Grid/lib/qcd/action/pseudofermion/TwoFlavourRatio.h

/*************************************************************************************

    Grid physics library, www.github.com/paboyle/Grid 

    Source file: ./lib/qcd/action/pseudofermion/TwoFlavourRatio.h

    Copyright (C) 2015

Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: Peter Boyle <peterboyle@Peters-MacBook-Pro-2.local>
Author: paboyle <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_TWO_FLAVOUR_RATIO_H
#define QCD_PSEUDOFERMION_TWO_FLAVOUR_RATIO_H

NAMESPACE_BEGIN(Grid);

///////////////////////////////////////
// Two flavour ratio
///////////////////////////////////////
template<class Impl>
class TwoFlavourRatioPseudoFermionAction : public Action<typename Impl::GaugeField> {
public:
  INHERIT_IMPL_TYPES(Impl);

private:
  FermionOperator<Impl> & NumOp;// the basic operator
  FermionOperator<Impl> & DenOp;// the basic operator

  OperatorFunction<FermionField> &DerivativeSolver;
  OperatorFunction<FermionField> &ActionSolver;

  FermionField Phi; // the pseudo fermion field for this trajectory

public:
  TwoFlavourRatioPseudoFermionAction(FermionOperator<Impl>  &_NumOp, 
				     FermionOperator<Impl>  &_DenOp, 
				     OperatorFunction<FermionField> & DS,
				     OperatorFunction<FermionField> & AS
				     ) : NumOp(_NumOp), DenOp(_DenOp), DerivativeSolver(DS), ActionSolver(AS), Phi(_NumOp.FermionGrid()) {};
      
  virtual std::string action_name(){return "TwoFlavourRatioPseudoFermionAction";}

  virtual std::string LogParameters(){
    std::stringstream sstream;
    sstream << GridLogMessage << "["<<action_name()<<"] has no parameters" << std::endl;
    return sstream.str();
  }  
      
  virtual void refresh(const GaugeField &U, GridParallelRNG& pRNG) {

    // P(phi) = e^{- phi^dag V (MdagM)^-1 Vdag phi}
    //
    // NumOp == V
    // DenOp == M
    //
    // Take phi = Vdag^{-1} Mdag eta  ; eta = Mdag^{-1} Vdag Phi
    //
    // 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) and must multiply by 0.707....
    //
    RealD scale = std::sqrt(0.5);

    FermionField eta(NumOp.FermionGrid());
    FermionField tmp(NumOp.FermionGrid());

    gaussian(pRNG,eta);

    NumOp.ImportGauge(U);
    DenOp.ImportGauge(U);

    // Note: this hard codes normal equations type solvers; alternate implementation needed for 
    // non-herm style solvers.
    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(NumOp);

    DenOp.Mdag(eta,Phi);            // Mdag eta
    tmp = zero;
    ActionSolver(MdagMOp,Phi,tmp);  // (VdagV)^-1 Mdag eta = V^-1 Vdag^-1 Mdag eta
    NumOp.M(tmp,Phi);               // Vdag^-1 Mdag eta

    Phi=Phi*scale;
	
  };

  //////////////////////////////////////////////////////
  // S = phi^dag V (Mdag M)^-1 Vdag phi
  //////////////////////////////////////////////////////
  virtual RealD S(const GaugeField &U) {

    NumOp.ImportGauge(U);
    DenOp.ImportGauge(U);

    FermionField X(NumOp.FermionGrid());
    FermionField Y(NumOp.FermionGrid());
	
    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(DenOp);

    NumOp.Mdag(Phi,Y);              // Y= Vdag phi
    X=zero;
    ActionSolver(MdagMOp,Y,X);      // X= (MdagM)^-1 Vdag phi
    DenOp.M(X,Y);                  // Y=  Mdag^-1 Vdag phi

    RealD action = norm2(Y);

    return action;
  };

  //////////////////////////////////////////////////////
  // dS/du = phi^dag dV (Mdag M)^-1 V^dag  phi
  //       - phi^dag V (Mdag M)^-1 [ Mdag dM + dMdag M ]  (Mdag M)^-1 V^dag  phi
  //       + phi^dag V (Mdag M)^-1 dV^dag  phi
  //////////////////////////////////////////////////////
  virtual void deriv(const GaugeField &U,GaugeField & dSdU) {

    NumOp.ImportGauge(U);
    DenOp.ImportGauge(U);

    MdagMLinearOperator<FermionOperator<Impl> ,FermionField> MdagMOp(DenOp);

    FermionField  X(NumOp.FermionGrid());
    FermionField  Y(NumOp.FermionGrid());

    GaugeField   force(NumOp.GaugeGrid());	


    //Y=Vdag phi
    //X = (Mdag M)^-1 V^dag phi
    //Y = (Mdag)^-1 V^dag  phi
    NumOp.Mdag(Phi,Y);              // Y= Vdag phi
    X=zero;
    DerivativeSolver(MdagMOp,Y,X);      // X= (MdagM)^-1 Vdag phi
    DenOp.M(X,Y);                  // Y=  Mdag^-1 Vdag phi

    // phi^dag V (Mdag M)^-1 dV^dag  phi
    NumOp.MDeriv(force , X, Phi, DaggerYes );  dSdU=force;
  
    // phi^dag dV (Mdag M)^-1 V^dag  phi
    NumOp.MDeriv(force , Phi, X ,DaggerNo  );  dSdU=dSdU+force;

    //    -    phi^dag V (Mdag M)^-1 Mdag dM   (Mdag M)^-1 V^dag  phi
    //    -    phi^dag V (Mdag M)^-1 dMdag M   (Mdag M)^-1 V^dag  phi
    DenOp.MDeriv(force,Y,X,DaggerNo);   dSdU=dSdU-force;
    DenOp.MDeriv(force,X,Y,DaggerYes);  dSdU=dSdU-force;

    dSdU *= -1.0;
    //dSdU = - Ta(dSdU);

  };
};

NAMESPACE_END(Grid):

#endif