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Two flavour HMC for Wilson/Wilson is conserving energy.

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Still to check plaq and <e(-dH)>, but nevertheless this is
progress
This commit is contained in:
Peter Boyle
2015-07-29 17:53:39 +09:00
parent 4cc2ef84d3
commit 4fe110bd07
20 changed files with 259 additions and 76 deletions
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95
tests/Test_wilson_force.cc
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@ -48,17 +48,19 @@ int main (int argc, char ** argv)
LatticeGaugeField tmp(&Grid);
Dw.MDeriv(tmp , Mphi, phi,DaggerNo ); UdSdU=tmp;
Dw.MDeriv(tmp , phi, Mphi,DaggerYes ); UdSdU=UdSdU+tmp;
Dw.MDeriv(tmp , phi, Mphi,DaggerYes ); UdSdU=(UdSdU+tmp);
LatticeFermion Ftmp (&Grid);
////////////////////////////////////
// Modify the gauge field a little
////////////////////////////////////
RealD dt = 1.0e-6;
RealD dt = 0.0001;
RealD Hmom = 0.0;
RealD Hmomprime = 0.0;
RealD Hmompp = 0.0;
LatticeColourMatrix mommu(&Grid);
LatticeColourMatrix forcemu(&Grid);
LatticeGaugeField mom(&Grid);
LatticeGaugeField Uprime(&Grid);
@ -66,13 +68,26 @@ int main (int argc, char ** argv)
SU3::GaussianLieAlgebraMatrix(pRNG, mommu); // Traceless antihermitian momentum; gaussian in lie alg
Hmom -= real(sum(trace(mommu*mommu)));
PokeIndex<LorentzIndex>(mom,mommu,mu);
// fourth order exponential approx
parallel_for(auto i=mom.begin();i<mom.end();i++){
Uprime[i](mu) =U[i](mu)+ mom[i](mu)*U[i](mu)*dt;
Uprime[i](mu) =
U[i](mu)
+ mom[i](mu)*U[i](mu)*dt
+ mom[i](mu) *mom[i](mu) *U[i](mu)*(dt*dt/2.0)
+ mom[i](mu) *mom[i](mu) *mom[i](mu) *U[i](mu)*(dt*dt*dt/6.0)
+ mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *U[i](mu)*(dt*dt*dt*dt/24.0)
+ mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *U[i](mu)*(dt*dt*dt*dt*dt/120.0)
+ mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *mom[i](mu) *U[i](mu)*(dt*dt*dt*dt*dt*dt/720.0)
;
}
}
std::cout << GridLogMessage <<"Initial mom hamiltonian is "<< Hmom <<std::endl;
Dw.DoubleStore(Dw.Umu,Uprime);
Dw.M (phi,MphiPrime);
@ -81,21 +96,75 @@ int main (int argc, char ** argv)
//////////////////////////////////////////////
// Use derivative to estimate dS
//////////////////////////////////////////////
LatticeComplex dS(&Grid); dS = zero;
parallel_for(auto i=mom.begin();i<mom.end();i++){
for(int mu=0;mu<Nd;mu++){
// dS[i]() = dS[i]()+trace(mom[i](mu) * UdSdU[i](mu) - mom[i](mu)* adj( UdSdU[i](mu)) )*dt;
dS[i]() = dS[i]()+trace(mom[i](mu) * (UdSdU[i](mu)))*dt;
dS[i]() = dS[i]()-trace(mom[i](mu) * adj(UdSdU[i](mu)))*dt;
}
for(int mu=0;mu<Nd;mu++){
std::cout << "" <<std::endl;
mommu = PeekIndex<LorentzIndex>(mom,mu);
std::cout << GridLogMessage<< " Mommu " << norm2(mommu)<<std::endl;
mommu = mommu+adj(mommu);
std::cout << GridLogMessage<< " Mommu + Mommudag " << norm2(mommu)<<std::endl;
mommu = PeekIndex<LorentzIndex>(UdSdU,mu);
std::cout << GridLogMessage<< " dsdumu " << norm2(mommu)<<std::endl;
mommu = mommu+adj(mommu);
std::cout << GridLogMessage<< " dsdumu + dag " << norm2(mommu)<<std::endl;
}
LatticeComplex dS(&Grid); dS = zero;
LatticeComplex dSmom(&Grid); dSmom = zero;
LatticeComplex dSmom2(&Grid); dSmom2 = zero;
for(int mu=0;mu<Nd;mu++){
mommu = PeekIndex<LorentzIndex>(UdSdU,mu);
mommu=Ta(mommu)*2.0;
PokeIndex<LorentzIndex>(UdSdU,mommu,mu);
}
for(int mu=0;mu<Nd;mu++){
mommu = PeekIndex<LorentzIndex>(mom,mu);
std::cout << GridLogMessage<< " Mommu " << norm2(mommu)<<std::endl;
mommu = mommu+adj(mommu);
std::cout << GridLogMessage<< " Mommu + Mommudag " << norm2(mommu)<<std::endl;
mommu = PeekIndex<LorentzIndex>(UdSdU,mu);
std::cout << GridLogMessage<< " dsdumu " << norm2(mommu)<<std::endl;
mommu = mommu+adj(mommu);
std::cout << GridLogMessage<< " dsdumu + dag " << norm2(mommu)<<std::endl;
}
for(int mu=0;mu<Nd;mu++){
forcemu = PeekIndex<LorentzIndex>(UdSdU,mu);
mommu = PeekIndex<LorentzIndex>(mom,mu);
// Update PF action density
dS = dS+trace(mommu*forcemu)*dt;
dSmom = dSmom - trace(mommu*forcemu) * dt;
dSmom2 = dSmom2 - trace(forcemu*forcemu) *(0.25* dt*dt);
// Update mom action density
mommu = mommu + forcemu*(dt*0.5);
Hmomprime -= real(sum(trace(mommu*mommu)));
}
Complex dSpred = sum(dS);
Complex dSm = sum(dSmom);
Complex dSm2 = sum(dSmom2);
std::cout << GridLogMessage <<"Initial mom hamiltonian is "<< Hmom <<std::endl;
std::cout << GridLogMessage <<"Final mom hamiltonian is "<< Hmomprime <<std::endl;
std::cout << GridLogMessage <<"Delta mom hamiltonian is "<< Hmomprime-Hmom <<std::endl;
std::cout << GridLogMessage << " S "<<S<<std::endl;
std::cout << GridLogMessage << " Sprime "<<Sprime<<std::endl;
std::cout << GridLogMessage << "dS "<<Sprime-S<<std::endl;
std::cout << GridLogMessage << "predict dS "<< dSpred <<std::endl;
std::cout << GridLogMessage <<"dSm "<< dSm<<std::endl;
std::cout << GridLogMessage <<"dSm2"<< dSm2<<std::endl;
std::cout << GridLogMessage << "Total dS "<< Hmomprime - Hmom + Sprime - S <<std::endl;
std::cout<< GridLogMessage << "Done" <<std::endl;
Grid_finalize();