Grid/lib/lattice/Lattice_reduction.h

/*************************************************************************************
    Grid physics library, www.github.com/paboyle/Grid 
    Source file: ./lib/lattice/Lattice_reduction.h
    Copyright (C) 2015
Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: paboyle <paboyle@ph.ed.ac.uk>
    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
    See the full license in the file "LICENSE" in the top level distribution directory
    *************************************************************************************/
    /*  END LEGAL */
#ifndef GRID_LATTICE_REDUCTION_H
#define GRID_LATTICE_REDUCTION_H

#include <Grid/Grid_Eigen_Dense.h>

namespace Grid {
#ifdef GRID_WARN_SUBOPTIMAL
#warning "Optimisation alert all these reduction loops are NOT threaded "
#endif     

  ////////////////////////////////////////////////////////////////////////////////////////////////////
  // Deterministic Reduction operations
  ////////////////////////////////////////////////////////////////////////////////////////////////////
template<class vobj> inline RealD norm2(const Lattice<vobj> &arg){
  auto nrm = innerProduct(arg,arg);
  return std::real(nrm); 
}

// Double inner product
template<class vobj>
inline ComplexD innerProduct(const Lattice<vobj> &left,const Lattice<vobj> &right)
{
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_typeD vector_type;
  GridBase *grid = left._grid;
  const int pad = 8;

  ComplexD  inner;
  Vector<ComplexD> sumarray(grid->SumArraySize()*pad);

  parallel_for(int thr=0;thr<grid->SumArraySize();thr++){
    int nwork, mywork, myoff;
    GridThread::GetWork(left._grid->oSites(),thr,mywork,myoff);
    
    decltype(innerProductD(left._odata[0],right._odata[0])) vinner=zero; // private to thread; sub summation
    for(int ss=myoff;ss<mywork+myoff; ss++){
      vinner = vinner + innerProductD(left._odata[ss],right._odata[ss]);
    }
    // All threads sum across SIMD; reduce serial work at end
    // one write per cacheline with streaming store
    ComplexD tmp = Reduce(TensorRemove(vinner)) ;
    vstream(sumarray[thr*pad],tmp);
  }
  inner=0.0;
  for(int i=0;i<grid->SumArraySize();i++){
    inner = inner+sumarray[i*pad];
  } 
  right._grid->GlobalSum(inner);
  return inner;
}

/////////////////////////
// Fast axpby_norm
// z = a x + b y
// return norm z
/////////////////////////
template<class sobj,class vobj> strong_inline RealD 
axpy_norm_fast(Lattice<vobj> &z,sobj a,const Lattice<vobj> &x,const Lattice<vobj> &y) 
{
  sobj one(1.0);
  return axpby_norm_fast(z,a,one,x,y);
}

template<class sobj,class vobj> strong_inline RealD 
axpby_norm_fast(Lattice<vobj> &z,sobj a,sobj b,const Lattice<vobj> &x,const Lattice<vobj> &y) 
{
  const int pad = 8;
  z.checkerboard = x.checkerboard;
  conformable(z,x);
  conformable(x,y);

  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_typeD vector_type;
  RealD  nrm;
  
  GridBase *grid = x._grid;
  
  Vector<RealD> sumarray(grid->SumArraySize()*pad);
  
  parallel_for(int thr=0;thr<grid->SumArraySize();thr++){
    int nwork, mywork, myoff;
    GridThread::GetWork(x._grid->oSites(),thr,mywork,myoff);
    
    // private to thread; sub summation
    decltype(innerProductD(z._odata[0],z._odata[0])) vnrm=zero; 
    for(int ss=myoff;ss<mywork+myoff; ss++){
      vobj tmp = a*x._odata[ss]+b*y._odata[ss];
      vnrm = vnrm + innerProductD(tmp,tmp);
      vstream(z._odata[ss],tmp);
    }
    vstream(sumarray[thr*pad],real(Reduce(TensorRemove(vnrm)))) ;
  }
  
  nrm = 0.0; // sum across threads; linear in thread count but fast
  for(int i=0;i<grid->SumArraySize();i++){
    nrm = nrm+sumarray[i*pad];
  } 
  z._grid->GlobalSum(nrm);
  return nrm; 
}

 
template<class Op,class T1>
inline auto sum(const LatticeUnaryExpression<Op,T1> & expr)
  ->typename decltype(expr.first.func(eval(0,std::get<0>(expr.second))))::scalar_object
{
  return sum(closure(expr));
}

template<class Op,class T1,class T2>
inline auto sum(const LatticeBinaryExpression<Op,T1,T2> & expr)
      ->typename decltype(expr.first.func(eval(0,std::get<0>(expr.second)),eval(0,std::get<1>(expr.second))))::scalar_object
{
  return sum(closure(expr));
}


template<class Op,class T1,class T2,class T3>
inline auto sum(const LatticeTrinaryExpression<Op,T1,T2,T3> & expr)
  ->typename decltype(expr.first.func(eval(0,std::get<0>(expr.second)),
				      eval(0,std::get<1>(expr.second)),
				      eval(0,std::get<2>(expr.second))
				      ))::scalar_object
{
  return sum(closure(expr));
}

template<class vobj>
inline typename vobj::scalar_object sum(const Lattice<vobj> &arg)
{
  GridBase *grid=arg._grid;
  int Nsimd = grid->Nsimd();
  
  std::vector<vobj,alignedAllocator<vobj> > sumarray(grid->SumArraySize());
  for(int i=0;i<grid->SumArraySize();i++){
    sumarray[i]=zero;
  }
  
  parallel_for(int thr=0;thr<grid->SumArraySize();thr++){
    int nwork, mywork, myoff;
    GridThread::GetWork(grid->oSites(),thr,mywork,myoff);
    
    vobj vvsum=zero;
    for(int ss=myoff;ss<mywork+myoff; ss++){
      vvsum = vvsum + arg._odata[ss];
    }
    sumarray[thr]=vvsum;
  }
  
  vobj vsum=zero;  // sum across threads
  for(int i=0;i<grid->SumArraySize();i++){
    vsum = vsum+sumarray[i];
  } 
  
  typedef typename vobj::scalar_object sobj;
  sobj ssum=zero;
  
  std::vector<sobj>               buf(Nsimd);
  extract(vsum,buf);
  
  for(int i=0;i<Nsimd;i++) ssum = ssum + buf[i];
  arg._grid->GlobalSum(ssum);
  
  return ssum;
}


//////////////////////////////////////////////////////////////////////////////////////////////////////////////
// sliceSum, sliceInnerProduct, sliceAxpy, sliceNorm etc...
//////////////////////////////////////////////////////////////////////////////////////////////////////////////

template<class vobj> inline void sliceSum(const Lattice<vobj> &Data,std::vector<typename vobj::scalar_object> &result,int orthogdim)
{
  ///////////////////////////////////////////////////////
  // FIXME precision promoted summation
  // may be important for correlation functions
  // But easily avoided by using double precision fields
  ///////////////////////////////////////////////////////
  typedef typename vobj::scalar_object sobj;
  GridBase  *grid = Data._grid;
  assert(grid!=NULL);

  const int    Nd = grid->_ndimension;
  const int Nsimd = grid->Nsimd();

  assert(orthogdim >= 0);
  assert(orthogdim < Nd);

  int fd=grid->_fdimensions[orthogdim];
  int ld=grid->_ldimensions[orthogdim];
  int rd=grid->_rdimensions[orthogdim];

  std::vector<vobj,alignedAllocator<vobj> > lvSum(rd); // will locally sum vectors first
  std::vector<sobj> lsSum(ld,zero);                    // sum across these down to scalars
  std::vector<sobj> extracted(Nsimd);                  // splitting the SIMD

  result.resize(fd); // And then global sum to return the same vector to every node 
  for(int r=0;r<rd;r++){
    lvSum[r]=zero;
  }

  int e1=    grid->_slice_nblock[orthogdim];
  int e2=    grid->_slice_block [orthogdim];
  int stride=grid->_slice_stride[orthogdim];

  // sum over reduced dimension planes, breaking out orthog dir
  // Parallel over orthog direction
  parallel_for(int r=0;r<rd;r++){

    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 

    for(int n=0;n<e1;n++){
      for(int b=0;b<e2;b++){
	int ss= so+n*stride+b;
	lvSum[r]=lvSum[r]+Data._odata[ss];
      }
    }
  }

  // Sum across simd lanes in the plane, breaking out orthog dir.
  std::vector<int> icoor(Nd);

  for(int rt=0;rt<rd;rt++){

    extract(lvSum[rt],extracted);

    for(int idx=0;idx<Nsimd;idx++){

      grid->iCoorFromIindex(icoor,idx);

      int ldx =rt+icoor[orthogdim]*rd;

      lsSum[ldx]=lsSum[ldx]+extracted[idx];

    }
  }
  
  // sum over nodes.
  sobj gsum;
  for(int t=0;t<fd;t++){
    int pt = t/ld; // processor plane
    int lt = t%ld;
    if ( pt == grid->_processor_coor[orthogdim] ) {
      gsum=lsSum[lt];
    } else {
      gsum=zero;
    }

    grid->GlobalSum(gsum);

    result[t]=gsum;
  }
}

template<class vobj>
static void mySliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim)
{
  std::cout << GridLogMessage << "Start mySliceInnerProductVector" << std::endl;

  typedef typename vobj::scalar_type scalar_type;
  std::vector<scalar_type> lsSum;
  localSliceInnerProductVector(result, lhs, rhs, lsSum, orthogdim);
  globalSliceInnerProductVector(result, lhs, lsSum, orthogdim);
  std::cout << GridLogMessage << "End mySliceInnerProductVector" << std::endl;
}

template <class vobj>
static void localSliceInnerProductVector(std::vector<ComplexD> &result, const Lattice<vobj> &lhs, const Lattice<vobj> &rhs, std::vector<typename vobj::scalar_type> &lsSum, int orthogdim)
{
  std::cout << GridLogMessage << "Start prep" << std::endl;
  typedef typename vobj::vector_type   vector_type;
  typedef typename vobj::scalar_type   scalar_type;
  GridBase  *grid = lhs._grid;
  assert(grid!=NULL);
  conformable(grid,rhs._grid);

  const int    Nd = grid->_ndimension;
  const int Nsimd = grid->Nsimd();

  assert(orthogdim >= 0);
  assert(orthogdim < Nd);

  int fd=grid->_fdimensions[orthogdim];
  int ld=grid->_ldimensions[orthogdim];
  int rd=grid->_rdimensions[orthogdim];
  // std::cout << GridLogMessage << "Start alloc" << std::endl;

  std::vector<vector_type,alignedAllocator<vector_type> > lvSum(rd); // will locally sum vectors first
  lsSum.resize(ld,scalar_type(0.0));                    // sum across these down to scalars
  std::vector<iScalar<scalar_type>> extracted(Nsimd);   // splitting the SIMD  
  // std::cout << GridLogMessage << "End alloc" << std::endl;

  result.resize(fd); // And then global sum to return the same vector to every node for IO to file
  for(int r=0;r<rd;r++){
    lvSum[r]=zero;
  }

  int e1=    grid->_slice_nblock[orthogdim];
  int e2=    grid->_slice_block [orthogdim];
  int stride=grid->_slice_stride[orthogdim];
  // std::cout << GridLogMessage << "End prep" << std::endl;
  // std::cout << GridLogMessage << "Start parallel inner product, _rd = " << rd << std::endl;
  vector_type vv;
  parallel_for(int r=0;r<rd;r++)
  {

    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 

    for(int n=0;n<e1;n++){
      for(int b=0;b<e2;b++){
        int ss = so + n * stride + b;
        vv = TensorRemove(innerProduct(lhs._odata[ss], rhs._odata[ss]));
        lvSum[r] = lvSum[r] + vv;
      }
    }
  }
  // std::cout << GridLogMessage << "End parallel inner product" << std::endl;

  // Sum across simd lanes in the plane, breaking out orthog dir.
  std::vector<int> icoor(Nd);
  for(int rt=0;rt<rd;rt++){

    iScalar<vector_type> temp; 
    temp._internal = lvSum[rt];
    extract(temp,extracted);

    for(int idx=0;idx<Nsimd;idx++){

      grid->iCoorFromIindex(icoor,idx);

      int ldx =rt+icoor[orthogdim]*rd;

      lsSum[ldx]=lsSum[ldx]+extracted[idx]._internal;

    }
  }
  // std::cout << GridLogMessage << "End sum over simd lanes" << std::endl;
}
template <class vobj>
static void globalSliceInnerProductVector(std::vector<ComplexD> &result, const Lattice<vobj> &lhs, std::vector<typename vobj::scalar_type> &lsSum, int orthogdim)
{
  typedef typename vobj::scalar_type scalar_type;
  GridBase *grid = lhs._grid;
  int fd = result.size();
  int ld = lsSum.size();
  // sum over nodes.
  std::vector<scalar_type> gsum;
  gsum.resize(fd, scalar_type(0.0));
  // std::cout << GridLogMessage << "Start of gsum[t] creation:" << std::endl;
  for(int t=0;t<fd;t++){
    int pt = t/ld; // processor plane
    int lt = t%ld;
    if ( pt == grid->_processor_coor[orthogdim] ) {
      gsum[t]=lsSum[lt];
    }
  }
  // std::cout << GridLogMessage << "End of gsum[t] creation:" << std::endl;
  // std::cout << GridLogMessage << "Start of GlobalSumVector:" << std::endl;
  grid->GlobalSumVector(&gsum[0], fd);
  // std::cout << GridLogMessage << "End of GlobalSumVector:" << std::endl;

  result = gsum;
}
template<class vobj>
static void sliceInnerProductVector( std::vector<ComplexD> & result, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int orthogdim) 
{
  typedef typename vobj::vector_type   vector_type;
  typedef typename vobj::scalar_type   scalar_type;
  GridBase  *grid = lhs._grid;
  assert(grid!=NULL);
  conformable(grid,rhs._grid);

  const int    Nd = grid->_ndimension;
  const int Nsimd = grid->Nsimd();

  assert(orthogdim >= 0);
  assert(orthogdim < Nd);

  int fd=grid->_fdimensions[orthogdim];
  int ld=grid->_ldimensions[orthogdim];
  int rd=grid->_rdimensions[orthogdim];

  std::vector<vector_type,alignedAllocator<vector_type> > lvSum(rd); // will locally sum vectors first
  std::vector<scalar_type > lsSum(ld,scalar_type(0.0));                    // sum across these down to scalars
  std::vector<iScalar<scalar_type> > extracted(Nsimd);                  // splitting the SIMD

  result.resize(fd); // And then global sum to return the same vector to every node for IO to file
  for(int r=0;r<rd;r++){
    lvSum[r]=zero;
  }

  int e1=    grid->_slice_nblock[orthogdim];
  int e2=    grid->_slice_block [orthogdim];
  int stride=grid->_slice_stride[orthogdim];

  parallel_for(int r=0;r<rd;r++){

    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 

    for(int n=0;n<e1;n++){
      for(int b=0;b<e2;b++){
	int ss= so+n*stride+b;
	vector_type vv = TensorRemove(innerProduct(lhs._odata[ss],rhs._odata[ss]));
	lvSum[r]=lvSum[r]+vv;
      }
    }
  }

  // Sum across simd lanes in the plane, breaking out orthog dir.
  std::vector<int> icoor(Nd);
  for(int rt=0;rt<rd;rt++){

    iScalar<vector_type> temp; 
    temp._internal = lvSum[rt];
    extract(temp,extracted);

    for(int idx=0;idx<Nsimd;idx++){

      grid->iCoorFromIindex(icoor,idx);

      int ldx =rt+icoor[orthogdim]*rd;

      lsSum[ldx]=lsSum[ldx]+extracted[idx]._internal;

    }
  }
  
  // sum over nodes.
  scalar_type gsum;
  for(int t=0;t<fd;t++){
    int pt = t/ld; // processor plane
    int lt = t%ld;
    if ( pt == grid->_processor_coor[orthogdim] ) {
      gsum=lsSum[lt];
    } else {
      gsum=scalar_type(0.0);
    }

    grid->GlobalSum(gsum);

    result[t]=gsum;
  }
}
template<class vobj>
static void sliceNorm (std::vector<RealD> &sn,const Lattice<vobj> &rhs,int Orthog) 
{
  typedef typename vobj::scalar_object sobj;
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_type vector_type;
  
  int Nblock = rhs._grid->GlobalDimensions()[Orthog];
  std::vector<ComplexD> ip(Nblock);
  sn.resize(Nblock);
  
  sliceInnerProductVector(ip,rhs,rhs,Orthog);
  for(int ss=0;ss<Nblock;ss++){
    sn[ss] = real(ip[ss]);
  }
};


template<class vobj>
static void sliceMaddVector(Lattice<vobj> &R,std::vector<RealD> &a,const Lattice<vobj> &X,const Lattice<vobj> &Y,
			    int orthogdim,RealD scale=1.0) 
{    
  typedef typename vobj::scalar_object sobj;
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_type vector_type;
  typedef typename vobj::tensor_reduced tensor_reduced;
  
  scalar_type zscale(scale);

  GridBase *grid  = X._grid;

  int Nsimd  =grid->Nsimd();
  int Nblock =grid->GlobalDimensions()[orthogdim];

  int fd     =grid->_fdimensions[orthogdim];
  int ld     =grid->_ldimensions[orthogdim];
  int rd     =grid->_rdimensions[orthogdim];

  int e1     =grid->_slice_nblock[orthogdim];
  int e2     =grid->_slice_block [orthogdim];
  int stride =grid->_slice_stride[orthogdim];

  std::vector<int> icoor;

  for(int r=0;r<rd;r++){

    int so=r*grid->_ostride[orthogdim]; // base offset for start of plane 

    vector_type    av;

    for(int l=0;l<Nsimd;l++){
      grid->iCoorFromIindex(icoor,l);
      int ldx =r+icoor[orthogdim]*rd;
      scalar_type *as =(scalar_type *)&av;
      as[l] = scalar_type(a[ldx])*zscale;
    }

    tensor_reduced at; at=av;

    parallel_for_nest2(int n=0;n<e1;n++){
      for(int b=0;b<e2;b++){
	int ss= so+n*stride+b;
	R._odata[ss] = at*X._odata[ss]+Y._odata[ss];
      }
    }
  }
};

/*
inline GridBase         *makeSubSliceGrid(const GridBase *BlockSolverGrid,int Orthog)
{
  int NN    = BlockSolverGrid->_ndimension;
  int nsimd = BlockSolverGrid->Nsimd();
  
  std::vector<int> latt_phys(0);
  std::vector<int> simd_phys(0);
  std::vector<int>  mpi_phys(0);
  
  for(int d=0;d<NN;d++){
    if( d!=Orthog ) { 
      latt_phys.push_back(BlockSolverGrid->_fdimensions[d]);
      simd_phys.push_back(BlockSolverGrid->_simd_layout[d]);
      mpi_phys.push_back(BlockSolverGrid->_processors[d]);
    }
  }
  return (GridBase *)new GridCartesian(latt_phys,simd_phys,mpi_phys); 
}
*/

template<class vobj>
static void sliceMaddMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,const Lattice<vobj> &Y,int Orthog,RealD scale=1.0) 
{    
  typedef typename vobj::scalar_object sobj;
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_type vector_type;

  int Nblock = X._grid->GlobalDimensions()[Orthog];

  GridBase *FullGrid  = X._grid;
  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);

  //  Lattice<vobj> Xslice(SliceGrid);
  //  Lattice<vobj> Rslice(SliceGrid);

  assert( FullGrid->_simd_layout[Orthog]==1);
  int nh =  FullGrid->_ndimension;
  //  int nl = SliceGrid->_ndimension;
  int nl = nh-1;

  //FIXME package in a convenient iterator
  //Should loop over a plane orthogonal to direction "Orthog"
  int stride=FullGrid->_slice_stride[Orthog];
  int block =FullGrid->_slice_block [Orthog];
  int nblock=FullGrid->_slice_nblock[Orthog];
  int ostride=FullGrid->_ostride[Orthog];
#pragma omp parallel 
  {
    std::vector<vobj> s_x(Nblock);

#pragma omp for collapse(2)
    for(int n=0;n<nblock;n++){
    for(int b=0;b<block;b++){
      int o  = n*stride + b;

      for(int i=0;i<Nblock;i++){
	s_x[i] = X[o+i*ostride];
      }

      vobj dot;
      for(int i=0;i<Nblock;i++){
	dot = Y[o+i*ostride];
	for(int j=0;j<Nblock;j++){
	  dot = dot + s_x[j]*(scale*aa(j,i));
	}
	R[o+i*ostride]=dot;
      }
    }}
  }
};

template<class vobj>
static void sliceMulMatrix (Lattice<vobj> &R,Eigen::MatrixXcd &aa,const Lattice<vobj> &X,int Orthog,RealD scale=1.0) 
{    
  typedef typename vobj::scalar_object sobj;
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_type vector_type;

  int Nblock = X._grid->GlobalDimensions()[Orthog];

  GridBase *FullGrid  = X._grid;
  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
  //  Lattice<vobj> Xslice(SliceGrid);
  //  Lattice<vobj> Rslice(SliceGrid);

  assert( FullGrid->_simd_layout[Orthog]==1);
  int nh =  FullGrid->_ndimension;
  //  int nl = SliceGrid->_ndimension;
  int nl=1;

  //FIXME package in a convenient iterator
  //Should loop over a plane orthogonal to direction "Orthog"
  int stride=FullGrid->_slice_stride[Orthog];
  int block =FullGrid->_slice_block [Orthog];
  int nblock=FullGrid->_slice_nblock[Orthog];
  int ostride=FullGrid->_ostride[Orthog];
#pragma omp parallel 
  {
    std::vector<vobj> s_x(Nblock);

#pragma omp for collapse(2)
    for(int n=0;n<nblock;n++){
    for(int b=0;b<block;b++){
      int o  = n*stride + b;

      for(int i=0;i<Nblock;i++){
	s_x[i] = X[o+i*ostride];
      }

      vobj dot;
      for(int i=0;i<Nblock;i++){
	dot = s_x[0]*(scale*aa(0,i));
	for(int j=1;j<Nblock;j++){
	  dot = dot + s_x[j]*(scale*aa(j,i));
	}
	R[o+i*ostride]=dot;
      }
    }}
  }

};


template<class vobj>
static void sliceInnerProductMatrix(  Eigen::MatrixXcd &mat, const Lattice<vobj> &lhs,const Lattice<vobj> &rhs,int Orthog) 
{
  typedef typename vobj::scalar_object sobj;
  typedef typename vobj::scalar_type scalar_type;
  typedef typename vobj::vector_type vector_type;
  
  GridBase *FullGrid  = lhs._grid;
  //  GridBase *SliceGrid = makeSubSliceGrid(FullGrid,Orthog);
  
  int Nblock = FullGrid->GlobalDimensions()[Orthog];
  
  //  Lattice<vobj> Lslice(SliceGrid);
  //  Lattice<vobj> Rslice(SliceGrid);
  
  mat = Eigen::MatrixXcd::Zero(Nblock,Nblock);

  assert( FullGrid->_simd_layout[Orthog]==1);
  int nh =  FullGrid->_ndimension;
  //  int nl = SliceGrid->_ndimension;
  int nl = nh-1;

  //FIXME package in a convenient iterator
  //Should loop over a plane orthogonal to direction "Orthog"
  int stride=FullGrid->_slice_stride[Orthog];
  int block =FullGrid->_slice_block [Orthog];
  int nblock=FullGrid->_slice_nblock[Orthog];
  int ostride=FullGrid->_ostride[Orthog];

  typedef typename vobj::vector_typeD vector_typeD;

#pragma omp parallel 
  {
    std::vector<vobj> Left(Nblock);
    std::vector<vobj> Right(Nblock);
    Eigen::MatrixXcd  mat_thread = Eigen::MatrixXcd::Zero(Nblock,Nblock);

#pragma omp for collapse(2)
    for(int n=0;n<nblock;n++){
    for(int b=0;b<block;b++){

      int o  = n*stride + b;

      for(int i=0;i<Nblock;i++){
	Left [i] = lhs[o+i*ostride];
	Right[i] = rhs[o+i*ostride];
      }

      for(int i=0;i<Nblock;i++){
      for(int j=0;j<Nblock;j++){
	auto tmp = innerProduct(Left[i],Right[j]);
	auto rtmp = TensorRemove(tmp);
	mat_thread(i,j) += Reduce(rtmp);
      }}
    }}
#pragma omp critical
    {
      mat += mat_thread;
    }  
  }

  for(int i=0;i<Nblock;i++){
  for(int j=0;j<Nblock;j++){
    ComplexD sum = mat(i,j);
    FullGrid->GlobalSum(sum);
    mat(i,j)=sum;
  }}

  return;
}

} /*END NAMESPACE GRID*/
#endif