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Merge branch 'develop' into feature/scidac-wp1

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This commit is contained in:
Peter Boyle 2023-10-02 17:24:55 -04:00
commit 8a70314f54
90 changed files with 5007 additions and 1615 deletions
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4
Grid/Makefile.am
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@ -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

4
Grid/communicator/SharedMemoryMPI.cc
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@ -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;

1
Grid/lattice/Lattice.h
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@ -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>

4
Grid/lattice/Lattice_ET.h
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@ -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

59
Grid/lattice/Lattice_trace.h
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@ -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

126
Grid/lattice/Lattice_transfer.h
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@ -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
}

52
Grid/lattice/PaddedCell.h
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@ -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;
}

10
Grid/qcd/action/fermion/Fermion.h
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@ -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;

18
Grid/qcd/action/fermion/WilsonImpl.h
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@ -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);

1
Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonCloverFermionInstantiationSpWilsonImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonFermionInstantiationSpWilsonImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonKernelsInstantiationSpWilsonImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplD/WilsonTMFermionInstantiationSpWilsonImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonTMFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplD/impl.h Normal file
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@ -0,0 +1 @@
#define IMPLEMENTATION SpWilsonImplD

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Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonCloverFermionInstantiationSpWilsonImplF.cc Symbolic link
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@ -0,0 +1 @@
../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonFermionInstantiationSpWilsonImplF.cc Symbolic link
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@ -0,0 +1 @@
../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonKernelsInstantiationSpWilsonImplF.cc Symbolic link
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../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplF/WilsonTMFermionInstantiationSpWilsonImplF.cc Symbolic link
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../WilsonTMFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonImplF/impl.h Normal file
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@ -0,0 +1 @@
#define IMPLEMENTATION SpWilsonImplF

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc Symbolic link
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../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc Symbolic link
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../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplD.cc Symbolic link
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@ -0,0 +1 @@
../WilsonTMFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplD/impl.h Normal file
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@ -0,0 +1 @@
#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplD

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc Symbolic link
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../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc Symbolic link
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../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc Symbolic link
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@ -0,0 +1 @@
../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexAntiSymmetricImplF.cc Symbolic link
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../WilsonTMFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexAntiSymmetricImplF/impl.h Normal file
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@ -0,0 +1 @@
#define IMPLEMENTATION SpWilsonTwoIndexAntiSymmetricImplF

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc Symbolic link
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../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc Symbolic link
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../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplD.cc Symbolic link
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../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplD.cc Symbolic link
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../WilsonTMFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplD/impl.h Normal file
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#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplD

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonCloverFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc Symbolic link
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../WilsonCloverFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc Symbolic link
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../WilsonFermionInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonKernelsInstantiationSpWilsonTwoIndexSymmetricImplF.cc Symbolic link
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../WilsonKernelsInstantiation.cc.master

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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/WilsonTMFermionInstantiationSpWilsonTwoIndexSymmetricImplF.cc Symbolic link
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Grid/qcd/action/fermion/instantiation/SpWilsonTwoIndexSymmetricImplF/impl.h Normal file
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@ -0,0 +1 @@
#define IMPLEMENTATION SpWilsonTwoIndexSymmetricImplF

6
Grid/qcd/action/fermion/instantiation/generate_instantiations.sh
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@ -10,12 +10,18 @@ WILSON_IMPL_LIST=" \
WilsonImplF \
WilsonImplD \
WilsonImplD2 \
SpWilsonImplF \
SpWilsonImplD \
WilsonAdjImplF \
WilsonAdjImplD \
WilsonTwoIndexSymmetricImplF \
WilsonTwoIndexSymmetricImplD \
WilsonTwoIndexAntiSymmetricImplF \
WilsonTwoIndexAntiSymmetricImplD \
SpWilsonTwoIndexAntiSymmetricImplF \
SpWilsonTwoIndexAntiSymmetricImplD \
SpWilsonTwoIndexSymmetricImplF \
SpWilsonTwoIndexSymmetricImplD \
GparityWilsonImplF \
GparityWilsonImplD "

3
Grid/qcd/action/gauge/Gauge.h
View File

@ -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;

28
Grid/qcd/action/gauge/GaugeImplTypes.h
View File

@ -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

7
Grid/qcd/action/gauge/GaugeImplementations.h
View File

@ -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

19
Grid/qcd/action/gauge/PlaqPlusRectangleAction.h
View File

@ -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);
}

12
Grid/qcd/hmc/GenericHMCrunner.h
View File

@ -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>;

7
Grid/qcd/representations/fundamental.h
View File

@ -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);

31
Grid/qcd/representations/two_index.h
View File

@ -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);

9
Grid/qcd/utils/CovariantCshift.h
View File

@ -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)
{

470
Grid/qcd/utils/GaugeGroup.h Normal file
View File

@ -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

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////////////////////////////////////////////////////////////////////////
//
// * 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

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/*************************************************************************************
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

578
Grid/qcd/utils/SUn.impl.h Normal file
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@ -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);
}

14
Grid/qcd/utils/SUnAdjoint.h
View File

@ -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);
}
}

273
Grid/qcd/utils/SUnTwoIndex.h
View File

@ -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

317
Grid/qcd/utils/Sp2n.impl.h Normal file
View File

@ -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;
}

4
Grid/qcd/utils/Utils.h
View File

@ -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

529
Grid/qcd/utils/WilsonLoops.h
View File

@ -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();
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();
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
//////////////////////////////////////////////////

104
Grid/stencil/GeneralLocalStencil.h
View File

@ -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;
}
}
});
}
};

1
Grid/stencil/Stencil.h
View File

@ -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

20
Grid/tensors/Tensor_SIMT.h
View File

@ -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);

135
Grid/tensors/Tensor_Ta.h
View File

@ -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

1
Grid/tensors/Tensor_exp.h
View File

@ -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>

24
configure.ac
View File

@ -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

BIN
documentation/Grid.pdf
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Binary file not shown.

72
documentation/GridXcode/readme.md
View File

@ -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:

98
documentation/manual.rst
View File

@ -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
----------------

5
scripts/filelist
View File

@ -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`

53
systems/OEM/README Normal file
View File

@ -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

18
systems/OEM/benchmarks/bench.sh Executable file
View File

@ -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

13
systems/OEM/benchmarks/select_gpu.sh Executable file
View File

@ -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"
"$@"

15
systems/OEM/config-command Normal file
View File

@ -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 "

3
systems/OEM/setup.sh Normal file
View File

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

2
systems/mac-arm/config-command-mpi
View File

@ -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

2
tests/Makefile.am
View File

@ -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

4
tests/core/Test_compact_wilson_clover_speedup.cc
View File

@ -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();
}

326
tests/core/Test_lie_generators.cc
View File

@ -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();
}

12
tests/core/Test_reunitarise.cc
View File

@ -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();
}

188
tests/debug/Test_iwasaki_action_newstaple.cc Normal file
View File

@ -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();
}

94
tests/debug/Test_optimized_staple_gaugebc.cc Normal file
View File

@ -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();
}

580
tests/debug/Test_padded_cell_staple.cc Normal file
View File

@ -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();
}

11
tests/solver/Test_coarse_even_odd.cc
View File

@ -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;

8
tests/sp2n/Makefile.am Normal file
View File

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

149
tests/sp2n/Test_2as_base.cc Normal file
View File

@ -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>();
}

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#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();
}

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#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();
}

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#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();
}

74
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#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();
}

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/*************************************************************************************
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

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#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();
}

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tests/sp2n/Test_sp2n_lie_gen.cc Normal file
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#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();
}