coalescedReadGeneralPermute now working

Feature/paddedcellgauge

Grid/Makefile.am

@@ -66,6 +66,10 @@ 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/GeneralCoarsenedMatrix.h

@@ -344,8 +344,8 @@ public:
 	    int ss = sss/nbasis;
 	    int b  = sss%nbasis;
 
-	    auto SE = Stencil_v.GetEntry(point,ss);
-	    auto nbr = coalescedRead(in_v[SE->_offset]);
+	    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);

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::level_zero>(theGridAccelerator->get_device());
-    auto zeContext   = cl::sycl::get_native<cl::sycl::backend::level_zero>(theGridAccelerator->get_context());
+    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());
       
     ze_ipc_mem_handle_t ihandle;
     clone_mem_t handle;

Grid/lattice/Lattice.h

@@ -47,3 +47,4 @@ 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

@@ -345,7 +345,9 @@ 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));
@@ -456,7 +458,9 @@ 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_trace.h

@@ -66,6 +66,65 @@ 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

@@ -697,8 +697,68 @@ 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;
@@ -738,6 +798,8 @@ void localCopyRegion(const Lattice<vobj> &From,Lattice<vobj> & To,Coordinate Fro
 #endif
     }
   });
+
+#endif
 }
 
 
@@ -830,6 +892,8 @@ 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)
 {
@@ -851,6 +915,65 @@ 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);
@@ -866,6 +989,7 @@ void InsertSliceLocal(const Lattice<vobj> &lowDim, Lattice<vobj> & higherDim,int
       pokeLocalSite(s,higherDimv,hcoor);
     }
   });
+#endif
 }
 
 

Grid/lattice/PaddedCell.h

@@ -26,14 +26,32 @@ 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();
@@ -78,7 +96,7 @@ public:
     }
   };
   template<class vobj>
-  inline Lattice<vobj> Extract(Lattice<vobj> &in)
+  inline Lattice<vobj> Extract(const Lattice<vobj> &in) const
   {
     Lattice<vobj> out(unpadded_grid);
 
@@ -89,19 +107,19 @@ public:
     return out;
   }
   template<class vobj>
-  inline Lattice<vobj> Exchange(Lattice<vobj> &in)
+  inline Lattice<vobj> Exchange(const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
     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); // rvalue && assignment
+      tmp = Expand(d,tmp,cshift); // rvalue && assignment
     }
     return tmp;
   }
   // expand up one dim at a time
   template<class vobj>
-  inline Lattice<vobj> Expand(int dim,Lattice<vobj> &in)
+  inline Lattice<vobj> Expand(int dim, const Lattice<vobj> &in, const CshiftImplBase<vobj> &cshift = CshiftImplDefault<vobj>()) const
   {
     GridBase *old_grid = in.Grid();
     GridCartesian *new_grid = grids[dim];//These are new grids
@@ -112,21 +130,41 @@ public:
     if(dim==0) conformable(old_grid,unpadded_grid);
     else       conformable(old_grid,grids[dim-1]);
 
-    //    std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
+    std::cout << " dim "<<dim<<" local "<<local << " padding to "<<plocal<<std::endl;
+
+    double tins=0, tshift=0;
+    
     // 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
-    shifted = Cshift(in,dim,depth);
+    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
-    shifted = Cshift(in,dim,-depth);
+    t = usecond();
+    shifted = cshift.Cshift(in,dim,-depth);
+    tshift += usecond() - t;
+    
+    t = usecond();
     for(int x=0;x<depth;x++){
       InsertSliceLocal(shifted,padded,x,x,dim);
     }
+    tins += usecond() - t;
+
+    std::cout << GridLogPerformance << "PaddedCell::Expand timings: cshift:" << tshift/1000 << "ms, insert-slice:" << tins/1000 << "ms" << std::endl;
+    
     return padded;
   }
 

Grid/qcd/action/fermion/Fermion.h

@@ -126,6 +126,16 @@ 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/WilsonImpl.h

@@ -261,6 +261,22 @@ 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/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

@@ -10,12 +10,18 @@ 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

@@ -39,6 +39,9 @@ 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 GaugeImplTypes {
+template <class S, int Nrepresentation = Nc, int Nexp = 12, class Group = SU<Nc> > class GaugeImplTypes {
 public:
   typedef S Simd;
   typedef typename Simd::scalar_type scalar_type;
@@ -78,8 +78,6 @@ 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
@@ -119,6 +117,7 @@ public:
     //
     LinkField Pmu(P.Grid());
     Pmu = Zero();
+
     for (int mu = 0; mu < Nd; mu++) {
       Group::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
       RealD scale = ::sqrt(HMC_MOMENTUM_DENOMINATOR) ;
@@ -126,8 +125,12 @@ public:
       PokeIndex<LorentzIndex>(P, Pmu, mu);
     }
   }
-
-  static inline Field projectForce(Field &P) { return Ta(P); }
+    
+  static inline Field projectForce(Field &P) {
+      Field ret(P.Grid());
+      Group::taProj(P, ret);
+      return ret;
+    }
 
   static inline void update_field(Field& P, Field& U, double ep){
     //static std::chrono::duration<double> diff;
@@ -137,14 +140,15 @@ public:
     autoView(P_v,P,AcceleratorRead);
     accelerator_for(ss, P.Grid()->oSites(),1,{
       for (int mu = 0; mu < Nd; mu++) {
-        U_v[ss](mu) = ProjectOnGroup(Exponentiate(P_v[ss](mu), ep, Nexp) * U_v[ss](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));
       }
     });
    //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();
@@ -157,7 +161,7 @@ public:
   }
 
   static inline void Project(Field &U) {
-    ProjectSUn(U);
+    Group::ProjectOnSpecialGroup(U);
   }
 
   static inline void HotConfiguration(GridParallelRNG &pRNG, Field &U) {
@@ -171,6 +175,7 @@ public:
   static inline void ColdConfiguration(GridParallelRNG &pRNG, Field &U) {
     Group::ColdConfiguration(pRNG, U);
   }
+
 };
 
 
@@ -178,10 +183,17 @@ 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(std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
+  static inline void       setDirections(const std::vector<int> &conjDirs) { _conjDirs=conjDirs; }
   static inline std::vector<int> getDirections(void) { return _conjDirs; }
   static inline bool isPeriodicGaugeField(void) { return false; }
 };
@@ -193,6 +193,11 @@ 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){};
 
@@ -79,27 +79,18 @@ 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++){
-
-      // 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;
+      dSdU_mu = Ta(U[mu]*Staple[mu])*factor_p;
+      dSdU_mu = dSdU_mu + Ta(U[mu]*RectStaple[mu])*factor_r;
 	  
       PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
     }

Grid/qcd/hmc/GenericHMCrunner.h

@@ -225,6 +225,18 @@ 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>
+template <int ncolour, class group_name>
 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 SU<ncolour>::LatticeMatrix LatticeMatrix;
+  typedef typename GaugeGroup<ncolour,group_name>::LatticeMatrix LatticeMatrix;
   typedef LatticeGaugeField LatticeField;
   
   explicit FundamentalRep(GridBase* grid) {} //do nothing
@@ -45,7 +45,8 @@ public:
     
 
   
-typedef	 FundamentalRep<Nc> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::SU> FundamentalRepresentation;
+typedef	 FundamentalRep<Nc,GroupName::Sp> SpFundamentalRepresentation;
 
 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>
+template <int ncolour, TwoIndexSymmetry S, class group_name = GroupName::SU>
 class TwoIndexRep {
 public:
   // typdef to be used by the Representations class in HMC to get the
   // types for the higher representation fields
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexMatrix LatticeMatrix;
-  typedef typename SU_TwoIndex<ncolour, S>::LatticeTwoIndexField LatticeField;
-  static const int Dimension = ncolour * (ncolour + S) / 2;
+  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;
   static const bool isFundamental = false;
 
   LatticeField U;
@@ -43,10 +43,10 @@ public:
     U = Zero();
     LatticeColourMatrix tmp(Uin.Grid());
 
-    Vector<typename SU<ncolour>::Matrix> eij(Dimension);
+    Vector<typename GaugeGroup<ncolour,group_name>::Matrix> eij(Dimension);
 
     for (int a = 0; a < Dimension; a++)
-      SU_TwoIndex<ncolour, S>::base(a, eij[a]);
+      GaugeGroupTwoIndex<ncolour, S, group_name>::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 SU<ncolour>::LatticeAlgebraVector h(in.Grid());
+      typename GaugeGroup<ncolour, group_name>::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);
@@ -80,20 +80,23 @@ public:
   }
 
 private:
-  void projectOnAlgebra(typename SU<ncolour>::LatticeAlgebraVector &h_out,
+  void projectOnAlgebra(typename GaugeGroup<ncolour, group_name>::LatticeAlgebraVector &h_out,
                         const LatticeMatrix &in, Real scale = 1.0) const {
-    SU_TwoIndex<ncolour, S>::projectOnAlgebra(h_out, in, scale);
+    GaugeGroupTwoIndex<ncolour, S,group_name>::projectOnAlgebra(h_out, in, scale);
   }
 
   void FundamentalLieAlgebraMatrix(
-				   typename SU<ncolour>::LatticeAlgebraVector &h,
-				   typename SU<ncolour>::LatticeMatrix &out, Real scale = 1.0) const {
-    SU<ncolour>::FundamentalLieAlgebraMatrix(h, out, scale);
+				   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);
   }
 };
 
-typedef TwoIndexRep<Nc, Symmetric> TwoIndexSymmetricRepresentation;
-typedef TwoIndexRep<Nc, AntiSymmetric> TwoIndexAntiSymmetricRepresentation;
+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;
 
 NAMESPACE_END(Grid);
 

Grid/qcd/utils/CovariantCshift.h

@@ -37,13 +37,14 @@ 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)
@@ -52,19 +53,19 @@ 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

@@ -0,0 +1,470 @@
+/*************************************************************************************
+
+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

@@ -0,0 +1,371 @@
+////////////////////////////////////////////////////////////////////////
+//
+// * 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

@@ -1,932 +0,0 @@
-/*************************************************************************************
-
-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

@@ -0,0 +1,578 @@
+// 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

@@ -51,6 +51,10 @@ 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>
@@ -58,8 +62,8 @@ public:
     // returns i(T_Adj)^index necessary for the projectors
     // see definitions above
     iAdjTa = Zero();
-    Vector<typename SU<ncolour>::template iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
-    typename SU<ncolour>::template iSUnMatrix<cplx> tmp;
+    Vector<iSUnMatrix<cplx> > ta(ncolour * ncolour - 1);
+    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]);
@@ -67,8 +71,7 @@ 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++) {
-        typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
-	  2.0 * tmp * ta[b];  // 2.0 from the normalization
+        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;
@@ -134,8 +137,7 @@ public:
 
     for (int a = 0; a < Dimension; a++) {
       generator(a, iTa);
-      LatticeComplex tmp = real(trace(iTa * in)) * coefficient;
-      pokeColour(h_out, tmp, a);
+      pokeColour(h_out, real(trace(iTa * in)) * coefficient, a);
     }
   }
 

Grid/qcd/utils/SUnTwoIndex.h

@@ -1,273 +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_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

@@ -0,0 +1,317 @@
+// 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/SUn.h>
+#include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/SUnTwoIndex.h>
+#include <Grid/qcd/utils/GaugeGroupTwoIndex.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 staples on each site
+  // the sum over all nu-oriented staples for nu != mu on each site
   //////////////////////////////////////////////////
   static void Staple(GaugeMat &staple, const GaugeLorentz &Umu, int mu) {
 
@@ -300,6 +300,10 @@ 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++) {
@@ -335,6 +339,202 @@ 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
   //////////////////////////////////////////////////
@@ -707,18 +907,14 @@ public:
   // the sum over all staples on each site
   //////////////////////////////////////////////////
   static void RectStapleDouble(GaugeMat &U2, const GaugeMat &U, int mu) {
-    U2 = U * Cshift(U, mu, 1);
+    U2 = U * Gimpl::CshiftLink(U, mu, 1);
   }
 
   ////////////////////////////////////////////////////////////////////////////
-  // 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 .
+  // Hop by two optimisation strategy. Use RectStapleDouble to obtain 'U2'
   ////////////////////////////////////////////////////////////////////////////
-  static void RectStapleOptimised(GaugeMat &Stap, std::vector<GaugeMat> &U2,
-                                  std::vector<GaugeMat> &U, int mu) {
+  static void RectStapleOptimised(GaugeMat &Stap, const std::vector<GaugeMat> &U2,
+                                  const std::vector<GaugeMat> &U, int mu) {
 
     Stap = Zero();
 
@@ -732,9 +928,9 @@ public:
 
         // Up staple    ___ ___
         //             |       |
-        tmp = Cshift(adj(U[nu]), nu, -1);
+        tmp = Gimpl::CshiftLink(adj(U[nu]), nu, -1);
         tmp = adj(U2[mu]) * tmp;
-        tmp = Cshift(tmp, mu, -2);
+        tmp = Gimpl::CshiftLink(tmp, mu, -2);
 
         Staple2x1 = Gimpl::CovShiftForward(U[nu], nu, tmp);
 
@@ -742,14 +938,14 @@ public:
         //             |___ ___|
         //
         tmp = adj(U2[mu]) * U[nu];
-        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Cshift(tmp, mu, -2));
+        Staple2x1 += Gimpl::CovShiftBackward(U[nu], nu, Gimpl::CshiftLink(tmp, mu, -2));
 
         //              ___ ___
         //             |    ___|
         //             |___ ___|
         //
 
-        Stap += Cshift(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
+        Stap += Gimpl::CshiftLink(Gimpl::CovShiftForward(U[mu], mu, Staple2x1), mu, 1);
 
         //              ___ ___
         //             |___    |
@@ -758,7 +954,7 @@ public:
 
         //  tmp= Staple2x1* Cshift(U[mu],mu,-2);
         //  Stap+= Cshift(tmp,mu,1) ;
-        Stap += Cshift(Staple2x1, mu, 1) * Cshift(U[mu], mu, -1);
+        Stap += Gimpl::CshiftLink(Staple2x1, mu, 1) * Gimpl::CshiftLink(U[mu], mu, -1);
         ;
 
         //       --
@@ -766,10 +962,10 @@ public:
         //
         //      |  |
 
-        tmp = Cshift(adj(U2[nu]), nu, -2);
+        tmp = Gimpl::CshiftLink(adj(U2[nu]), nu, -2);
         tmp = Gimpl::CovShiftBackward(U[mu], mu, tmp);
-        tmp = U2[nu] * Cshift(tmp, nu, 2);
-        Stap += Cshift(tmp, mu, 1);
+        tmp = U2[nu] * Gimpl::CshiftLink(tmp, nu, 2);
+        Stap += Gimpl::CshiftLink(tmp, mu, 1);
 
         //      |  |
         //
@@ -778,25 +974,12 @@ public:
 
         tmp = Gimpl::CovShiftBackward(U[mu], mu, U2[nu]);
         tmp = adj(U2[nu]) * tmp;
-        tmp = Cshift(tmp, nu, -2);
-        Stap += Cshift(tmp, mu, 1);
+        tmp = Gimpl::CshiftLink(tmp, nu, -2);
+        Stap += Gimpl::CshiftLink(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();
@@ -895,6 +1078,288 @@ 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

@@ -79,60 +79,60 @@ public:
     this->_entries.resize(npoints* osites);
     this->_entries_p = &_entries[0];
 
+    thread_for(site, osites, {
+	Coordinate Coor;
+	Coordinate NbrCoor;
 
-    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;
+	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;
 	}
-	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

@@ -32,6 +32,7 @@
 
 #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

@@ -73,6 +73,16 @@ 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)
 {
@@ -83,7 +93,7 @@ void coalescedWriteNonTemporal(vobj & __restrict__ vec,const vobj & __restrict__
 {
   vstream(vec, extracted);
 }
-#else
+#else //==GRID_SIMT
 
 
 //#ifndef GRID_SYCL
@@ -166,6 +176,14 @@ 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

@@ -66,13 +66,61 @@ 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;
@@ -90,10 +138,12 @@ 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
@@ -102,7 +152,7 @@ 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 = 1.0/nrm;
+    nrm = one/nrm;
     for(int c2=0;c2<N;c2++)
       ret._internal[c1][c2]*= nrm;
       
@@ -127,7 +177,7 @@ 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 = 1.0/nrm;
+    nrm = one/nrm;
     for(int c2=0;c2<N;c2++)
       ret._internal[c1][c2]*= nrm;
   }
@@ -135,6 +185,85 @@ 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

@@ -53,7 +53,6 @@ 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> 

configure.ac

@@ -41,7 +41,7 @@ AC_PROG_RANLIB
 
 ############### Get compiler informations
 AC_LANG([C++])
-AX_CXX_COMPILE_STDCXX_11([noext],[mandatory])
+AX_CXX_COMPILE_STDCXX(14,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])
@@ -191,10 +191,28 @@ 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])],
@@ -737,7 +755,7 @@ case ${ac_TIMERS} in
 esac
 
 ############### Chroma regression test
-AC_ARG_ENABLE([chroma],[AS_HELP_STRING([--enable-chroma],[Expect chroma compiled under c++11 ])],ac_CHROMA=yes,ac_CHROMA=no)
+AC_ARG_ENABLE([chroma],[AS_HELP_STRING([--enable-chroma],[Expect chroma compiled under c++14 ])],ac_CHROMA=yes,ac_CHROMA=no)
 
 case ${ac_CHROMA} in
      yes|no)
@@ -819,6 +837,7 @@ FFTW                        : `if test "x$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'`
@@ -847,6 +866,7 @@ 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

@@ -10,9 +10,8 @@ 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 Open MPI ***optional***
-4. Install and build Grid pre-requisites
-5. Install, Configure and Build Grid
+3. Install and build Grid pre-requisites
+4. 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].
 
@@ -92,60 +91,33 @@ launchctl setenv GridPkg /opt/local</string>
 </plist>
 ```
 
-## 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
+## 3. Install and build Grid pre-requisites
 
 To simplify the installation of **Grid pre-requisites**, you can use your favourite package manager, e.g.:
 
-### 1. [MacPorts][MacPorts]
+### 3.1. [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 <portname>
+    sudo port install openmpi git-flow-avh gmp hdf5 mpfr fftw-3-single lapack wget autoconf automake bison cmake gawk libomp
 
-These are the `portname`s for mandatory Grid libraries:
+On a Mac without GPUs:
 
-* git-flow-avh
-* gmp
-* hdf5
-* mpfr
+    sudo port install OpenBLAS +native
 
-and these are the `portname`s for optional Grid libraries:
+To use `Gnu sha256sum`:
 
-* fftw-3-single
-* lapack
-* doxygen
-* OpenBLAS
+    pushd /opt/local/bin; sudo ln -s gsha256sum sha256sum; popd 
 
-***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?***
+These `port`s are not strictly necessary, but they are helpful:
 
-### 2. [Homebrew][Homebrew]
+    sudo port install gnuplot gsl h5utils nasm rclone texinfo tree xorg-server
 
-[Homebrew]: https://brew.sh "Homebrew package manager"
+***Please update this list with any packages I've missed!***
 
-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***
+#### Install LIME
 
 There isn't currently a port for [C-LIME][C-LIME], so download the source and then build it:
 
@@ -154,9 +126,19 @@ 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
 
-## 5. Install, Configure and Build Grid
+### 3.2. [Homebrew][Homebrew]
 
-### 5.1 Install 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
 
 [Grid]: https://github.com/paboyle/Grid
 
@@ -174,7 +156,7 @@ or
 
 depending on how many times you like to enter your password.
 
-### 5.2 Configure Grid
+### 4.2 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).
 
@@ -198,7 +180,7 @@ 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
 
-### 5.3 Build Grid
+### 4.3 Build Grid
 
 Each configuration must be built before they can be used. You can either:
 

documentation/manual.rst

@@ -2778,47 +2778,81 @@ and there are associated reconstruction routines for assembling four spinors fro
 
 These ca
 
-
-SU(N)
+Gauge Group
 --------
+A generic Nc qcd/utils/GaugeGroup.h is provided. This defines a template class that can be specialised to different gauge groups::
 
-A generic Nc qcd/utils/SUn.h is provided. This defines a template class::
+  template <int ncolour, class group_name>
+  class GaugeGroup {...}
 
-  template <int ncolour> class SU ;
+Supported groups are SU(N) and Sp(2N). The group can be specified through the GroupName namespace::
 
-The most important external methods are::
+  namespace GroupName {
+  class SU {};
+  class Sp {};
+  }
+
+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::
 
-  static void printGenerators(void) ;
   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::
 
   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++){
@@ -2857,6 +2891,16 @@ 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

@@ -15,6 +15,8 @@ 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 $HPPFILES > Make.inc
@@ -27,13 +29,14 @@ echo STAG_FERMION_FILES=$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/OEM/README

@@ -0,0 +1,53 @@
+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

@@ -0,0 +1,18 @@
+#!/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

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

@@ -0,0 +1,15 @@
+../../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

@@ -0,0 +1,3 @@
+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 +1,3 @@
 BREW=/opt/local/
-CXXFLAGS=-fsanitize=address CXX=g++ ../../configure --enable-simd=NEONv8 --enable-comms=none --enable-unified=yes --prefix $HOME/QCD/GridInstall --with-lime=/Users/peterboyle/QCD/SciDAC/install/ --with-openssl=$BREW --disable-gparity --disable-fermion-reps 
+MPICXX=mpicxx ../../configure --enable-simd=GEN --enable-comms=mpi-auto --enable-unified=yes --prefix $HOME/QCD/GridInstall --with-lime=/Users/peterboyle/QCD/SciDAC/install/ --with-openssl=$BREW --disable-fermion-reps --disable-gparity --disable-debug
 

tests/Makefile.am

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

@@ -29,13 +29,14 @@ 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/SUn.h>
+#include <Grid/qcd/utils/GaugeGroup.h>
 #include <Grid/qcd/utils/SUnAdjoint.h>
-#include <Grid/qcd/utils/SUnTwoIndex.h>
+#include <Grid/qcd/utils/GaugeGroupTwoIndex.h>
 
 #include <Grid/qcd/representations/adjoint.h>
 #include <Grid/qcd/representations/two_index.h>
@@ -43,7 +44,6 @@ directory
 
 using namespace std;
 using namespace Grid;
-;
 
 int main(int argc, char** argv) {
   Grid_init(&argc, &argv);
@@ -62,20 +62,17 @@ int main(int argc, char** argv) {
   SU2::printGenerators();
   std::cout << "Dimension of adjoint representation: "<< SU2Adjoint::Dimension << 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(Nc" << std::endl;
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for SU(3)" << std::endl;
   std::cout << GridLogMessage << "*********************************************"
-	    << std::endl;
+            << std::endl;
   SU3::printGenerators();
   std::cout << "Dimension of adjoint representation: "<< SU3Adjoint::Dimension << std::endl;
   SU3Adjoint::printGenerators();
@@ -94,22 +91,22 @@ int main(int argc, char** argv) {
   // Projectors 
   GridParallelRNG gridRNG(grid);
   gridRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
-  SU3Adjoint::LatticeAdjMatrix Gauss(grid);
-  SU3::LatticeAlgebraVector ha(grid);
-  SU3::LatticeAlgebraVector hb(grid);
+  SU_Adjoint<Nc>::LatticeAdjMatrix Gauss(grid);
+  SU<Nc>::LatticeAlgebraVector ha(grid);
+  SU<Nc>::LatticeAlgebraVector hb(grid);
   random(gridRNG,Gauss);
 
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3Adjoint::projectOnAlgebra(ha, Gauss);
+  SU_Adjoint<Nc>::projectOnAlgebra(ha, Gauss);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3Adjoint::projector(hb, Gauss);
+  SU_Adjoint<Nc>::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
 
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3Adjoint::projector(hb, Gauss);
+  SU_Adjoint<Nc>::projector(hb, Gauss);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff = ha -hb;
+  SU<Nc>::LatticeAlgebraVector diff = ha -hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
 
 
@@ -119,17 +116,17 @@ 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);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V);
-    
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U);
+  SU<Nc>::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++) {
-    SU3::LatticeMatrix Umu = peekLorentz(U,mu);
-    SU3::LatticeMatrix Vmu = peekLorentz(V,mu);
+    SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
+    SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
     pokeLorentz(UV,Umu*Vmu, mu);
   }
     
@@ -151,6 +148,7 @@ 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;
@@ -176,19 +174,19 @@ 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
-  SU3::LatticeAlgebraVector h_adj(grid);
+  SU<Nc>::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
-  SU3::LatticeAlgebraVector h_adj2(grid);
+  SU<Nc>::LatticeAlgebraVector h_adj2(grid);
   SU_Adjoint<Nc>::projectOnAlgebra(h_adj2, Ar);
-  SU3::LatticeAlgebraVector h_diff = h_adj - h_adj2;
+  SU<Nc>::LatticeAlgebraVector h_diff = h_adj - h_adj2;
   std::cout << GridLogMessage << "Projections structure check vector difference (Adjoint representation) : " << norm2(h_diff) << std::endl;
     
   // Exponentiate
@@ -210,14 +208,14 @@ int main(int argc, char** argv) {
 	    << std::endl;
     
   // Construct the fundamental matrix in the group
-  SU3::LatticeMatrix Af(grid);
-  SU3::FundamentalLieAlgebraMatrix(h_adj,Af);
-  SU3::LatticeMatrix Ufund(grid);
+  SU<Nc>::LatticeMatrix Af(grid);
+  SU<Nc>::FundamentalLieAlgebraMatrix(h_adj,Af);
+  SU<Nc>::LatticeMatrix Ufund(grid);
   Ufund  = expMat(Af, 1.0, 16);
   // Check unitarity
-  SU3::LatticeMatrix uno_f(grid);
+  SU<Nc>::LatticeMatrix uno_f(grid);
   uno_f = 1.0;
-  SU3::LatticeMatrix UnitCheck(grid);
+  SU<Nc>::LatticeMatrix UnitCheck(grid);
   UnitCheck = Ufund * adj(Ufund) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck)
 	    << std::endl;
@@ -280,20 +278,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two Index Symmetric projectors"
 	    << std::endl;
   // Projectors 
-  SU3TwoIndexSymm::LatticeTwoIndexMatrix Gauss2(grid);
+  SU_TwoIndex<Nc, Symmetric>::LatticeTwoIndexMatrix Gauss2(grid);
   random(gridRNG,Gauss2);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3TwoIndexSymm::projectOnAlgebra(ha, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projectOnAlgebra(ha, Gauss2);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3TwoIndexSymm::projector(hb, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3TwoIndexSymm::projector(hb, Gauss2);
+  SU_TwoIndex<Nc, Symmetric>::projector(hb, Gauss2);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff2 = ha - hb;
+  SU<Nc>::LatticeAlgebraVector diff2 = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
 	    << std::endl;
@@ -304,20 +302,20 @@ int main(int argc, char** argv) {
   std::cout << GridLogMessage << "Test for the Two index anti-Symmetric projectors"
 	    << std::endl;
   // Projectors
-  SU3TwoIndexAntiSymm::LatticeTwoIndexMatrix Gauss2a(grid);
+  SU_TwoIndex<Nc, AntiSymmetric>::LatticeTwoIndexMatrix Gauss2a(grid);
   random(gridRNG,Gauss2a);
   
   std::cout << GridLogMessage << "Start projectOnAlgebra" << std::endl;
-  SU3TwoIndexAntiSymm::projectOnAlgebra(ha, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projectOnAlgebra(ha, Gauss2a);
   std::cout << GridLogMessage << "end projectOnAlgebra" << std::endl;
   std::cout << GridLogMessage << "Start projector" << std::endl;
-  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
   
   std::cout << GridLogMessage << "ReStart projector" << std::endl;
-  SU3TwoIndexAntiSymm::projector(hb, Gauss2a);
+  SU_TwoIndex<Nc, AntiSymmetric>::projector(hb, Gauss2a);
   std::cout << GridLogMessage << "end projector" << std::endl;
-  SU3::LatticeAlgebraVector diff2a = ha - hb;
+  SU<Nc>::LatticeAlgebraVector diff2a = ha - hb;
   std::cout << GridLogMessage << "Difference: " << norm2(diff2a) << std::endl;
   std::cout << GridLogMessage << "*********************************************"
 	    << std::endl;
@@ -326,55 +324,59 @@ 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);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
-  SU3::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
-    
+
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, U2);
+  SU<Nc>::HotConfiguration<LatticeGaugeField>(gridRNG, V2);
+
   LatticeGaugeField UV2(grid);
   UV2 = Zero();
   for (int mu = 0; mu < Nd; mu++) {
-    SU3::LatticeMatrix Umu2 = peekLorentz(U2,mu);
-    SU3::LatticeMatrix Vmu2 = peekLorentz(V2,mu);
+    SU<Nc>::LatticeMatrix Umu2 = peekLorentz(U2,mu);
+    SU<Nc>::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
-  SU3::LatticeAlgebraVector h_sym(grid);
+  SU<Nc>::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
-  SU3::LatticeAlgebraVector h_sym2(grid);
+  SU<Nc>::LatticeAlgebraVector h_sym2(grid);
   SU_TwoIndex< Nc, Symmetric>::projectOnAlgebra(h_sym2, Ar_sym);
-  SU3::LatticeAlgebraVector h_diff_sym = h_sym - h_sym2;
+  SU<Nc>::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
@@ -396,11 +398,11 @@ int main(int argc, char** argv) {
 	    << std::endl;
     
   // Construct the fundamental matrix in the group
-  SU3::LatticeMatrix Af_sym(grid);
-  SU3::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
-  SU3::LatticeMatrix Ufund2(grid);
+  SU<Nc>::LatticeMatrix Af_sym(grid);
+  SU<Nc>::FundamentalLieAlgebraMatrix(h_sym,Af_sym);
+  SU<Nc>::LatticeMatrix Ufund2(grid);
   Ufund2  = expMat(Af_sym, 1.0, 16);
-  SU3::LatticeMatrix UnitCheck2(grid);
+  SU<Nc>::LatticeMatrix UnitCheck2(grid);
   UnitCheck2 = Ufund2 * adj(Ufund2) - uno_f;
   std::cout << GridLogMessage << "unitarity check 1: " << norm2(UnitCheck2)
 	    << std::endl;
@@ -425,115 +427,113 @@ 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);
+  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);
+  // 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++) {
-      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;
+  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);
   }
+  
+  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;
 
-#endif
+  
+  // 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;
+}
   
   Grid_finalize();
 }
+

tests/core/Test_reunitarise.cc

@@ -26,6 +26,7 @@ Author: Peter Boyle <paboyle@ph.ed.ac.uk>
     See the full license in the file "LICENSE" in the top level distribution directory
     *************************************************************************************/
     /*  END LEGAL */
+
 #include <Grid/Grid.h>
 
 using namespace std;
@@ -121,8 +122,9 @@ int main (int argc, char ** argv)
   detU=detU-1.0;
   std::cout << "Determinant defect before projection " <<norm2(detU)<<std::endl;
   tmp = U*adj(U) - ident;
-  std::cout << "Unitarity check before projection    " << norm2(tmp)<<std::endl; 
-#if (Nc == 3)
+  std::cout << "Unitarity check before projection    " << norm2(tmp)<<std::endl;
+    
+#if Nc==3
   ProjectSU3(U);
   detU= Determinant(U) ;
   detU= detU -1.0;
@@ -130,7 +132,7 @@ int main (int argc, char ** argv)
   tmp = U*adj(U) - ident;
   std::cout << "Unitarity check after projection    " << norm2(tmp)<<std::endl; 
 #endif
-  
+    
   ProjectSUn(UU);
   detUU= Determinant(UU);
   detUU= detUU -1.0;
@@ -140,7 +142,3 @@ int main (int argc, char ** argv)
   
   Grid_finalize();
 }
-
-
-
-

tests/debug/Test_iwasaki_action_newstaple.cc

@@ -0,0 +1,188 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_iwasaki_action_newstaple.cc
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@bnl.gov>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+
+using namespace std;
+using namespace Grid;
+
+////////////////////////////////////////////////////////////////////////
+// PlaqPlusRectangleActoin
+////////////////////////////////////////////////////////////////////////
+template<class Gimpl>
+class PlaqPlusRectangleActionOrig : public Action<typename Gimpl::GaugeField> {
+public:
+
+  INHERIT_GIMPL_TYPES(Gimpl);
+
+private:
+  RealD c_plaq;
+  RealD c_rect;
+
+public:
+  PlaqPlusRectangleActionOrig(RealD b,RealD c): c_plaq(b),c_rect(c){};
+
+  virtual std::string action_name(){return "PlaqPlusRectangleActionOrig";}
+      
+  virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {}; // noop as no pseudoferms
+      
+  virtual std::string LogParameters(){
+    std::stringstream sstream;
+    sstream << GridLogMessage << "["<<action_name() <<"] c_plaq: " << c_plaq << std::endl;
+    sstream << GridLogMessage << "["<<action_name() <<"] c_rect: " << c_rect << std::endl;
+    return sstream.str();
+  }
+
+
+  virtual RealD S(const GaugeField &U) {
+    RealD vol = U.Grid()->gSites();
+
+    RealD plaq = WilsonLoops<Gimpl>::avgPlaquette(U);
+    RealD rect = WilsonLoops<Gimpl>::avgRectangle(U);
+
+    RealD action=c_plaq*(1.0 -plaq)*(Nd*(Nd-1.0))*vol*0.5
+      +c_rect*(1.0 -rect)*(Nd*(Nd-1.0))*vol;
+
+    return action;
+  };
+
+  virtual void deriv(const GaugeField &Umu,GaugeField & dSdU) {
+    //extend Ta to include Lorentz indexes
+    RealD factor_p = c_plaq/RealD(Nc)*0.5;
+    RealD factor_r = c_rect/RealD(Nc)*0.5;
+
+    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);
+    }
+
+    GaugeLinkField dSdU_mu(grid);
+    GaugeLinkField staple(grid);
+
+    for (int mu=0; mu < Nd; mu++){
+
+      // 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);
+    }
+
+  };
+
+};
+
+// Convenience for common physically defined cases.
+//
+// RBC c1 parameterisation is not really RBC but don't have good
+// reference and we are happy to change name if prior use of this plaq coeff
+// parameterisation is made known to us. 
+template<class Gimpl>
+class RBCGaugeActionOrig : public PlaqPlusRectangleActionOrig<Gimpl> {
+public:
+  INHERIT_GIMPL_TYPES(Gimpl);
+  RBCGaugeActionOrig(RealD beta,RealD c1) : PlaqPlusRectangleActionOrig<Gimpl>(beta*(1.0-8.0*c1), beta*c1) {};
+  virtual std::string action_name(){return "RBCGaugeActionOrig";}
+};
+
+template<class Gimpl>
+class IwasakiGaugeActionOrig : public RBCGaugeActionOrig<Gimpl> {
+public:
+  INHERIT_GIMPL_TYPES(Gimpl);
+  IwasakiGaugeActionOrig(RealD beta) : RBCGaugeActionOrig<Gimpl>(beta,-0.331) {};
+  virtual std::string action_name(){return "IwasakiGaugeActionOrig";}
+};
+
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  Coordinate latt_size  = GridDefaultLatt();
+  Coordinate simd_layout= GridDefaultSimd(Nd,vComplexD::Nsimd());
+  Coordinate mpi_layout = GridDefaultMpi();
+  std::cout << " mpi "<<mpi_layout<<std::endl;
+  std::cout << " simd "<<simd_layout<<std::endl;
+  std::cout << " latt "<<latt_size<<std::endl;
+  GridCartesian GRID(latt_size,simd_layout,mpi_layout);
+
+  GridParallelRNG   pRNG(&GRID);
+  pRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
+  LatticeGaugeField U(&GRID);
+
+  SU<Nc>::HotConfiguration(pRNG,U);
+
+  //#define PRD
+#ifdef PRD
+  typedef PeriodicGimplD Gimpl;
+#else
+  typedef ConjugateGimplD Gimpl;
+  std::vector<int> conj_dirs(Nd,0); conj_dirs[0]=1; conj_dirs[3]=1;
+  Gimpl::setDirections(conj_dirs);
+#endif
+
+  typedef typename WilsonLoops<Gimpl>::GaugeMat GaugeMat;
+  typedef typename WilsonLoops<Gimpl>::GaugeLorentz GaugeLorentz;
+
+  GaugeLorentz derivOrig(&GRID), derivNew(&GRID);
+  double beta = 2.13;
+  IwasakiGaugeActionOrig<Gimpl> action_orig(beta);
+  IwasakiGaugeAction<Gimpl> action_new(beta);
+
+  double torig=0, tnew=0;
+  int ntest = 10;
+  for(int i=0;i<ntest;i++){
+    double t0 = usecond();
+    action_orig.deriv(U, derivOrig);
+    double t1 = usecond();
+    action_new.deriv(U, derivNew);
+    double t2 = usecond();
+
+    GaugeLorentz diff = derivOrig - derivNew;
+    double n = norm2(diff);
+    std::cout << GridLogMessage << "Difference " << n << " (expect 0)" << std::endl;
+    assert(n<1e-10);
+
+    std::cout << GridLogMessage << "Timings orig: " << (t1-t0)/1000 << "ms,  new: " << (t2-t1)/1000 << "ms" << std::endl;
+    torig += (t1-t0)/1000; tnew += (t2-t1)/1000;
+  }
+  std::cout << GridLogMessage << "Avg timings " << ntest << " iterations: orig:" << torig/ntest << "ms,   new:" << tnew/ntest << "ms" << std::endl;
+  
+  Grid_finalize();
+}

tests/debug/Test_optimized_staple_gaugebc.cc

@@ -0,0 +1,94 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_optimized_staple_gaugebc.cc
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@bnl.gov>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+using namespace std;
+using namespace Grid;
+ 
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  Coordinate latt_size  = GridDefaultLatt();
+  Coordinate simd_layout= GridDefaultSimd(Nd,vComplexD::Nsimd());
+  Coordinate mpi_layout = GridDefaultMpi();
+  std::cout << " mpi "<<mpi_layout<<std::endl;
+  std::cout << " simd "<<simd_layout<<std::endl;
+  std::cout << " latt "<<latt_size<<std::endl;
+  GridCartesian GRID(latt_size,simd_layout,mpi_layout);
+
+  GridParallelRNG   pRNG(&GRID);
+  pRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
+  LatticeGaugeField U(&GRID);
+
+  SU<Nc>::HotConfiguration(pRNG,U);
+
+  //#define PRD
+#ifdef PRD
+  typedef PeriodicGimplD Gimpl;
+#else
+  typedef ConjugateGimplD Gimpl;
+  std::vector<int> conj_dirs(Nd,0); conj_dirs[0]=1; conj_dirs[3]=1;
+  Gimpl::setDirections(conj_dirs);
+#endif
+
+  typedef typename WilsonLoops<Gimpl>::GaugeMat GaugeMat;
+  typedef typename WilsonLoops<Gimpl>::GaugeLorentz GaugeLorentz;
+
+  int count = 0;
+  double torig=0, topt=0;
+     
+  std::vector<GaugeMat> Umu(Nd,&GRID), U2(Nd,&GRID);
+  for(int mu=0;mu<Nd;mu++){
+    Umu[mu] = PeekIndex<LorentzIndex>(U,mu);
+    WilsonLoops<Gimpl>::RectStapleDouble(U2[mu], Umu[mu], mu);
+  }
+
+  std::cout << GridLogMessage << "Checking optimized vs unoptimized RectStaple" << std::endl;
+  for(int mu=0;mu<Nd;mu++){
+    GaugeMat staple_orig(&GRID), staple_opt(&GRID), staple_U2(&GRID);
+    double t0 = usecond();
+    WilsonLoops<Gimpl>::RectStapleUnoptimised(staple_orig,U,mu);
+    double t1 = usecond();
+    WilsonLoops<Gimpl>::RectStapleOptimised(staple_opt, U2, Umu, mu);
+    double t2 = usecond();
+    torig += t1-t0;  topt += t2-t1;
+    ++count;
+    
+    GaugeMat diff = staple_orig - staple_opt;
+    double n = norm2(diff);
+    std::cout << GridLogMessage << mu << " " << n << std::endl;
+    assert(n<1e-10);
+  }
+  std::cout << GridLogMessage << "RectStaple timings orig: " << torig/1000/count << "ms,  optimized: " << topt/1000/count << "ms" << std::endl;
+  
+  Grid_finalize();
+}

tests/debug/Test_padded_cell_staple.cc

@@ -0,0 +1,580 @@
+    /*************************************************************************************
+
+    Grid physics library, www.github.com/paboyle/Grid 
+
+    Source file: ./tests/Test_padded_cell_staple.cc
+
+    Copyright (C) 2015
+
+Author: Christopher Kelly <ckelly@bnl.gov>
+Author: Peter Boyle <paboyle@ph.ed.ac.uk>
+
+    This program is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License along
+    with this program; if not, write to the Free Software Foundation, Inc.,
+    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+    See the full license in the file "LICENSE" in the top level distribution directory
+    *************************************************************************************/
+    /*  END LEGAL */
+#include <Grid/Grid.h>
+#include <Grid/lattice/PaddedCell.h>
+#include <Grid/stencil/GeneralLocalStencil.h>
+
+using namespace std;
+using namespace Grid;
+
+template <class Gimpl> class WilsonLoopsTest : public Gimpl {
+public:
+  INHERIT_GIMPL_TYPES(Gimpl);
+
+  typedef typename Gimpl::GaugeLinkField GaugeMat;
+  typedef typename Gimpl::GaugeField GaugeLorentz;
+
+
+  //Original implementation
+  static void StapleOrig(GaugeMat &staple, const GaugeLorentz &Umu, int mu,
+			 int nu) {
+
+    GridBase *grid = Umu.Grid();
+
+    std::vector<GaugeMat> U(Nd, grid);
+    for (int d = 0; d < Nd; d++) {
+      U[d] = PeekIndex<LorentzIndex>(Umu, d);
+    }
+    staple = Zero();
+
+    if (nu != mu) {
+
+      // mu
+      // ^
+      // |__>  nu
+
+      //    __
+      //      |
+      //    __|
+      //
+
+      //Forward: Out(x) = Link(x)*field(x+mu)
+      //Backward: Out(x) = Link^dag(x-mu)*field(x-mu)
+      //ShiftStaple: Link(x) = Link(x+mu)
+
+      //tmp1 = U^dag_nu(x-nu)
+      //tmp2 = U^dag_mu(x-mu) tmp1(x-mu) = U^dag_mu(x-mu) U^dag_nu(x-nu-mu)
+      //tmp3 = U_nu(x) tmp2(x+nu) = U_nu(x)U^dag_mu(x-mu+nu) U^dag_nu(x-mu)
+      //tmp4 = tmp(x+mu) = U_nu(x+mu)U^dag_mu(x+nu) U^dag_nu(x)
+
+      staple += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftForward(
+							  U[nu], nu,
+							  Gimpl::CovShiftBackward(
+										  U[mu], mu, Gimpl::CovShiftIdentityBackward(U[nu], nu))),
+				   mu);
+
+      //  __
+      // |
+      // |__
+      //
+      //
+    
+      //tmp1 = U_mu^dag(x-mu) U_nu(x-mu)
+      //tmp2 = U_nu^dag(x-nu) tmp1(x-nu) = U_nu^dag(x-nu) U_mu^dag(x-mu-nu) U_nu(x-mu-nu)
+      //tmp3 = tmp2(x+mu) = U_nu^dag(x-nu+mu) U_mu^dag(x-nu) U_nu(x-nu)
+      staple += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftBackward(U[nu], nu,
+							   Gimpl::CovShiftBackward(U[mu], mu, U[nu])),
+				   mu);
+    }
+  }
+
+  static void StaplePadded(GaugeMat &staple, const GaugeLorentz &U, int mu,
+			   int nu) {
+    if(nu==mu){
+      staple = Zero();
+      return;
+    }
+    double peek = 0, construct = 0, exchange = 0, coord = 0, stencil =0, kernel = 0, extract = 0, total = 0;
+    
+    double tstart = usecond();
+    double t=tstart;
+    
+    PaddedCell Ghost(1, (GridCartesian*)U.Grid());
+
+    construct += usecond() - t;
+      
+    t=usecond();      
+    GaugeMat U_mu = PeekIndex<LorentzIndex>(U, mu);
+    GaugeMat U_nu = PeekIndex<LorentzIndex>(U, nu);
+    peek += usecond() - t;
+
+    t=usecond();
+    CshiftImplGauge<Gimpl> cshift_impl;
+    GaugeMat Ug_mu = Ghost.Exchange(U_mu, cshift_impl);
+    GaugeMat Ug_nu = Ghost.Exchange(U_nu, cshift_impl);
+    exchange += usecond() - t;
+    
+    GridBase *ggrid = Ug_mu.Grid();
+
+    GaugeMat gStaple(ggrid);
+
+    t=usecond();
+    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;
+
+    std::vector<Coordinate> shifts;
+
+    //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);
+    coord += usecond()-t;
+
+    t=usecond();
+    GeneralLocalStencil gStencil(ggrid,shifts);
+    stencil += usecond() -t;
+
+    t=usecond();
+    {
+      autoView( gStaple_v , gStaple, AcceleratorWrite);
+      auto gStencil_v = gStencil.View();
+      autoView( Ug_mu_v , Ug_mu, AcceleratorRead);
+      autoView( Ug_nu_v , Ug_nu, AcceleratorRead);
+  
+      accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
+	  GeneralStencilEntry const* e = gStencil_v.GetEntry(0,ss);
+	  auto Udag_nu_x = adj(coalescedReadGeneralPermute(Ug_nu_v[e->_offset], e->_permute, Nd));
+	  e = gStencil_v.GetEntry(1,ss);
+	  auto Udag_mu_xpnu = adj(coalescedReadGeneralPermute(Ug_mu_v[e->_offset], e->_permute, Nd));
+	  e = gStencil_v.GetEntry(2,ss);
+	  auto U_nu_xpmu = coalescedReadGeneralPermute(Ug_nu_v[e->_offset], e->_permute, Nd);
+      
+	  auto stencil_ss = U_nu_xpmu * Udag_mu_xpnu * Udag_nu_x;
+
+	  e = gStencil_v.GetEntry(3,ss);
+	  auto U_nu_xmnu = coalescedReadGeneralPermute(Ug_nu_v[e->_offset], e->_permute, Nd);
+	  e = gStencil_v.GetEntry(4,ss);
+	  auto Udag_mu_xmnu = adj(coalescedReadGeneralPermute(Ug_mu_v[e->_offset], e->_permute, Nd));
+	  e = gStencil_v.GetEntry(5,ss);
+	  auto Udag_nu_xmnu_pmu = adj(coalescedReadGeneralPermute(Ug_nu_v[e->_offset], e->_permute, Nd));
+
+	  stencil_ss = stencil_ss + Udag_nu_xmnu_pmu * Udag_mu_xmnu * U_nu_xmnu;
+      
+	  coalescedWrite(gStaple_v[ss],stencil_ss);
+	}
+	);
+    } //ensure views are all closed!
+    kernel += usecond() - t;
+
+    t=usecond();
+    staple = Ghost.Extract(gStaple);
+    extract += usecond()-t;
+    
+    total += usecond() - tstart;
+    std::cout << GridLogMessage << "StaplePadded timings peek:" << peek << " construct:" << construct << " exchange:" << exchange << " coord:" << coord << " stencil:" << stencil << " kernel:" << kernel << " extract:" << extract << " total:" << total << std::endl;
+  }
+
+  static void RectStapleOrig(GaugeMat &Stap, const GaugeLorentz &Umu,
+			     int mu) {
+    GridBase *grid = Umu.Grid();
+
+    std::vector<GaugeMat> U(Nd, grid);
+    for (int d = 0; d < Nd; d++) {
+      U[d] = PeekIndex<LorentzIndex>(Umu, d);
+    }
+
+    Stap = Zero();
+
+    for (int nu = 0; nu < Nd; nu++) {
+      if (nu != mu) {
+        //           __ ___
+        //          |    __ |
+        //
+	//tmp1 = U_nu^dag(x-nu)
+	//tmp2 = U_mu^dag(x-mu)tmp1(x-mu) = U_mu^dag(x-mu) U_nu^dag(x-nu-mu)
+	//tmp3 = U_mu^dag(x-mu)tmp2(x-mu) = U_mu^dag(x-mu) U_mu^dag(x-2mu) U_nu^dag(x-nu-2mu)
+	//tmp4 = U_nu(x)tmp3(x+nu) = U_nu(x)U_mu^dag(x-mu+nu) U_mu^dag(x-2mu+nu) U_nu^dag(x-2mu)
+	//tmp5 = U_mu(x)tmp4(x+mu) = U_mu(x)U_nu(x+mu)U_mu^dag(x+nu) U_mu^dag(x-mu+nu) U_nu^dag(x-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)
+	
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftForward(
+							  U[mu], mu,
+							  Gimpl::CovShiftForward(
+										 U[nu], nu,
+										 Gimpl::CovShiftBackward(
+													 U[mu], mu,
+													 Gimpl::CovShiftBackward(
+																 U[mu], mu,
+																 Gimpl::CovShiftIdentityBackward(U[nu], nu))))),
+				   mu);
+
+        //              __
+        //          |__ __ |
+
+	//tmp1 = U^dag_mu(x-mu)U_nu(x-mu)
+	//tmp2 = U^dag_mu(x-mu)tmp1(x-mu) = U^dag_mu(x-mu)U^dag_mu(x-2mu)U_nu(x-2mu)
+	//tmp3 = U^dag_nu(x-nu)tmp2(x-nu) = U^dag_nu(x-nu)U^dag_mu(x-mu-nu)U^dag_mu(x-2mu-nu)U_nu(x-2mu-nu)
+	//tmp4 = U_mu(x)tmp3(x+mu) = U_mu(x)U^dag_nu(x-nu+mu)U^dag_mu(x-nu)U^dag_mu(x-mu-nu)U_nu(x-mu-nu)
+	//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)
+	
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftForward(
+							  U[mu], mu,
+							  Gimpl::CovShiftBackward(
+										  U[nu], nu,
+										  Gimpl::CovShiftBackward(
+													  U[mu], mu, Gimpl::CovShiftBackward(U[mu], mu, U[nu])))),
+				   mu);
+
+        //           __
+        //          |__ __ |
+	//Forward: Out(x) = Link(x)*field(x+mu)
+	//Backward: Out(x) = Link^dag(x-mu)*field(x-mu)
+	//ShiftStaple: Link(x) = Link(x+mu)
+
+	//tmp1 = U_nu(x)U_mu(x+nu)
+	//tmp2 = U^dag_mu(x-mu)tmp1(x-mu) = U^dag_mu(x-mu)U_nu(x-mu)U_mu(x+nu-mu)
+	//tmp3 = U^dag_mu(x-mu)tmp2(x-mu) = U^dag_mu(x-mu)U^dag_mu(x-2mu)U_nu(x-2mu)U_mu(x+nu-2mu)
+	//tmp4 = U^dag_nu(x-nu)tmp3(x-nu) = U^dag_nu(x-nu)U^dag_mu(x-mu-nu)U^dag_mu(x-2mu-nu)U_nu(x-2mu-nu)U_mu(x-2mu)
+	//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)
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftBackward(
+							   U[nu], nu,
+							   Gimpl::CovShiftBackward(
+										   U[mu], mu,
+										   Gimpl::CovShiftBackward(
+													   U[mu], mu, Gimpl::CovShiftForward(U[nu], nu, U[mu])))),
+				   mu);
+
+        //           __ ___
+        //          |__    |
+	//tmp1 = U_nu^dag(x-nu)U_mu(x-nu)
+	//tmp2 = U_mu^dag(x-mu)tmp1(x-mu) = U_mu^dag(x-mu)U_nu^dag(x-mu-nu)U_mu(x-mu-nu)
+	//tmp3 = U_mu^dag(x-mu)tmp2(x-mu) = U_mu^dag(x-mu)U_mu^dag(x-2mu)U_nu^dag(x-2mu-nu)U_mu(x-2mu-nu)
+	//tmp4 = U_nu(x)tmp3(x+nu) = U_nu(x)U_mu^dag(x-mu+nu)U_mu^dag(x-2mu+nu)U_nu^dag(x-2mu)U_mu(x-2mu)
+	//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)
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftForward(
+							  U[nu], nu,
+							  Gimpl::CovShiftBackward(
+										  U[mu], mu,
+										  Gimpl::CovShiftBackward(
+													  U[mu], mu, Gimpl::CovShiftBackward(U[nu], nu, U[mu])))),
+				   mu);
+
+        //       --
+        //      |  |
+        //
+        //      |  |
+	//tmp1 = U_nu^dag(x-nu)
+	//tmp2 = U_nu^dag(x-nu)tmp1(x-nu) = U_nu^dag(x-nu)U_nu^dag(x-2nu)
+	//tmp3 = U_mu^dag(x-mu)tmp2(x-mu) = U_mu^dag(x-mu)U_nu^dag(x-mu-nu)U_nu^dag(x-mu-2nu)
+	//tmp4 = U_nu(x)tmp3(x+nu) = U_nu(x)U_mu^dag(x-mu+nu)U_nu^dag(x-mu)U_nu^dag(x-mu-nu)
+	//tmp5 = U_nu(x)tmp4(x+nu) = U_nu(x)U_nu(x+nu)U_mu^dag(x-mu+2nu)U_nu^dag(x-mu+nu)U_nu^dag(x-mu)
+	//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)
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftForward(
+							  U[nu], nu,
+							  Gimpl::CovShiftForward(
+										 U[nu], nu,
+										 Gimpl::CovShiftBackward(
+													 U[mu], mu,
+													 Gimpl::CovShiftBackward(
+																 U[nu], nu,
+																 Gimpl::CovShiftIdentityBackward(U[nu], nu))))),
+				   mu);
+
+        //      |  |
+        //
+        //      |  |
+        //       --
+	//tmp1 = U_nu(x)U_nu(x+nu)
+	//tmp2 = U_mu^dag(x-mu)tmp1(x-mu) = U_mu^dag(x-mu)U_nu(x-mu)U_nu(x-mu+nu)
+	//tmp3 = U_nu^dag(x-nu)tmp2(x-nu) = U_nu^dag(x-nu)U_mu^dag(x-mu-nu)U_nu(x-mu-nu)U_nu(x-mu)
+	//tmp4 = U_nu^dag(x-nu)tmp3(x-nu) = U_nu^dag(x-nu)U_nu^dag(x-2nu)U_mu^dag(x-mu-2nu)U_nu(x-mu-2nu)U_nu(x-mu-nu)
+	//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)
+        Stap += Gimpl::ShiftStaple(
+				   Gimpl::CovShiftBackward(
+							   U[nu], nu,
+							   Gimpl::CovShiftBackward(
+										   U[nu], nu,
+										   Gimpl::CovShiftBackward(
+													   U[mu], mu, Gimpl::CovShiftForward(U[nu], nu, U[nu])))),
+				   mu);
+      }
+    }
+  }
+
+
+  static void RectStaplePadded(GaugeMat &Stap, const GaugeLorentz &U,
+			       int mu) {
+    PaddedCell Ghost(2,(GridCartesian*)U.Grid());
+    GridBase *ggrid = Ghost.grids.back();
+    
+    CshiftImplGauge<Gimpl> cshift_impl;
+    std::vector<GaugeMat> Ug_dirs(Nd,ggrid);
+    for(int i=0;i<Nd;i++) Ug_dirs[i] = Ghost.Exchange(PeekIndex<LorentzIndex>(U, i), cshift_impl);
+
+    GaugeMat gStaple(ggrid);
+
+    std::vector<Coordinate> shifts;
+    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));
+      }
+    }
+    size_t nshift = shifts.size();
+
+    GeneralLocalStencil gStencil(ggrid,shifts);
+    {
+      autoView( gStaple_v , gStaple, AcceleratorWrite);
+      auto gStencil_v = gStencil.View();
+
+      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] = Ug_dirs[i].View(AcceleratorRead);
+      GaugeViewType* Ug_dirs_v = (GaugeViewType*)acceleratorAllocDevice(vsize);
+      acceleratorCopyToDevice(Ug_dirs_v_host,Ug_dirs_v,vsize);
+
+      accelerator_for(ss, ggrid->oSites(), ggrid->Nsimd(), {
+	  decltype(coalescedRead(Ug_dirs_v[0][0])) stencil_ss;
+	  stencil_ss = Zero();
+	  int s=0;
+	  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;   
+
+	    }
+	  }
+	  assert(s==nshift);
+	  coalescedWrite(gStaple_v[ss],stencil_ss);
+	}
+	);
+  
+      for(int i=0;i<Nd;i++) Ug_dirs_v_host[i].ViewClose();
+      free(Ug_dirs_v_host);
+      acceleratorFreeDevice(Ug_dirs_v);
+    }   
+    Stap = Ghost.Extract(gStaple);    
+  }
+
+
+
+};  
+  
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  Coordinate latt_size  = GridDefaultLatt();
+  Coordinate simd_layout= GridDefaultSimd(Nd,vComplexD::Nsimd());
+  Coordinate mpi_layout = GridDefaultMpi();
+  std::cout << " mpi "<<mpi_layout<<std::endl;
+  std::cout << " simd "<<simd_layout<<std::endl;
+  std::cout << " latt "<<latt_size<<std::endl;
+  GridCartesian GRID(latt_size,simd_layout,mpi_layout);
+
+  GridParallelRNG   pRNG(&GRID);
+  pRNG.SeedFixedIntegers(std::vector<int>({45,12,81,9}));
+  LatticeGaugeField U(&GRID);
+
+  SU<Nc>::HotConfiguration(pRNG,U);
+
+  //typedef PeriodicGimplD Gimpl;
+  typedef ConjugateGimplD Gimpl;
+  std::vector<int> conj_dirs(Nd,0); conj_dirs[0]=1; conj_dirs[3]=1;
+  Gimpl::setDirections(conj_dirs);
+
+  typedef typename WilsonLoopsTest<Gimpl>::GaugeMat GaugeMat;
+  typedef typename WilsonLoopsTest<Gimpl>::GaugeLorentz GaugeLorentz;
+
+  std::cout << GridLogMessage << "Checking Staple" << std::endl;
+  int count = 0;
+  double torig=0, tpadded=0;
+  
+  for(int mu=0;mu<Nd;mu++){
+    for(int nu=0;nu<Nd;nu++){
+      if(mu != nu){
+	GaugeMat staple_orig(&GRID), staple_padded(&GRID);
+	double t0 = usecond();
+	WilsonLoopsTest<Gimpl>::StapleOrig(staple_orig,U,mu,nu);
+	double t1 = usecond();
+	WilsonLoopsTest<Gimpl>::StaplePadded(staple_padded,U,mu,nu);
+	double t2 = usecond();
+	torig += t1-t0;  tpadded += t2-t1;
+	++count;
+	
+	GaugeMat diff = staple_orig - staple_padded;
+	double n = norm2(diff);
+	std::cout << GridLogMessage << mu << " " << nu << " " << n << std::endl;
+	assert(n<1e-10);
+      }
+    }
+  }
+  std::cout << GridLogMessage << "Staple timings orig: " << torig/1000/count << "ms,  padded: " << tpadded/1000/count << "ms" << std::endl;
+  count=0; torig=tpadded=0;
+    
+  std::cout << GridLogMessage << "Checking RectStaple" << std::endl;
+  for(int mu=0;mu<Nd;mu++){
+    GaugeMat staple_orig(&GRID), staple_padded(&GRID);
+    double t0 = usecond();
+    WilsonLoopsTest<Gimpl>::RectStapleOrig(staple_orig,U,mu);
+    double t1 = usecond();
+    WilsonLoopsTest<Gimpl>::RectStaplePadded(staple_padded,U,mu);
+    double t2 = usecond();
+    torig += t1-t0;  tpadded += t2-t1;
+    ++count;
+    
+    GaugeMat diff = staple_orig - staple_padded;
+    double n = norm2(diff);
+    std::cout << GridLogMessage << mu << " " << n << std::endl;
+    assert(n<1e-10);
+  }
+  std::cout << GridLogMessage << "RectStaple timings orig: " << torig/1000/count << "ms,  padded: " << tpadded/1000/count << "ms" << std::endl;
+  
+  Grid_finalize();
+}

tests/solver/Test_coarse_even_odd.cc

@@ -93,16 +93,9 @@ int main(int argc, char** argv) {
   //                    Setup of Dirac Matrix and Operator                   //
   /////////////////////////////////////////////////////////////////////////////
 
+
   LatticeGaugeField Umu(Grid_f);
-#if (Nc==2)
-  SU2::HotConfiguration(pRNG_f, Umu);
-#elif (defined Nc==3)
-  SU3::HotConfiguration(pRNG_f, Umu);
-#elif (defined Nc==4)
-  SU4::HotConfiguration(pRNG_f, Umu);
-#elif (defined Nc==5)
-  SU5::HotConfiguration(pRNG_f, Umu);
-#endif
+  SU<Nc>::HotConfiguration(pRNG_f, Umu);
   RealD checkTolerance = (getPrecision<LatticeFermion>::value == 1) ? 1e-7 : 1e-15;
 
   RealD mass = -0.30;

tests/sp2n/Makefile.am

@@ -0,0 +1,8 @@
+.PHONY: check
+
+include Make.inc
+
+check: tests
+	./Test_project_on_Sp
+	./Test_sp2n_lie_gen
+	./Test_Sp_start

tests/sp2n/Test_2as_base.cc

@@ -0,0 +1,149 @@
+#include <Grid/Grid.h>
+
+#define verbose 0
+
+using namespace Grid;
+
+template<int this_nc>
+static void check_dimensions() {
+    
+    const int this_n = this_nc/2;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    
+    RealD realA;
+    std::cout << GridLogMessage << "Nc = " << this_n << " 2as dimension is " << Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension << std::endl;
+    std::cout << GridLogMessage << "Nc = " << this_n << " 2s dimension is " << Sp_TwoIndex<this_nc, Symmetric>::Dimension << std::endl;
+    std::cout << GridLogMessage << "Nc = " << this_n << " algebra dimension is " << this_algebra_dim << std::endl;
+    realA = Sp_TwoIndex<this_nc, AntiSymmetric>::Dimension + Sp_TwoIndex<this_nc, Symmetric>::Dimension;
+    std::cout << GridLogMessage << "Checking dim(2AS) + dim(AS) + 1 = Nc * Nc " << this_algebra_dim << std::endl;
+    assert ( realA == this_nc * this_nc - 1); // Nc x Nc = dim(2indxS) + dim(2indxAS) + dim(singlet)
+}
+
+template<int this_nc, TwoIndexSymmetry S>
+static void run_symmetry_checks() {
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    Matrix eij_c;
+    Matrix e_sum;
+    RealD realS = S;
+    
+    std::cout << GridLogMessage << "checking base has symmetry " << S << std::endl;
+    for (int a=0; a < this_irrep_dim; a++)
+    {
+        Sp_TwoIndex<this_nc, S>::base(a, eij_c);
+        e_sum = eij_c - realS * transpose(eij_c);
+        std::cout << GridLogMessage << "e_ab - (" << S << " * e_ab^T ) = " << norm2(e_sum) << std::endl;
+        assert(norm2(e_sum) < 1e-8);
+          
+    }
+}
+
+template<int this_nc, TwoIndexSymmetry S>
+static void run_traces_checks() {
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    Matrix eij_a;
+    Matrix eij_b;
+    Matrix Omega;
+    Sp<this_nc>::Omega(Omega);
+    RealD realS = S;
+    RealD realA;
+    
+    std::cout << GridLogMessage << "Checking Tr (e^(ab) Omega ) = 0 and Tr (e^(ab) e^(cd) = delta^((ab)(cd)) ) " << std::endl;
+    for (int a=0; a < Sp_TwoIndex<this_nc, S>::Dimension; a++) {
+        Sp_TwoIndex<this_nc, S>::base(a, eij_a);
+        realA = norm2(trace(Omega*eij_a));
+        std::cout << GridLogMessage << "Checkig Omega-trace for e_{ab=" << a << "} " << std::endl;
+        //std::cout << GridLogMessage << "Tr ( Omega e_{ab=" << a << "} ) = " << realA << std::endl;
+        assert(realA < 1e-8);
+        for (int b=0; b < Sp_TwoIndex<this_nc, S>::Dimension; b++) {
+            Sp_TwoIndex<this_nc, S>::base(b, eij_b);
+            auto d_ab = TensorRemove(trace(eij_a * eij_b));
+    #if verbose
+            std::cout << GridLogMessage << "Tr( e_{ab=" << a << "} e_{cd=" << b << "} ) = " << d_ab << std::endl;
+    #endif
+            std::cout << GridLogMessage << "Checking orthonormality for e_{ab = " << a << "} " << std::endl;
+            if (a==b) {
+                assert(real(d_ab) - realS < 1e-8);
+            } else {
+                assert(real(d_ab) < 1e-8);
+            }
+            assert(imag(d_ab) < 1e-8);
+            assert(imag(d_ab) < 1e-8);
+        }
+    }
+    
+}
+
+template<int this_nc, TwoIndexSymmetry S>
+static void run_generators_checks() {
+    const int this_n = this_nc/2;
+    const int this_irrep_dim = Sp_TwoIndex<this_nc, S>::Dimension;
+    const int this_algebra_dim = Sp<this_nc>::AlgebraDimension;
+    typedef typename Sp_TwoIndex<this_nc, S>::template iGroupMatrix<Complex> Matrix;
+    int sum = 0;
+    int sum_im = 0;
+    Vector<Matrix> ta_fund(this_algebra_dim);
+    Vector<Matrix> eij(this_irrep_dim);
+    Matrix tmp_l;
+    Matrix tmp_r;
+    for (int n = 0; n < this_algebra_dim; n++)
+    {
+        Sp<this_nc>::generator(n, ta_fund[n]);  // generators in the fundamental
+    }
+      for (int a = 0; a < this_irrep_dim; a++)
+    {
+        Sp_TwoIndex<this_nc, S>::base(a, eij[a]);   // base functions e_ij^a for upgrading gauge links from fund to 2-index
+    }
+    for (int gen_id = 0; gen_id < this_algebra_dim; gen_id++)
+    {
+        sum = 0;
+        sum_im = 0;
+        std::cout << GridLogMessage <<  "generator number " << gen_id << std::endl;
+        for (int a = 0; a < this_irrep_dim; a++)
+        {
+          
+            tmp_l = adj(eij[a])*ta_fund[gen_id]*eij[a];
+            tmp_r = adj(eij[a])*eij[a]*transpose(ta_fund[gen_id]);
+    #if verbose
+            std::cout << GridLogMessage << " as_indx = " << a << " eDag T_F e = " << std::endl << tmp_l << std::endl;
+            std::cout << GridLogMessage << " as_indx = " << a << " eDag e T_F^T = " << std::endl << tmp_r << std::endl;
+    #endif
+            //std::cout << GridLogMessage << " as_indx = " << a << " Tr(eDag T_F e + eDag e T_F^T) = " << TensorRemove(trace(tmp_l+tmp_r)) << std::endl;
+            sum += real(TensorRemove(trace(tmp_l+tmp_r)));
+            sum_im += imag(TensorRemove(trace(tmp_l+tmp_r)));
+        }
+        std::cout << GridLogMessage << "re-evaluated trace of the generator " << gen_id << " is " << sum << " " << sum_im << std::endl;
+        assert ( sum < 1e-8) ;
+        assert ( sum_im < 1e-8) ;
+    }
+    
+}
+    
+template<int this_nc, TwoIndexSymmetry S>
+static void run_base_checks() {
+    std::cout << GridLogMessage << " ****** " << std::endl;
+    std::cout << GridLogMessage << "Running checks for Nc = " << this_nc << " TwoIndex Symmetry = " << S << std::endl;
+    run_symmetry_checks<this_nc, S>();
+    run_traces_checks<this_nc, S>();
+    run_generators_checks<this_nc, S>();
+}
+
+int main(int argc, char** argv) {
+    check_dimensions<2>();
+    check_dimensions<4>();
+    check_dimensions<6>();
+    check_dimensions<8>();
+    
+    run_base_checks<2, Symmetric>();    // For Nc=2 the AS is the singlet
+    run_base_checks<4, Symmetric>();
+    run_base_checks<4, AntiSymmetric>();
+    run_base_checks<6, Symmetric>();
+    run_base_checks<6, AntiSymmetric>();
+    run_base_checks<8, Symmetric>();
+    run_base_checks<8, AntiSymmetric>();
+}

tests/sp2n/Test_Sp_start.cc

@@ -0,0 +1,110 @@
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+template <typename T>
+bool has_correct_group_block_structure(const T& U) {
+  std::cout << GridLogMessage << "Checking the structure is " << std::endl;
+  std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+  std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
+  std::cout << GridLogMessage << std::endl;
+
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
+  for (int c1 = 0; c1 < nsp; c1++)  // check on W
+  {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto W = PeekIndex<ColourIndex>(U, c1, c2);
+      auto Wstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2 + nsp);
+      auto Ww = conjugate(Wstar);
+      auto amizero = sum(W - Ww);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+
+  for (int c1 = 0; c1 < nsp; c1++) {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto X = PeekIndex<ColourIndex>(U, c1, c2 + nsp);
+      auto minusXstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2);
+      auto minusXx = conjugate(minusXstar);
+      auto amizero = sum(X + minusXx);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+  return true;
+};
+
+template <typename T>
+bool is_element_of_sp2n_group(const T& U) {
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
+
+  std::cout << GridLogMessage << "Unitary check" << std::endl;
+  aux = U * adj(U) - identity;
+  std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  aux = Omega - (U * Omega * transpose(U));
+  std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)
+            << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  std::cout << GridLogMessage
+            << "|Det| = " << norm2(Determinant(U)) / U.Grid()->gSites()
+            << std::endl;
+  assert(norm2(Determinant(U)) / U.Grid()->gSites() - 1 < 1e-8);
+
+  return has_correct_group_block_structure(U);
+}
+
+int main (int argc, char **argv)
+{
+    Grid_init(&argc,&argv);
+    
+    Coordinate latt_size   = GridDefaultLatt();
+    Coordinate simd_layout = GridDefaultSimd(Nd,vComplex::Nsimd());
+    Coordinate mpi_layout  = GridDefaultMpi();
+
+    GridCartesian             Grid(latt_size,simd_layout,mpi_layout);
+    GridRedBlackCartesian     RBGrid(&Grid);
+    
+    LatticeGaugeField Umu(&Grid);
+    LatticeColourMatrixD U(&Grid);
+    
+    std::vector<int> pseeds({1,2,3,4,5});
+    std::vector<int> sseeds({6,7,8,9,10});
+    GridParallelRNG  pRNG(&Grid); pRNG.SeedFixedIntegers(pseeds);
+    GridSerialRNG    sRNG;       sRNG.SeedFixedIntegers(sseeds);
+    
+    std::cout << GridLogMessage << "Checking Cold Configuration " << std::endl;
+    Sp<Nc>::ColdConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    assert(is_element_of_sp2n_group(U));
+    
+    std::cout << GridLogMessage << "Checking Hot Configuration" << std::endl;
+    Sp<Nc>::HotConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    assert(is_element_of_sp2n_group(U));
+    
+    std::cout << GridLogMessage << "Checking Tepid Configuration" << std::endl;
+    Sp<Nc>::TepidConfiguration(pRNG,Umu);
+    U = PeekIndex<LorentzIndex>(Umu,1);
+    assert(is_element_of_sp2n_group(U));
+    
+    Grid_finalize();
+
+
+    }
+

tests/sp2n/Test_hmc_Sp_WF_2_Fund_3_2AS.cc

@@ -0,0 +1,97 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+
+  typedef Representations< SpFundamentalRepresentation, SpTwoIndexAntiSymmetricRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper;
+
+  typedef SpWilsonTwoIndexAntiSymmetricImplR TwoIndexFermionImplPolicy;
+  typedef SpWilsonTwoIndexAntiSymmetricFermionD TwoIndexFermionAction;
+  typedef typename TwoIndexFermionAction::FermionField TwoIndexFermionField;
+
+  typedef SpWilsonImplR FundFermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionD FundFermionAction;                                     // ok
+  typedef typename FundFermionAction::FermionField FundFermionField;
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+
+  HMCWrapper TheHMC;
+
+  TheHMC.Resources.AddFourDimGrid("gauge");
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+
+  typedef PolyakovMod<HMCWrapper::ImplPolicy> PolyakovObs;
+  TheHMC.Resources.AddObservable<PolyakovObs>();
+
+  RealD beta = 6 ;
+
+  SpWilsonGaugeActionR Waction(beta);
+
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+
+  SpFundamentalRepresentation::LatticeField fundU(GridPtr);
+  SpTwoIndexAntiSymmetricRepresentation::LatticeField asU(GridPtr);
+    //LatticeGaugeField U(GridPtr);
+
+  RealD Fundmass = -0.71;
+  RealD ASmass = -0.71;
+  std::vector<Complex> boundary = {-1,-1,-1,-1};
+    
+  FundFermionAction::ImplParams bc(boundary);
+  TwoIndexFermionAction::ImplParams bbc(boundary);
+
+  FundFermionAction FundFermOp(fundU, *GridPtr, *GridRBPtr, Fundmass, bbc);
+  TwoIndexFermionAction TwoIndexFermOp(asU, *GridPtr, *GridRBPtr, ASmass, bbc);
+  ConjugateGradient<FundFermionField> fCG(1.0e-8, 2000, false);
+  ConjugateGradient<TwoIndexFermionField> asCG(1.0e-8, 2000, false);
+  OneFlavourRationalParams Params(1.0e-6, 64.0, 2000, 1.0e-6, 16);
+
+  TwoFlavourPseudoFermionAction<FundFermionImplPolicy> fundNf2(FundFermOp, fCG, fCG);
+  TwoFlavourPseudoFermionAction<TwoIndexFermionImplPolicy> asNf2(TwoIndexFermOp, asCG, asCG);
+  OneFlavourRationalPseudoFermionAction<TwoIndexFermionImplPolicy> asNf1(TwoIndexFermOp,Params);
+
+  fundNf2.is_smeared = false;
+  asNf2.is_smeared = false;
+  asNf1.is_smeared = false;
+  
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+  Level1.push_back(&fundNf2);
+  Level1.push_back(&asNf2);
+  Level1.push_back(&asNf1);
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+  Level2.push_back(&Waction);
+
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
+
+  TheHMC.Parameters.MD.MDsteps = 28;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
+
+  Grid_finalize();
+}

tests/sp2n/Test_hmc_Sp_Wilson2ASFermionGauge.cc

@@ -0,0 +1,81 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+
+  typedef Representations<SpFundamentalRepresentation,
+                          SpTwoIndexAntiSymmetricRepresentation>
+      TheRepresentations;
+
+  Grid_init(&argc, &argv);
+
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2>
+      HMCWrapper;
+  typedef SpWilsonTwoIndexAntiSymmetricImplR FermionImplPolicy;
+  typedef SpWilsonTwoIndexAntiSymmetricFermionD FermionAction;
+  typedef typename FermionAction::FermionField FermionField;
+
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+
+  HMCWrapper TheHMC;
+
+  TheHMC.Resources.AddFourDimGrid("gauge");
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 100;
+  CPparams.format = "IEEE64BIG";
+
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+
+  RealD beta = 6.7;
+
+  SpWilsonGaugeActionR Waction(beta);
+
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+
+  SpTwoIndexAntiSymmetricRepresentation::LatticeField U(GridPtr);
+  // LatticeGaugeField U(GridPtr);
+
+  RealD mass = -0.115;
+
+  std::vector<Complex> boundary = {-1, -1, -1, -1};
+  FermionAction::ImplParams bc(boundary);
+  FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass, bc);
+
+  ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
+
+  TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
+
+  Nf2.is_smeared = false;
+  std::cout << GridLogMessage << "mass " << mass << std::endl;
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations> Level1(1);
+  Level1.push_back(&Nf2);
+
+  ActionLevel<HMCWrapper::Field, TheRepresentations> Level2(4);
+  Level2.push_back(&Waction);
+
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
+
+  TheHMC.Parameters.MD.MDsteps = 16;
+  TheHMC.Parameters.MD.trajL = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
+
+  Grid_finalize();
+}

tests/sp2n/Test_hmc_Sp_WilsonFundFermionGauge.cc

@@ -0,0 +1,74 @@
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) {
+  using namespace Grid;
+   
+  typedef Representations< SpFundamentalRepresentation > TheRepresentations;
+
+  Grid_init(&argc, &argv);
+    
+  typedef GenericSpHMCRunnerHirep<TheRepresentations, MinimumNorm2> HMCWrapper; // ok
+  typedef SpWilsonImplR FermionImplPolicy;                                    // ok
+  typedef SpWilsonFermionD FermionAction;                                     // ok
+  typedef typename FermionAction::FermionField FermionField;                  // ok?
+ 
+  //::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+   
+  HMCWrapper TheHMC;
+    
+  TheHMC.Resources.AddFourDimGrid("gauge");
+    
+  // Checkpointer definition
+  CheckpointerParameters CPparams;
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 100;
+  CPparams.format = "IEEE64BIG";
+    
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "1 2 3 4 5";
+  RNGpar.parallel_seeds = "6 7 8 9 10";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+    
+  RealD beta = 7.2 ;
+    
+  SpWilsonGaugeActionR Waction(beta);
+    
+  auto GridPtr = TheHMC.Resources.GetCartesian();
+  auto GridRBPtr = TheHMC.Resources.GetRBCartesian();
+    
+  SpFundamentalRepresentation::LatticeField U(GridPtr);
+    
+  RealD mass = -0.76;
+
+  FermionAction FermOp(U, *GridPtr, *GridRBPtr, mass);
+
+  ConjugateGradient<FermionField> CG(1.0e-8, 2000, false);
+  
+  TwoFlavourPseudoFermionAction<FermionImplPolicy> Nf2(FermOp, CG, CG);
+    
+  Nf2.is_smeared = false;
+  
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level1(1);
+  Level1.push_back(&Nf2);
+    
+  ActionLevel<HMCWrapper::Field, TheRepresentations > Level2(4);
+  Level2.push_back(&Waction);
+    
+  TheHMC.TheAction.push_back(Level1);
+  TheHMC.TheAction.push_back(Level2);
+    
+  TheHMC.Parameters.MD.MDsteps = 36;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+    
+  TheHMC.ReadCommandLine(argc, argv);
+  TheHMC.Run();
+    
+  Grid_finalize();
+}

tests/sp2n/Test_hmc_Sp_pureGaugeWilson.cc

@@ -0,0 +1,99 @@
+/*************************************************************************************
+
+Grid physics library, www.github.com/paboyle/Grid
+
+Source file: ./tests/Test_hmc_WilsonFermionGauge.cc
+
+Copyright (C) 2015
+
+Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
+Author: neo <cossu@post.kek.jp>
+Author: Guido Cossu <guido.cossu@ed.ac.uk>
+
+This program is free software; you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation; either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License along
+with this program; if not, write to the Free Software Foundation, Inc.,
+51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
+
+See the full license in the file "LICENSE" in the top level distribution
+directory
+*************************************************************************************/
+/*  END LEGAL */
+#include <Grid/Grid.h>
+
+int main(int argc, char **argv) 
+{
+  using namespace Grid;
+
+  Grid_init(&argc, &argv);
+  GridLogLayout();
+
+  typedef GenericSpHMCRunner<MinimumNorm2> HMCWrapper;
+  HMCWrapper TheHMC;
+
+  TheHMC.Resources.AddFourDimGrid("gauge");
+
+  // Checkpointer definition
+  CheckpointerParameters CPparams;  
+  CPparams.config_prefix = "ckpoint_lat";
+  CPparams.rng_prefix = "ckpoint_rng";
+  CPparams.saveInterval = 5;
+  CPparams.format = "IEEE64BIG";
+  
+  TheHMC.Resources.LoadNerscCheckpointer(CPparams);
+
+  RNGModuleParameters RNGpar;
+  RNGpar.serial_seeds = "12 22 32 42 52";
+  RNGpar.parallel_seeds = "76 77 87 79 70";
+  TheHMC.Resources.SetRNGSeeds(RNGpar);
+
+  // Construct observables
+  // here there is too much indirection 
+  typedef PlaquetteMod<HMCWrapper::ImplPolicy> PlaqObs;
+  typedef TopologicalChargeMod<HMCWrapper::ImplPolicy> QObs;
+  TheHMC.Resources.AddObservable<PlaqObs>();
+  TopologyObsParameters TopParams;
+  TopParams.interval = 5;
+  TopParams.do_smearing = true;
+  TopParams.Smearing.init_step_size = 0.01;
+  TopParams.Smearing.tolerance = 1e-5;
+  //TopParams.Smearing.steps = 200;
+  //TopParams.Smearing.step_size = 0.01;
+  TopParams.Smearing.meas_interval = 50;
+  TopParams.Smearing.maxTau = 2.0; 
+  TheHMC.Resources.AddObservable<QObs>(TopParams);
+  //////////////////////////////////////////////
+
+  /////////////////////////////////////////////////////////////
+  // Collect actions, here use more encapsulation
+  // need wrappers of the fermionic classes 
+  // that have a complex construction
+  // standard
+  RealD beta = 8.0 ;
+  SpWilsonGaugeActionR Waction(beta);
+  
+  ActionLevel<HMCWrapper::Field> Level1(1);
+  Level1.push_back(&Waction);
+  //Level1.push_back(WGMod.getPtr());
+  TheHMC.TheAction.push_back(Level1);
+  /////////////////////////////////////////////////////////////
+
+  // HMC parameters are serialisable 
+  TheHMC.Parameters.MD.MDsteps = 10;
+  TheHMC.Parameters.MD.trajL   = 1.0;
+
+  TheHMC.ReadCommandLine(argc, argv); // these can be parameters from file
+  TheHMC.Run();  // no smearing
+
+  Grid_finalize();
+
+} // main

tests/sp2n/Test_project_on_Sp.cc

@@ -0,0 +1,240 @@
+#include <Grid/Grid.h>
+
+using namespace Grid;
+
+template <typename T>
+bool has_correct_group_block_structure(const T& U) {
+  std::cout << GridLogMessage << "Checking the structure is " << std::endl;
+  std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+  std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
+  std::cout << GridLogMessage << std::endl;
+
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
+  for (int c1 = 0; c1 < nsp; c1++)  // check on W
+  {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto W = PeekIndex<ColourIndex>(U, c1, c2);
+      auto Wstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2 + nsp);
+      auto Ww = conjugate(Wstar);
+      auto amizero = sum(W - Ww);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+
+  for (int c1 = 0; c1 < nsp; c1++) {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto X = PeekIndex<ColourIndex>(U, c1, c2 + nsp);
+      auto minusXstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2);
+      auto minusXx = conjugate(minusXstar);
+      auto amizero = sum(X + minusXx);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+  return true;
+};
+
+template <typename T>
+bool is_element_of_sp2n_group(const T& U) {
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
+
+  std::cout << GridLogMessage << "Unitary check" << std::endl;
+  aux = U * adj(U) - identity;
+  std::cout << GridLogMessage << "U adjU - 1 = " << norm2(aux) << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  aux = Omega - (U * Omega * transpose(U));
+  std::cout << GridLogMessage << "Omega - U Omega transpose(U) = " << norm2(aux)
+            << std::endl;
+  assert(norm2(aux) < 1e-8);
+
+  std::cout << GridLogMessage
+            << "|Det| = " << norm2(Determinant(U)) / U.Grid()->gSites()
+            << std::endl;
+  assert(norm2(Determinant(U)) / U.Grid()->gSites() - 1 < 1e-8);
+
+  return has_correct_group_block_structure(U);
+}
+
+template <typename T>
+void test_group_projections(T U) {
+  RealD Delta = 666.;
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << "Group" << std::endl;
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << std::endl;
+
+  std::string name = "ProjectOnSpGroup";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  U = ProjectOnSpGroup(U);
+  assert(is_element_of_sp2n_group(U));
+
+  name = "ProjectOnGeneralGroup";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  U = Sp<Nc>::ProjectOnGeneralGroup(U);
+  assert(is_element_of_sp2n_group(U));
+
+  name = "ProjectOnSpecialGroup";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  Sp<Nc>::ProjectOnSpecialGroup(U);
+  assert(is_element_of_sp2n_group(U));
+
+  name = "ProjectSpn";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  ProjectSpn(U);
+  assert(is_element_of_sp2n_group(U));
+}
+
+template <typename T>
+bool has_correct_algebra_block_structure(const T& U) {
+  // this only checks for the anti-hermitian part of the algebra
+  const int nsp = Nc / 2;
+  Complex i(0., 1.);
+  std::cout << GridLogMessage << "Checking the structure is " << std::endl;
+  std::cout << GridLogMessage << "U  =  (   W    X   )  " << std::endl;
+  std::cout << GridLogMessage << "      (  -X^*  W^* )  " << std::endl;
+  for (int c1 = 0; c1 < nsp; c1++)  // check on W
+  {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto W = PeekIndex<ColourIndex>(U, c1, c2);
+      auto Wstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2 + nsp);
+      auto Ww = conjugate(Wstar);
+      auto amizero = sum(W - Ww);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+  for (int c1 = 0; c1 < nsp; c1++) {
+    for (int c2 = 0; c2 < nsp; c2++) {
+      auto X = PeekIndex<ColourIndex>(U, c1, c2 + nsp);
+      auto minusXstar = PeekIndex<ColourIndex>(U, c1 + nsp, c2);
+      auto minusXx = conjugate(minusXstar);
+      auto amizero = sum(X + minusXx);
+      auto amizeroo = TensorRemove(amizero);
+      assert(amizeroo.real() < 10e-6);
+      amizeroo *= i;
+      assert(amizeroo.real() < 10e-6);
+    }
+  }
+
+  return true;
+}
+
+template <typename T>
+bool is_element_of_sp2n_algebra(const T& U) {
+  LatticeColourMatrixD aux(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+  LatticeColourMatrixD Omega(U.Grid());
+  Sp<Nc>::Omega(Omega);
+
+  std::cout << GridLogMessage << "Check matrix is non-zero " << std::endl;
+  assert(norm2(U) > 1e-8);
+
+  aux = U - adj(U);
+  std::cout << GridLogMessage << "T - Tda = " << norm2(aux)
+            << " (not supposed to vanish)" << std::endl;
+
+  aux = U + adj(U);
+  std::cout << GridLogMessage << "T + Tda = " << norm2(aux)
+            << " (supposed to vanish)" << std::endl;
+  assert(norm2(aux) - 1 < 1e-8);
+
+  std::cout << GridLogMessage << "Check that Omega T Omega + conj(T) = 0 "
+            << std::endl;
+  aux = Omega * U * Omega + conjugate(U);
+  assert(norm2(aux) < 1e-8);
+
+  return has_correct_algebra_block_structure(U);
+}
+
+template <typename T>
+void test_algebra_projections(T U) {
+  RealD Delta = 666.;
+  LatticeColourMatrixD tmp(U.Grid());
+  LatticeColourMatrixD identity(U.Grid());
+  identity = 1.0;
+
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << "Algebra" << std::endl;
+  std::cout << GridLogMessage << "#   #   #   #" << std::endl;
+  std::cout << GridLogMessage << std::endl;
+
+  std::string name = "SpTa";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  U = SpTa(U);
+  assert(is_element_of_sp2n_algebra(U));
+
+  name = "TaProj";
+  std::cout << GridLogMessage << "Testing " << name << std::endl;
+  std::cout << GridLogMessage << "Apply to deformed matrix" << std::endl;
+
+  U = U + Delta * identity;
+  Sp<Nc>::taProj(U, tmp);
+  U = tmp;
+  assert(is_element_of_sp2n_algebra(U));
+}
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+
+  Coordinate latt_size = GridDefaultLatt();
+  Coordinate simd_layout = GridDefaultSimd(Nd, vComplex::Nsimd());
+  Coordinate mpi_layout = GridDefaultMpi();
+
+  GridCartesian Grid(latt_size, simd_layout, mpi_layout);
+
+  LatticeGaugeField Umu(&Grid);
+  LatticeColourMatrixD U(&Grid);
+
+  // Will test resimplectification-related functionalities (from
+  // ProjectOnGeneralGroup, ProjectOnSpGroup, ProjectOnSpecialGroup) and projection on the
+  // algebra (from SpTa)
+  // ProjectOnGeneralGroup, ProjectOnSpGroup project on the non-special group allowi for complex determinants of module 1
+  // ProjectOnSpecialGroup projects on the full gauge group providing a determinant equals to 1
+
+  std::vector<int> pseeds({1, 2, 3, 4, 5});
+  GridParallelRNG pRNG(&Grid);
+  pRNG.SeedFixedIntegers(pseeds);
+
+  SU<Nc>::HotConfiguration(pRNG, Umu);
+  U = PeekIndex<LorentzIndex>(Umu, 0);
+  test_group_projections(U);
+  U = PeekIndex<LorentzIndex>(Umu, 1);
+  test_algebra_projections(U);
+
+  Grid_finalize();
+}

tests/sp2n/Test_sp2n_lie_gen.cc

@@ -0,0 +1,65 @@
+#include <Grid/Grid.h>
+
+#include <iostream>
+
+using namespace Grid;
+
+template <int ngroup>
+std::ostream& operator<<(std::ostream& o, Sp<ngroup> g) {
+  return o << "Sp(" << ngroup << ") Fundamental";
+}
+
+template <int ngroup, TwoIndexSymmetry S>
+std::ostream& operator<<(std::ostream& o, Sp_TwoIndex<ngroup, S> g) {
+  return o << "Sp(" << ngroup << ") TwoIndex "
+           << (S == Symmetric ? "Symmetric" : "AntiSymmetric");
+}
+
+template <class Group>
+void run_check_on(bool print_generators = false) {
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+  std::cout << GridLogMessage << "* Generators for " << Group() << std::endl;
+  std::cout << GridLogMessage << "*********************************************"
+            << std::endl;
+
+  if (print_generators) {
+    Group::printGenerators();
+  }
+  Group::testGenerators();
+}
+
+template <int ngroup>
+void run_checks() {
+  run_check_on<Sp<ngroup>>();
+  run_check_on<Sp_TwoIndex<ngroup, Symmetric>>();
+  run_check_on<Sp_TwoIndex<ngroup, AntiSymmetric>>();
+}
+
+template <>
+void run_checks<2>() {
+  // Print generators because they are small enough to be actually helpful.
+  run_check_on<Sp<2>>(true);
+  run_check_on<Sp_TwoIndex<2, Symmetric>>(true);
+  // The AntiSymmetric representation is 0 dimensional. This makes problems in
+  // device code.
+}
+
+template <>
+void run_checks<4>() {
+  // Print generators because they are small enough to be actually helpful.
+  run_check_on<Sp<4>>(true);
+  run_check_on<Sp_TwoIndex<4, Symmetric>>(true);
+  run_check_on<Sp_TwoIndex<4, AntiSymmetric>>(true);
+}
+
+int main(int argc, char** argv) {
+  Grid_init(&argc, &argv);
+
+  run_checks<2>();
+  run_checks<4>();
+  run_checks<6>();
+  run_checks<8>();
+
+  Grid_finalize();
+}