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https://github.com/paboyle/Grid.git
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155c164b0c
So valence sector looks ok. FermionOperatorImpl.h provides the policy classes. Expect HMC will introduce a smearing policy and a fermion representation change policy template param. Will also probably need multi-precision work. * HMC is running even-odd and non-checkerboarded (checked 4^4 wilson fermion/wilson gauge). There appears to be a bug in the multi-level integrator -- <e-dH> passes with single level but not with multi-level. In any case there looks to be quite a bit to clean up. This is the "const det" style implementation that is not appropriate yet for clover since it assumes that Mee is indept of the gauge fields. Easily fixed in future.
210 lines
6.5 KiB
C++
210 lines
6.5 KiB
C++
#ifndef QCD_PSEUDOFERMION_TWO_FLAVOUR_H
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#define QCD_PSEUDOFERMION_TWO_FLAVOUR_H
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namespace Grid{
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namespace QCD{
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// Placeholder comments:
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///////////////////////////////////////
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// Two flavour ratio
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///////////////////////////////////////
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// S = phi^dag V (Mdag M)^-1 V^dag phi
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// dS/du = phi^dag dV (Mdag M)^-1 V^dag phi
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// - phi^dag V (Mdag M)^-1 [ Mdag dM + dMdag M ] (Mdag M)^-1 V^dag phi
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// + phi^dag V (Mdag M)^-1 dV^dag phi
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///////////////////////////////////////
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// One flavour rational
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///////////////////////////////////////
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// S_f = chi^dag * N(M^dag*M)/D(M^dag*M) * chi
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//
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// Here, M is some operator
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// N and D makeup the rat. poly
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//
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// Need
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// dS_f/dU = chi^dag P/Q d[N/D] P/Q chi
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//
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// Here N/D \sim R_{-1/2} ~ (M^dagM)^{-1/2}
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//
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// N/D is expressed as partial fraction expansion:
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//
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// a0 + \sum_k ak/(M^dagM + bk)
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//
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// d[N/D] is then
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//
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// \sum_k -ak [M^dagM+bk]^{-1} [ dM^dag M + M^dag dM ] [M^dag M + bk]^{-1}
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//
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// Need
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//
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// Mf Phi_k = [MdagM+bk]^{-1} Phi
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// Mf Phi = \sum_k ak [MdagM+bk]^{-1} Phi
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//
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// With these building blocks
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//
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// dS/dU = \sum_k -ak Mf Phi_k^dag [ dM^dag M + M^dag dM ] Mf Phi_k
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// S = innerprodReal(Phi,Mf Phi);
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///////////////////////////////////////
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// One flavour rational ratio
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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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// 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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//
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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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//
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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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//
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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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// With these building blocks
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//
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// dS/dU =
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// \sum_k -ak MpvPhi_k^dag [ dV^dag V + V^dag dV ] MpvMfMpvPhi_k <- deriv on P left
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// + \sum_k -ak MpvMfMpvPhi_k^\dag [ dV^dag V + V^dag dV ] MpvPhi_k
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// + \sum_k -ak MfMpvPhi_k^dag [ dM^dag M + M^dag dM ] MfMpvPhi_k
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////////////////////////////////////////////////////////////////////////
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// Two flavour pseudofermion action for any dop
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////////////////////////////////////////////////////////////////////////
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template<class Impl>
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class TwoFlavourPseudoFermionAction : public Action<typename Impl::GaugeField> {
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public:
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INHERIT_IMPL_TYPES(Impl);
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private:
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FermionOperator<Impl> & FermOp;// the basic operator
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OperatorFunction<FermionField> &DerivativeSolver;
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OperatorFunction<FermionField> &ActionSolver;
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FermionField Phi; // the pseudo fermion field for this trajectory
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public:
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/////////////////////////////////////////////////
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// Pass in required objects.
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/////////////////////////////////////////////////
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TwoFlavourPseudoFermionAction(FermionOperator<Impl> &Op,
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OperatorFunction<FermionField> & DS,
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OperatorFunction<FermionField> & AS
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) : FermOp(Op), DerivativeSolver(DS), ActionSolver(AS), Phi(Op.FermionGrid()) {
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};
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//////////////////////////////////////////////////////////////////////////////////////
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// Push the gauge field in to the dops. Assume any BC's and smearing already applied
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//////////////////////////////////////////////////////////////////////////////////////
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virtual void init(const GaugeField &U, GridParallelRNG& pRNG) {
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// P(phi) = e^{- phi^dag (MdagM)^-1 phi}
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// Phi = Mdag eta
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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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// and must multiply by 0.707....
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//
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// Chroma has this scale factor: two_flavor_monomial_w.h
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// IroIro: does not use this scale. It is absorbed by a change of vars
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// in the Phi integral, and thus is only an irrelevant prefactor for the partition function.
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//
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RealD scale = std::sqrt(0.5);
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FermionField eta(FermOp.FermionGrid());
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gaussian(pRNG,eta);
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FermOp.ImportGauge(U);
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FermOp.Mdag(eta,Phi);
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Phi=Phi*scale;
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};
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//////////////////////////////////////////////////////
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// S = phi^dag (Mdag M)^-1 phi
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//////////////////////////////////////////////////////
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virtual RealD S(const GaugeField &U) {
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FermOp.ImportGauge(U);
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FermionField X(FermOp.FermionGrid());
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FermionField Y(FermOp.FermionGrid());
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MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(FermOp);
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X=zero;
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ActionSolver(MdagMOp,Phi,X);
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MdagMOp.Op(X,Y);
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RealD action = norm2(Y);
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std::cout << GridLogMessage << "Pseudofermion action "<<action<<std::endl;
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return action;
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};
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//////////////////////////////////////////////////////
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// dS/du = - phi^dag (Mdag M)^-1 [ Mdag dM + dMdag M ] (Mdag M)^-1 phi
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// = - phi^dag M^-1 dM (MdagM)^-1 phi - phi^dag (MdagM)^-1 dMdag dM (Mdag)^-1 phi
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//
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// = - Ydag dM X - Xdag dMdag Y
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//
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//////////////////////////////////////////////////////
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virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
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FermOp.ImportGauge(U);
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FermionField X(FermOp.FermionGrid());
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FermionField Y(FermOp.FermionGrid());
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GaugeField tmp(FermOp.GaugeGrid());
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MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(FermOp);
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X=zero;
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DerivativeSolver(MdagMOp,Phi,X);
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MdagMOp.Op(X,Y);
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// Our conventions really make this UdSdU; We do not differentiate wrt Udag here.
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// So must take dSdU - adj(dSdU) and left multiply by mom to get dS/dt.
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FermOp.MDeriv(tmp , Y, X,DaggerNo ); dSdU=tmp;
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FermOp.MDeriv(tmp , X, Y,DaggerYes); dSdU=dSdU+tmp;
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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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