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

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 Grid {
namespace QCD {

///////////////////////////////////////
// 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 void refresh(const GaugeField &U, 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);

    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);
  };
};
}
}

#endif