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HMC for Adjoint fermions works

Browse Source 
Accepts and reproduces known results

Check initial instability of inverters
when starting from hot configurations
This commit is contained in:
Guido Cossu
2016-08-30 11:31:25 +01:00
parent 9c2e8d5e28
commit b512ccbee6
8 changed files with 45 additions and 57 deletions
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25
lib/qcd/action/pseudofermion/TwoFlavour.h
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@@ -130,32 +130,9 @@ class TwoFlavourPseudoFermionAction : public Action<typename Impl::GaugeField> {
MdagMLinearOperator<FermionOperator<Impl>, FermionField> MdagMOp(FermOp);
X = zero;
DerivativeSolver(MdagMOp, Phi, X); // X = (MdagM)^-1 phi
DerivativeSolver(MdagMOp, Phi, X); // X = (MdagM)^-1 phi
MdagMOp.Op(X, Y); // Y = M X = (Mdag)^-1 phi
// Check hermiticity
std::vector<int> seeds({1,2,3,4});
GridParallelRNG RNG(U._grid); RNG.SeedFixedIntegers(seeds);
FermionField RNGphi(FermOp.FermionGrid());
FermionField RNGchi(FermOp.FermionGrid());
FermionField Achi(FermOp.FermionGrid());
FermionField Aphi(FermOp.FermionGrid());
random(RNG, RNGphi);
random(RNG, RNGchi);
MdagMOp.HermOp(RNGchi, Achi);
MdagMOp.HermOp(RNGphi, Aphi);
ComplexD pAc = innerProduct(RNGphi, Achi);
ComplexD cAp = innerProduct(RNGchi, Aphi);
//these should be real
ComplexD pAp = innerProduct(RNGphi, Aphi);
ComplexD cAc = innerProduct(RNGchi, Achi);
std::cout<<GridLogMessage<< "pAc "<<pAc<<" cAp "<< cAp<< " diff "<<pAc-adj(cAp)<<std::endl;
// These ones should be real
std::cout << GridLogMessage << "pAp " << pAp << " cAc " << cAc << std::endl;
// Our conventions really make this UdSdU; We do not differentiate wrt Udag
// here.
// So must take dSdU - adj(dSdU) and left multiply by mom to get dS/dt.

6
lib/qcd/hmc/integrators/Integrator.h
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@@ -120,12 +120,11 @@ class Integrator {
FieldType forceR(U._grid);
// Implement smearing only for the fundamental representation now
repr_set.at(a)->deriv(Rep.U, forceR);
forceR -= adj(forceR);
GF force =
Rep.RtoFundamentalProject(forceR); // Ta for the fundamental rep
std::cout << GridLogIntegrator << "Hirep Force average: "
<< norm2(force) / (U._grid->gSites()) << std::endl;
Mom -= force * ep;
Mom -= force * ep ;
}
}
} update_P_hireps{};
@@ -163,13 +162,14 @@ class Integrator {
<< " dt " << ep << " : t_U " << t_U << std::endl;
}
void update_U(GaugeField& Mom, GaugeField& U, double ep) {
// rewrite exponential to deal automatically with the lorentz index?
// rewrite exponential to deal internally with the lorentz index?
for (int mu = 0; mu < Nd; mu++) {
auto Umu = PeekIndex<LorentzIndex>(U, mu);
auto Pmu = PeekIndex<LorentzIndex>(Mom, mu);
Umu = expMat(Pmu, ep, Params.Nexp) * Umu;
PokeIndex<LorentzIndex>(U, ProjectOnGroup(Umu), mu);
}
// Update the smeared fields, can be implemented as observer
Smearer.set_GaugeField(U);
// Update the higher representations fields

19
lib/qcd/representations/adjoint.h
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@@ -29,7 +29,7 @@ class AdjointRep {
explicit AdjointRep(GridBase *grid) : U(grid) {}
void update_representation(const LatticeGaugeField &Uin) {
std::cout << GridLogDebug << "Updating adjoint representation\n" ;
std::cout << GridLogDebug << "Updating adjoint representation\n";
// Uin is in the fundamental representation
// get the U in AdjointRep
// (U_adj)_B = tr[e^a U e^b U^dag]
@@ -43,8 +43,8 @@ class AdjointRep {
Vector<typename SU<ncolour>::Matrix> ta(Dimension);
// Debug lines
//LatticeMatrix uno(Uin._grid);
//uno = 1.0;
// LatticeMatrix uno(Uin._grid);
// uno = 1.0;
////////////////
// FIXME probably not very efficient to get all the generators
@@ -53,11 +53,11 @@ class AdjointRep {
for (int mu = 0; mu < Nd; mu++) {
auto Uin_mu = peekLorentz(Uin, mu);
auto U_mu = peekLorentz(U, mu);
auto U_mu = peekLorentz(U, mu);
for (int a = 0; a < Dimension; a++) {
tmp = 2.0 * adj(Uin_mu) * ta[a] * Uin_mu;
for (int b = 0; b < Dimension; b++)
pokeColour(U_mu, trace(tmp * ta[b]), b, a);
pokeColour(U_mu, trace(tmp * ta[b]), a, b);
}
pokeLorentz(U, U_mu, mu);
// Check matrix U_mu, must be real orthogonal
@@ -71,7 +71,6 @@ class AdjointRep {
std::cout << GridLogMessage << "orthogonality check: " << norm2(Ucheck) <<
std::endl;
*/
}
}
@@ -87,11 +86,11 @@ class AdjointRep {
out_mu = zero;
typename SU<ncolour>::LatticeAlgebraVector h(in._grid);
projectOnAlgebra(h, in_mu, scale);
FundamentalLieAlgebraMatrix(h, out_mu, 1.0); // apply scale only once
projectOnAlgebra(h, in_mu, double(Nc) * 2.0); // factor C(r)/C(fund)
FundamentalLieAlgebraMatrix(h, out_mu); // apply scale only once
pokeLorentz(out, out_mu, mu);
// Returns traceless antihermitian matrix Nc * Nc.
// Confirmed
// Returns traceless antihermitian matrix Nc * Nc.
// Confirmed
}
return out;
}

14
lib/qcd/utils/SUn.h
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@@ -160,8 +160,9 @@ class SU {
else
generatorSigmaX(su2Index, ta);
}
template <class cplx>
static void generatorSigmaX(int su2Index, iSUnMatrix<cplx> &ta) {
static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
ta = zero;
int i1, i2;
su2SubGroupIndex(i1, i2, su2Index);
@@ -170,15 +171,16 @@ class SU {
ta = ta * 0.5;
}
template <class cplx>
static void generatorSigmaY(int su2Index, iSUnMatrix<cplx> &ta) {
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()()(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, ...)
@@ -651,9 +653,10 @@ class SU {
for (int a = 0; a < AdjointDimension; a++) {
gaussian(pRNG, ca);
generator(a, ta);
la = toComplex(ca) * ci * ta;
la = toComplex(ca) * ta;
out += la;
}
out *= ci;
}
static void FundamentalLieAlgebraMatrix(const LatticeAlgebraVector &h,
@@ -684,7 +687,6 @@ class SU {
auto tmp = - 2.0 * (trace(timesI(Ta) * in)) * scale;// 2.0 for the normalization of the trace in the fundamental rep
pokeColour(h_out, tmp, a);
}
std::cout << "h_out " << h_out << std::endl;
}

17
lib/qcd/utils/SUnAdjoint.h
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@@ -75,7 +75,8 @@ class SU_Adjoint : public SU<ncolour> {
typename SU<ncolour>::template iSUnMatrix<cplx> tmp1 =
2.0 * tmp * ta[b]; // 2.0 from the normalization
Complex iTr = TensorRemove(timesI(trace(tmp1)));
iAdjTa()()(b, a) = iTr;
//iAdjTa()()(b, a) = iTr;
iAdjTa()()(a, b) = iTr;
}
}
}
@@ -121,9 +122,10 @@ class SU_Adjoint : public SU<ncolour> {
out = zero;
for (int a = 0; a < Dimension; a++) {
generator(a, iTa);
la = peekColour(h, a) * iTa * scale;
la = peekColour(h, a) * iTa;
out += la;
}
out *= scale;
}
// Projects the algebra components a lattice matrix (of dimension ncol*ncol -1 )
@@ -131,16 +133,16 @@ class SU_Adjoint : public SU<ncolour> {
conformable(h_out, in);
h_out = zero;
AMatrix iTa;
Real coefficient = - 1.0/(ncolour) * scale;// 1/Nc for the normalization of the trace in the adj rep
for (int a = 0; a < Dimension; a++) {
generator(a, iTa);
auto tmp = - 1.0/(ncolour) * (trace(iTa * in)) * scale;// 1/Nc for the normalization of the trace in the adj rep
auto tmp = real(trace(iTa * in)) * coefficient;
pokeColour(h_out, tmp, a);
}
//std::cout << "h_out " << h_out << std::endl;
}
// a projector that keeps the generators stored to avoid the overhead of recomputing.
// a projector that keeps the generators stored to avoid the overhead of recomputing them
static void projector(typename SU<ncolour>::LatticeAlgebraVector &h_out, const LatticeAdjMatrix &in, Real scale = 1.0) {
conformable(h_out, in);
static std::vector<AMatrix> iTa(Dimension); // to store the generators
@@ -151,8 +153,11 @@ class SU_Adjoint : public SU<ncolour> {
for (int a = 0; a < Dimension; a++) generator(a, iTa[a]);
}
Real coefficient = -1.0 / (ncolour)*scale; // 1/Nc for the normalization of
// the trace in the adj rep
for (int a = 0; a < Dimension; a++) {
auto tmp = - 1.0/(ncolour) * (trace(iTa[a] * in)) * scale;
auto tmp = real(trace(iTa[a] * in)) * coefficient;
pokeColour(h_out, tmp, a);
}
}

5
tests/Test_hmc_WilsonAdjointFermionGauge.cc
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@@ -65,14 +65,15 @@ class HmcRunner : public NerscHmcRunnerHirep< TheRepresentations > {
AdjointRepresentation::LatticeField U(UGrid);
// Gauge action
WilsonGaugeActionR Waction(2.0);
WilsonGaugeActionR Waction(2.25);
Real mass = -1.0;
Real mass = -0.95;
FermionAction FermOp(U, *FGrid, *FrbGrid, mass);
ConjugateGradient<FermionField> CG(1.0e-8, 10000);
ConjugateResidual<FermionField> CR(1.0e-8, 10000);
// Pass two solvers: one for the force computation and one for the action
TwoFlavourPseudoFermionAction<ImplPolicy> Nf2(FermOp, CG, CG);
// Set smearing (true/false), default: false

6
tests/Test_lie_generators.cc
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@@ -121,6 +121,7 @@ int main(int argc, char** argv) {
// Test group structure
// (U_f * V_f)_r = U_r * V_r
LatticeGaugeField UV(grid);
UV = zero;
for (int mu = 0; mu < Nd; mu++) {
SU<Nc>::LatticeMatrix Umu = peekLorentz(U,mu);
SU<Nc>::LatticeMatrix Vmu = peekLorentz(V,mu);
@@ -138,6 +139,7 @@ int main(int argc, char** argv) {
typename AdjointRep<Nc>::LatticeField Vr = AdjRep.U; // V_r
typename AdjointRep<Nc>::LatticeField UrVr(grid);
UrVr = zero;
for (int mu = 0; mu < Nd; mu++) {
typename AdjointRep<Nc>::LatticeMatrix Urmu = peekLorentz(Ur,mu);
typename AdjointRep<Nc>::LatticeMatrix Vrmu = peekLorentz(Vr,mu);
@@ -145,9 +147,9 @@ int main(int argc, char** argv) {
}
typename AdjointRep<Nc>::LatticeField Diff_check = UVr - UrVr;
std::cout << GridLogMessage << "Group structure check difference : " << norm2(Diff_check) << std::endl;
std::cout << GridLogMessage << "Group structure SU("<<Nc<<") check difference : " << norm2(Diff_check) << std::endl;
// Check correspondence of algebra and group transformations
// Check correspondence of algebra and group transformations
// Create a random vector
SU<Nc>::LatticeAlgebraVector h_adj(grid);
typename AdjointRep<Nc>::LatticeMatrix Ar(grid);

10
tests/Test_wilson_force.cc
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@@ -58,8 +58,8 @@ int main (int argc, char ** argv)
LatticeGaugeField U(&Grid);
SU2::HotConfiguration(pRNG,U);
// SU3::ColdConfiguration(pRNG,U);
//SU2::HotConfiguration(pRNG,U);
SU3::ColdConfiguration(pRNG,U);
////////////////////////////////////
// Unmodified matrix element
@@ -95,7 +95,7 @@ int main (int argc, char ** argv)
for(int mu=0;mu<Nd;mu++){
SU2::GaussianFundamentalLieAlgebraMatrix(pRNG, mommu); // Traceless antihermitian momentum; gaussian in lie alg
SU3::GaussianFundamentalLieAlgebraMatrix(pRNG, mommu); // Traceless antihermitian momentum; gaussian in lie alg
Hmom -= real(sum(trace(mommu*mommu)));
@@ -142,11 +142,13 @@ int main (int argc, char ** argv)
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);
@@ -170,7 +172,7 @@ int main (int argc, char ** argv)
dSmom2 = dSmom2 - trace(forcemu*forcemu) *(0.25* dt*dt);
// Update mom action density
mommu = mommu + forcemu*(dt*0.5);
mommu = mommu + forcemu*(dt * 0.5);
Hmomprime -= real(sum(trace(mommu*mommu)));