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4D pseudofermion in Cayley action
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Peter Boyle
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Grid/qcd/action/pseudofermion/TwoFlavourRatio4DPseudoFermion.h
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Grid/qcd/action/pseudofermion/TwoFlavourRatio4DPseudoFermion.h
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/*************************************************************************************
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Grid physics library, www.github.com/paboyle/Grid
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Source file: ./lib/qcd/action/pseudofermion/TwoFlavourRatio.h
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Copyright (C) 2015
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Author: Peter Boyle <paboyle@ph.ed.ac.uk>
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Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
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Author: paboyle <paboyle@ph.ed.ac.uk>
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License along
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with this program; if not, write to the Free Software Foundation, Inc.,
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51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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See the full license in the file "LICENSE" in the top level distribution directory
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*************************************************************************************/
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/* END LEGAL */
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#pragma once
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NAMESPACE_BEGIN(Grid);
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///////////////////////////////////////
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// Two flavour ratio
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///////////////////////////////////////
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template<class Impl>
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class TwoFlavourRatio4DPseudoFermionAction : 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> & NumOp;// the basic operator
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FermionOperator<Impl> & DenOp;// the basic operator
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OperatorFunction<FermionField> &DerivativeSolver;
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OperatorFunction<FermionField> &ActionSolver;
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FermionField phi4; // the pseudo fermion field for this trajectory
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public:
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TwoFlavourRatio4DPseudoFermionAction(FermionOperator<Impl> &_NumOp,
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FermionOperator<Impl> &_DenOp,
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OperatorFunction<FermionField> & DS,
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OperatorFunction<FermionField> & AS
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) : NumOp(_NumOp),
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DenOp(_DenOp),
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DerivativeSolver(DS),
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ActionSolver(AS),
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phi4(_NumOp.GaugeGrid())
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{};
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virtual std::string action_name(){return "TwoFlavourRatio4DPseudoFermionAction";}
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virtual std::string LogParameters(){
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std::stringstream sstream;
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sstream << GridLogMessage << "["<<action_name()<<"] has no parameters" << std::endl;
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return sstream.str();
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}
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virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {
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// P(phi) = e^{- phi^dag (V^dag M^-dag)_11 (M^-1 V)_11 phi}
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//
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// NumOp == V
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// DenOp == M
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//
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// Take phi = (V^{-1} M)_11 eta ; eta = (M^{-1} V)_11 Phi
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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) and must multiply by 0.707....
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//
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RealD scale = std::sqrt(0.5);
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FermionField eta4(NumOp.GaugeGrid());
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FermionField eta5(NumOp.FermionGrid());
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FermionField tmp(NumOp.FermionGrid());
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FermionField phi5(NumOp.FermionGrid());
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gaussian(pRNG,eta4);
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NumOp.ImportFourDimPseudoFermion(eta4,eta5);
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NumOp.ImportGauge(U);
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DenOp.ImportGauge(U);
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MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(NumOp);
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DenOp.M(eta5,phi5); // M eta
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NumOp.Mdag(phi5,tmp); // Vdag M eta
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phi5 = Zero();
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ActionSolver(MdagMOp,tmp,phi5); // (VdagV)^-1 M eta = V^-1 Vdag^-1 Vdag M eta = V^-1 M eta
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phi5=phi5*scale;
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// Project to 4d
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NumOp.ExportFourDimPseudoFermion(phi5,phi4);
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};
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//////////////////////////////////////////////////////
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// S = phi^dag (V^dag M^-dag)_11 (M^-1 V)_11 phi
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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 Y4(NumOp.GaugeGrid());
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FermionField X(NumOp.FermionGrid());
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FermionField Y(NumOp.FermionGrid());
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FermionField phi5(NumOp.FermionGrid());
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MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(DenOp);
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NumOp.ImportFourDimPseudoFermion(phi4,phi5);
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NumOp.M(phi5,Y); // Y= V phi
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DenOp.Mdag(Y,X); // X= Mdag V phi
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Y=Zero();
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ActionSolver(MdagMOp,X,Y); // Y= (MdagM)^-1 Mdag Vdag phi = M^-1 V phi
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NumOp.ExportFourDimPseudoFermion(Y,Y4);
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RealD action = norm2(Y4);
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return action;
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};
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//////////////////////////////////////////////////////
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// dS/du = 2 Re phi^dag (V^dag M^-dag)_11 (M^-1 d V)_11 phi
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// - 2 Re phi^dag (dV^dag M^-dag)_11 (M^-1 dM M^-1 V)_11 phi
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//////////////////////////////////////////////////////
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virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
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NumOp.ImportGauge(U);
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DenOp.ImportGauge(U);
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MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(DenOp);
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FermionField X(NumOp.FermionGrid());
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FermionField Y(NumOp.FermionGrid());
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FermionField phi(NumOp.FermionGrid());
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FermionField Vphi(NumOp.FermionGrid());
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FermionField MinvVphi(NumOp.FermionGrid());
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FermionField tmp4(NumOp.GaugeGrid());
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FermionField MdagInvMinvVphi(NumOp.FermionGrid());
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GaugeField force(NumOp.GaugeGrid());
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//Y=V phi
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//X = (Mdag V phi
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//Y = (Mdag M)^-1 Mdag V phi = M^-1 V Phi
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NumOp.ImportFourDimPseudoFermion(phi4,phi);
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NumOp.M(phi,Vphi); // V phi
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DenOp.Mdag(Vphi,X); // X= Mdag V phi
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Y=Zero();
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DerivativeSolver(MdagMOp,X,MinvVphi);// M^-1 V phi
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// Projects onto the physical space and back
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NumOp.ExportFourDimPseudoFermion(MinvVphi,tmp4);
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NumOp.ImportFourDimPseudoFermion(tmp4,Y);
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X=Zero();
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DerivativeSolver(MdagMOp,Y,X);// X = (MdagM)^-1 proj M^-1 V phi
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DenOp.M(X,MdagInvMinvVphi);
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// phi^dag (Vdag Mdag^-1) (M^-1 dV) phi
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NumOp.MDeriv(force ,MdagInvMinvVphi , phi, DaggerNo ); dSdU=force;
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// phi^dag (dVdag Mdag^-1) (M^-1 V) phi
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NumOp.MDeriv(force , phi, MdagInvMinvVphi ,DaggerYes ); dSdU=dSdU+force;
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// - 2 Re phi^dag (dV^dag M^-dag)_11 (M^-1 dM M^-1 V)_11 phi
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DenOp.MDeriv(force,MdagInvMinvVphi,MinvVphi,DaggerNo); dSdU=dSdU-force;
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DenOp.MDeriv(force,MinvVphi,MdagInvMinvVphi,DaggerYes); dSdU=dSdU-force;
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dSdU *= -1.0;
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//dSdU = - Ta(dSdU);
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};
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};
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NAMESPACE_END(Grid);
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