OneFlavourEvenOddRational.h

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/*************************************************************************************
 
Grid physics library, www.github.com/paboyle/Grid
 
Source file: ./lib/qcd/action/pseudofermion/OneFlavourEvenOddRational.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_EVEN_ODD_RATIONAL_H
#define QCD_PSEUDOFERMION_ONE_FLAVOUR_EVEN_ODD_RATIONAL_H
 
NAMESPACE_BEGIN(Grid);

// One flavour rational
 
// S_f = chi^dag *  N(Mpc^dag*Mpc)/D(Mpc^dag*Mpc) * chi
//
// Here, M is some operator
// N and D makeup the rat. poly
//
 
template <class Impl>
class OneFlavourEvenOddRationalPseudoFermionAction : 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 PhiEven;  // the pseudo fermion field for this trajectory
  FermionField PhiOdd;   // the pseudo fermion field for this trajectory
 
public:
  OneFlavourEvenOddRationalPseudoFermionAction(FermionOperator<Impl> &Op,
                                               Params &p)
    : FermOp(Op),
      PhiEven(Op.FermionRedBlackGrid()),
      PhiOdd(Op.FermionRedBlackGrid()),
      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 "OneFlavourEvenOddRationalPseudoFermionAction";}
 
  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 (MpcdagMpc)^-1/2 phi}
    //        = e^{- phi^dag (MpcdagMpc)^-1/4 (MpcdagMpc)^-1/4 phi}
    // Phi = MpcdagMpc^{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());
    FermionField etaOdd(FermOp.FermionRedBlackGrid());
    FermionField etaEven(FermOp.FermionRedBlackGrid());
 
    gaussian(pRNG, eta);
    eta = eta * scale;
 
    pickCheckerboard(Even, etaEven, eta);
    pickCheckerboard(Odd, etaOdd, eta);
 
    FermOp.ImportGauge(U);
 
    // mutishift CG
    SchurDifferentiableOperator<Impl> Mpc(FermOp);
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter, PowerQuarter);
    msCG(Mpc, etaOdd, PhiOdd);

    // FIXME : Clover term not yet..
 
    assert(FermOp.ConstEE() == 1);
    PhiEven = Zero();
  };

  // S = phi^dag (Mdag M)^-1/2 phi
  virtual RealD S(const GaugeField &U) {
    FermOp.ImportGauge(U);
 
    FermionField Y(FermOp.FermionRedBlackGrid());
 
    SchurDifferentiableOperator<Impl> Mpc(FermOp);
 
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter,
                                                   PowerNegQuarter);
 
    msCG(Mpc, PhiOdd, Y);
 
    auto grid = FermOp.FermionGrid();
    auto r=rand();
    grid->Broadcast(0,r);
    if ( (r%param.BoundsCheckFreq)==0 ) { 
      FermionField gauss(FermOp.FermionRedBlackGrid());
      gauss = PhiOdd;
      HighBoundCheck(Mpc,gauss,param.hi);
      InverseSqrtBoundsCheck(param.MaxIter,param.tolerance*100,Mpc,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.FermionRedBlackGrid());
 
    FermionField X(FermOp.FermionRedBlackGrid());
    FermionField Y(FermOp.FermionRedBlackGrid());
 
    GaugeField tmp(FermOp.GaugeGrid());
 
    FermOp.ImportGauge(U);
 
    SchurDifferentiableOperator<Impl> Mpc(FermOp);
 
    ConjugateGradientMultiShift<FermionField> msCG(param.MaxIter, PowerNegHalf);
 
    msCG(Mpc, PhiOdd, MPhi_k);
 
    dSdU = Zero();
    for (int k = 0; k < Npole; k++) {
      RealD ak = PowerNegHalf.residues[k];
 
      X = MPhi_k[k];
 
      Mpc.Mpc(X, Y);
      Mpc.MpcDeriv(tmp, Y, X);
      dSdU = dSdU + ak * tmp;
      Mpc.MpcDagDeriv(tmp, X, Y);
      dSdU = dSdU + ak * tmp;
    }
 
    // dSdU = Ta(dSdU);
  };
};
 
NAMESPACE_END(Grid);
 
#endif