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Grid/lib/lattice/Lattice_reduction.h

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/*************************************************************************************
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 mySsliceInnerProductVector" << 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
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