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

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

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

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

Copyright (C) 2015

Author: Peter Boyle <pabobyle@ph.ed.ac.uk>
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_TWO_FLAVOUR_H
#define QCD_PSEUDOFERMION_TWO_FLAVOUR_H

namespace Grid {
namespace QCD {

////////////////////////////////////////////////////////////////////////
// Two flavour pseudofermion action for any dop
////////////////////////////////////////////////////////////////////////
template <class Impl>
class TwoFlavourPseudoFermionAction : public Action<typename Impl::GaugeField> {
 public:
  INHERIT_IMPL_TYPES(Impl);

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

  OperatorFunction<FermionField> &DerivativeSolver;

  OperatorFunction<FermionField> &ActionSolver;

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

 public:
  /////////////////////////////////////////////////
  // Pass in required objects.
  /////////////////////////////////////////////////
  TwoFlavourPseudoFermionAction(FermionOperator<Impl> &Op,
                                OperatorFunction<FermionField> &DS,
                                OperatorFunction<FermionField> &AS)
      : FermOp(Op),
        DerivativeSolver(DS),
        ActionSolver(AS),
        Phi(Op.FermionGrid()){};

  //////////////////////////////////////////////////////////////////////////////////////
  // Push the gauge field in to the dops. Assume any BC's and smearing already
  // applied
  //////////////////////////////////////////////////////////////////////////////////////
  virtual void refresh(const GaugeField &U, GridParallelRNG &pRNG) {
    // P(phi) = e^{- phi^dag (MdagM)^-1 phi}
    // Phi = Mdag 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).
    // and must multiply by 0.707....
    //
    // Chroma has this scale factor: two_flavor_monomial_w.h
    // IroIro: does not use this scale. It is absorbed by a change of vars
    //         in the Phi integral, and thus is only an irrelevant prefactor for
    //         the partition function.
    //
    RealD scale = std::sqrt(0.5);
    FermionField eta(FermOp.FermionGrid());

    gaussian(pRNG, eta);

    FermOp.ImportGauge(U);
    FermOp.Mdag(eta, Phi);

    Phi = Phi * scale;
  };

  //////////////////////////////////////////////////////
  // S = phi^dag (Mdag M)^-1 phi
  //////////////////////////////////////////////////////
  virtual RealD S(const GaugeField &U) {
    FermOp.ImportGauge(U);

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

    MdagMLinearOperator<FermionOperator<Impl>, FermionField> MdagMOp(FermOp);
    X = zero;
    ActionSolver(MdagMOp, Phi, X);
    MdagMOp.Op(X, Y);

    RealD action = norm2(Y);
    std::cout << GridLogMessage << "Pseudofermion action " << action
              << std::endl;
    return action;
  };

  //////////////////////////////////////////////////////
  // dS/du = - phi^dag  (Mdag M)^-1 [ Mdag dM + dMdag M ]  (Mdag M)^-1 phi
  //       = - phi^dag M^-1 dM (MdagM)^-1 phi -  phi^dag (MdagM)^-1 dMdag dM
  //       (Mdag)^-1 phi
  //
  //       = - Ydag dM X  - Xdag dMdag Y
  //
  //////////////////////////////////////////////////////
  virtual void deriv(const GaugeField &U, GaugeField &dSdU) {
    FermOp.ImportGauge(U);

    FermionField X(FermOp.FermionGrid());
    FermionField Y(FermOp.FermionGrid());
    GaugeField tmp(FermOp.GaugeGrid());

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

    X = zero;
    DerivativeSolver(MdagMOp, Phi, X);
    MdagMOp.Op(X, Y);

    // Check hermiticity
    /*
    std::vector<int> seeds({1,2,3,4});
    GridParallelRNG          RNG(U._grid);   RNG.SeedFixedIntegers(seeds);
    FermionField RNGphi(FermOp.FermionGrid());
    FermionField RNGchi(FermOp.FermionGrid());
    FermionField Achi(FermOp.FermionGrid());
    FermionField Aphi(FermOp.FermionGrid());

    random(RNG, RNGphi);
    random(RNG, RNGchi);
    MdagMOp.Op(RNGchi, Achi);
    MdagMOp.Op(RNGphi, Aphi);
    ComplexD pAc = innerProduct(RNGphi, Achi);
    ComplexD cAp = innerProduct(RNGchi, Aphi);
    //these should be real
    ComplexD pAp = innerProduct(RNGphi, Aphi);
    ComplexD cAc = innerProduct(RNGchi, Achi);

    std::cout<<GridLogMessage<< "pAc "<<pAc<<" cAp "<< cAp<< " diff "<<pAc-adj(cAp)<<std::endl;
    std::cout << GridLogMessage << "pAp " << pAp << " cAc " << cAc << std::endl;
*/
    // Our conventions really make this UdSdU; We do not differentiate wrt Udag
    // here.
    // So must take dSdU - adj(dSdU) and left multiply by mom to get dS/dt.

    FermOp.MDeriv(tmp, Y, X, DaggerNo);
    dSdU = tmp;
    FermOp.MDeriv(tmp, X, Y, DaggerYes);
    dSdU = dSdU + tmp;

    // not taking here the traceless antihermitian component
  };
};
}
}

#endif