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

    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, 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);

    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