#include <Grid.h>
#include <qcd/utils/CovariantCshift.h>
#include <qcd/utils/WilsonLoops.h>
using namespace std;
using namespace Grid;
using namespace Grid::QCD;
/* For Metropolis */
class Metropolis {
public:
GridSerialRNG & sRNG;
Metropolis(GridSerialRNG & _sRNG) : sRNG(_sRNG) {};
bool AcceptReject(const RealD Delta)
{
RealD rand;
if(Delta <=0.0) return true;
random(sRNG,rand);
if(rand <= exp(-Delta))
return true;
else
return false;
}
};
void RectPlaq(const std::vector<LatticeColourMatrix> &U, LatticeComplex &RectPlaqValue )
{
RectPlaqValue=zero;
// 12 * vol loops
for(int mu=1;mu<Nd;mu++){
for(int nu=0;nu<mu;nu++){
RectPlaqValue = RectPlaqValue + trace(
CovShiftForward(U[mu],mu,CovShiftForward(U[mu],mu,U[nu]))* // ->->|
adj(CovShiftForward(U[nu],nu,CovShiftForward(U[mu],mu,U[mu]))) );
RectPlaqValue = RectPlaqValue + trace(
CovShiftForward(U[mu],mu,CovShiftForward(U[nu],nu,U[nu]))* // ->||
adj(CovShiftForward(U[nu],nu,CovShiftForward(U[nu],nu,U[mu]))) );
}
}
}
void RectPlaqDeriv(const std::vector<LatticeColourMatrix> &U, LatticeComplex &RectPlaqValue )
{
}
int main (int argc, char ** argv)
{
Grid_init(&argc,&argv);
std::vector<int> simd_layout = GridDefaultSimd(4,vComplex::Nsimd());
std::vector<int> mpi_layout = GridDefaultMpi();
std::vector<int> latt_size ({16,16,16,32});
std::vector<int> clatt_size ({4,4,4,8});
int orthodir=3;
int orthosz =latt_size[orthodir];
GridCartesian Fine(latt_size,simd_layout,mpi_layout);
GridCartesian Coarse(clatt_size,simd_layout,mpi_layout);
LatticeGaugeField Umu(&Fine);
std::vector<LatticeColourMatrix> U(4,&Fine);
NerscField header;
std::string file("./ckpoint_lat.4000");
NerscIO::readConfiguration(Umu,header,file);
for(int mu=0;mu<Nd;mu++){
U[mu] = PeekIndex<LorentzIndex>(Umu,mu);
}
// Painful ; fix syntactical niceness : to check reader
LatticeComplex LinkTrace(&Fine);
LinkTrace=zero;
for(int mu=0;mu<Nd;mu++){
LinkTrace = LinkTrace + trace(U[mu]);
}
LatticeComplex Plaq(&Fine);
LatticeComplex cPlaq(&Coarse);
Plaq = zero;
for(int mu=1;mu<Nd;mu++){
for(int nu=0;nu<mu;nu++){
Plaq = Plaq + trace(CovShiftForward(U[mu],mu,U[nu])*adj(CovShiftForward(U[nu],nu,U[mu])));
}
}
LatticeComplex RectPlaqValue(&Fine);
double vol = Fine.gSites();
Complex PlaqScale(1.0/vol/6.0/3.0);
Complex RectScale(1.0/vol/12.0/3.0);
std::cout<<GridLogMessage <<"PlaqScale" << PlaqScale<<std::endl;
std::cout<<GridLogMessage <<"RectScale" << RectScale<<std::endl;
RectPlaq(U,RectPlaqValue);
TComplex TRp = sum(RectPlaqValue);
Complex rp = TensorRemove(TRp);
std::cout<<GridLogMessage << "calculated Rect plaquettes A " <<rp*RectScale<<std::endl;
// Rect Plaq Calc Deriv
LatticeComplex RectPlaq_d(&Fine);
RectPlaq_d = zero;
LatticeColourMatrix ds_U(&Fine);
LatticeColourMatrix left_2(&Fine);
LatticeColourMatrix upper_l(&Fine);
LatticeColourMatrix upper_staple(&Fine);
LatticeColourMatrix down_staple(&Fine);
LatticeColourMatrix tmp(&Fine);
// 2x1 // Each link has 2*(Nd-1) + 4*(Nd-1) = 6(Nd-1) , 1x2 and 2x1 loops attached.
// //
// // For producing the rectangle term normalised to number of loops
// // there are Vol x Nd.(Nd-1) x 2 / 2 distinct loops total. (mu<nu, mu>nu)
// //
// // Expect scale factor to be
// //
for(int mu=0;mu<Nd;mu++){
ds_U=zero; // dS / dUmu
for(int nu=0;nu<Nd;nu++){
if ( nu != mu ) {
/*
(x) ---> ---> : U(x,mu)*U(x+mu, mu)
*/
left_2= CovShiftForward(U[mu],mu,U[mu]);
/*
upper_l = <---- <---
^
| =>tmp
(x+2mu)
Unu(x+2mu) Umudag(x+mu+nu) Umudag(x+nu)
*/
tmp=Cshift(U[nu],mu,2);
upper_l= CovShiftForward(tmp,nu,adj(left_2)); // i.e. upper_l
/*
upper_staple= <---- <--- ^
| |
V (x) (x + 2mu)
*/
// Unu(x+2mu) Umudag(x+mu+nu) Umudag(x+nu) Unudag(x)
upper_staple= upper_l*adj(U[nu]);
/*
down_staple= ^
| |
(x) <----- <---- V x + 2mu
*/
down_staple= adj(left_2*tmp)*U[nu];
/*
ds_U+= <---- <--- ^
| |
(x-mu) V-----> (x + mu)
*/
tmp=upper_staple*U[mu];
ds_U+= Cshift(tmp,mu,-1);
/*
ds_U+= (x-mu) ^----> (x + mu)
| |
<-----<--- V
*/
tmp=CovShiftBackward(U[mu],nu,down_staple);
ds_U+=Cshift(tmp,mu,-1);
/*
ds_U+= <----<---- ^
| |
(x) V -----> (x + 2mu)
*/
tmp=Cshift(U[mu],mu,1);
/*
ds_U+= (x) ^ ----> (x + 2mu)
| |
<---- <----V
*/
ds_U+=tmp*(upper_staple+down_staple);
/*****Part 2********/
/*
^
|
upper= ^
|
(x)
*/
LatticeColourMatrix up2= CovShiftForward(U[nu],nu,U[nu]);
/*
<----^
|
upper_l= ^
|
(x)
*/
// Unu(x+mu)Unu(x+mu+nu) UmuDag(x+nu+nu) lives at X
upper_l= CovShiftForward(Cshift(up2,mu,1),nu,Cshift(adj(U[mu]),nu,1));
/*
|<----^
upper_staple = V |
| ^
(x) V |
*/
ds_U+= upper_l*adj(up2);
/*
|
V
downer_l= |
(x)<----V
*/
upper_l= adj(CovShiftForward(U[mu],mu,up2)); //downer_l
/*
^ |
down_staple = | V
^ |
| V
(x)<----
down_staple= upper*upper_l;
*/
tmp= upper_l*up2;
ds_U+= Cshift(tmp,nu,-2);
//TRp = sum(RectPlaq_d);
//rp = TensorRemove(TRp);
//std::cout << GridLogMessage<< " Rect[" << " " << "] = "<< TensorRemove(TRp) <<std::endl;
}}
RectPlaq_d += trace( U[mu]*ds_U) * 0.25;
}
TRp = sum(RectPlaq_d);
rp = TensorRemove(TRp);
std::cout<<GridLogMessage << "calculated Rect plaquettes_d " <<rp*RectScale<<std::endl;
std::vector<TComplex> Plaq_T(orthosz);
sliceSum(Plaq,Plaq_T,Nd-1);
int Nt = Plaq_T.size();
TComplex Plaq_T_sum;
Plaq_T_sum=zero;
for(int t=0;t<Nt;t++){
Plaq_T_sum = Plaq_T_sum+Plaq_T[t];
Complex Pt=TensorRemove(Plaq_T[t]);
std::cout<<GridLogMessage << "sliced ["<<t<<"]" <<Pt*PlaqScale*Real(Nt) << std::endl;
}
{
Complex Pt = TensorRemove(Plaq_T_sum);
std::cout<<GridLogMessage << "total " <<Pt*PlaqScale<<std::endl;
}
TComplex Tp = sum(Plaq);
Complex p = TensorRemove(Tp);
std::cout<<GridLogMessage << "calculated plaquettes " <<p*PlaqScale<<std::endl;
RealD avg_plaq = ColourWilsonLoops::avgPlaquette(Umu);
std::cout<<GridLogMessage << "NEW : calculated real plaquettes " <<avg_plaq<<std::endl;
// Staple Plaq
RealD StapScale(1.0/vol/6.0/3.0);
RealD stap_plaq=0.0;
LatticeColourMatrix stap(&Fine);
LatticeComplex stap_tr(&Fine);
for(int mu=0;mu<Nd;mu++){
ColourWilsonLoops::Staple(stap,Umu,mu);
stap_tr = trace(U[mu]*stap);
TComplex Ts = sum(stap_tr);
Complex s = TensorRemove(Ts);
stap_plaq+=real(s);
}
std::cout<<GridLogMessage << "NEW : plaquette via staples"<< stap_plaq*StapScale*0.25<< std::endl;
Complex LinkTraceScale(1.0/vol/4.0/3.0);
TComplex Tl = sum(LinkTrace);
Complex l = TensorRemove(Tl);
std::cout<<GridLogMessage << "calculated link trace " <<l*LinkTraceScale<<std::endl;
blockSum(cPlaq,Plaq);
TComplex TcP = sum(cPlaq);
Complex ll= TensorRemove(TcP);
std::cout<<GridLogMessage << "coarsened plaquettes sum to " <<ll*PlaqScale<<std::endl;
Grid_finalize();
}