OneFlavourRational.h

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    /*************************************************************************************
 
    Grid physics library, www.github.com/paboyle/Grid 
 
    Source file: ./lib/qcd/action/pseudofermion/OneFlavourRational.h
 
    Copyright (C) 2015
 
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
 
    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License along
    with this program; if not, write to the Free Software Foundation, Inc.,
    51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 
    See the full license in the file "LICENSE" in the top level distribution directory
    *************************************************************************************/
    /*  END LEGAL */
#ifndef QCD_PSEUDOFERMION_ONE_FLAVOUR_RATIONAL_H
#define QCD_PSEUDOFERMION_ONE_FLAVOUR_RATIONAL_H
 
NAMESPACE_BEGIN(Grid);

    // One flavour rational
 
    // S_f = chi^dag *  N(M^dag*M)/D(M^dag*M) * chi
    //
    // Here, M is some operator 
    // N and D makeup the rat. poly 
    //
  
    template<class Impl>
    class OneFlavourRationalPseudoFermionAction : public Action<typename Impl::GaugeField> {
    public:
      INHERIT_IMPL_TYPES(Impl);
 
      typedef OneFlavourRationalParams Params;
      Params param;
 
      MultiShiftFunction PowerHalf   ;
      MultiShiftFunction PowerNegHalf;
      MultiShiftFunction PowerQuarter;
      MultiShiftFunction PowerNegQuarter;
 
    private:
     
      FermionOperator<Impl> & FermOp;// the basic operator
 
      // NOT using "Nroots"; IroIro is -- perhaps later, but this wasn't good for us historically
      // and hasenbusch works better
 
      FermionField Phi; // the pseudo fermion field for this trajectory
 
    public:
 
      OneFlavourRationalPseudoFermionAction(FermionOperator<Impl>  &Op, 
                        Params & p
                        ) : FermOp(Op), Phi(Op.FermionGrid()), param(p) 
      {
    AlgRemez remez(param.lo,param.hi,param.precision);
 
    // MdagM^(+- 1/2)
    std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/2)"<<std::endl;
    remez.generateApprox(param.degree,1,2);
    PowerHalf.Init(remez,param.tolerance,false);
    PowerNegHalf.Init(remez,param.tolerance,true);
 
    // MdagM^(+- 1/4)
    std::cout<<GridLogMessage << "Generating degree "<<param.degree<<" for x^(1/4)"<<std::endl;
    remez.generateApprox(param.degree,1,4);
    PowerQuarter.Init(remez,param.tolerance,false);
    PowerNegQuarter.Init(remez,param.tolerance,true);
      };
 
      virtual std::string action_name(){return "OneFlavourRationalPseudoFermionAction";}
 
      virtual std::string LogParameters(){
    std::stringstream sstream;
    sstream << GridLogMessage << "["<<action_name()<<"] Low            :" << param.lo <<  std::endl;
    sstream << GridLogMessage << "["<<action_name()<<"] High           :" << param.hi <<  std::endl;
    sstream << GridLogMessage << "["<<action_name()<<"] Max iterations :" << param.MaxIter <<  std::endl;
    sstream << GridLogMessage << "["<<action_name()<<"] Tolerance      :" << param.tolerance <<  std::endl;
    sstream << GridLogMessage << "["<<action_name()<<"] Degree         :" << param.degree <<  std::endl;
    sstream << GridLogMessage << "["<<action_name()<<"] Precision      :" << param.precision <<  std::endl;
    return sstream.str();
      }  
 
 
      
      virtual void refresh(const GaugeField &U, GridSerialRNG &sRNG, GridParallelRNG& pRNG) {
 
    
    // P(phi) = e^{- phi^dag (MdagM)^-1/2 phi}
    //        = e^{- phi^dag (MdagM)^-1/4 (MdagM)^-1/4 phi}
    // Phi = Mdag^{1/4} eta 
    // P(eta) = e^{- eta^dag eta}
    //
    // e^{x^2/2 sig^2} => sig^2 = 0.5.
    // 
    // So eta should be of width sig = 1/sqrt(2).
 
    RealD scale = std::sqrt(0.5);
 
    FermionField eta(FermOp.FermionGrid());
 
    gaussian(pRNG,eta);
 
    FermOp.ImportGauge(U);
 
    // mutishift CG
    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(FermOp);
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter,PowerQuarter);
    msCG(MdagMOp,eta,Phi);
 
    Phi=Phi*scale;
    
      };

      // S = phi^dag (Mdag M)^-1/2 phi
      virtual RealD S(const GaugeField &U) {
 
    FermOp.ImportGauge(U);
 
    FermionField Y(FermOp.FermionGrid());
    
    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(FermOp);
 
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter,PowerNegQuarter);
 
    msCG(MdagMOp,Phi,Y);
 
    auto grid = FermOp.FermionGrid();
        auto r=rand();
        grid->Broadcast(0,r);
        if ( (r%param.BoundsCheckFreq)==0 ) { 
      FermionField gauss(FermOp.FermionGrid());
      gauss = Phi;
      HighBoundCheck(MdagMOp,gauss,param.hi);
      InverseSqrtBoundsCheck(param.MaxIter,param.tolerance*100,MdagMOp,gauss,PowerNegHalf);
    }
 
 
    RealD action = norm2(Y);
    std::cout << GridLogMessage << "Pseudofermion action FIXME -- is -1/4 solve or -1/2 solve faster??? "<<action<<std::endl;
    return action;
      };

      // Need
      // dS_f/dU = chi^dag   d[N/D]  chi
      //
      // N/D is expressed as partial fraction expansion:
      //
      //           a0 + \sum_k ak/(M^dagM + bk)
      //
      // d[N/D] is then
      //
      //          \sum_k -ak [M^dagM+bk]^{-1}  [ dM^dag M + M^dag dM ] [M^dag M + bk]^{-1}
      //
      // Need
      //       Mf Phi_k = [MdagM+bk]^{-1} Phi
      //       Mf Phi   = \sum_k ak [MdagM+bk]^{-1} Phi
      //
      // With these building blocks
      //
      //       dS/dU =  \sum_k -ak Mf Phi_k^dag      [ dM^dag M + M^dag dM ] Mf Phi_k
      //        S    = innerprodReal(Phi,Mf Phi);
      virtual void deriv(const GaugeField &U,GaugeField & dSdU) {
 
    const int Npole = PowerNegHalf.poles.size();
 
    std::vector<FermionField> MPhi_k (Npole,FermOp.FermionGrid());
 
    FermionField X(FermOp.FermionGrid());
    FermionField Y(FermOp.FermionGrid());
 
    GaugeField   tmp(FermOp.GaugeGrid());
 
    FermOp.ImportGauge(U);
 
    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(FermOp);
 
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter,PowerNegHalf);
 
    msCG(MdagMOp,Phi,MPhi_k);
 
    dSdU = Zero();
    for(int k=0;k<Npole;k++){
 
      RealD ak = PowerNegHalf.residues[k];
 
      X  = MPhi_k[k];
 
      FermOp.M(X,Y);
 
      FermOp.MDeriv(tmp , Y, X,DaggerNo );  dSdU=dSdU+ak*tmp;
      FermOp.MDeriv(tmp , X, Y,DaggerYes);  dSdU=dSdU+ak*tmp;
 
    }
 
    //dSdU = Ta(dSdU);
 
      };
    };
 
NAMESPACE_END(Grid);
 
#endif