(site, lcoor);
+    iScalar<iScalar<iMatrix<ComplexD, N> > > Us;
+    iScalar<iScalar<iMatrix<ComplexD, N> > > Ui;
+    peekLocalSite(Us, Umu_v, lcoor);
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	EigenU(i,j) = Us()()(i,j);
+      }}
+    Eigen::MatrixXcd EigenUinv = EigenU.inverse();
+    for(int i=0;i<N;i++){
+      for(int j=0;j<N;j++){
+	Ui()()(i,j) = EigenUinv(i,j);
+      }}
+    pokeLocalSite(Ui,ret_v,lcoor);
+  });
+  return ret;
+}
+// Explicit specialisation for SU(3).
+// Explicit specialisation for SU(3).
+static void
+ProjectSU3 (Lattice<iScalar<iScalar<iMatrix<vComplexD, 3> > > > &Umu)
+{
+  GridBase *grid=Umu.Grid();
+  const int x=0;
+  const int y=1;
+  const int z=2;
+  // Reunitarise
+  Umu = ProjectOnGroup(Umu);
+  autoView(Umu_v,Umu,CpuWrite);
+  thread_for(ss,grid->oSites(),{
+      auto cm = Umu_v[ss];
+      cm()()(2,x) = adj(cm()()(0,y)*cm()()(1,z)-cm()()(0,z)*cm()()(1,y)); //x= yz-zy
+      cm()()(2,y) = adj(cm()()(0,z)*cm()()(1,x)-cm()()(0,x)*cm()()(1,z)); //y= zx-xz
+      cm()()(2,z) = adj(cm()()(0,x)*cm()()(1,y)-cm()()(0,y)*cm()()(1,x)); //z= xy-yx
+      Umu_v[ss]=cm;
+  });
+}
+static void ProjectSU3(Lattice<iVector<iScalar<iMatrix<vComplexD, 3> >,Nd> > &U)
+{
+  GridBase *grid=U.Grid();
+  // Reunitarise
+  for(int mu=0;mu<Nd;mu++){
+    auto Umu = PeekIndex<LorentzIndex>(U,mu);
+    Umu      = ProjectOnGroup(Umu);
+    ProjectSU3(Umu);
+    PokeIndex<LorentzIndex>(U,Umu,mu);
+  }
+}
+
+typedef SU<2> SU2;
+typedef SU<3> SU3;
+typedef SU<4> SU4;
+typedef SU<5> SU5;
+
+
+typedef SU<Nc> FundamentalMatrices;
+
+NAMESPACE_END(Grid);
+#endif

Grid/qcd/utils/SUn.impl.h

@@ -1,578 +0,0 @@
-// This file is #included into the body of the class template definition of
-// GaugeGroup. So, image there to be
-//
-// template <int ncolour, class group_name>
-// class GaugeGroup {
-//
-// around it.
-//
-// Please note that the unconventional file extension makes sure that it
-// doesn't get found by the scripts/filelist during bootstrapping.
-
-private:
-template <ONLY_IF_SU>
-static int su2subgroups(GroupName::SU) { return (ncolour * (ncolour - 1)) / 2; }
-////////////////////////////////////////////////////////////////////////
-// There are N^2-1 generators for SU(N).
-//
-// We take a traceless hermitian generator basis as follows
-//
-// * Normalisation: trace ta tb = 1/2 delta_ab = T_F delta_ab
-//   T_F = 1/2  for SU(N) groups
-//
-// * Off diagonal
-//    - pairs of rows i1,i2 behaving like pauli matrices signma_x, sigma_y
-//
-//    - there are (Nc-1-i1) slots for i2 on each row [ x  0  x ]
-//      direct count off each row
-//
-//    - Sum of all pairs is Nc(Nc-1)/2: proof arithmetic series
-//
-//      (Nc-1) + (Nc-2)+...  1      ==> Nc*(Nc-1)/2
-//      1+ 2+          +   + Nc-1
-//
-//    - There are 2 x Nc (Nc-1)/ 2 of these = Nc^2 - Nc
-//
-//    - We enumerate the row-col pairs.
-//    - for each row col pair there is a (sigma_x) and a (sigma_y) like
-//    generator
-//
-//
-//   t^a_ij = { in 0.. Nc(Nc-1)/2 -1} =>  1/2(delta_{i,i1} delta_{j,i2} +
-//   delta_{i,i1} delta_{j,i2})
-//   t^a_ij = { in Nc(Nc-1)/2 ... Nc(Nc-1) - 1} =>  i/2( delta_{i,i1}
-//   delta_{j,i2} - i delta_{i,i1} delta_{j,i2})
-//
-// * Diagonal; must be traceless and normalised
-//   - Sequence is
-//   N  (1,-1,0,0...)
-//   N  (1, 1,-2,0...)
-//   N  (1, 1, 1,-3,0...)
-//   N  (1, 1, 1, 1,-4,0...)
-//
-//   where 1/2 = N^2 (1+.. m^2)etc.... for the m-th diagonal generator
-//   NB this gives the famous SU3 result for su2 index 8
-//
-//   N= sqrt(1/2 . 1/6 ) = 1/2 . 1/sqrt(3)
-//
-//   ( 1      )
-//   (    1   ) / sqrt(3) /2  = 1/2 lambda_8
-//   (      -2)
-//
-////////////////////////////////////////////////////////////////////////
-template <class cplx, ONLY_IF_SU>
-static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::SU) {
-  // map lie index to which type of generator
-  int diagIndex;
-  int su2Index;
-  int sigxy;
-  int NNm1 = ncolour * (ncolour - 1);
-  if (lieIndex >= NNm1) {
-    diagIndex = lieIndex - NNm1;
-    generatorDiagonal(diagIndex, ta);
-    return;
-  }
-  sigxy = lieIndex & 0x1;  // even or odd
-  su2Index = lieIndex >> 1;
-  if (sigxy)
-    generatorSigmaY(su2Index, ta);
-  else
-    generatorSigmaX(su2Index, ta);
-}
-
-template <class cplx, ONLY_IF_SU>
-static void generatorSigmaY(int su2Index, iGroupMatrix<cplx> &ta) {
-  ta = Zero();
-  int i1, i2;
-  su2SubGroupIndex(i1, i2, su2Index);
-  ta()()(i1, i2) = 1.0;
-  ta()()(i2, i1) = 1.0;
-  ta = ta * 0.5;
-}
-
-template <class cplx, ONLY_IF_SU>
-static void generatorSigmaX(int su2Index, iGroupMatrix<cplx> &ta) {
-  ta = Zero();
-  cplx i(0.0, 1.0);
-  int i1, i2;
-  su2SubGroupIndex(i1, i2, su2Index);
-  ta()()(i1, i2) = i;
-  ta()()(i2, i1) = -i;
-  ta = ta * 0.5;
-}
-
-template <class cplx, ONLY_IF_SU>
-static void generatorDiagonal(int diagIndex, iGroupMatrix<cplx> &ta) {
-  // diag ({1, 1, ..., 1}(k-times), -k, 0, 0, ...)
-  ta = Zero();
-  int k = diagIndex + 1;                  // diagIndex starts from 0
-  for (int i = 0; i <= diagIndex; i++) {  // k iterations
-    ta()()(i, i) = 1.0;
-  }
-  ta()()(k, k) = -k;  // indexing starts from 0
-  RealD nrm = 1.0 / std::sqrt(2.0 * k * (k + 1));
-  ta = ta * nrm;
-}
-
-////////////////////////////////////////////////////////////////////////
-// Map a su2 subgroup number to the pair of rows that are non zero
-////////////////////////////////////////////////////////////////////////
-static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::SU) {
-  assert((su2_index >= 0) && (su2_index < (ncolour * (ncolour - 1)) / 2));
-
-  int spare = su2_index;
-  for (i1 = 0; spare >= (ncolour - 1 - i1); i1++) {
-    spare = spare - (ncolour - 1 - i1);  // remove the Nc-1-i1 terms
-  }
-  i2 = i1 + 1 + spare;
-}
-
-public:
-//////////////////////////////////////////////////////////////////////////////////////////
-// Pull out a subgroup and project on to real coeffs x pauli basis
-//////////////////////////////////////////////////////////////////////////////////////////
-template <class vcplx, ONLY_IF_SU>
-static void su2Extract(Lattice<iSinglet<vcplx> > &Determinant,
-                       Lattice<iSU2Matrix<vcplx> > &subgroup,
-                       const Lattice<iGroupMatrix<vcplx> > &source,
-                       int su2_index) {
-  GridBase *grid(source.Grid());
-  conformable(subgroup, source);
-  conformable(subgroup, Determinant);
-  int i0, i1;
-  su2SubGroupIndex(i0, i1, su2_index);
-
-  autoView(subgroup_v, subgroup, AcceleratorWrite);
-  autoView(source_v, source, AcceleratorRead);
-  autoView(Determinant_v, Determinant, AcceleratorWrite);
-  accelerator_for(ss, grid->oSites(), 1, {
-    subgroup_v[ss]()()(0, 0) = source_v[ss]()()(i0, i0);
-    subgroup_v[ss]()()(0, 1) = source_v[ss]()()(i0, i1);
-    subgroup_v[ss]()()(1, 0) = source_v[ss]()()(i1, i0);
-    subgroup_v[ss]()()(1, 1) = source_v[ss]()()(i1, i1);
-
-    iSU2Matrix<vcplx> Sigma = subgroup_v[ss];
-
-    Sigma = Sigma - adj(Sigma) + trace(adj(Sigma));
-
-    subgroup_v[ss] = Sigma;
-
-    // this should be purely real
-    Determinant_v[ss] =
-        Sigma()()(0, 0) * Sigma()()(1, 1) - Sigma()()(0, 1) * Sigma()()(1, 0);
-  });
-}
-
-//////////////////////////////////////////////////////////////////////////////////////////
-// Set matrix to one and insert a pauli subgroup
-//////////////////////////////////////////////////////////////////////////////////////////
-template <class vcplx, ONLY_IF_SU>
-static void su2Insert(const Lattice<iSU2Matrix<vcplx> > &subgroup,
-                      Lattice<iGroupMatrix<vcplx> > &dest, int su2_index) {
-  GridBase *grid(dest.Grid());
-  conformable(subgroup, dest);
-  int i0, i1;
-  su2SubGroupIndex(i0, i1, su2_index);
-
-  dest = 1.0;  // start out with identity
-  autoView(dest_v, dest, AcceleratorWrite);
-  autoView(subgroup_v, subgroup, AcceleratorRead);
-  accelerator_for(ss, grid->oSites(), 1, {
-    dest_v[ss]()()(i0, i0) = subgroup_v[ss]()()(0, 0);
-    dest_v[ss]()()(i0, i1) = subgroup_v[ss]()()(0, 1);
-    dest_v[ss]()()(i1, i0) = subgroup_v[ss]()()(1, 0);
-    dest_v[ss]()()(i1, i1) = subgroup_v[ss]()()(1, 1);
-  });
-}
-
-///////////////////////////////////////////////
-// Generate e^{ Re Tr Staple Link} dlink
-//
-// *** Note Staple should be appropriate linear compbination between all
-// staples.
-// *** If already by beta pass coefficient 1.0.
-// *** This routine applies the additional 1/Nc factor that comes after trace
-// in action.
-//
-///////////////////////////////////////////////
-template <ONLY_IF_SU>
-static void SubGroupHeatBath(
-    GridSerialRNG &sRNG, GridParallelRNG &pRNG,
-    RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
-    LatticeMatrix &link,
-    const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
-    int su2_subgroup, int nheatbath, LatticeInteger &wheremask) {
-  GridBase *grid = link.Grid();
-
-  const RealD twopi = 2.0 * M_PI;
-
-  LatticeMatrix staple(grid);
-
-  staple = barestaple * (beta / ncolour);
-
-  LatticeMatrix V(grid);
-  V = link * staple;
-
-  // Subgroup manipulation in the lie algebra space
-  LatticeSU2Matrix u(
-      grid);  // Kennedy pendleton "u" real projected normalised Sigma
-  LatticeSU2Matrix uinv(grid);
-  LatticeSU2Matrix ua(grid);  // a in pauli form
-  LatticeSU2Matrix b(grid);   // rotated matrix after hb
-
-  // Some handy constant fields
-  LatticeComplex ones(grid);
-  ones = 1.0;
-  LatticeComplex zeros(grid);
-  zeros = Zero();
-  LatticeReal rones(grid);
-  rones = 1.0;
-  LatticeReal rzeros(grid);
-  rzeros = Zero();
-  LatticeComplex udet(grid);  // determinant of real(staple)
-  LatticeInteger mask_true(grid);
-  mask_true = 1;
-  LatticeInteger mask_false(grid);
-  mask_false = 0;
-
-  /*
-    PLB 156 P393 (1985) (Kennedy and Pendleton)
-
-    Note: absorb "beta" into the def of sigma compared to KP paper; staple
-    passed to this routine has "beta" already multiplied in
-
-    Action linear in links h and of form:
-
-    beta S = beta  Sum_p (1 - 1/Nc Re Tr Plaq )
-
-    Writing Sigma = 1/Nc (beta Sigma') where sum over staples is "Sigma' "
-
-    beta S = const - beta/Nc Re Tr h Sigma'
-    = const - Re Tr h Sigma
-
-    Decompose h and Sigma into (1, sigma_j) ; h_i real, h^2=1, Sigma_i complex
-    arbitrary.
-
-    Tr h Sigma = h_i Sigma_j Tr (sigma_i sigma_j)  = h_i Sigma_j 2 delta_ij
-    Re Tr h Sigma = 2 h_j Re Sigma_j
-
-    Normalised re Sigma_j = xi u_j
-
-    With u_j a unit vector and U can be in SU(2);
-
-    Re Tr h Sigma = 2 h_j Re Sigma_j = 2 xi (h.u)
-
-    4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-    u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-    xi = sqrt(Det)/2;
-
-    Write a= u h in SU(2); a has pauli decomp a_j;
-
-    Note: Product b' xi is unvariant because scaling Sigma leaves
-    normalised vector "u" fixed; Can rescale Sigma so b' = 1.
-  */
-
-  ////////////////////////////////////////////////////////
-  // Real part of Pauli decomposition
-  // Note a subgroup can project to zero in cold start
-  ////////////////////////////////////////////////////////
-  su2Extract(udet, u, V, su2_subgroup);
-
-  //////////////////////////////////////////////////////
-  // Normalising this vector if possible; else identity
-  //////////////////////////////////////////////////////
-  LatticeComplex xi(grid);
-
-  LatticeSU2Matrix lident(grid);
-
-  SU2Matrix ident = Complex(1.0);
-  SU2Matrix pauli1;
-  GaugeGroup<2, GroupName::SU>::generator(0, pauli1);
-  SU2Matrix pauli2;
-  GaugeGroup<2, GroupName::SU>::generator(1, pauli2);
-  SU2Matrix pauli3;
-  GaugeGroup<2, GroupName::SU>::generator(2, pauli3);
-  pauli1 = timesI(pauli1) * 2.0;
-  pauli2 = timesI(pauli2) * 2.0;
-  pauli3 = timesI(pauli3) * 2.0;
-
-  LatticeComplex cone(grid);
-  LatticeReal adet(grid);
-  adet = abs(toReal(udet));
-  lident = Complex(1.0);
-  cone = Complex(1.0);
-  Real machine_epsilon = 1.0e-7;
-  u = where(adet > machine_epsilon, u, lident);
-  udet = where(adet > machine_epsilon, udet, cone);
-
-  xi = 0.5 * sqrt(udet);        // 4xi^2 = Det [ Sig - Sig^dag  + 1 Tr Sigdag]
-  u = 0.5 * u * pow(xi, -1.0);  //  u   = 1/2xi [ Sig - Sig^dag  + 1 Tr Sigdag]
-
-  // Debug test for sanity
-  uinv = adj(u);
-  b = u * uinv - 1.0;
-  assert(norm2(b) < 1.0e-4);
-
-  /*
-    Measure: Haar measure dh has d^4a delta(1-|a^2|)
-    In polars:
-    da = da0 r^2 sin theta dr dtheta dphi delta( 1 - r^2 -a0^2)
-    = da0 r^2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r)(sqrt(1-a0^) +
-    r) )
-    = da0 r/2 sin theta dr dtheta dphi delta( (sqrt(1-a0^) - r) )
-
-    Action factor Q(h) dh  = e^-S[h]  dh =  e^{  xi Tr uh} dh    // beta
-    enters through xi =  e^{2 xi (h.u)} dh =  e^{2 xi h0u0}.e^{2 xi h1u1}.e^{2
-    xi h2u2}.e^{2 xi h3u3} dh
-
-    Therefore for each site, take xi for that site
-    i) generate  |a0|<1 with dist
-    (1-a0^2)^0.5 e^{2 xi a0 } da0
-
-    Take alpha = 2 xi  = 2 xi [ recall 2 beta/Nc unmod staple norm];
-    hence 2.0/Nc factor in Chroma ] A. Generate two uniformly distributed
-    pseudo-random numbers R and R', R'', R''' in the unit interval; B. Set X =
-    -(ln R)/alpha, X' =-(ln R')/alpha; C. Set C = cos^2(2pi R"), with R"
-    another uniform random number in [0,1] ; D. Set A = XC; E. Let d  = X'+A;
-    F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-    G. Set a0 = 1 - d;
-
-    Note that in step D setting B ~ X - A and using B in place of A in step E
-    will generate a second independent a 0 value.
-  */
-
-  /////////////////////////////////////////////////////////
-  // count the number of sites by picking "1"'s out of hat
-  /////////////////////////////////////////////////////////
-  Integer hit = 0;
-  LatticeReal rtmp(grid);
-  rtmp = where(wheremask, rones, rzeros);
-  RealD numSites = sum(rtmp);
-  RealD numAccepted;
-  LatticeInteger Accepted(grid);
-  Accepted = Zero();
-  LatticeInteger newlyAccepted(grid);
-
-  std::vector<LatticeReal> xr(4, grid);
-  std::vector<LatticeReal> a(4, grid);
-  LatticeReal d(grid);
-  d = Zero();
-  LatticeReal alpha(grid);
-
-  //    std::cout<<GridLogMessage<<"xi "<<xi <<std::endl;
-  xi = 2.0 * xi;
-  alpha = toReal(xi);
-
-  do {
-    // A. Generate two uniformly distributed pseudo-random numbers R and R',
-    // R'', R''' in the unit interval;
-    random(pRNG, xr[0]);
-    random(pRNG, xr[1]);
-    random(pRNG, xr[2]);
-    random(pRNG, xr[3]);
-
-    // B. Set X = - ln R/alpha, X' = -ln R'/alpha
-    xr[1] = -log(xr[1]) / alpha;
-    xr[2] = -log(xr[2]) / alpha;
-
-    // C. Set C = cos^2(2piR'')
-    xr[3] = cos(xr[3] * twopi);
-    xr[3] = xr[3] * xr[3];
-
-    LatticeReal xrsq(grid);
-
-    // D. Set A = XC;
-    // E. Let d  = X'+A;
-    xrsq = xr[2] + xr[1] * xr[3];
-
-    d = where(Accepted, d, xr[2] + xr[1] * xr[3]);
-
-    // F. If R'''^2 :> 1 - 0.5 d,  go back to A;
-    LatticeReal thresh(grid);
-    thresh = 1.0 - d * 0.5;
-    xrsq = xr[0] * xr[0];
-    LatticeInteger ione(grid);
-    ione = 1;
-    LatticeInteger izero(grid);
-    izero = Zero();
-
-    newlyAccepted = where(xrsq < thresh, ione, izero);
-    Accepted = where(newlyAccepted, newlyAccepted, Accepted);
-    Accepted = where(wheremask, Accepted, izero);
-
-    // FIXME need an iSum for integer to avoid overload on return type??
-    rtmp = where(Accepted, rones, rzeros);
-    numAccepted = sum(rtmp);
-
-    hit++;
-
-  } while ((numAccepted < numSites) && (hit < nheatbath));
-
-  // G. Set a0 = 1 - d;
-  a[0] = Zero();
-  a[0] = where(wheremask, 1.0 - d, a[0]);
-
-  //////////////////////////////////////////
-  //    ii) generate a_i uniform on two sphere radius (1-a0^2)^0.5
-  //////////////////////////////////////////
-
-  LatticeReal a123mag(grid);
-  a123mag = sqrt(abs(1.0 - a[0] * a[0]));
-
-  LatticeReal cos_theta(grid);
-  LatticeReal sin_theta(grid);
-  LatticeReal phi(grid);
-
-  random(pRNG, phi);
-  phi = phi * twopi;  // uniform in [0,2pi]
-  random(pRNG, cos_theta);
-  cos_theta = (cos_theta * 2.0) - 1.0;  // uniform in [-1,1]
-  sin_theta = sqrt(abs(1.0 - cos_theta * cos_theta));
-
-  a[1] = a123mag * sin_theta * cos(phi);
-  a[2] = a123mag * sin_theta * sin(phi);
-  a[3] = a123mag * cos_theta;
-
-  ua = toComplex(a[0]) * ident + toComplex(a[1]) * pauli1 +
-       toComplex(a[2]) * pauli2 + toComplex(a[3]) * pauli3;
-
-  b = 1.0;
-  b = where(wheremask, uinv * ua, b);
-  su2Insert(b, V, su2_subgroup);
-
-  // mask the assignment back based on Accptance
-  link = where(Accepted, V * link, link);
-
-  //////////////////////////////
-  // Debug Checks
-  // SU2 check
-  LatticeSU2Matrix check(grid);  // rotated matrix after hb
-  u = Zero();
-  check = ua * adj(ua) - 1.0;
-  check = where(Accepted, check, u);
-  assert(norm2(check) < 1.0e-4);
-
-  check = b * adj(b) - 1.0;
-  check = where(Accepted, check, u);
-  assert(norm2(check) < 1.0e-4);
-
-  LatticeMatrix Vcheck(grid);
-  Vcheck = Zero();
-  Vcheck = where(Accepted, V * adj(V) - 1.0, Vcheck);
-  //    std::cout<<GridLogMessage << "SU3 check " <<norm2(Vcheck)<<std::endl;
-  assert(norm2(Vcheck) < 1.0e-4);
-
-  // Verify the link stays in SU(3)
-  //    std::cout<<GridLogMessage <<"Checking the modified link"<<std::endl;
-  Vcheck = link * adj(link) - 1.0;
-  assert(norm2(Vcheck) < 1.0e-4);
-  /////////////////////////////////
-}
-
-template <ONLY_IF_SU>
-static void testGenerators(GroupName::SU) {
-  Matrix ta;
-  Matrix tb;
-  std::cout << GridLogMessage
-            << "Fundamental - Checking trace ta tb is 0.5 delta_ab"
-            << std::endl;
-  for (int a = 0; a < AdjointDimension; a++) {
-    for (int b = 0; b < AdjointDimension; b++) {
-      generator(a, ta);
-      generator(b, tb);
-      Complex tr = TensorRemove(trace(ta * tb));
-      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
-                << std::endl;
-      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-      if (a != b) assert(abs(tr) < 1.0e-6);
-    }
-    std::cout << GridLogMessage << std::endl;
-  }
-  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
-            << std::endl;
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, ta);
-    std::cout << GridLogMessage << a << std::endl;
-    assert(norm2(ta - adj(ta)) < 1.0e-6);
-  }
-  std::cout << GridLogMessage << std::endl;
-
-  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
-            << std::endl;
-  for (int a = 0; a < AdjointDimension; a++) {
-    generator(a, ta);
-    Complex tr = TensorRemove(trace(ta));
-    std::cout << GridLogMessage << a << " " << std::endl;
-    assert(abs(tr) < 1.0e-6);
-  }
-  std::cout << GridLogMessage << std::endl;
-}
-
-
-template <int N, class vtype>
-static Lattice<iScalar<iScalar<iMatrix<vtype, N> > > >
-ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vtype, N> > > > &Umu, GroupName::SU) {
-  return ProjectOnGroup(Umu);
-}
-
-template <class vtype>
-accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::SU) {
-  return ProjectOnGroup(r);
-}
-
-template <class vtype, int N>
-accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::SU) {
-  return ProjectOnGroup(r);
-}
-
-template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::SU) {
-  return ProjectOnGroup(arg);
-}
-
-template <typename LatticeMatrixType>
-static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
-  out = Ta(in);
-}
-
-/*
- * Fundamental rep gauge xform
- */
-template<typename Fundamental,typename GaugeMat>
-static void GaugeTransformFundamental( Fundamental &ferm, GaugeMat &g){
-  GridBase *grid = ferm._grid;
-  conformable(grid,g._grid);
-  ferm = g*ferm;
-}
-/*
- * Adjoint rep gauge xform
- */
-
-template<typename Gimpl>
-static void GaugeTransform(typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
-  GridBase *grid = Umu.Grid();
-  conformable(grid,g.Grid());
-
-  typename Gimpl::GaugeLinkField U(grid);
-  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
-
-  for(int mu=0;mu<Nd;mu++){
-    U= PeekIndex<LorentzIndex>(Umu,mu);
-    U = g*U*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
-    PokeIndex<LorentzIndex>(Umu,U,mu);
-  }
-}
-template<typename Gimpl>
-static void GaugeTransform( std::vector<typename Gimpl::GaugeLinkField> &U, typename Gimpl::GaugeLinkField &g){
-  GridBase *grid = g.Grid();
-  typename Gimpl::GaugeLinkField ag(grid); ag = adj(g);
-  for(int mu=0;mu<Nd;mu++){
-    U[mu] = g*U[mu]*Gimpl::CshiftLink(ag, mu, 1); //BC-aware
-  }
-}
-template<typename Gimpl>
-static void RandomGaugeTransform(GridParallelRNG &pRNG, typename Gimpl::GaugeField &Umu, typename Gimpl::GaugeLinkField &g){
-  LieRandomize(pRNG,g,1.0);
-  GaugeTransform<Gimpl>(Umu,g);
-}

Grid/qcd/utils/SUnAdjoint.h

@@ -51,10 +51,6 @@ public:
   typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> > LatticeAdjFieldF;
   typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> > LatticeAdjFieldD;
 
-
-  template <typename vtype>
-  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
-
   typedef Lattice<iScalar<iScalar<iVector<vComplex, Dimension> > > >  LatticeAdjVector;
 
   template <class cplx>
@@ -62,8 +58,8 @@ public:
     // returns i(T_Adj)^index necessary for the projectors
     // see definitions above
     iAdjTa = Zero();
-    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
-    iSUnMatrix<cplx> tmp;
+    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
+    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
 
     // FIXME not very efficient to get all the generators everytime
     for (int a = 0; a < Dimension; a++) SU<ncolour>::generator(a, ta[a]);
@@ -71,7 +67,8 @@ public:
     for (int a = 0; a < Dimension; a++) {
       tmp = ta[a] * ta[Index] - ta[Index] * ta[a];
       for (int b = 0; b < (ncolour * ncolour - 1); b++) {
-        iSUnMatrix<cplx> tmp1 = 2.0 * tmp * ta[b];  // 2.0 from the normalization
+        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
+	  2.0 * tmp * ta[b];  // 2.0 from the normalization
         Complex iTr = TensorRemove(timesI(trace(tmp1)));
         //iAdjTa()()(b, a) = iTr;
         iAdjTa()()(a, b) = iTr;
@@ -137,7 +134,8 @@ public:
 
     for (int a = 0; a < Dimension; a++) {
       generator(a, iTa);
-      pokeColour(h_out, real(trace(iTa * in)) * coefficient, a);
+      LatticeComplex tmp = real(trace(iTa * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
     }
   }
 

Grid/qcd/utils/SUnTwoIndex.h

@@ -0,0 +1,273 @@
+////////////////////////////////////////////////////////////////////////
+//
+// * Two index representation generators
+//
+// * Normalisation for the fundamental generators:
+//   trace ta tb = 1/2 delta_ab = T_F delta_ab
+//   T_F = 1/2  for SU(N) groups
+//
+//
+//   base for NxN two index (anti-symmetric) matrices
+//   normalized to 1 (d_ij is the kroenecker delta)
+//
+//   (e^(ij)_{kl} = 1 / sqrt(2) (d_ik d_jl +/- d_jk d_il)
+//
+//   Then the generators are written as
+//
+//   (iT_a)^(ij)(lk) = i * ( tr[e^(ij)^dag e^(lk) T^trasp_a] +
+//   tr[e^(lk)e^(ij)^dag T_a] )  //
+//   
+//
+////////////////////////////////////////////////////////////////////////
+
+// Authors: David Preti, Guido Cossu
+
+#ifndef QCD_UTIL_SUN2INDEX_H
+#define QCD_UTIL_SUN2INDEX_H
+
+
+NAMESPACE_BEGIN(Grid);
+
+enum TwoIndexSymmetry { Symmetric = 1, AntiSymmetric = -1 };
+
+inline Real delta(int a, int b) { return (a == b) ? 1.0 : 0.0; }
+
+template <int ncolour, TwoIndexSymmetry S>
+class SU_TwoIndex : public SU<ncolour> {
+public:
+  static const int Dimension = ncolour * (ncolour + S) / 2;
+  static const int NumGenerators = SU<ncolour>::AdjointDimension;
+
+  template <typename vtype>
+  using iSUnTwoIndexMatrix = iScalar<iScalar<iMatrix<vtype, Dimension> > >;
+
+  typedef iSUnTwoIndexMatrix<Complex> TIMatrix;
+  typedef iSUnTwoIndexMatrix<ComplexF> TIMatrixF;
+  typedef iSUnTwoIndexMatrix<ComplexD> TIMatrixD;
+
+  typedef iSUnTwoIndexMatrix<vComplex> vTIMatrix;
+  typedef iSUnTwoIndexMatrix<vComplexF> vTIMatrixF;
+  typedef iSUnTwoIndexMatrix<vComplexD> vTIMatrixD;
+
+  typedef Lattice<vTIMatrix> LatticeTwoIndexMatrix;
+  typedef Lattice<vTIMatrixF> LatticeTwoIndexMatrixF;
+  typedef Lattice<vTIMatrixD> LatticeTwoIndexMatrixD;
+
+  typedef Lattice<iVector<iScalar<iMatrix<vComplex, Dimension> >, Nd> >
+  LatticeTwoIndexField;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexF, Dimension> >, Nd> >
+  LatticeTwoIndexFieldF;
+  typedef Lattice<iVector<iScalar<iMatrix<vComplexD, Dimension> >, Nd> >
+  LatticeTwoIndexFieldD;
+
+  template <typename vtype>
+  using iSUnMatrix = iScalar<iScalar<iMatrix<vtype, ncolour> > >;
+
+  typedef iSUnMatrix<Complex> Matrix;
+  typedef iSUnMatrix<ComplexF> MatrixF;
+  typedef iSUnMatrix<ComplexD> MatrixD;
+
+  template <class cplx>
+  static void base(int Index, iSUnMatrix<cplx> &eij) {
+    // returns (e)^(ij)_{kl} necessary for change of base U_F -> U_R
+    assert(Index < NumGenerators);
+    eij = Zero();
+
+    // for the linearisation of the 2 indexes 
+    static int a[ncolour * (ncolour - 1) / 2][2]; // store the a <-> i,j
+    static bool filled = false;
+    if (!filled) {
+      int counter = 0;
+      for (int i = 1; i < ncolour; i++) {
+        for (int j = 0; j < i; j++) {
+          a[counter][0] = i;
+          a[counter][1] = j;
+          counter++;
+        }
+      }
+      filled = true;
+    }
+
+    if (Index < ncolour * (ncolour - 1) / 2) {
+      baseOffDiagonal(a[Index][0], a[Index][1], eij);
+    } else {
+      baseDiagonal(Index, eij);
+    }
+  }
+
+  template <class cplx>
+  static void baseDiagonal(int Index, iSUnMatrix<cplx> &eij) {
+    eij = Zero();
+    eij()()(Index - ncolour * (ncolour - 1) / 2,
+            Index - ncolour * (ncolour - 1) / 2) = 1.0;
+  }
+
+  template <class cplx>
+  static void baseOffDiagonal(int i, int j, iSUnMatrix<cplx> &eij) {
+    eij = Zero();
+    for (int k = 0; k < ncolour; k++)
+      for (int l = 0; l < ncolour; l++)
+        eij()()(l, k) = delta(i, k) * delta(j, l) +
+	  S * delta(j, k) * delta(i, l);
+
+    RealD nrm = 1. / std::sqrt(2.0);
+    eij = eij * nrm;
+  }
+
+  static void printBase(void) {
+    for (int gen = 0; gen < Dimension; gen++) {
+      Matrix tmp;
+      base(gen, tmp);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << tmp << std::endl;
+    }
+  }
+
+  template <class cplx>
+  static void generator(int Index, iSUnTwoIndexMatrix<cplx> &i2indTa) {
+    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(
+								ncolour * ncolour - 1);
+    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > eij(Dimension);
+    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
+    i2indTa = Zero();
+    
+    for (int a = 0; a < ncolour * ncolour - 1; a++)
+      SU<ncolour>::generator(a, ta[a]);
+    
+    for (int a = 0; a < Dimension; a++) base(a, eij[a]);
+
+    for (int a = 0; a < Dimension; a++) {
+      tmp = transpose(ta[Index]) * adj(eij[a]) + adj(eij[a]) * ta[Index];
+      for (int b = 0; b < Dimension; b++) {
+        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
+	  tmp * eij[b]; 
+        Complex iTr = TensorRemove(timesI(trace(tmp1)));
+        i2indTa()()(a, b) = iTr;
+      }
+    }
+  }
+
+  static void printGenerators(void) {
+    for (int gen = 0; gen < ncolour * ncolour - 1; gen++) {
+      TIMatrix i2indTa;
+      generator(gen, i2indTa);
+      std::cout << GridLogMessage << "Nc = " << ncolour << " t_" << gen
+                << std::endl;
+      std::cout << GridLogMessage << i2indTa << std::endl;
+    }
+  }
+
+  static void testGenerators(void) {
+    TIMatrix i2indTa, i2indTb;
+    std::cout << GridLogMessage << "2IndexRep - Checking if traceless"
+              << std::endl;
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(trace(i2indTa)) < 1.0e-6);
+    }
+    std::cout << GridLogMessage << std::endl;
+
+    std::cout << GridLogMessage << "2IndexRep - Checking if antihermitean"
+              << std::endl;
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      generator(a, i2indTa);
+      std::cout << GridLogMessage << a << std::endl;
+      assert(norm2(adj(i2indTa) + i2indTa) < 1.0e-6);
+    }
+
+    std::cout << GridLogMessage << std::endl;
+    std::cout << GridLogMessage
+              << "2IndexRep - Checking Tr[Ta*Tb]=delta(a,b)*(N +- 2)/2"
+              << std::endl;
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      for (int b = 0; b < ncolour * ncolour - 1; b++) {
+        generator(a, i2indTa);
+        generator(b, i2indTb);
+
+        // generator returns iTa, so we need a minus sign here
+        Complex Tr = -TensorRemove(trace(i2indTa * i2indTb));
+        std::cout << GridLogMessage << "a=" << a << "b=" << b << "Tr=" << Tr
+                  << std::endl;
+      }
+    }
+    std::cout << GridLogMessage << std::endl;
+  }
+
+  static void TwoIndexLieAlgebraMatrix(
+				       const typename SU<ncolour>::LatticeAlgebraVector &h,
+				       LatticeTwoIndexMatrix &out, Real scale = 1.0) {
+    conformable(h, out);
+    GridBase *grid = out.Grid();
+    LatticeTwoIndexMatrix la(grid);
+    TIMatrix i2indTa;
+
+    out = Zero();
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      generator(a, i2indTa);
+      la = peekColour(h, a) * i2indTa;
+      out += la;
+    }
+    out *= scale;
+  }
+
+  // Projects the algebra components 
+  // of a lattice matrix ( of dimension ncol*ncol -1 )
+  static void projectOnAlgebra(
+			       typename SU<ncolour>::LatticeAlgebraVector &h_out,
+			       const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    h_out = Zero();
+    TIMatrix i2indTa;
+    Real coefficient = -2.0 / (ncolour + 2 * S) * scale;
+    // 2/(Nc +/- 2) for the normalization of the trace in the two index rep
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      generator(a, i2indTa);
+      auto tmp = real(trace(i2indTa * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
+    }
+  }
+
+  // a projector that keeps the generators stored to avoid the overhead of
+  // recomputing them
+  static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out,
+                        const LatticeTwoIndexMatrix &in, Real scale = 1.0) {
+    conformable(h_out, in);
+    // to store the generators
+    static std::vector<TIMatrix> i2indTa(ncolour * ncolour -1); 
+    h_out = Zero();
+    static bool precalculated = false;
+    if (!precalculated) {
+      precalculated = true;
+      for (int a = 0; a < ncolour * ncolour - 1; a++) generator(a, i2indTa[a]);
+    }
+
+    Real coefficient =
+      -2.0 / (ncolour + 2 * S) * scale;  // 2/(Nc +/- 2) for the normalization
+    // of the trace in the two index rep
+
+    for (int a = 0; a < ncolour * ncolour - 1; a++) {
+      auto tmp = real(trace(i2indTa[a] * in)) * coefficient;
+      pokeColour(h_out, tmp, a);
+    }
+  }
+};
+
+// Some useful type names
+typedef SU_TwoIndex<Nc, Symmetric> TwoIndexSymmMatrices;
+typedef SU_TwoIndex<Nc, AntiSymmetric> TwoIndexAntiSymmMatrices;
+
+typedef SU_TwoIndex<2, Symmetric> SU2TwoIndexSymm;
+typedef SU_TwoIndex<3, Symmetric> SU3TwoIndexSymm;
+typedef SU_TwoIndex<4, Symmetric> SU4TwoIndexSymm;
+typedef SU_TwoIndex<5, Symmetric> SU5TwoIndexSymm;
+
+typedef SU_TwoIndex<2, AntiSymmetric> SU2TwoIndexAntiSymm;
+typedef SU_TwoIndex<3, AntiSymmetric> SU3TwoIndexAntiSymm;
+typedef SU_TwoIndex<4, AntiSymmetric> SU4TwoIndexAntiSymm;
+typedef SU_TwoIndex<5, AntiSymmetric> SU5TwoIndexAntiSymm;
+
+NAMESPACE_END(Grid);
+
+#endif

Grid/qcd/utils/Sp2n.impl.h

@@ -1,317 +0,0 @@
-// This file is #included into the body of the class template definition of
-// GaugeGroup. So, image there to be
-//
-// template <int ncolour, class group_name>
-// class GaugeGroup {
-//
-// around it.
-//
-// Please note that the unconventional file extension makes sure that it
-// doesn't get found by the scripts/filelist during bootstrapping.
-
-private:
-template <ONLY_IF_Sp>
-static int su2subgroups(GroupName::Sp) { return (ncolour/2 * (ncolour/2 - 1)) / 2; }
-
-// Sp(2N) has N(2N+1) = 2N^2+N generators
-//
-// normalise the generators such that
-// Trace ( Ta Tb) = 1/2 delta_ab
-//
-// N generators in the cartan, 2N^2 off
-// off diagonal:
-//     there are 6 types named a,b,c,d and w,z
-//     abcd are N(N-1)/2 each while wz are N each
-
-template <class cplx, ONLY_IF_Sp>
-static void generator(int lieIndex, iGroupMatrix<cplx> &ta, GroupName::Sp) {
-  // map lie index into type of generators: diagonal, abcd type, wz type
-
-  const int nsp = ncolour/2;
-  int diagIndex;
-  int aIndex, bIndex, cIndex, dIndex;
-  int wIndex, zIndex;  // a,b,c,d are N(N-1)/2 and w,z are N
-  const int mod = nsp * (nsp - 1) * 0.5;
-  const int offdiag =
-      2 * nsp * nsp;  // number of generators not in the cartan subalgebra
-  const int wmod = 4 * mod;
-  const int zmod = wmod + nsp;
-  if (lieIndex >= offdiag) {
-    diagIndex = lieIndex - offdiag;  // 0, ... ,N-1
-    // std::cout << GridLogMessage << "diag type " << std::endl;
-    generatorDiagtype(diagIndex, ta);
-    return;
-  }
-  if ((lieIndex >= wmod) && (lieIndex < zmod)) {
-    // std::cout << GridLogMessage << "w type " << std::endl;
-    wIndex = lieIndex - wmod;  // 0, ... ,N-1
-    generatorWtype(wIndex, ta);
-    return;
-  }
-  if ((lieIndex >= zmod) && (lieIndex < offdiag)) {
-    // std::cout << GridLogMessage << "z type " << std::endl;
-    // std::cout << GridLogMessage << "lie index " << lieIndex << std::endl;
-    // std::cout << GridLogMessage << "z mod " << zmod << std::endl;
-    zIndex = lieIndex - zmod;  // 0, ... ,N-1
-    generatorZtype(zIndex, ta);
-    return;
-  }
-  if (lieIndex < mod) {  // atype 0, ... , N(N-1)/2=mod
-    // std::cout << GridLogMessage << "a type " << std::endl;
-    aIndex = lieIndex;
-    // std::cout << GridLogMessage << "a indx " << aIndex << std::endl;
-    generatorAtype(aIndex, ta);
-    return;
-  }
-  if ((lieIndex >= mod) && lieIndex < 2 * mod) {  // btype mod, ... , 2mod-1
-    // std::cout << GridLogMessage << "b type " << std::endl;
-    bIndex = lieIndex - mod;
-    generatorBtype(bIndex, ta);
-    return;
-  }
-  if ((lieIndex >= 2 * mod) &&
-      lieIndex < 3 * mod) {  // ctype 2mod, ... , 3mod-1
-    // std::cout << GridLogMessage << "c type " << std::endl;
-    cIndex = lieIndex - 2 * mod;
-    generatorCtype(cIndex, ta);
-    return;
-  }
-  if ((lieIndex >= 3 * mod) &&
-      lieIndex < wmod) {  // ctype 3mod, ... , 4mod-1 = wmod-1
-    // std::cout << GridLogMessage << "d type " << std::endl;
-    dIndex = lieIndex - 3 * mod;
-    generatorDtype(dIndex, ta);
-    return;
-  }
-
-}  // end of generator
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorDiagtype(int diagIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,i) = - ta(i+N,i+N) = 1/2 for each i index of the cartan subalgebra
-
-  const int nsp=ncolour/2;
-  ta = Zero();
-  RealD nrm = 1.0 / 2;
-
-  ta()()(diagIndex, diagIndex) = nrm;
-  ta()()(diagIndex + nsp, diagIndex + nsp) = -nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorAtype(int aIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,j) = ta(j,i) = -ta(i+N,j+N) = -ta(j+N,i+N) = 1 / 2 sqrt(2)
-  // with i<j and i=0,...,N-2
-  // follows that j=i+1, ... , N
-  int i1, i2;
-  const int nsp=ncolour/2;
-  ta = Zero();
-  RealD nrm = 1 / (2 * std::sqrt(2));
-
-  su2SubGroupIndex(i1, i2, aIndex);
-  ta()()(i1, i2) = 1;
-  ta()()(i2, i1) = 1;
-  ta()()(i1 + nsp, i2 + nsp) = -1;
-  ta()()(i2 + nsp, i1 + nsp) = -1;
-
-  ta = ta * nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorBtype(int bIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,j) = -ta(j,i) = ta(i+N,j+N) = -ta(j+N,i+N) = i / 1/ 2 sqrt(2)
-  // with i<j and i=0,...,N-2
-  // follows that j=i+1, ... , N-1
-
-  const int nsp=ncolour/2;
-  int i1, i2;
-  ta = Zero();
-  cplx i(0.0, 1.0);
-  RealD nrm = 1 / (2 * std::sqrt(2));
-  su2SubGroupIndex(i1, i2, bIndex);
-
-  ta()()(i1, i2) = i;
-  ta()()(i2, i1) = -i;
-  ta()()(i1 + nsp, i2 + nsp) = i;
-  ta()()(i2 + nsp, i1 + nsp) = -i;
-
-  ta = ta * nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorCtype(int cIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,j+N) = ta(j,i+N) = ta(i+N,j) = ta(j+N,i) = 1 / 2 sqrt(2)
-
-  const int nsp=ncolour/2;
-  int i1, i2;
-  ta = Zero();
-  RealD nrm = 1 / (2 * std::sqrt(2));
-  su2SubGroupIndex(i1, i2, cIndex);
-
-  ta()()(i1, i2 + nsp) = 1;
-  ta()()(i2, i1 + nsp) = 1;
-  ta()()(i1 + nsp, i2) = 1;
-  ta()()(i2 + nsp, i1) = 1;
-
-  ta = ta * nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorDtype(int dIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,j+N) = ta(j,i+N) = -ta(i+N,j) = -ta(j+N,i) = i /  2 sqrt(2)
-
-  const int nsp=ncolour/2;
-  int i1, i2;
-  ta = Zero();
-  cplx i(0.0, 1.0);
-  RealD nrm = 1 / (2 * std::sqrt(2));
-  su2SubGroupIndex(i1, i2, dIndex);
-
-  ta()()(i1, i2 + nsp) = i;
-  ta()()(i2, i1 + nsp) = i;
-  ta()()(i1 + nsp, i2) = -i;
-  ta()()(i2 + nsp, i1) = -i;
-
-  ta = ta * nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorWtype(int wIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,i+N) =  ta(i+N,i) = 1/2
-
-  const int nsp=ncolour/2;
-  ta = Zero();
-  RealD nrm = 1.0 / 2;  // check
-
-  ta()()(wIndex, wIndex + nsp) = 1;
-  ta()()(wIndex + nsp, wIndex) = 1;
-
-  ta = ta * nrm;
-}
-
-template <class cplx, ONLY_IF_Sp>
-static void generatorZtype(int zIndex, iGroupMatrix<cplx> &ta) {
-  // ta(i,i+N) = - ta(i+N,i) = i/2
-
-  const int nsp=ncolour/2;
-  ta = Zero();
-  RealD nrm = 1.0 / 2;  // check
-  cplx i(0.0, 1.0);
-  ta()()(zIndex, zIndex + nsp) = i;
-  ta()()(zIndex + nsp, zIndex) = -i;
-
-  ta = ta * nrm;
-}
-
-////////////////////////////////////////////////////////////////////////
-// Map a su2 subgroup number to the pair of rows that are non zero
-////////////////////////////////////////////////////////////////////////
-template <ONLY_IF_Sp>
-static void su2SubGroupIndex(int &i1, int &i2, int su2_index, GroupName::Sp) {
-  const int nsp=ncolour/2;
-  assert((su2_index >= 0) && (su2_index < (nsp * (nsp - 1)) / 2));
-
-  int spare = su2_index;
-  for (i1 = 0; spare >= (nsp - 1 - i1); i1++) {
-    spare = spare - (nsp - 1 - i1);  // remove the Nc-1-i1 terms
-  }
-  i2 = i1 + 1 + spare;
-}
-
-static void testGenerators(GroupName::Sp) {
-  Matrix ta;
-  Matrix tb;
-  std::cout << GridLogMessage
-            << "Fundamental - Checking trace ta tb is 0.5 delta_ab "
-            << std::endl;
-  for (int a = 0; a < AlgebraDimension; a++) {
-    for (int b = 0; b < AlgebraDimension; b++) {
-      generator(a, ta);
-      generator(b, tb);
-      Complex tr = TensorRemove(trace(ta * tb));
-      std::cout << GridLogMessage << "(" << a << "," << b << ") =  " << tr
-                << std::endl;
-      if (a == b) assert(abs(tr - Complex(0.5)) < 1.0e-6);
-      if (a != b) assert(abs(tr) < 1.0e-6);
-    }
-  }
-  std::cout << GridLogMessage << std::endl;
-  std::cout << GridLogMessage << "Fundamental - Checking if hermitian"
-            << std::endl;
-  for (int a = 0; a < AlgebraDimension; a++) {
-    generator(a, ta);
-    std::cout << GridLogMessage << a << std::endl;
-    assert(norm2(ta - adj(ta)) < 1.0e-6);
-  }
-  std::cout << GridLogMessage << std::endl;
-  std::cout << GridLogMessage << "Fundamental - Checking if traceless"
-            << std::endl;
-  for (int a = 0; a < AlgebraDimension; a++) {
-    generator(a, ta);
-    Complex tr = TensorRemove(trace(ta));
-    std::cout << GridLogMessage << a << std::endl;
-    assert(abs(tr) < 1.0e-6);
-  }
-}
-
-template <int N>
-static Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > >
-ProjectOnGeneralGroup(const Lattice<iScalar<iScalar<iMatrix<vComplexD, N> > > > &Umu, GroupName::Sp) {
-  return ProjectOnSpGroup(Umu);
-}
-
-template <class vtype>
-accelerator_inline static iScalar<vtype> ProjectOnGeneralGroup(const iScalar<vtype> &r, GroupName::Sp) {
-  return ProjectOnSpGroup(r);
-}
-
-template <class vtype, int N>
-accelerator_inline static iVector<vtype,N> ProjectOnGeneralGroup(const iVector<vtype,N> &r, GroupName::Sp) {
-  return ProjectOnSpGroup(r);
-}
-
-template <class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-accelerator_inline static iMatrix<vtype,N> ProjectOnGeneralGroup(const iMatrix<vtype,N> &arg, GroupName::Sp) {
-  return ProjectOnSpGroup(arg);
-}
-
-template <typename LatticeMatrixType>   
-static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
-  out = SpTa(in);
-}
-
-public:
-
-template <ONLY_IF_Sp>
-static void Omega(LatticeColourMatrixD &in) {
-  const int nsp=ncolour/2;
-  LatticeColourMatrixD OmegaLatt(in.Grid());
-  LatticeColourMatrixD identity(in.Grid());
-  ColourMatrix Omega;
-
-  OmegaLatt = Zero();
-  Omega = Zero();
-  identity = 1.;
-
-  for (int i = 0; i < nsp; i++) {
-    Omega()()(i, nsp + i) = 1.;
-    Omega()()(nsp + i, i) = -1;
-  }
-  OmegaLatt = OmegaLatt + (identity * Omega);
-  in = OmegaLatt;
-}
-
-template <ONLY_IF_Sp, class vtype, int N>
-static void Omega(iScalar<iScalar<iMatrix<vtype, N> > > &in) {
-  const int nsp=ncolour/2;
-    
-  iScalar<iScalar<iMatrix<vtype, N> > > Omega;
-  Omega = Zero();
-
-  for (int i = 0; i < nsp; i++) {
-    Omega()()(i, nsp + i) = 1.;
-    Omega()()(nsp + i, i) = -1;
-  }
-    
-  in = Omega;
-}

Grid/qcd/utils/Utils.h

@@ -8,9 +8,9 @@
 #include <Grid/qcd/utils/ScalarObjs.h>
 
 // Include representations
-#include <Grid/qcd/utils/GaugeGroup.h>
+#include <Grid/qcd/utils/SUn.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
+#include <Grid/qcd/utils/SUnTwoIndex.h>
 
 // All-to-all contraction kernels that touch the 
 // internal lattice structure

Grid/qcd/utils/WilsonLoops.h

@@ -290,7 +290,7 @@ public:
   }
 */
   //////////////////////////////////////////////////
-  // the sum over all nu-oriented staples for nu != mu on each site
+  // the sum over all staples on each site
   //////////////////////////////////////////////////
   static void Staple(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
 
@@ -300,10 +300,6 @@ public:
     for (int d = 0; d < Nd; d++) {
       U[d] = PeekIndex<LorentzIndex>(Umu, d);
     }
-    Staple(staple, U, mu);
-  }
-
-  static void Staple(GaugeMat &staple, const std::vector<GaugeMat> &U, int mu) {
     staple = Zero();
 
     for (int nu = 0; nu < Nd; nu++) {
@@ -339,202 +335,6 @@ public:
     }
   }
 
-  /////////////
-  //Staples for each direction mu, summed over nu != mu
-  //staple: output staples for each mu (Nd)
-  //U: link array (Nd)
-  /////////////
-  static void StapleAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U) {
-    assert(staple.size() == Nd); assert(U.size() == Nd);
-    for(int mu=0;mu<Nd;mu++) Staple(staple[mu], U, mu);
-  }
-
-
-  //A workspace class allowing reuse of the stencil
-  class WilsonLoopPaddedStencilWorkspace{
-    std::unique_ptr<GeneralLocalStencil> stencil;
-    size_t nshift;
-
-    void generateStencil(GridBase* padded_grid){
-      double t0 = usecond();
-      
-      //Generate shift arrays
-      std::vector<Coordinate> shifts = this->getShifts();
-      nshift = shifts.size();
-      
-      double t1 = usecond();
-      //Generate local stencil
-      stencil.reset(new GeneralLocalStencil(padded_grid,shifts));
-      double t2 = usecond();
-      std::cout << GridLogPerformance << " WilsonLoopPaddedWorkspace timings: coord:" << (t1-t0)/1000 << "ms, stencil:" << (t2-t1)/1000 << "ms" << std::endl;   
-    }
-  public:
-    //Get the stencil. If not already generated, or if generated using a different Grid than in PaddedCell, it will be created on-the-fly
-    const GeneralLocalStencil & getStencil(const PaddedCell &pcell){
-      assert(pcell.depth >= this->paddingDepth());
-      if(!stencil || stencil->Grid() != (GridBase*)pcell.grids.back() ) generateStencil((GridBase*)pcell.grids.back());
-      return *stencil;
-    }
-    size_t Nshift() const{ return nshift; }
-    
-    virtual std::vector<Coordinate> getShifts() const = 0;
-    virtual int paddingDepth() const = 0; //padding depth required
-    
-    virtual ~WilsonLoopPaddedStencilWorkspace(){}
-  };
-
-  //This workspace allows the sharing of a common PaddedCell object between multiple stencil workspaces
-  class WilsonLoopPaddedWorkspace{
-    std::vector<WilsonLoopPaddedStencilWorkspace*> stencil_wk;
-    std::unique_ptr<PaddedCell> pcell;
-
-    void generatePcell(GridBase* unpadded_grid){
-      assert(stencil_wk.size());
-      int max_depth = 0;
-      for(auto const &s : stencil_wk) max_depth=std::max(max_depth, s->paddingDepth());
-      
-      pcell.reset(new PaddedCell(max_depth, dynamic_cast<GridCartesian*>(unpadded_grid)));
-    }
-    
-  public:
-    //Add a stencil definition. This should be done before the first call to retrieve a stencil object.
-    //Takes ownership of the pointer
-    void addStencil(WilsonLoopPaddedStencilWorkspace *stencil){
-      assert(!pcell);
-      stencil_wk.push_back(stencil);
-    }
-
-    const GeneralLocalStencil & getStencil(const size_t stencil_idx, GridBase* unpadded_grid){
-      if(!pcell || pcell->unpadded_grid != unpadded_grid) generatePcell(unpadded_grid);
-      return stencil_wk[stencil_idx]->getStencil(*pcell);
-    }      
-    const PaddedCell & getPaddedCell(GridBase* unpadded_grid){
-      if(!pcell || pcell->unpadded_grid != unpadded_grid) generatePcell(unpadded_grid);
-      return *pcell;
-    }
-    
-    ~WilsonLoopPaddedWorkspace(){
-      for(auto &s : stencil_wk) delete s;
-    }
-  };
-
-  //A workspace class allowing reuse of the stencil
-  class StaplePaddedAllWorkspace: public WilsonLoopPaddedStencilWorkspace{
-  public:
-    std::vector<Coordinate> getShifts() const override{
-      std::vector<Coordinate> shifts;
-      for(int mu=0;mu<Nd;mu++){
-	for(int nu=0;nu<Nd;nu++){
-	  if(nu != mu){
-	    Coordinate shift_0(Nd,0);
-	    Coordinate shift_mu(Nd,0); shift_mu[mu]=1;
-	    Coordinate shift_nu(Nd,0); shift_nu[nu]=1;
-	    Coordinate shift_mnu(Nd,0); shift_mnu[nu]=-1;
-	    Coordinate shift_mnu_pmu(Nd,0); shift_mnu_pmu[nu]=-1; shift_mnu_pmu[mu]=1;
-      
-	    //U_nu(x+mu)U^dag_mu(x+nu) U^dag_nu(x)
-	    shifts.push_back(shift_0);
-	    shifts.push_back(shift_nu);
-	    shifts.push_back(shift_mu);
-      
-	    //U_nu^dag(x-nu+mu) U_mu^dag(x-nu) U_nu(x-nu)
-	    shifts.push_back(shift_mnu);
-	    shifts.push_back(shift_mnu);
-	    shifts.push_back(shift_mnu_pmu);
-	  }
-	}
-      }
-      return shifts;
-    }
-
-    int paddingDepth() const override{ return 1; }
-  }; 
-
-  //Padded cell implementation of the staple method for all mu, summed over nu != mu
-  //staple: output staple for each mu, summed over nu != mu (Nd)
-  //U_padded: the gauge link fields padded out using the PaddedCell class
-  //Cell: the padded cell class
-  static void StaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell) {
-    StaplePaddedAllWorkspace wk;
-    StaplePaddedAll(staple,U_padded,Cell,wk.getStencil(Cell));
-  }
-  
-  //Padded cell implementation of the staple method for all mu, summed over nu != mu
-  //staple: output staple for each mu, summed over nu != mu (Nd)
-  //U_padded: the gauge link fields padded out using the PaddedCell class
-  //Cell: the padded cell class
-  //gStencil: the precomputed generalized local stencil for the staple
-  static void StaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell, const GeneralLocalStencil &gStencil) {
-    double t0 = usecond();
-    assert(U_padded.size() == Nd); assert(staple.size() == Nd);
-    assert(U_padded[0].Grid() == (GridBase*)Cell.grids.back());
-    assert(Cell.depth >= 1);
-    GridBase *ggrid = U_padded[0].Grid(); //padded cell grid
-
-    int shift_mu_off = gStencil._npoints/Nd;
-    
-    //Open views to padded gauge links and keep open over mu loop
-    typedef LatticeView<typename GaugeMat::vector_object> GaugeViewType;
-    size_t vsize = Nd*sizeof(GaugeViewType);
-    GaugeViewType* Ug_dirs_v_host = (GaugeViewType*)malloc(vsize);
-    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i] = U_padded[i].View(AcceleratorRead);
-    GaugeViewType* Ug_dirs_v = (GaugeViewType*)acceleratorAllocDevice(vsize);
-    acceleratorCopyToDevice(Ug_dirs_v_host,Ug_dirs_v,vsize);
-    
-    GaugeMat gStaple(ggrid);
-
-    int outer_off = 0;
-    for(int mu=0;mu<Nd;mu++){
-      { //view scope
-	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View(AcceleratorRead);
-	
-	accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
-	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
-	    stencil_ss = Zero();
-	    int off = outer_off;
-	    
-	    for(int nu=0;nu<Nd;nu++){
-	      if(nu != mu){	  
-		GeneralStencilEntry const* e = gStencil_v.GetEntry(off++,ss);
-		auto U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(off++,ss);
-		auto U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(off++,ss);
-		auto U2 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-      
-		stencil_ss = stencil_ss + U2 * U1 * U0;
-
-		e = gStencil_v.GetEntry(off++,ss);
-		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(off++,ss);
-		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(off++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-
-		stencil_ss = stencil_ss + U2 * U1 * U0;
-	      }
-	    }
-		
-	    coalescedWrite(gStaple_v[ss],stencil_ss);
-	  }
-	  );
-      } //ensure views are all closed!
-      
-      staple[mu] = Cell.Extract(gStaple);
-      outer_off += shift_mu_off;
-    }//mu loop
-
-    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i].ViewClose();
-    free(Ug_dirs_v_host);
-    acceleratorFreeDevice(Ug_dirs_v);
-    
-    double t1=usecond();
-    
-    std::cout << GridLogPerformance << "StaplePaddedAll timing:" << (t1-t0)/1000 << "ms" << std::endl;   
-  }
-
-   
   //////////////////////////////////////////////////
   // the sum over all staples on each site in direction mu,nu, upper part
   //////////////////////////////////////////////////
@@ -907,14 +707,18 @@ public:
   // the sum over all staples on each site
   //////////////////////////////////////////////////
   static void RectStapleDouble(GaugeMat &U2, const GaugeMat &U, int mu) {
-    U2 = U * Gimpl::CshiftLink(U, mu, 1);
+    U2 = U * Cshift(U, mu, 1);
   }
 
   ////////////////////////////////////////////////////////////////////////////
-  // Hop by two optimisation strategy. Use RectStapleDouble to obtain 'U2'
+  // Hop by two optimisation strategy does not work nicely with Gparity. (could
+  // do,
+  // but need to track two deep where cross boundary and apply a conjugation).
+  // Must differentiate this in Gimpl, and use Gimpl::isPeriodicGaugeField to do
+  // so .
   ////////////////////////////////////////////////////////////////////////////
-  static void RectStapleOptimised(GaugeMat &Stap, const std::vector<GaugeMat> &U2,
-                                  const std::vector<GaugeMat> &U, int mu) {
+  static void RectStapleOptimised(GaugeMat &Stap, std::vector<GaugeMat> &U2,
+                                  std::vector<GaugeMat> &U, int mu) {
 
     Stap = Zero();
 
@@ -928,9 +732,9 @@ public:
 
         // Up staple    ___ ___
         //             |       |
-        tmp = Gimpl::CshiftLink(adj(U[nu]), nu, -1);
+        tmp = Cshift(adj(U[nu]), nu, -1);
         tmp = adj(U2[mu]) * tmp;
-        tmp = Gimpl::CshiftLink(tmp, mu, -2);
+        tmp = Cshift(tmp, mu, -2);
 
         Staple2x1 = Gimpl::CovShiftForward(U[nu], nu, tmp);
 
@@ -938,14 +742,14 @@ public:
         //             |___ ___|
         //
         tmp = adj(U2[mu]) * U[nu];
-        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Gimpl::CshiftLink(tmp, mu, -2));
+        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Cshift(tmp, mu, -2));
 
         //              ___ ___
         //             |    ___|
         //             |___ ___|
         //
 
-        Stap += Gimpl::CshiftLink(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
+        Stap += Cshift(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
 
         //              ___ ___
         //             |___    |
@@ -954,7 +758,7 @@ public:
 
         //  tmp= Staple2x1* Cshift(U[mu],mu,-2);
         //  Stap+= Cshift(tmp,mu,1) ;
-        Stap += Gimpl::CshiftLink(Staple2x1, mu, 1) * Gimpl::CshiftLink(U[mu], mu, -1);
+        Stap += Cshift(Staple2x1, mu, 1) * Cshift(U[mu], mu, -1);
         ;
 
         //       --
@@ -962,10 +766,10 @@ public:
         //
         //      |  |
 
-        tmp = Gimpl::CshiftLink(adj(U2[nu]), nu, -2);
+        tmp = Cshift(adj(U2[nu]), nu, -2);
         tmp = Gimpl::CovShiftBackward(U[mu], mu, tmp);
-        tmp = U2[nu] * Gimpl::CshiftLink(tmp, nu, 2);
-        Stap += Gimpl::CshiftLink(tmp, mu, 1);
+        tmp = U2[nu] * Cshift(tmp, nu, 2);
+        Stap += Cshift(tmp, mu, 1);
 
         //      |  |
         //
@@ -974,12 +778,25 @@ public:
 
         tmp = Gimpl::CovShiftBackward(U[mu], mu, U2[nu]);
         tmp = adj(U2[nu]) * tmp;
-        tmp = Gimpl::CshiftLink(tmp, nu, -2);
-        Stap += Gimpl::CshiftLink(tmp, mu, 1);
+        tmp = Cshift(tmp, nu, -2);
+        Stap += Cshift(tmp, mu, 1);
       }
     }
   }
 
+  static void RectStaple(GaugeMat &Stap, const GaugeLorentz &Umu, int mu) {
+    RectStapleUnoptimised(Stap, Umu, mu);
+  }
+  static void RectStaple(const GaugeLorentz &Umu, GaugeMat &Stap,
+                         std::vector<GaugeMat> &U2, std::vector<GaugeMat> &U,
+                         int mu) {
+    if (Gimpl::isPeriodicGaugeField()) {
+      RectStapleOptimised(Stap, U2, U, mu);
+    } else {
+      RectStapleUnoptimised(Stap, Umu, mu);
+    }
+  }
+
   static void RectStapleUnoptimised(GaugeMat &Stap, const GaugeLorentz &Umu,
                                     int mu) {
     GridBase *grid = Umu.Grid();
@@ -1078,288 +895,6 @@ public:
     }
   }
 
-  static void RectStaple(GaugeMat &Stap, const GaugeLorentz &Umu, int mu) {
-    RectStapleUnoptimised(Stap, Umu, mu);
-  }
-  static void RectStaple(const GaugeLorentz &Umu, GaugeMat &Stap,
-                         std::vector<GaugeMat> &U2, std::vector<GaugeMat> &U,
-                         int mu) {
-    RectStapleOptimised(Stap, U2, U, mu);
-  }
-  //////////////////////////////////////////////////////
-  //Compute the rectangular staples for all orientations
-  //Stap : Array of staples (Nd)
-  //U: Gauge links in each direction (Nd)
-  /////////////////////////////////////////////////////
-  static void RectStapleAll(std::vector<GaugeMat> &Stap, const std::vector<GaugeMat> &U){
-    assert(Stap.size() == Nd); assert(U.size() == Nd);
-    std::vector<GaugeMat> U2(Nd,U[0].Grid());
-    for(int mu=0;mu<Nd;mu++) RectStapleDouble(U2[mu], U[mu], mu);
-    for(int mu=0;mu<Nd;mu++) RectStapleOptimised(Stap[mu], U2, U, mu);
-  }
-
-  //A workspace class allowing reuse of the stencil
-  class RectStaplePaddedAllWorkspace: public WilsonLoopPaddedStencilWorkspace{
-  public:
-    std::vector<Coordinate> getShifts() const override{
-      std::vector<Coordinate> shifts;
-      for (int mu = 0; mu < Nd; mu++){
-	for (int nu = 0; nu < Nd; nu++) {
-	  if (nu != mu) {
-	    auto genShift = [&](int mushift,int nushift){
-	      Coordinate out(Nd,0); out[mu]=mushift; out[nu]=nushift; return out;
-	    };
-
-	    //tmp6 = tmp5(x+mu) = U_mu(x+mu)U_nu(x+2mu)U_mu^dag(x+nu+mu) U_mu^dag(x+nu) U_nu^dag(x)
-	    shifts.push_back(genShift(0,0));
-	    shifts.push_back(genShift(0,+1));
-	    shifts.push_back(genShift(+1,+1));
-	    shifts.push_back(genShift(+2,0));
-	    shifts.push_back(genShift(+1,0));
-
-	    //tmp5 = tmp4(x+mu) = U_mu(x+mu)U^dag_nu(x-nu+2mu)U^dag_mu(x-nu+mu)U^dag_mu(x-nu)U_nu(x-nu)
-	    shifts.push_back(genShift(0,-1));
-	    shifts.push_back(genShift(0,-1));
-	    shifts.push_back(genShift(+1,-1));
-	    shifts.push_back(genShift(+2,-1));
-	    shifts.push_back(genShift(+1,0));
-
-	    //tmp5 = tmp4(x+mu) = U^dag_nu(x-nu+mu)U^dag_mu(x-nu)U^dag_mu(x-mu-nu)U_nu(x-mu-nu)U_mu(x-mu)
-	    shifts.push_back(genShift(-1,0));
-	    shifts.push_back(genShift(-1,-1));
-	    shifts.push_back(genShift(-1,-1));
-	    shifts.push_back(genShift(0,-1));
-	    shifts.push_back(genShift(+1,-1));
-
-	    //tmp5 = tmp4(x+mu) = U_nu(x+mu)U_mu^dag(x+nu)U_mu^dag(x-mu+nu)U_nu^dag(x-mu)U_mu(x-mu)
-	    shifts.push_back(genShift(-1,0));
-	    shifts.push_back(genShift(-1,0));
-	    shifts.push_back(genShift(-1,+1));
-	    shifts.push_back(genShift(0,+1));
-	    shifts.push_back(genShift(+1,0));
-
-	    //tmp6 = tmp5(x+mu) = U_nu(x+mu)U_nu(x+mu+nu)U_mu^dag(x+2nu)U_nu^dag(x+nu)U_nu^dag(x)
-	    shifts.push_back(genShift(0,0));
-	    shifts.push_back(genShift(0,+1));
-	    shifts.push_back(genShift(0,+2));
-	    shifts.push_back(genShift(+1,+1));
-	    shifts.push_back(genShift(+1,0));
-
-	    //tmp5 = tmp4(x+mu) = U_nu^dag(x+mu-nu)U_nu^dag(x+mu-2nu)U_mu^dag(x-2nu)U_nu(x-2nu)U_nu(x-nu)
-	    shifts.push_back(genShift(0,-1));
-	    shifts.push_back(genShift(0,-2));
-	    shifts.push_back(genShift(0,-2));
-	    shifts.push_back(genShift(+1,-2));
-	    shifts.push_back(genShift(+1,-1));
-	  }
-	}
-      }
-      return shifts;
-    }
-
-    int paddingDepth() const override{ return 2; }
-  }; 
-
-  //Padded cell implementation of the rectangular staple method for all mu, summed over nu != mu
-  //staple: output staple for each mu, summed over nu != mu (Nd)
-  //U_padded: the gauge link fields padded out using the PaddedCell class
-  //Cell: the padded cell class
-  static void RectStaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell) {
-    RectStaplePaddedAllWorkspace wk;
-    RectStaplePaddedAll(staple,U_padded,Cell,wk.getStencil(Cell));
-  }
-  
-  //Padded cell implementation of the rectangular staple method for all mu, summed over nu != mu
-  //staple: output staple for each mu, summed over nu != mu (Nd)
-  //U_padded: the gauge link fields padded out using the PaddedCell class
-  //Cell: the padded cell class
-  //gStencil: the stencil
-  static void RectStaplePaddedAll(std::vector<GaugeMat> &staple, const std::vector<GaugeMat> &U_padded, const PaddedCell &Cell, const GeneralLocalStencil &gStencil) {
-    double t0 = usecond();
-    assert(U_padded.size() == Nd); assert(staple.size() == Nd);
-    assert(U_padded[0].Grid() == (GridBase*)Cell.grids.back());
-    assert(Cell.depth >= 2);
-    GridBase *ggrid = U_padded[0].Grid(); //padded cell grid
-
-    size_t nshift = gStencil._npoints;
-    int mu_off_delta = nshift / Nd;
-    
-    //Open views to padded gauge links and keep open over mu loop
-    typedef LatticeView<typename GaugeMat::vector_object> GaugeViewType;
-    size_t vsize = Nd*sizeof(GaugeViewType);
-    GaugeViewType* Ug_dirs_v_host = (GaugeViewType*)malloc(vsize);
-    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i] = U_padded[i].View(AcceleratorRead);
-    GaugeViewType* Ug_dirs_v = (GaugeViewType*)acceleratorAllocDevice(vsize);
-    acceleratorCopyToDevice(Ug_dirs_v_host,Ug_dirs_v,vsize);
-
-    GaugeMat gStaple(ggrid); //temp staple object on padded grid
-
-    int offset = 0;
-    for(int mu=0; mu<Nd; mu++){
-
-      { //view scope
-	autoView( gStaple_v , gStaple, AcceleratorWrite);
-	auto gStencil_v = gStencil.View(AcceleratorRead);
-
-	accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
-	    decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
-	    stencil_ss = Zero();
-	    int s=offset;
-	    for(int nu=0;nu<Nd;nu++){
-	      if(nu != mu){
-		//tmp6 = tmp5(x+mu) = U_mu(x+mu)U_nu(x+2mu)U_mu^dag(x+nu+mu) U_mu^dag(x+nu) U_nu^dag(x)
-		GeneralStencilEntry const* e = gStencil_v.GetEntry(s++,ss);
-		auto U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		auto U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		auto U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		auto U3 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		auto U4 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
-	    
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
-
-		//tmp5 = tmp4(x+mu) = U_mu(x+mu)U^dag_nu(x-nu+2mu)U^dag_mu(x-nu+mu)U^dag_mu(x-nu)U_nu(x-nu)
-		e = gStencil_v.GetEntry(s++,ss);
-		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U4 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
-
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
-
-		//tmp5 = tmp4(x+mu) = U^dag_nu(x-nu+mu)U^dag_mu(x-nu)U^dag_mu(x-mu-nu)U_nu(x-mu-nu)U_mu(x-mu)
-		e = gStencil_v.GetEntry(s++,ss);
-		U0 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U1 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U4 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
-
-		//tmp5 = tmp4(x+mu) = U_nu(x+mu)U_mu^dag(x+nu)U_mu^dag(x-mu+nu)U_nu^dag(x-mu)U_mu(x-mu)
-		e = gStencil_v.GetEntry(s++,ss);
-		U0 = coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U4 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;
-
-		//tmp6 = tmp5(x+mu) = U_nu(x+mu)U_nu(x+mu+nu)U_mu^dag(x+2nu)U_nu^dag(x+nu)U_nu^dag(x)
-		e = gStencil_v.GetEntry(s++,ss);
-		U0 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U1 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U3 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U4 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;   
-
-		//tmp5 = tmp4(x+mu) = U_nu^dag(x+mu-nu)U_nu^dag(x+mu-2nu)U_mu^dag(x-2nu)U_nu(x-2nu)U_nu(x-nu)
-		e = gStencil_v.GetEntry(s++,ss);
-		U0 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U1 = coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd);
-		e = gStencil_v.GetEntry(s++,ss);
-		U2 = adj(coalescedReadGeneralPermute(Ug_dirs_v[mu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U3 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-		e = gStencil_v.GetEntry(s++,ss);
-		U4 = adj(coalescedReadGeneralPermute(Ug_dirs_v[nu][e->_offset], e->_permute, Nd));
-
-		stencil_ss = stencil_ss + U4*U3*U2*U1*U0;   
-
-	      }
-	    }
-	    coalescedWrite(gStaple_v[ss],stencil_ss);
-	  }
-	  );
-	offset += mu_off_delta;
-      }//kernel/view scope
-
-      staple[mu] = Cell.Extract(gStaple);    
-    }//mu loop
-  
-    for(int i=0;i<Nd;i++) Ug_dirs_v_host[i].ViewClose();
-    free(Ug_dirs_v_host);
-    acceleratorFreeDevice(Ug_dirs_v);
-    
-    double t1 = usecond();
-    
-    std::cout << GridLogPerformance << "RectStaplePaddedAll timings:" << (t1-t0)/1000 << "ms" << std::endl;   
-  }
-
-  //A workspace for reusing the PaddedCell and GeneralLocalStencil objects
-  class StapleAndRectStapleAllWorkspace: public WilsonLoopPaddedWorkspace{
-  public:
-    StapleAndRectStapleAllWorkspace(){
-      this->addStencil(new StaplePaddedAllWorkspace);
-      this->addStencil(new RectStaplePaddedAllWorkspace);
-    }
-  };     
-    
-  //////////////////////////////////////////////////////
-  //Compute the 1x1 and 1x2 staples for all orientations
-  //Stap : Array of staples (Nd)
-  //RectStap: Array of rectangular staples (Nd)
-  //U: Gauge links in each direction (Nd)
-  /////////////////////////////////////////////////////
-  static void StapleAndRectStapleAll(std::vector<GaugeMat> &Stap, std::vector<GaugeMat> &RectStap, const std::vector<GaugeMat> &U){
-    StapleAndRectStapleAllWorkspace wk;
-    StapleAndRectStapleAll(Stap,RectStap,U,wk);
-  }
-  
-  //////////////////////////////////////////////////////
-  //Compute the 1x1 and 1x2 staples for all orientations
-  //Stap : Array of staples (Nd)
-  //RectStap: Array of rectangular staples (Nd)
-  //U: Gauge links in each direction (Nd)
-  //wk: a workspace containing stored PaddedCell and GeneralLocalStencil objects to maximize reuse
-  /////////////////////////////////////////////////////
-  static void StapleAndRectStapleAll(std::vector<GaugeMat> &Stap, std::vector<GaugeMat> &RectStap, const std::vector<GaugeMat> &U, StapleAndRectStapleAllWorkspace &wk){
-#if 0
-    StapleAll(Stap, U);
-    RectStapleAll(RectStap, U);
-#else
-    double t0 = usecond();
-
-    GridCartesian* unpadded_grid = dynamic_cast<GridCartesian*>(U[0].Grid());
-    const PaddedCell &Ghost = wk.getPaddedCell(unpadded_grid);
-        
-    CshiftImplGauge<Gimpl> cshift_impl;
-    std::vector<GaugeMat> U_pad(Nd, Ghost.grids.back());
-    for(int mu=0;mu<Nd;mu++) U_pad[mu] = Ghost.Exchange(U[mu], cshift_impl);
-    double t1 = usecond();
-    StaplePaddedAll(Stap, U_pad, Ghost, wk.getStencil(0,unpadded_grid) );
-    double t2 = usecond();
-    RectStaplePaddedAll(RectStap, U_pad, Ghost, wk.getStencil(1,unpadded_grid));
-    double t3 = usecond();
-    std::cout << GridLogPerformance << "StapleAndRectStapleAll timings: pad:" << (t1-t0)/1000 << "ms, staple:" << (t2-t1)/1000 << "ms, rect-staple:" << (t3-t2)/1000 << "ms" << std::endl;
-#endif
-  }
-
   //////////////////////////////////////////////////
   // Wilson loop of size (R1, R2), oriented in mu,nu plane
   //////////////////////////////////////////////////

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(int mode) const {
+  View_type View(void) const {
     View_type accessor(*( (View_type *) this));
     return accessor;
   }
@@ -79,60 +79,60 @@ public:
     this->_entries.resize(npoints* osites);
     this->_entries_p = &_entries[0];
 
-    thread_for(site, osites, {
-	Coordinate Coor;
-	Coordinate NbrCoor;
 
-	for(Integer ii=0;ii<npoints;ii++){
-	  Integer lex = site*npoints+ii;
-	  GeneralStencilEntry SE;
-	  ////////////////////////////////////////////////
-	  // Outer index of neighbour Offset calculation
-	  ////////////////////////////////////////////////
-	  grid->oCoorFromOindex(Coor,site);
-	  for(int d=0;d<Coor.size();d++){
-	    int rd = grid->_rdimensions[d];
-	    NbrCoor[d] = (Coor[d] + shifts[ii][d] + rd )%rd;
-	  }
-	  SE._offset      = grid->oIndexReduced(NbrCoor);
-
-	  ////////////////////////////////////////////////
-	  // Inner index permute calculation
-	  // Simpler version using icoor calculation
-	  ////////////////////////////////////////////////
-	  SE._permute =0;
-	  for(int d=0;d<Coor.size();d++){
-
-	    int fd = grid->_fdimensions[d];
-	    int rd = grid->_rdimensions[d];
-	    int ly = grid->_simd_layout[d];
-
-	    assert((ly==1)||(ly==2));
-
-	    int shift = (shifts[ii][d]+fd)%fd;  // make it strictly positive 0.. L-1
-	    int x = Coor[d];                // x in [0... rd-1] as an oSite 
-
-	    int permute_dim  = grid->PermuteDim(d);
-	    int permute_slice=0;
-	    if(permute_dim){    
-	      int  num = shift%rd; // Slice within dest osite cell of slice zero
-	      int wrap = shift/rd; // Number of osite local volume cells crossed through
-	      // x+num < rd dictates whether we are in same permute state as slice 0
-	      if ( x< rd-num ) permute_slice=wrap;
-	      else             permute_slice=(wrap+1)%ly;
-	    }
-	    if ( permute_slice ) {
-	      int ptype       =grid->PermuteType(d);
-	      uint8_t mask    =0x1<<ptype;
-	      SE._permute    |= mask;
-	    }
-	  }	
-	  ////////////////////////////////////////////////
-	  // Store in look up table
-	  ////////////////////////////////////////////////
-	  this->_entries[lex] = SE;
+    Coordinate Coor;
+    Coordinate NbrCoor;
+    for(Integer site=0;site<osites;site++){
+      for(Integer ii=0;ii<npoints;ii++){
+	Integer lex = site*npoints+ii;
+	GeneralStencilEntry SE;
+	////////////////////////////////////////////////
+	// Outer index of neighbour Offset calculation
+	////////////////////////////////////////////////
+	grid->oCoorFromOindex(Coor,site);
+	for(int d=0;d<Coor.size();d++){
+	  int rd = grid->_rdimensions[d];
+	  NbrCoor[d] = (Coor[d] + shifts[ii][d] + rd )%rd;
 	}
-      });
+	SE._offset      = grid->oIndexReduced(NbrCoor);
+
+	////////////////////////////////////////////////
+	// Inner index permute calculation
+	// Simpler version using icoor calculation
+	////////////////////////////////////////////////
+	SE._permute =0;
+	for(int d=0;d<Coor.size();d++){
+
+	  int fd = grid->_fdimensions[d];
+	  int rd = grid->_rdimensions[d];
+	  int ly = grid->_simd_layout[d];
+
+	  assert((ly==1)||(ly==2));
+
+	  int shift = (shifts[ii][d]+fd)%fd;  // make it strictly positive 0.. L-1
+	  int x = Coor[d];                // x in [0... rd-1] as an oSite 
+
+	  int permute_dim  = grid->PermuteDim(d);
+	  int permute_slice=0;
+	  if(permute_dim){    
+	    int  num = shift%rd; // Slice within dest osite cell of slice zero
+	    int wrap = shift/rd; // Number of osite local volume cells crossed through
+                                  // x+num < rd dictates whether we are in same permute state as slice 0
+	    if ( x< rd-num ) permute_slice=wrap;
+	    else             permute_slice=(wrap+1)%ly;
+	  }
+	  if ( permute_slice ) {
+	    int ptype       =grid->PermuteType(d);
+	    uint8_t mask    =0x1<<ptype;
+	    SE._permute    |= mask;
+	  }
+	}	
+	////////////////////////////////////////////////
+	// Store in look up table
+	////////////////////////////////////////////////
+	this->_entries[lex] = SE;
+      }
+    }      
   }
   
 };

Grid/stencil/Stencil.h

@@ -32,7 +32,6 @@
 
 #include <Grid/stencil/SimpleCompressor.h>   // subdir aggregate
 #include <Grid/stencil/Lebesgue.h>   // subdir aggregate
-#include <Grid/stencil/GeneralLocalStencil.h>
 
 //////////////////////////////////////////////////////////////////////////////////////////
 // Must not lose sight that goal is to be able to construct really efficient

Grid/tensors/Tensor_SIMT.h

@@ -73,16 +73,6 @@ vobj coalescedReadPermute(const vobj & __restrict__ vec,int ptype,int doperm,int
     return vec;
   }
 }
-//'perm_mask' acts as a bitmask
-template<class vobj> accelerator_inline
-vobj coalescedReadGeneralPermute(const vobj & __restrict__ vec,int perm_mask,int nd,int lane=0)
-{
-  auto obj = vec, tmp = vec;
-  for (int d=0;d<nd;d++)
-    if (perm_mask & (0x1 << d)) { permute(obj,tmp,d); tmp=obj;}
-  return obj;
-}
-
 template<class vobj> accelerator_inline
 void coalescedWrite(vobj & __restrict__ vec,const vobj & __restrict__ extracted,int lane=0)
 {
@@ -93,7 +83,7 @@ void coalescedWriteNonTemporal(vobj & __restrict__ vec,const vobj & __restrict__
 {
   vstream(vec, extracted);
 }
-#else //==GRID_SIMT
+#else
 
 
 //#ifndef GRID_SYCL
@@ -176,14 +166,6 @@ typename vobj::scalar_object coalescedReadPermute(const vobj & __restrict__ vec,
   return extractLane(plane,vec);
 }
 template<class vobj> accelerator_inline
-typename vobj::scalar_object coalescedReadGeneralPermute(const vobj & __restrict__ vec,int perm_mask,int nd,int lane=acceleratorSIMTlane(vobj::Nsimd()))
-{
-  int plane = lane;
-  for (int d=0;d<nd;d++)
-    plane = (perm_mask & (0x1 << d)) ? plane ^ (vobj::Nsimd() >> (d + 1)) : plane;
-  return extractLane(plane,vec);
-}
-template<class vobj> accelerator_inline
 void coalescedWrite(vobj & __restrict__ vec,const typename vobj::scalar_object & __restrict__ extracted,int lane=acceleratorSIMTlane(vobj::Nsimd()))
 {
   insertLane(lane,vec,extracted);

Grid/tensors/Tensor_Ta.h

@@ -66,61 +66,13 @@ template<class vtype,int N> accelerator_inline iMatrix<vtype,N> Ta(const iMatrix
   return ret;
 }
 
-template<class vtype> accelerator_inline iScalar<vtype> SpTa(const iScalar<vtype>&r)
-{
-  iScalar<vtype> ret;
-  ret._internal = SpTa(r._internal);
-  return ret;
-}
-template<class vtype,int N> accelerator_inline iVector<vtype,N> SpTa(const iVector<vtype,N>&r)
-{
-  iVector<vtype,N> ret;
-  for(int i=0;i<N;i++){
-    ret._internal[i] = SpTa(r._internal[i]);
-  }
-  return ret;
-}
-template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-accelerator_inline iMatrix<vtype,N> SpTa(const iMatrix<vtype,N> &arg)
-{
-  // Generalises Ta to Sp2n
-  // Applies the following projections
-  // P_{antihermitian} P_{antihermitian-Sp-algebra} P_{traceless}
-  // where the ordering matters
-  // P_{traceless} subtracts the trace
-  // P_{antihermitian-Sp-algebra} provides the block structure of the algebra based on U = exp(T) i.e. anti-hermitian generators
-  // P_{antihermitian} does in-adj(in) / 2
-  iMatrix<vtype,N> ret(arg);
-  double factor = (1.0/(double)N);
-  vtype nrm;
-  nrm = 0.5;
-    
-  ret = arg - (trace(arg)*factor);
-    
-  for(int c1=0;c1<N/2;c1++)
-  {
-      for(int c2=0;c2<N/2;c2++)
-      {
-          ret._internal[c1][c2] = nrm*(conjugate(ret._internal[c1+N/2][c2+N/2]) + ret._internal[c1][c2]); // new[up-left] = old[up-left]+old*[down-right]
-          ret._internal[c1][c2+N/2] = nrm*(ret._internal[c1][c2+N/2] - conjugate(ret._internal[c1+N/2][c2])); // new[up-right] = old[up-right]-old*[down-left]
-      }
-      for(int c2=N/2;c2<N;c2++)
-      {
-          ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);  //  reconstructs lower blocks
-          ret._internal[c1+N/2][c2] = conjugate(ret._internal[c1][c2-N/2]);   //  from upper blocks
-      }
-  }
-    
-  ret = (ret - adj(ret))*0.5;
-
-  return ret;
-}
 
 /////////////////////////////////////////////// 
 // ProjectOnGroup function for scalar, vector, matrix 
 // Projects on orthogonal, unitary group
 /////////////////////////////////////////////// 
 
+
 template<class vtype> accelerator_inline iScalar<vtype> ProjectOnGroup(const iScalar<vtype>&r)
 {
   iScalar<vtype> ret;
@@ -138,12 +90,10 @@ template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnGroup(c
 template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr> 
 accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
 {
-  typedef typename iMatrix<vtype,N>::scalar_type scalar;
   // need a check for the group type?
   iMatrix<vtype,N> ret(arg);
   vtype nrm;
   vtype inner;
-  scalar one(1.0);
   for(int c1=0;c1<N;c1++){
 
     // Normalises row c1
@@ -152,7 +102,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
       inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
 
     nrm = sqrt(inner);
-    nrm = one/nrm;
+    nrm = 1.0/nrm;
     for(int c2=0;c2<N;c2++)
       ret._internal[c1][c2]*= nrm;
       
@@ -177,7 +127,7 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
       inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
 
     nrm = sqrt(inner);
-    nrm = one/nrm;
+    nrm = 1.0/nrm;
     for(int c2=0;c2<N;c2++)
       ret._internal[c1][c2]*= nrm;
   }
@@ -185,85 +135,6 @@ accelerator_inline iMatrix<vtype,N> ProjectOnGroup(const iMatrix<vtype,N> &arg)
   return ret;
 }
 
-// re-do for sp2n
-
-// Ta cannot be defined here for Sp2n because I need the generators from the Sp class
-// It is defined in gauge impl types
-
-template<class vtype> accelerator_inline iScalar<vtype> ProjectOnSpGroup(const iScalar<vtype>&r)
-{
-  iScalar<vtype> ret;
-  ret._internal = ProjectOnSpGroup(r._internal);
-  return ret;
-}
-template<class vtype,int N> accelerator_inline iVector<vtype,N> ProjectOnSpGroup(const iVector<vtype,N>&r)
-{
-  iVector<vtype,N> ret;
-  for(int i=0;i<N;i++){
-    ret._internal[i] = ProjectOnSpGroup(r._internal[i]);
-  }
-  return ret;
-}
-
-
-// int N is 2n in Sp(2n)
-template<class vtype,int N, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0 >::type * =nullptr>
-accelerator_inline iMatrix<vtype,N> ProjectOnSpGroup(const iMatrix<vtype,N> &arg)
-{
-  // need a check for the group type?
-  iMatrix<vtype,N> ret(arg);
-  vtype nrm;
-  vtype inner;
-  
-  for(int c1=0;c1<N/2;c1++)
-  {
-      
-    for (int b=0; b<c1; b++)                  // remove the b-rows from U_c1
-    {
-      decltype(ret._internal[b][b]*ret._internal[b][b]) pr;
-      decltype(ret._internal[b][b]*ret._internal[b][b]) prn;
-      zeroit(pr);
-      zeroit(prn);
-          
-      for(int c=0; c<N; c++)
-      {
-        pr += conjugate(ret._internal[c1][c])*ret._internal[b][c];        // <U_c1 | U_b >
-        prn += conjugate(ret._internal[c1][c])*ret._internal[b+N/2][c];   // <U_c1 | U_{b+N} >
-      }
-       
-
-      for(int c=0; c<N; c++)
-      {
-        ret._internal[c1][c] -= (conjugate(pr) * ret._internal[b][c] + conjugate(prn) * ret._internal[b+N/2][c] );    //  U_c1 -= (  <U_c1 | U_b > U_b + <U_c1 | U_{b+N} > U_{b+N}  )
-      }
-    }
-    
-    zeroit(inner);
-    for(int c2=0;c2<N;c2++)
-    {
-      inner += innerProduct(ret._internal[c1][c2],ret._internal[c1][c2]);
-    }
-      
-    nrm = sqrt(inner);
-    nrm = 1.0/nrm;
-    for(int c2=0;c2<N;c2++)
-    {
-      ret._internal[c1][c2]*= nrm;
-    }
-      
-    for(int c2=0;c2<N/2;c2++)
-    {
-      ret._internal[c1+N/2][c2+N/2] = conjugate(ret._internal[c1][c2]);          // down right in the new matrix = (up-left)* of the old matrix
-    }
-      
-    for(int c2=N/2;c2<N;c2++)
-    {
-      ret._internal[c1+N/2][c2-N/2] = -conjugate(ret._internal[c1][c2]);;     // down left in the new matrix = -(up-right)* of the old
-    }
-  }
-  return ret;
-}
-
 NAMESPACE_END(Grid);
 
 #endif

Grid/tensors/Tensor_exp.h

@@ -53,6 +53,7 @@ template<class vtype, int N> accelerator_inline iVector<vtype, N> Exponentiate(c
 }
 
 
+
 // Specialisation: Cayley-Hamilton exponential for SU(3)
 #if 0
 template<class vtype, typename std::enable_if< GridTypeMapper<vtype>::TensorLevel == 0>::type * =nullptr> 

Grid/threads/Accelerator.h

@@ -137,18 +137,6 @@ 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,				\
@@ -169,20 +157,6 @@ 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)
 {
@@ -194,17 +168,6 @@ 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,
@@ -245,7 +208,6 @@ 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;
 };
@@ -498,9 +460,6 @@ 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

@@ -94,13 +94,6 @@ 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,int64_t index,const coor_t &dims){
+    static accelerator_inline void CoorFromIndex (coor_t& coor,int index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=0;d<nd;d++){
@@ -18,45 +18,28 @@ namespace Grid{
     }
 
     template<class coor_t>
-    static accelerator_inline void IndexFromCoor (const coor_t& coor,int64_t &index,const coor_t &dims){
+    static accelerator_inline void IndexFromCoor (const coor_t& coor,int &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=0;d<nd;d++){
-	index = index+(int64_t)stride*coor[d];
+	index = index+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,int64_t &index,const coor_t &dims){
+    static inline void IndexFromCoorReversed (const coor_t& coor,int &index,const coor_t &dims){
       int nd=dims.size();
       int stride=1;
       index=0;
       for(int d=nd-1;d>=0;d--){
-	index = index+(int64_t)stride*coor[d];
+	index = index+stride*coor[d];
 	stride=stride*dims[d];
       }
     }
     template<class coor_t>
-    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){
+    static inline void CoorFromIndexReversed (coor_t& coor,int index,const coor_t &dims){
       int nd= dims.size();
       coor.resize(nd);
       for(int d=nd-1;d>=0;d--){

configure.ac

@@ -41,7 +41,7 @@ AC_PROG_RANLIB
 
 ############### Get compiler informations
 AC_LANG([C++])
-AX_CXX_COMPILE_STDCXX(14,noext,mandatory)
+AX_CXX_COMPILE_STDCXX_11([noext],[mandatory])
 AX_COMPILER_VENDOR
 AC_DEFINE_UNQUOTED([CXX_COMP_VENDOR],["$ax_cv_cxx_compiler_vendor"],
       [vendor of C++ compiler that will compile the code])
@@ -191,28 +191,10 @@ case ${ac_Nc} in
         AC_DEFINE([Config_Nc],[4],[Gauge group Nc]);;
     5)
         AC_DEFINE([Config_Nc],[5],[Gauge group Nc]);;
-    8)
-        AC_DEFINE([Config_Nc],[8],[Gauge group Nc]);;
     *)
       AC_MSG_ERROR(["Unsupport gauge group choice Nc = ${ac_Nc}"]);;
 esac
 
-############### Symplectic group
-AC_ARG_ENABLE([Sp],
-    [AC_HELP_STRING([--enable-Sp=yes|no], [enable gauge group Sp2n])],
-    [ac_ENABLE_SP=${enable_Sp}], [ac_ENABLE_SP=no])
-
-AM_CONDITIONAL(BUILD_SP, [ test "${ac_ENABLE_SP}X" == "yesX" ])
-
-case ${ac_ENABLE_SP} in
-   yes)
-        AC_DEFINE([Sp2n_config],[1],[gauge group Sp2n], [have_sp2n=true]);;
-   no)
-        AC_DEFINE([Sp2n_config],[0],[gauge group SUn], [have_sp2n=false]);;
-    *)
-        AC_MSG_ERROR(["--enable-Sp is either yes or no"]);;
-esac
-
 ############### FP16 conversions
 AC_ARG_ENABLE([sfw-fp16],
     [AS_HELP_STRING([--enable-sfw-fp16=yes|no],[enable software fp16 comms])],
@@ -755,7 +737,7 @@ case ${ac_TIMERS} in
 esac
 
 ############### Chroma regression test
-AC_ARG_ENABLE([chroma],[AS_HELP_STRING([--enable-chroma],[Expect chroma compiled under c++14 ])],ac_CHROMA=yes,ac_CHROMA=no)
+AC_ARG_ENABLE([chroma],[AS_HELP_STRING([--enable-chroma],[Expect chroma compiled under c++11 ])],ac_CHROMA=yes,ac_CHROMA=no)
 
 case ${ac_CHROMA} in
      yes|no)
@@ -837,7 +819,6 @@ FFTW                        : `if test "x$have_fftw" = xtrue; then echo yes; els
 LIME (ILDG support)         : `if test "x$have_lime" = xtrue; then echo yes; else echo no; fi`
 HDF5                        : `if test "x$have_hdf5" = xtrue; then echo yes; else echo no; fi`
 build DOXYGEN documentation : `if test "$DX_FLAG_doc" = '1'; then echo yes; else echo no; fi`
-Sp2n                        : ${ac_ENABLE_SP}
 ----- BUILD FLAGS -------------------------------------
 CXXFLAGS:
 `echo ${AM_CXXFLAGS} ${CXXFLAGS} | tr ' ' '\n' | sed 's/^-/    -/g'`
@@ -866,7 +847,6 @@ AC_CONFIG_FILES(tests/lanczos/Makefile)
 AC_CONFIG_FILES(tests/smearing/Makefile)
 AC_CONFIG_FILES(tests/qdpxx/Makefile)
 AC_CONFIG_FILES(tests/testu01/Makefile)
-AC_CONFIG_FILES(tests/sp2n/Makefile)
 AC_CONFIG_FILES(benchmarks/Makefile)
 AC_CONFIG_FILES(examples/Makefile)
 AC_OUTPUT

documentation/GridXcode/readme.md

@@ -10,8 +10,9 @@ For first time setup of the Xcode and Grid build environment on Mac OS, you will
 
 1. Install Xcode and the Xcode command-line utilities
 2. Set Grid environment variables
-3. Install and build Grid pre-requisites
-4. Install, Configure and Build Grid
+3. Install and build Open MPI ***optional***
+4. Install and build Grid pre-requisites
+5. Install, Configure and Build Grid
 
 Apple's [Xcode website][Xcode] is the go-to reference for 1, and the definitive reference for 4 and 5 is the [Grid Documentation][GridDoc].
 
@@ -91,33 +92,60 @@ launchctl setenv GridPkg /opt/local</string>
 </plist>
 ```
 
-## 3. Install and build Grid pre-requisites
+## 3. Install and build Open MPI -- ***optional***
+
+Download the latest version of [Open MPI][OMPI] version 3.1 (I used 3.1.5) and build it like so:
+
+[OMPI]: https://www.open-mpi.org/software/ompi/v3.1/
+
+    ../configure CC=clang CXX=clang++ CXXFLAGS=-g --prefix=$GridPre/bin
+    make -j 4 all install
+
+***Note the `/bin` at the end of the prefix - this is required. As a quirk of the OpenMPI installer, `--prefix` must point to the `bin` subdirectory, with other files installed in `$GridPre/include`, `$GridPre/lib`, `$GridPre/share`, etc.***
+
+Grid does not have any dependencies on fortran, however many standard scientific packages do, so you may wish to download GNU fortran (e.g. MacPorts ``gfortran`` package) and add the following to your configure invocation:
+
+    F77=gfortran FC=gfortran
+
+## 4. Install and build Grid pre-requisites
 
 To simplify the installation of **Grid pre-requisites**, you can use your favourite package manager, e.g.:
 
-### 3.1. [MacPorts][MacPorts]
+### 1. [MacPorts][MacPorts]
 
 [MacPorts]: https://www.macports.org "MacPorts package manager"
 
 Install [MacPorts][MacPorts] if you haven't done so already, and then install packages with:
 
-    sudo port install openmpi git-flow-avh gmp hdf5 mpfr fftw-3-single lapack wget autoconf automake bison cmake gawk libomp
+    sudo port install <portname>
 
-On a Mac without GPUs:
+These are the `portname`s for mandatory Grid libraries:
 
-    sudo port install OpenBLAS +native
+* git-flow-avh
+* gmp
+* hdf5
+* mpfr
 
-To use `Gnu sha256sum`:
+and these are the `portname`s for optional Grid libraries:
 
-    pushd /opt/local/bin; sudo ln -s gsha256sum sha256sum; popd 
+* fftw-3-single
+* lapack
+* doxygen
+* OpenBLAS
 
-These `port`s are not strictly necessary, but they are helpful:
+***Please update this list with any packages I've missed! ... and double-check whether OpenBLAS is really for Grid. NB: lapack doesn't seem to work. Should it be scalapack?***
 
-    sudo port install gnuplot gsl h5utils nasm rclone texinfo tree xorg-server
+### 2. [Homebrew][Homebrew]
 
-***Please update this list with any packages I've missed!***
+[Homebrew]: https://brew.sh "Homebrew package manager"
 
-#### Install LIME
+Install [Homebrew][Homebrew] if you haven't done so already, and then install packages with:
+
+    sudo brew install <packagename>
+
+The same packages are available as from MacPorts.
+
+### Install LIME ***optional***
 
 There isn't currently a port for [C-LIME][C-LIME], so download the source and then build it:
 
@@ -126,19 +154,9 @@ There isn't currently a port for [C-LIME][C-LIME], so download the source and th
     ../configure CC=clang --prefix=$GridPre
     make -j 4 all install
 
-### 3.2. [Homebrew][Homebrew]
+## 5. Install, Configure and Build Grid
 
-[Homebrew]: https://brew.sh "Homebrew package manager"
-
-Install [Homebrew][Homebrew] if you haven't done so already, and then install packages with:
-
-    sudo brew install <packagename>
-
-I don't use Homebrew, so I'm not sure what the Brew package name equivalents are. ** Please update if you know **
-
-## 4. Install, Configure and Build Grid
-
-### 4.1 Install Grid
+### 5.1 Install Grid
 
 [Grid]: https://github.com/paboyle/Grid
 
@@ -156,7 +174,7 @@ or
 
 depending on how many times you like to enter your password.
 
-### 4.2 Configure Grid
+### 5.2 Configure Grid
 
 The Xcode build system supports multiple configurations for each project, by default: `Debug` and `Release`, but more configurations can be defined. We will create separate Grid build directories for each configuration, using the Grid **Autoconf** build system to make each configuration. NB: it is **not** necessary to run `make install` on them once they are built (IDE features such as *jump to definition* will work better of you don't).
 
@@ -180,7 +198,7 @@ Debug configuration with MPI:
 
     ../configure CXX=clang++ CXXFLAGS="-I$GridPkg/include/libomp -Xpreprocessor -fopenmp -std=c++11" LDFLAGS="-L$GridPkg/lib/libomp" LIBS="-lomp" --with-hdf5=$GridPkg --with-gmp=$GridPkg --with-mpfr=$GridPkg --with-fftw=$GridPkg --with-lime=$GridPre --enable-simd=GEN --enable-comms=mpi-auto MPICXX=$GridPre/bin/mpicxx --prefix=$GridPre/MPIDebug
 
-### 4.3 Build Grid
+### 5.3 Build Grid
 
 Each configuration must be built before they can be used. You can either:
 

documentation/manual.rst

@@ -2778,81 +2778,47 @@ and there are associated reconstruction routines for assembling four spinors fro
 
 These ca
 
-Gauge Group
+
+SU(N)
 --------
-A generic Nc qcd/utils/GaugeGroup.h is provided. This defines a template class that can be specialised to different gauge groups::
 
-  template <int ncolour, class group_name>
-  class GaugeGroup {...}
+A generic Nc qcd/utils/SUn.h is provided. This defines a template class::
 
-Supported groups are SU(N) and Sp(2N). The group can be specified through the GroupName namespace::
+  template <int ncolour> class SU ;
 
-  namespace GroupName {
-  class SU {};
-  class Sp {};
-  }
+The most important external methods are::
 
-A simpler interface is achieved by aliasing the GaugeGroup class with a specific group::
-
-  template <int ncolour>
-  using SU = GaugeGroup<ncolour, GroupName::SU>;
-
-  template <int ncolour>
-  using Sp = GaugeGroup<ncolour, GroupName::Sp>;
-  
-Specific aliases are then defined::
-
-  typedef SU<2> SU2;
-  typedef SU<3> SU3;
-  typedef SU<4> SU4;
-  typedef SU<5> SU5;
-  typedef Sp<2> Sp2;
-  typedef Sp<4> Sp4;
-  typedef Sp<6> Sp6;
-  typedef Sp<8> Sp8;
-
-Some methods are common to both gauge groups. Common external methods are::
-
-  template <class cplx>  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
-  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG, LatticeMatrix &out, Real scale = 1.0) ;
-  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
-  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
-  static void ColdConfiguration(GaugeField &out);
-  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out);
-  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
   static void printGenerators(void) ;
-   
-Whenever needed, a different implementation of these methods for the gauge groups is achieved by overloading. For example,::
-
-  template <typename LatticeMatrixType> //  shared interface for the traceless-antihermitian projection
-  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out) {
-    taProj(in, out, group_name());
-  }
-  
-  template <typename LatticeMatrixType> //  overloaded function to SU(N) simply perform Ta
-  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::SU) {
-    out = Ta(in);
-  }
-  
-  template <typename LatticeMatrixType> //  overloaded function to Sp(2N) must use a modified Ta function
-  static void taProj(const LatticeMatrixType &in, LatticeMatrixType &out, GroupName::Sp) {
-    out = SpTa(in);
-  }
-
-Gauge Group: SU(N)
---------
-The specialisation of GaugeGroup to SU(N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/SUn.impl
-It contains methods that are only implemented for SU(N), and specialisations of shared methods to the special unitary group
-
-Public methods are::
+  template <class cplx>  static void generator(int lieIndex, iSUnMatrix<cplx> &ta) ;
 
   static void SubGroupHeatBath(GridSerialRNG &sRNG, GridParallelRNG &pRNG, RealD beta,  // coeff multiplying staple in action (with no 1/Nc)
                                LatticeMatrix &link,
 			       const LatticeMatrix &barestaple,  // multiplied by action coeffs so th
 			       int su2_subgroup, int nheatbath, LatticeInteger &wheremask);
+
+  static void GaussianFundamentalLieAlgebraMatrix(GridParallelRNG &pRNG,
+                                                  LatticeMatrix &out,
+                                                  Real scale = 1.0) ;
   static void GaugeTransform( GaugeField &Umu, GaugeMat &g)
   static void RandomGaugeTransform(GridParallelRNG &pRNG, GaugeField &Umu, GaugeMat &g);
 
+  static void HotConfiguration(GridParallelRNG &pRNG, GaugeField &out) ;
+  static void TepidConfiguration(GridParallelRNG &pRNG,GaugeField &out);
+  static void ColdConfiguration(GaugeField &out);
+
+  static void taProj( const LatticeMatrixType &in,  LatticeMatrixType &out);
+  static void taExp(const LatticeMatrixType &x, LatticeMatrixType &ex) ;
+
+  static int su2subgroups(void) ; // returns how many subgroups
+
+
+Specific instantiations are defined::
+
+	 typedef SU<2> SU2;
+	 typedef SU<3> SU3;
+	 typedef SU<4> SU4;
+	 typedef SU<5> SU5;
+
 For example, Quenched QCD updating may be run as (tests/core/Test_quenched_update.cc)::
 
   for(int sweep=0;sweep<1000;sweep++){
@@ -2891,16 +2857,6 @@ For example, Quenched QCD updating may be run as (tests/core/Test_quenched_updat
     }
   }
 
-Gauge Group: Sp(2N)
---------
-The specialisation of GaugeGroup to Sp(2N), formally part of qcd/utils/GaugeGroup.h, is found in the file qcd/utils/Sp(2N).impl
-It contains methods that are only implemented for Sp(2N), and specialisations of shared methods to the special unitary group
-
-External methods are::
-
-  static void Omega(LatticeColourMatrixD &in) // Symplectic matrix left invariant by Sp(2N)
-
-Generation of Sp(2N) gauge fields is only supported via HMC.
 
 Space time grids
 ----------------

scripts/filelist

@@ -15,8 +15,6 @@ STAG_FERMION_FILES=`  find . -name '*.cc' -path '*/instantiation/*' -path '*/ins
 GP_FERMION_FILES=`    find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/Gparity*' `
 ADJ_FERMION_FILES=`   find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonAdj*' `
 TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/WilsonTwoIndex*'`
-SP_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonImpl*'`
-SP_TWOIND_FERMION_FILES=`find . -name '*.cc' -path '*/instantiation/*' -path '*/instantiation/SpWilsonTwo*'`
 
 HPPFILES=`find . -type f -name '*.hpp'`
 echo HFILES=$HFILES $HPPFILES > Make.inc
@@ -29,14 +27,13 @@ echo STAG_FERMION_FILES=$STAG_FERMION_FILES   >> Make.inc
 echo GP_FERMION_FILES=$GP_FERMION_FILES   >> Make.inc
 echo ADJ_FERMION_FILES=$ADJ_FERMION_FILES   >> Make.inc
 echo TWOIND_FERMION_FILES=$TWOIND_FERMION_FILES   >> Make.inc
-echo SP_FERMION_FILES=$SP_FERMION_FILES >> Make.inc
-echo SP_TWOIND_FERMION_FILES=$SP_TWOIND_FERMION_FILES >> Make.inc
 
 # tests Make.inc
 cd $home/tests
 dirs=`find . -type d -not -path '*/\.*'`
 for subdir in $dirs; do
     cd $home/tests/$subdir
+    pwd
     TESTS=`ls T*.cc`
     TESTLIST=`echo ${TESTS} | sed s/.cc//g `
     PREF=`[ $subdir = '.' ] && echo noinst || echo EXTRA`

systems/Frontier/benchmarks/bench2.slurm

@@ -1,43 +0,0 @@
-#!/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

@@ -1,23 +0,0 @@
-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

@@ -1,13 +0,0 @@
-#!/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

@@ -1,13 +0,0 @@
-. /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

@@ -1,9 +0,0 @@
-#!/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/OEM/README

@@ -1,53 +0,0 @@
-1. Prerequisites:
-===================
-Make sure you have the latest Intel ipcx release loaded (via modules or similar)
-Make sure you have SYCL aware MPICH or Intel MPI loaded (assumed as mpicxx)
-
-2. Obtain Grid:
-===================
-
-bash$
-git clone https://github.com/paboyle/Grid
-cd Grid
-./bootstrap.sh
-cd systems/PVC
-
-3. Build Grid:
-===================
-
-Here, configure command is stored in file config-command:
-
-bash$
-../../configure \
-	--enable-simd=GPU \
-	--enable-gen-simd-width=64 \
-	--enable-comms=mpi-auto \
-	--enable-accelerator-cshift \
-	--disable-gparity \
-	--disable-fermion-reps \
-	--enable-shm=nvlink \
-	--enable-accelerator=sycl \
-	--enable-unified=no \
-	MPICXX=mpicxx \
-	CXX=icpx \
-	LDFLAGS="-fiopenmp  -fsycl -fsycl-device-code-split=per_kernel -fsycl-device-lib=all -lze_loader " \
-	CXXFLAGS="-fiopenmp -fsycl-unnamed-lambda -fsycl -Wno-tautological-compare "
-
-make all
-
-4. Run a benchmark:
-===================
-
-*** Assumes interactive access to node. ***
-
-run Benchmark_dwf_fp32 using benchmarks/bench.sh
-
-bash$
-cd benchmarks
-./bench.sh
-
-
-
-
-
-

systems/OEM/benchmarks/bench.sh

@@ -1,18 +0,0 @@
-#!/bin/bash
-
-export EnableImplicitScaling=0
-export ZE_ENABLE_PCI_ID_DEVICE_ORDER=1
-export ZE_AFFINITY_MASK=$gpu_id.$tile_id
-export ONEAPI_DEVICE_FILTER=gpu,level_zero
-export SYCL_PI_LEVEL_ZERO_DEVICE_SCOPE_EVENTS=0
-export SYCL_PI_LEVEL_ZERO_USE_IMMEDIATE_COMMANDLISTS=1
-export SYCL_PI_LEVEL_ZERO_USE_COPY_ENGINE=0:2
-export SYCL_PI_LEVEL_ZERO_USE_COPY_ENGINE_FOR_D2D_COPY=1
-
-mpiexec -launcher ssh -n 1 -host localhost ./select_gpu.sh ./Benchmark_dwf_fp32 --mpi 1.1.1.1 --grid 32.32.32.32 --accelerator-threads 16 --shm-mpi 1 --shm 2048 --device-mem 32768 | tee 1tile.log
-mpiexec -launcher ssh -n 2 -host localhost ./select_gpu.sh ./Benchmark_dwf_fp32 --mpi 1.1.1.2 --grid 32.32.32.64 --accelerator-threads 16 --shm-mpi 1 --shm 2048 --device-mem 32768 | tee 2tile.log
-
-#mpiexec -launcher ssh -n 4 -host localhost ./select_gpu.sh ./Benchmark_dwf_fp32 --mpi 1.1.2.2 --grid 16.16.64.64 --accelerator-threads 16 --shm-mpi 0 --shm 2048 --device-mem 32768 | tee 4tile.log
-#mpiexec -launcher ssh -n 8 -host localhost ./select_gpu.sh ./Benchmark_dwf_fp32 --mpi 1.1.2.4 --grid 16.16.64.128 --accelerator-threads 16 --shm-mpi 0 --shm 2048 --device-mem 32768 | tee 8tile.log
-
-

systems/OEM/benchmarks/select_gpu.sh

@@ -1,13 +0,0 @@
-#!/bin/bash
-
-num_tile=2
-
-gpu_id=$(( (MPI_LOCAL_RANKID % num_tile ) ))
-tile_id=$((MPI_LOCAL_RANKID / num_tile))
-
-export ZE_AFFINITY_MASK=$gpu_id.$tile_id
-
-echo "local rank $MPI_LOCALRANKID ; ZE_AFFINITY_MASK=$ZE_AFFINITY_MASK"
-
-"$@"
-

systems/OEM/config-command

@@ -1,15 +0,0 @@
-../../configure \
-	--enable-simd=GPU \
-	--enable-gen-simd-width=64 \
-	--enable-comms=mpi-auto \
-	--enable-accelerator-cshift \
-	--disable-gparity \
-	--disable-fermion-reps \
-	--enable-shm=nvlink \
-	--enable-accelerator=sycl \
-	--enable-unified=no \
-	MPICXX=mpicxx \
-	CXX=icpx \
-	LDFLAGS="-fiopenmp  -fsycl -fsycl-device-code-split=per_kernel -fsycl-device-lib=all -lze_loader " \
-	CXXFLAGS="-fiopenmp -fsycl-unnamed-lambda -fsycl -Wno-tautological-compare "
-

systems/OEM/setup.sh

@@ -1,3 +0,0 @@
-export https_proxy=http://proxy-chain.intel.com:911
-module load intel-release
-module load intel/mpich

systems/mac-arm/config-command-mpi

@@ -1,3 +1,4 @@
 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
+CXX=mpicxx-openmpi-mp ../../configure --enable-simd=GEN --enable-comms=mpi --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/Makefile.am

@@ -1,4 +1,4 @@
-SUBDIRS = . core forces hmc solver debug smearing IO lanczos sp2n
+SUBDIRS = . core forces hmc solver debug smearing IO lanczos
 
 if BUILD_CHROMA_REGRESSION
   SUBDIRS+= qdpxx

tests/core/Test_compact_wilson_clover_speedup.cc

@@ -218,9 +218,9 @@ void runBenchmark(int* argc, char*** argv) {
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
-#if Nc==3
+
   runBenchmark<vComplexD>(&argc, &argv);
   runBenchmark<vComplexF>(&argc, &argv);
-#endif
+
   Grid_finalize();
 }

tests/core/Test_lie_generators.cc

@@ -29,14 +29,13 @@ See the full license in the file "LICENSE" in the top level distribution
 directory
 *************************************************************************************/
 /*  END LEGAL */
-
 #include <Grid/Grid.h>
 
 #include <Grid/qcd/utils/CovariantCshift.h>
 
-#include <Grid/qcd/utils/GaugeGroup.h>
+#include <Grid/qcd/utils/SUn.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
+#include <Grid/qcd/utils/SUnTwoIndex.h>
 
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
@@ -44,6 +43,7 @@ directory
 
 using namespace std;
 using namespace Grid;
+;
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
@@ -62,17 +62,20 @@ int main(int argc, char** argv) {
   SU2::printGenerators();
   std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << std::endl;
 
-  std::cout << " Printing  Adjoint Generators"<< std::endl;
+  // guard as this code fails to compile for Nc != 3
+#if 1
 
+  std::cout << " Printing  Adjoint Generators"<< std::endl;
+    
   SU2Adjoint::printGenerators();
   SU2::testGenerators();
   SU2Adjoint::testGenerators();
-
+    
   std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
-  std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
+	    << std::endl;
+  std::cout << GridLogMessage << "* Generators for SU(Nc" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
-            << std::endl;
+	    << std::endl;
   SU3::printGenerators();
   std::cout << "Dimension of adjoint representation: "<< SU3Adjoint::Dimension << std::endl;
   SU3Adjoint::printGenerators();
@@ -91,22 +94,22 @@ int main(int argc, char** argv) {
   // Projectors 
   GridParallelRNG gridRNG(grid);
   gridRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
-  SU_Adjoint<Nc>::LatticeAdjMatrix Gauss(grid);
-  SU<Nc>::LatticeAlgebraVector ha(grid);
-  SU<Nc>::LatticeAlgebraVector hb(grid);
+  SU3Adjoint::LatticeAdjMatrix Gauss(grid);
+  SU3::LatticeAlgebraVector ha(grid);
+  SU3::LatticeAlgebraVector hb(grid);
   random(gridRNG,Gauss);
 
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU_Adjoint<Nc>::projectOnAlgebra(ha, Gauss);
+  SU3Adjoint::projectOnAlgebra(ha, Gauss);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU_Adjoint<Nc>::projector(hb, Gauss);
+  SU3Adjoint::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
 
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU_Adjoint<Nc>::projector(hb, Gauss);
+  SU3Adjoint::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU<Nc>::LatticeAlgebraVector diff = ha -hb;
+  SU3::LatticeAlgebraVector diff = ha -hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
 
 
@@ -116,17 +119,17 @@ int main(int argc, char** argv) {
   // AdjointRepresentation has the predefined number of colours Nc
   //  Representations<FundamentalRepresentation, AdjointRepresentation, TwoIndexSymmetricRepresentation> RepresentationTypes(grid);  
   LatticeGaugeField U(grid), V(grid);
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V);
-
+  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U);
+  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V);
+    
   // Adjoint representation
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r
   LatticeGaugeField UV(grid);
   UV = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
-    SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
+    SU3::LatticeMatrix Umu = peekLorentz(U,mu);
+    SU3::LatticeMatrix Vmu = peekLorentz(V,mu);
     pokeLorentz(UV,Umu*Vmu, mu);
   }
     
@@ -148,7 +151,6 @@ int main(int argc, char** argv) {
     pokeLorentz(UrVr,Urmu*Vrmu, mu);
   }
 
-#if Nc==3
   typedef typename SU_Adjoint<Nc>::AMatrix AdjointMatrix;
   typename AdjointRep<Nc>::LatticeField Diff_check = UVr - UrVr;
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Adjoint representation) : " << norm2(Diff_check) << std::endl;
@@ -174,19 +176,19 @@ int main(int argc, char** argv) {
     assert(abs( (2.0*tr1-tr2) ) < 1.0e-7);
     std::cout << "------------------"<<std::endl;
   }}}
-#endif
+  
   // Check correspondence of algebra and group transformations
   // Create a random vector
-  SU<Nc>::LatticeAlgebraVector h_adj(grid);
+  SU3::LatticeAlgebraVector h_adj(grid);
   typename AdjointRep<Nc>::LatticeMatrix Ar(grid);
   random(gridRNG,h_adj);
   h_adj = real(h_adj);
   SU_Adjoint<Nc>::AdjointLieAlgebraMatrix(h_adj,Ar);
     
   // Re-extract h_adj
-  SU<Nc>::LatticeAlgebraVector h_adj2(grid);
+  SU3::LatticeAlgebraVector h_adj2(grid);
   SU_Adjoint<Nc>::projectOnAlgebra(h_adj2, Ar);
-  SU<Nc>::LatticeAlgebraVector h_diff = h_adj - h_adj2;
+  SU3::LatticeAlgebraVector h_diff = h_adj - h_adj2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Adjoint representation) : " << norm2(h_diff) << std::endl;
     
   // Exponentiate
@@ -208,14 +210,14 @@ int main(int argc, char** argv) {
 	    << std::endl;
     
   // Construct the fundamental matrix in the group
-  SU<Nc>::LatticeMatrix Af(grid);
-  SU<Nc>::FundamentalLieAlgebraMatrix(h_adj,Af);
-  SU<Nc>::LatticeMatrix Ufund(grid);
+  SU3::LatticeMatrix Af(grid);
+  SU3::FundamentalLieAlgebraMatrix(h_adj,Af);
+  SU3::LatticeMatrix Ufund(grid);
   Ufund  = expMat(Af, 1.0, 16);
   // Check unitarity
-  SU<Nc>::LatticeMatrix uno_f(grid);
+  SU3::LatticeMatrix uno_f(grid);
   uno_f = 1.0;
-  SU<Nc>::LatticeMatrix UnitCheck(grid);
+  SU3::LatticeMatrix UnitCheck(grid);
   UnitCheck = Ufund * adj(Ufund) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck)
 	    << std::endl;
@@ -278,20 +280,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two Index Symmetric projectors"
 	    << std::endl;
   // Projectors 
-  SU_TwoIndex<Nc, Symmetric>::LatticeTwoIndexMatrix Gauss2(grid);
+  SU3TwoIndexSymm::LatticeTwoIndexMatrix Gauss2(grid);
   random(gridRNG,Gauss2);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU_TwoIndex<Nc, Symmetric>::projectOnAlgebra(ha, Gauss2);
+  SU3TwoIndexSymm::projectOnAlgebra(ha, Gauss2);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
+  SU3TwoIndexSymm::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
+  SU3TwoIndexSymm::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU<Nc>::LatticeAlgebraVector diff2 = ha - hb;
+  SU3::LatticeAlgebraVector diff2 = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
 	    << std::endl;
@@ -302,20 +304,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two index anti-Symmetric projectors"
 	    << std::endl;
   // Projectors
-  SU_TwoIndex<Nc, AntiSymmetric>::LatticeTwoIndexMatrix Gauss2a(grid);
+  SU3TwoIndexAntiSymm::LatticeTwoIndexMatrix Gauss2a(grid);
   random(gridRNG,Gauss2a);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU_TwoIndex<Nc, AntiSymmetric>::projectOnAlgebra(ha, Gauss2a);
+  SU3TwoIndexAntiSymm::projectOnAlgebra(ha, Gauss2a);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
+  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
+  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU<Nc>::LatticeAlgebraVector diff2a = ha - hb;
+  SU3::LatticeAlgebraVector diff2a = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff2a) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
 	    << std::endl;
@@ -324,59 +326,55 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Two index Symmetric: Checking Group Structure"
 	    << std::endl;
   // Testing HMC representation classes
-  TwoIndexRep< Nc, Symmetric> TIndexRep(grid);
+  TwoIndexRep< Nc, Symmetric > TIndexRep(grid);
 
   // Test group structure
   // (U_f * V_f)_r = U_r * V_r
   LatticeGaugeField U2(grid), V2(grid);
-
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
-
+  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
+  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
+    
   LatticeGaugeField UV2(grid);
   UV2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU<Nc>::LatticeMatrix Umu2 = peekLorentz(U2,mu);
-    SU<Nc>::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
+    SU3::LatticeMatrix Umu2 = peekLorentz(U2,mu);
+    SU3::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
     pokeLorentz(UV2,Umu2*Vmu2, mu);
   }
     
   TIndexRep.update_representation(UV2);
-
   typename TwoIndexRep< Nc, Symmetric >::LatticeField UVr2 = TIndexRep.U;  // (U_f * V_f)_r
-  
+    
   TIndexRep.update_representation(U2);
   typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2 = TIndexRep.U;  // U_r
-  
+    
   TIndexRep.update_representation(V2);
   typename TwoIndexRep< Nc, Symmetric >::LatticeField Vr2 = TIndexRep.U;  // V_r
     
   typename TwoIndexRep< Nc, Symmetric >::LatticeField Ur2Vr2(grid);
-
   Ur2Vr2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
-    typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
+    typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Urmu2 = peekLorentz(Ur2,mu);
+    typename TwoIndexRep< Nc, Symmetric >::LatticeMatrix Vrmu2 = peekLorentz(Vr2,mu);
     pokeLorentz(Ur2Vr2,Urmu2*Vrmu2, mu);
   }
     
   typename TwoIndexRep< Nc, Symmetric >::LatticeField Diff_check2 = UVr2 - Ur2Vr2;
-
   std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index Symmetric): " << norm2(Diff_check2) << std::endl;
     
     
   // Check correspondence of algebra and group transformations
   // Create a random vector
-  SU<Nc>::LatticeAlgebraVector h_sym(grid);
+  SU3::LatticeAlgebraVector h_sym(grid);
   typename TwoIndexRep< Nc, Symmetric>::LatticeMatrix Ar_sym(grid);
   random(gridRNG,h_sym);
   h_sym = real(h_sym);
   SU_TwoIndex<Nc,Symmetric>::TwoIndexLieAlgebraMatrix(h_sym,Ar_sym);
     
   // Re-extract h_sym
-  SU<Nc>::LatticeAlgebraVector h_sym2(grid);
+  SU3::LatticeAlgebraVector h_sym2(grid);
   SU_TwoIndex< Nc, Symmetric>::projectOnAlgebra(h_sym2, Ar_sym);
-  SU<Nc>::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
+  SU3::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Two Index Symmetric): " << norm2(h_diff_sym) << std::endl;
     
   // Exponentiate
@@ -398,11 +396,11 @@ int main(int argc, char** argv) {
 	    << std::endl;
     
   // Construct the fundamental matrix in the group
-  SU<Nc>::LatticeMatrix Af_sym(grid);
-  SU<Nc>::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
-  SU<Nc>::LatticeMatrix Ufund2(grid);
+  SU3::LatticeMatrix Af_sym(grid);
+  SU3::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
+  SU3::LatticeMatrix Ufund2(grid);
   Ufund2  = expMat(Af_sym, 1.0, 16);
-  SU<Nc>::LatticeMatrix UnitCheck2(grid);
+  SU3::LatticeMatrix UnitCheck2(grid);
   UnitCheck2 = Ufund2 * adj(Ufund2) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2)
 	    << std::endl;
@@ -427,113 +425,115 @@ int main(int argc, char** argv) {
     std::cout << GridLogMessage << "*********************************************"
 	      << std::endl;
     
-  std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
-      << std::endl;
-  // Testing HMC representation classes
-  TwoIndexRep< Nc, AntiSymmetric> TIndexRepA(grid);
-
-
-  // Test group structure
-  // (U_f * V_f)_r = U_r * V_r
-  LatticeGaugeField U2A(grid), V2A(grid);
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
-  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
   
-  LatticeGaugeField UV2A(grid);
-  UV2A = Zero();
-  for (int mu = 0; mu < Nd; mu++) {
-    SU<Nc>::LatticeMatrix Umu2A = peekLorentz(U2,mu);
-    SU<Nc>::LatticeMatrix Vmu2A = peekLorentz(V2,mu);
-    pokeLorentz(UV2A,Umu2A*Vmu2A, mu);
+    std::cout << GridLogMessage << "Two Index anti-Symmetric: Check Group Structure"
+	      << std::endl;
+    // Testing HMC representation classes
+    TwoIndexRep< Nc, AntiSymmetric > TIndexRepA(grid);
+
+
+    // Test group structure
+    // (U_f * V_f)_r = U_r * V_r
+    LatticeGaugeField U2A(grid), V2A(grid);
+    SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2A);
+    SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2A);
+  
+    LatticeGaugeField UV2A(grid);
+    UV2A = Zero();
+    for (int mu = 0; mu < Nd; mu++) {
+      SU3::LatticeMatrix Umu2A = peekLorentz(U2,mu);
+      SU3::LatticeMatrix Vmu2A = peekLorentz(V2,mu);
+      pokeLorentz(UV2A,Umu2A*Vmu2A, mu);
+    }
+  
+    TIndexRep.update_representation(UV2A);
+    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
+  
+    TIndexRep.update_representation(U2A);
+    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2A = TIndexRepA.U;  // U_r
+  
+    TIndexRep.update_representation(V2A);
+    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Vr2A = TIndexRepA.U;  // V_r
+  
+    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Ur2Vr2A(grid);
+    Ur2Vr2A = Zero();
+    for (int mu = 0; mu < Nd; mu++) {
+      typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
+      typename TwoIndexRep< Nc, AntiSymmetric >::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
+      pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
+    }
+  
+    typename TwoIndexRep< Nc, AntiSymmetric >::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
+    std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
+
+  
+    // Check correspondence of algebra and group transformations
+    // Create a random vector
+    SU3::LatticeAlgebraVector h_Asym(grid);
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
+    random(gridRNG,h_Asym);
+    h_Asym = real(h_Asym);
+    SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
+  
+    // Re-extract h_sym
+    SU3::LatticeAlgebraVector h_Asym2(grid);
+    SU_TwoIndex< Nc, AntiSymmetric>::projectOnAlgebra(h_Asym2, Ar_Asym);
+    SU3::LatticeAlgebraVector h_diff_Asym = h_Asym - h_Asym2;
+    std::cout << GridLogMessage << "Projections structure check vector difference (Two Index anti-Symmetric): " << norm2(h_diff_Asym) << std::endl;
+
+  
+    // Exponentiate
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
+    U2iAS  = expMat(Ar_Asym, 1.0, 16);
+  
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
+    uno2iAS = 1.0;
+    // Check matrix U2iS, must be real orthogonal
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
+    std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
+	      << std::endl;
+  
+    Ucheck2iAS = U2iAS * adj(U2iAS) - uno2iAS;
+    std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck2iAS)
+	      << std::endl;
+    Ucheck2iAS = adj(U2iAS) * U2iAS - uno2iAS;
+    std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck2iAS)
+	      << std::endl;
+  
+  
+  
+    // Construct the fundamental matrix in the group
+    SU3::LatticeMatrix Af_Asym(grid);
+    SU3::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
+    SU3::LatticeMatrix Ufund2A(grid);
+    Ufund2A  = expMat(Af_Asym, 1.0, 16);
+    SU3::LatticeMatrix UnitCheck2A(grid);
+    UnitCheck2A = Ufund2A * adj(Ufund2A) - uno_f;
+    std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2A)
+	      << std::endl;
+    UnitCheck2A = adj(Ufund2A) * Ufund2A - uno_f;
+    std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck2A)
+	      << std::endl;
+  
+
+    // Tranform to the 2Index Sym representation
+    U = Zero(); // fill this with only one direction
+    pokeLorentz(U,Ufund2A,0); // the representation transf acts on full gauge fields
+  
+    TIndexRepA.update_representation(U);
+    Ur2A = TIndexRepA.U;  // U_r  
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
+  
+    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
+    std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
+  
+  } else  {
+    std::cout << GridLogMessage << "Skipping Two Index anti-Symmetric tests "
+      "because representation is trivial (dim = 1)"
+	      << std::endl;
   }
-  
-  TIndexRep.update_representation(UV2A);
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField UVr2A = TIndexRepA.U;  // (U_f * V_f)_r
-  
-  TIndexRep.update_representation(U2A);
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2A = TIndexRepA.U;  // U_r
-  
-  TIndexRep.update_representation(V2A);
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Vr2A = TIndexRepA.U;  // V_r
-  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Ur2Vr2A(grid);
-  Ur2Vr2A = Zero();
-  for (int mu = 0; mu < Nd; mu++) {
-    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Urmu2A = peekLorentz(Ur2A,mu);
-    typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Vrmu2A = peekLorentz(Vr2A,mu);
-    pokeLorentz(Ur2Vr2A,Urmu2A*Vrmu2A, mu);
-  }
-  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeField Diff_check2A = UVr2A - Ur2Vr2A;
-  std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference (Two Index anti-Symmetric): " << norm2(Diff_check2A) << std::endl;
 
-  
-  // Check correspondence of algebra and group transformations
-  // Create a random vector
-  SU<Nc>::LatticeAlgebraVector h_Asym(grid);
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ar_Asym(grid);
-  random(gridRNG,h_Asym);
-  h_Asym = real(h_Asym);
-  SU_TwoIndex< Nc, AntiSymmetric>::TwoIndexLieAlgebraMatrix(h_Asym,Ar_Asym);
-  
-  // Re-extract h_sym
-  SU<Nc>::LatticeAlgebraVector h_Asym2(grid);
-  SU_TwoIndex< Nc, AntiSymmetric>::projectOnAlgebra(h_Asym2, Ar_Asym);
-  SU<Nc>::LatticeAlgebraVector h_diff_Asym = h_Asym - h_Asym2;
-  std::cout << GridLogMessage << "Projections structure check vector difference (Two Index anti-Symmetric): " << norm2(h_diff_Asym) << std::endl;
-
-  
-  // Exponentiate
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix U2iAS(grid);
-  U2iAS  = expMat(Ar_Asym, 1.0, 16);
-  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix uno2iAS(grid);
-  uno2iAS = 1.0;
-  // Check matrix U2iS, must be real orthogonal
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ucheck2iAS = U2iAS - conjugate(U2iAS);
-  std::cout << GridLogMessage << "Reality check: " << norm2(Ucheck2iAS)
-      << std::endl;
-  
-  Ucheck2iAS = U2iAS * adj(U2iAS) - uno2iAS;
-  std::cout << GridLogMessage << "orthogonality check 1: " << norm2(Ucheck2iAS)
-      << std::endl;
-  Ucheck2iAS = adj(U2iAS) * U2iAS - uno2iAS;
-  std::cout << GridLogMessage << "orthogonality check 2: " << norm2(Ucheck2iAS)
-      << std::endl;
-  
-  
-  
-  // Construct the fundamental matrix in the group
-  SU<Nc>::LatticeMatrix Af_Asym(grid);
-  SU<Nc>::FundamentalLieAlgebraMatrix(h_Asym,Af_Asym);
-  SU<Nc>::LatticeMatrix Ufund2A(grid);
-  Ufund2A  = expMat(Af_Asym, 1.0, 16);
-  SU<Nc>::LatticeMatrix UnitCheck2A(grid);
-  UnitCheck2A = Ufund2A * adj(Ufund2A) - uno_f;
-  std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2A)
-      << std::endl;
-  UnitCheck2A = adj(Ufund2A) * Ufund2A - uno_f;
-  std::cout << GridLogMessage << "unitarity check 2: " << norm2(UnitCheck2A)
-      << std::endl;
-  
-
-  // Tranform to the 2Index Sym representation
-  U = Zero(); // fill this with only one direction
-  pokeLorentz(U,Ufund2A,0); // the representation transf acts on full gauge fields
-  
-  TIndexRepA.update_representation(U);
-  Ur2A = TIndexRepA.U;  // U_r  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Ur02A = peekLorentz(Ur2A,0); // this should be the same as U2iS
-  
-  typename TwoIndexRep< Nc, AntiSymmetric>::LatticeMatrix Diff_check_mat2A = Ur02A - U2iAS;
-  std::cout << GridLogMessage << "Projections structure check group difference (Two Index anti-Symmetric): " << norm2(Diff_check_mat2A) << std::endl;
-  
-} else  {
-  std::cout << GridLogMessage << "Skipping Two Index anti-Symmetric tests "
-                                 "because representation is trivial (dim = 1)"
-            << std::endl;
-}
+#endif
   
   Grid_finalize();
 }
-