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241 lines
7.5 KiB
C++
241 lines
7.5 KiB
C++
#ifndef QCD_PSEUDOFERMION_ONE_FLAVOUR_EVEN_ODD_RATIONAL_RATIO_H
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#define QCD_PSEUDOFERMION_ONE_FLAVOUR_EVEN_ODD_RATIONAL_RATIO_H
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namespace Grid{
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namespace QCD{
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///////////////////////////////////////
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// One flavour rational
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///////////////////////////////////////
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// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
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//
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// Here P/Q \sim R_{1/4} ~ (V^dagV)^{1/4}
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// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
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template<class Impl>
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class OneFlavourEvenOddRatioRationalPseudoFermionAction : public Action<typename Impl::GaugeField> {
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public:
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INHERIT_IMPL_TYPES(Impl);
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typedef OneFlavourRationalParams Params;
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Params param;
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MultiShiftFunction PowerHalf ;
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MultiShiftFunction PowerNegHalf;
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MultiShiftFunction PowerQuarter;
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MultiShiftFunction PowerNegQuarter;
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private:
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FermionOperator<Impl> & NumOp;// the basic operator
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FermionOperator<Impl> & DenOp;// the basic operator
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FermionField PhiEven; // the pseudo fermion field for this trajectory
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FermionField PhiOdd; // the pseudo fermion field for this trajectory
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public:
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OneFlavourEvenOddRatioRationalPseudoFermionAction(FermionOperator<Impl> &_NumOp,
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FermionOperator<Impl> &_DenOp,
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Params & p
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) :
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NumOp(_NumOp),
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DenOp(_DenOp),
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PhiOdd (_NumOp.FermionRedBlackGrid()),
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PhiEven(_NumOp.FermionRedBlackGrid()),
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param(p)
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{
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AlgRemez remez(param.lo,param.hi,param.precision);
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// MdagM^(+- 1/2)
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std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/2)"<<std::endl;
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remez.generateApprox(param.degree,1,2);
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PowerHalf.Init(remez,param.tolerance,false);
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PowerNegHalf.Init(remez,param.tolerance,true);
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// MdagM^(+- 1/4)
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std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/4)"<<std::endl;
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remez.generateApprox(param.degree,1,4);
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PowerQuarter.Init(remez,param.tolerance,false);
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PowerNegQuarter.Init(remez,param.tolerance,true);
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};
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virtual void refresh(const GaugeField &U, GridParallelRNG& pRNG) {
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// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
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//
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// P(phi) = e^{- phi^dag (VdagV)^1/4 (MdagM)^-1/2 (VdagV)^1/4 phi}
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// = e^{- phi^dag (VdagV)^1/4 (MdagM)^-1/4 (MdagM)^-1/4 (VdagV)^1/4 phi}
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//
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// Phi = (VdagV)^-1/4 Mdag^{1/4} eta
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//
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// P(eta) = e^{- eta^dag eta}
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//
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// e^{x^2/2 sig^2} => sig^2 = 0.5.
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//
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// So eta should be of width sig = 1/sqrt(2).
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RealD scale = std::sqrt(0.5);
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FermionField eta(NumOp.FermionGrid());
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FermionField etaOdd (NumOp.FermionRedBlackGrid());
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FermionField etaEven(NumOp.FermionRedBlackGrid());
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FermionField tmp(NumOp.FermionRedBlackGrid());
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gaussian(pRNG,eta); eta=eta*scale;
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pickCheckerboard(Even,etaEven,eta);
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pickCheckerboard(Odd,etaOdd,eta);
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NumOp.ImportGauge(U);
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DenOp.ImportGauge(U);
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// MdagM^1/4 eta
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SchurDifferentiableOperator<Impl> MdagM(DenOp);
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ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,PowerQuarter);
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msCG_M(MdagM,etaOdd,tmp);
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// VdagV^-1/4 MdagM^1/4 eta
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SchurDifferentiableOperator<Impl> VdagV(NumOp);
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ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,PowerNegQuarter);
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msCG_V(VdagV,tmp,PhiOdd);
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assert(NumOp.ConstEE() == 1);
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assert(DenOp.ConstEE() == 1);
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PhiEven = zero;
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};
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//////////////////////////////////////////////////////
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// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
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//////////////////////////////////////////////////////
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virtual RealD S(const GaugeField &U) {
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NumOp.ImportGauge(U);
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DenOp.ImportGauge(U);
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FermionField X(NumOp.FermionRedBlackGrid());
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FermionField Y(NumOp.FermionRedBlackGrid());
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// VdagV^1/4 Phi
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SchurDifferentiableOperator<Impl> VdagV(NumOp);
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ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,PowerQuarter);
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msCG_V(VdagV,PhiOdd,X);
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// MdagM^-1/4 VdagV^1/4 Phi
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SchurDifferentiableOperator<Impl> MdagM(DenOp);
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ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,PowerNegQuarter);
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msCG_M(MdagM,X,Y);
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// Phidag VdagV^1/4 MdagM^-1/4 MdagM^-1/4 VdagV^1/4 Phi
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RealD action = norm2(Y);
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return action;
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};
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// S_f = chi^dag* P(V^dag*V)/Q(V^dag*V)* N(M^dag*M)/D(M^dag*M)* P(V^dag*V)/Q(V^dag*V)* chi
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//
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// Here, M is some 5D operator and V is the Pauli-Villars field
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// N and D makeup the rat. poly of the M term and P and & makeup the rat.poly of the denom term
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//
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// Need
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// dS_f/dU = chi^dag d[P/Q] N/D P/Q chi
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// + chi^dag P/Q d[N/D] P/Q chi
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// + chi^dag P/Q N/D d[P/Q] chi
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//
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// P/Q is expressed as partial fraction expansion:
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//
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// a0 + \sum_k ak/(V^dagV + bk)
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//
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// d[P/Q] is then
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//
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// \sum_k -ak [V^dagV+bk]^{-1} [ dV^dag V + V^dag dV ] [V^dag V + bk]^{-1}
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//
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// and similar for N/D.
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//
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// Need
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// MpvPhi_k = [Vdag V + bk]^{-1} chi
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// MpvPhi = {a0 + \sum_k ak [Vdag V + bk]^{-1} }chi
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//
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// MfMpvPhi_k = [MdagM+bk]^{-1} MpvPhi
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// MfMpvPhi = {a0 + \sum_k ak [Mdag M + bk]^{-1} } MpvPhi
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//
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// MpvMfMpvPhi_k = [Vdag V + bk]^{-1} MfMpvchi
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//
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virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
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const int n_f = PowerNegHalf.poles.size();
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const int n_pv = PowerQuarter.poles.size();
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std::vector<FermionField> MpvPhi_k (n_pv,NumOp.FermionRedBlackGrid());
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std::vector<FermionField> MpvMfMpvPhi_k(n_pv,NumOp.FermionRedBlackGrid());
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std::vector<FermionField> MfMpvPhi_k (n_f ,NumOp.FermionRedBlackGrid());
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FermionField MpvPhi(NumOp.FermionRedBlackGrid());
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FermionField MfMpvPhi(NumOp.FermionRedBlackGrid());
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FermionField MpvMfMpvPhi(NumOp.FermionRedBlackGrid());
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FermionField Y(NumOp.FermionRedBlackGrid());
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GaugeField tmp(NumOp.GaugeGrid());
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NumOp.ImportGauge(U);
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DenOp.ImportGauge(U);
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SchurDifferentiableOperator<Impl> VdagV(NumOp);
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SchurDifferentiableOperator<Impl> MdagM(DenOp);
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ConjugateGradientMultiShift<FermionField> msCG_V(param.MaxIter,PowerQuarter);
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ConjugateGradientMultiShift<FermionField> msCG_M(param.MaxIter,PowerNegHalf);
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msCG_V(VdagV,PhiOdd,MpvPhi_k,MpvPhi);
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msCG_M(MdagM,MpvPhi,MfMpvPhi_k,MfMpvPhi);
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msCG_V(VdagV,MfMpvPhi,MpvMfMpvPhi_k,MpvMfMpvPhi);
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RealD ak;
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dSdU = zero;
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// With these building blocks
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//
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// dS/dU =
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// \sum_k -ak MfMpvPhi_k^dag [ dM^dag M + M^dag dM ] MfMpvPhi_k (1)
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// + \sum_k -ak MpvMfMpvPhi_k^\dag [ dV^dag V + V^dag dV ] MpvPhi_k (2)
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// -ak MpvPhi_k^dag [ dV^dag V + V^dag dV ] MpvMfMpvPhi_k (3)
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//(1)
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for(int k=0;k<n_f;k++){
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ak = PowerNegHalf.residues[k];
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MdagM.Mpc(MfMpvPhi_k[k],Y);
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MdagM.MpcDagDeriv(tmp , MfMpvPhi_k[k], Y ); dSdU=dSdU+ak*tmp;
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MdagM.MpcDeriv(tmp , Y, MfMpvPhi_k[k] ); dSdU=dSdU+ak*tmp;
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}
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//(2)
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//(3)
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for(int k=0;k<n_pv;k++){
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ak = PowerQuarter.residues[k];
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VdagV.Mpc(MpvPhi_k[k],Y);
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VdagV.MpcDagDeriv(tmp,MpvMfMpvPhi_k[k],Y); dSdU=dSdU+ak*tmp;
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VdagV.MpcDeriv (tmp,Y,MpvMfMpvPhi_k[k]); dSdU=dSdU+ak*tmp;
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VdagV.Mpc(MpvMfMpvPhi_k[k],Y); // V as we take Ydag
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VdagV.MpcDeriv (tmp,Y, MpvPhi_k[k]); dSdU=dSdU+ak*tmp;
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VdagV.MpcDagDeriv(tmp,MpvPhi_k[k], Y); dSdU=dSdU+ak*tmp;
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}
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dSdU = Ta(dSdU);
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};
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};
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}
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}
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#endif
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