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379 lines
10 KiB
C++
379 lines
10 KiB
C++
#ifndef QCD_UTILS_WILSON_LOOPS_H
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#define QCD_UTILS_WILSON_LOOPS_H
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namespace Grid {
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namespace QCD {
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// Common wilson loop observables
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template<class GaugeLorentz>
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class WilsonLoops {
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public:
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typedef LorentzScalar<GaugeLorentz> GaugeMat;
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//////////////////////////////////////////////////
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// directed plaquette oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void dirPlaquette(GaugeMat &plaq,const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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plaq=CovShiftForward(U[mu],mu,U[nu])*adj(CovShiftForward(U[nu],nu,U[mu]));
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}
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//////////////////////////////////////////////////
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// trace of directed plaquette oriented in mu,nu plane
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//////////////////////////////////////////////////
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static void traceDirPlaquette(LatticeComplex &plaq, const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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GaugeMat sp(U[0]._grid);
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dirPlaquette(sp,U,mu,nu);
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plaq=trace(sp);
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}
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//////////////////////////////////////////////////
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// sum over all planes of plaquette
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//////////////////////////////////////////////////
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static void sitePlaquette(LatticeComplex &Plaq,const std::vector<GaugeMat> &U)
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{
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LatticeComplex sitePlaq(U[0]._grid);
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Plaq=zero;
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for(int mu=1;mu<Nd;mu++){
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for(int nu=0;nu<mu;nu++){
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traceDirPlaquette(sitePlaq,U,mu,nu);
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Plaq = Plaq + sitePlaq;
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}
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}
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD sumPlaquette(const GaugeLorentz &Umu){
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std::vector<GaugeMat> U(4,Umu._grid);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
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}
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LatticeComplex Plaq(Umu._grid);
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sitePlaquette(Plaq,U);
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TComplex Tp = sum(Plaq);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD avgPlaquette(const GaugeLorentz &Umu){
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RealD sumplaq = sumPlaquette(Umu);
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double vol = Umu._grid->gSites();
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double faces = (1.0*Nd*(Nd-1))/2.0;
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return sumplaq/vol/faces/Nc; // Nd , Nc dependent... FIXME
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}
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static RealD linkTrace(const GaugeLorentz &Umu){
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std::vector<GaugeMat> U(4,Umu._grid);
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LatticeComplex Tr(Umu._grid); Tr=zero;
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for(int mu=0;mu<Nd;mu++){
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U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
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Tr = Tr+trace(U[mu]);
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}
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TComplex Tp = sum(Tr);
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Complex p = TensorRemove(Tp);
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double vol = Umu._grid->gSites();
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return p.real()/vol/4.0/3.0;
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};
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//////////////////////////////////////////////////
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// the sum over all staples on each site
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//////////////////////////////////////////////////
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static void Staple(GaugeMat &staple,const GaugeLorentz &Umu,int mu){
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GridBase *grid = Umu._grid;
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std::vector<GaugeMat> U(4,grid);
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for(int d=0;d<Nd;d++){
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U[d] = PeekIndex<LorentzIndex>(Umu,d);
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}
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staple = zero;
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GaugeMat tmp(grid);
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for(int nu=0;nu<Nd;nu++){
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if(nu != mu) {
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// mu
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// ^
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// |__> nu
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// __ __
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// | |
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// __| = __| *
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//
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// staple += CovShiftForward(U[nu],nu,U[mu])*Cshift(adj(U[nu]),mu,+1);
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staple +=
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Cshift(CovShiftForward (U[nu],nu,
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CovShiftBackward(U[mu],mu,Cshift(adj(U[nu]),nu,-1))),mu,1);
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// Unu(x) Umu(x+nu) Unu^dag(x+mu) ; left mult by Umu^dag(x) to close ring
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//
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// __ __
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// | |
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// |__ = | * __
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//
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//
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staple +=
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Cshift(
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CovShiftBackward(U[nu],nu,
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CovShiftBackward(U[mu],mu,U[nu])),mu,1);
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// tmp = CovShiftForward (U[mu],mu,U[nu]);
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// staple+= CovShiftBackward(U[nu],nu,tmp);
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// Unu^dag(x-nu) Umu(x-nu) Unu(x+mu-nu) ; left mult by Umu^dag(x) to close ring.
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}
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}
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}
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//////////////////////////////////////////////////////
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// Similar to above for rectangle is required
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//////////////////////////////////////////////////////
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static void dirRectangle(GaugeMat &rect,const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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rect = CovShiftForward(U[mu],mu,CovShiftForward(U[mu],mu,U[nu]))* // ->->|
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adj(CovShiftForward(U[nu],nu,CovShiftForward(U[mu],mu,U[mu]))) ;
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rect = rect +
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CovShiftForward(U[mu],mu,CovShiftForward(U[nu],nu,U[nu]))* // ->||
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adj(CovShiftForward(U[nu],nu,CovShiftForward(U[nu],nu,U[mu]))) ;
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}
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static void traceDirRectangle(LatticeComplex &rect, const std::vector<GaugeMat> &U, const int mu, const int nu)
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{
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GaugeMat sp(U[0]._grid);
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dirRectangle(sp,U,mu,nu);
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rect=trace(sp);
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}
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static void siteRectangle(LatticeComplex &Rect,const std::vector<GaugeMat> &U)
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{
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LatticeComplex siteRect(U[0]._grid);
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Rect=zero;
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for(int mu=1;mu<Nd;mu++){
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for(int nu=0;nu<mu;nu++){
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traceDirRectangle(siteRect,U,mu,nu);
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Rect = Rect + siteRect;
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}
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}
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}
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//////////////////////////////////////////////////
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// sum over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD sumRectangle(const GaugeLorentz &Umu){
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std::vector<GaugeMat> U(4,Umu._grid);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
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}
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LatticeComplex Rect(Umu._grid);
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siteRectangle(Rect,U);
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TComplex Tp = sum(Rect);
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Complex p = TensorRemove(Tp);
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return p.real();
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}
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//////////////////////////////////////////////////
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// average over all x,y,z,t and over all planes of plaquette
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//////////////////////////////////////////////////
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static RealD avgRectangle(const GaugeLorentz &Umu){
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RealD sumrect = sumRectangle(Umu);
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double vol = Umu._grid->gSites();
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double faces = (1.0*Nd*(Nd-1)); // 2 distinct orientations summed
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return sumrect/vol/faces/Nc; // Nd , Nc dependent... FIXME
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}
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//////////////////////////////////////////////////
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// the sum over all staples on each site
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//////////////////////////////////////////////////
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static void RectStapleDouble(GaugeMat &U2,const GaugeMat & U,int mu){
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U2 = U * Cshift(U,mu,1);
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}
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static void RectStapleOptimised(GaugeMat &Stap,std::vector<GaugeMat> &U2,std::vector<GaugeMat> &U,int mu){
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Stap = zero;
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GridBase *grid = U[0]._grid;
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GaugeMat Staple2x1 (grid);
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GaugeMat tmp (grid);
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for(int nu=0;nu<Nd;nu++){
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if ( nu!=mu) {
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// Up staple ___ ___
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// | |
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tmp = Cshift(adj(U[nu]),nu,-1);
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tmp = adj(U2[mu])*tmp;
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tmp = Cshift(tmp,mu,-2);
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Staple2x1 = CovShiftForward (U[nu],nu,tmp);
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// Down staple
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// |___ ___|
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//
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tmp = adj(U2[mu])*U[nu];
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Staple2x1+= CovShiftBackward(U[nu],nu,Cshift(tmp,mu,-2));
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// ___ ___
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// | ___|
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// |___ ___|
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//
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Stap+= Cshift(CovShiftForward (U[mu],mu,Staple2x1),mu,1);
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// ___ ___
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// |___ |
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// |___ ___|
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//
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// tmp= Staple2x1* Cshift(U[mu],mu,-2);
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// Stap+= Cshift(tmp,mu,1) ;
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Stap+= Cshift(Staple2x1,mu,1)*Cshift(U[mu],mu,-1); ;
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// --
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// | |
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//
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// | |
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tmp = Cshift(adj(U2[nu]),nu,-2);
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tmp = CovShiftBackward(U[mu],mu,tmp);
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tmp = U2[nu]*Cshift(tmp,nu,2);
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Stap+= Cshift(tmp, mu, 1);
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// | |
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//
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// | |
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// --
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tmp = CovShiftBackward(U[mu],mu,U2[nu]);
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tmp = adj(U2[nu])*tmp;
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tmp = Cshift(tmp,nu,-2);
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Stap+=Cshift(tmp, mu, 1);
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}}
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}
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static void RectStaple(GaugeMat &Stap,const GaugeLorentz &Umu,int mu){
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#if 1
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RectStapleUnoptimised(Stap,Umu,mu);
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#else
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GridBase *grid = Umu._grid;
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std::vector<GaugeMat> U (Nd,grid);
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std::vector<GaugeMat> U2(Nd,grid);
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for(int mu=0;mu<Nd;mu++){
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U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
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RectStapleDouble(U2[mu],U[mu],mu);
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}
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RectStapleOptimised(Stap,U2,U,mu);
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#endif
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}
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static void RectStapleUnoptimised(GaugeMat &Stap,const GaugeLorentz &Umu,int mu){
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GridBase *grid = Umu._grid;
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std::vector<GaugeMat> U(4,grid);
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for(int d=0;d<Nd;d++){
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U[d] = PeekIndex<LorentzIndex>(Umu,d);
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}
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Stap=zero;
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for(int nu=0;nu<Nd;nu++){
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if ( nu!=mu) {
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// __ ___
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// | __ |
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//
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Stap+= Cshift(CovShiftForward (U[mu],mu,
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CovShiftForward (U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[mu],mu,
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Cshift(adj(U[nu]),nu,-1))))) , mu, 1);
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// __
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// |__ __ |
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Stap+= Cshift(CovShiftForward (U[mu],mu,
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CovShiftBackward(U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[mu],mu, U[nu])))) , mu, 1);
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// __
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// |__ __ |
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Stap+= Cshift(CovShiftBackward(U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[mu],mu,
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CovShiftForward(U[nu],nu,U[mu])))) , mu, 1);
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// __ ___
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// |__ |
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Stap+= Cshift(CovShiftForward (U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[nu],nu,U[mu])))) , mu, 1);
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// --
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// | |
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//
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// | |
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Stap+= Cshift(CovShiftForward(U[nu],nu,
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CovShiftForward(U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftBackward(U[nu],nu,
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Cshift(adj(U[nu]),nu,-1))))) , mu, 1);
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// | |
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//
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// | |
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// --
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Stap+= Cshift(CovShiftBackward(U[nu],nu,
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CovShiftBackward(U[nu],nu,
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CovShiftBackward(U[mu],mu,
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CovShiftForward (U[nu],nu,U[nu])))) , mu, 1);
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}}
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}
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};
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typedef WilsonLoops<LatticeGaugeField> ColourWilsonLoops;
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typedef WilsonLoops<LatticeGaugeField> U1WilsonLoops;
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typedef WilsonLoops<LatticeGaugeField> SU2WilsonLoops;
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typedef WilsonLoops<LatticeGaugeField> SU3WilsonLoops;
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}}
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#endif
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