Grid/lib/qcd/action/gauge/WilsonGaugeAction.h

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

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

Source file: ./lib/qcd/action/gauge/WilsonGaugeAction.h

Copyright (C) 2015

Author: Azusa Yamaguchi <ayamaguc@staffmail.ed.ac.uk>
Author: Peter Boyle <paboyle@ph.ed.ac.uk>
Author: neo <cossu@post.kek.jp>
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_WILSON_GAUGE_ACTION_H
#define QCD_WILSON_GAUGE_ACTION_H

namespace Grid {
namespace QCD {

////////////////////////////////////////////////////////////////////////
// Wilson Gauge Action .. should I template the Nc etc..
////////////////////////////////////////////////////////////////////////
template <class Gimpl>
class WilsonGaugeAction : public Action<typename Gimpl::GaugeField> {
 public:
  INHERIT_GIMPL_TYPES(Gimpl);

  //      typedef LorentzScalar<GaugeField> GaugeLinkField;

 private:
  RealD beta;

 public:
  WilsonGaugeAction(RealD b) : beta(b){};

  virtual void refresh(const GaugeField &U,
                       GridParallelRNG &pRNG){};  // noop as no pseudoferms

  virtual RealD S(const GaugeField &U) {
    RealD plaq = WilsonLoops<Gimpl>::avgPlaquette(U);
    RealD vol = U._grid->gSites();
    RealD action = beta * (1.0 - plaq) * (Nd * (Nd - 1.0)) * vol * 0.5;
    return action;
  };

  virtual void deriv(const GaugeField &U, GaugeField &dSdU) {
    // not optimal implementation FIXME
    // extend Ta to include Lorentz indexes

    // RealD factor = 0.5*beta/RealD(Nc);
    RealD factor = 0.5 * beta / RealD(Nc);

    GaugeLinkField Umu(U._grid);
    GaugeLinkField dSdU_mu(U._grid);
    for (int mu = 0; mu < Nd; mu++) {
      Umu = PeekIndex<LorentzIndex>(U, mu);

      // Staple in direction mu
      WilsonLoops<Gimpl>::Staple(dSdU_mu, U, mu);
      dSdU_mu = Ta(Umu * dSdU_mu) * factor;

      PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
    }
  };
};

template <class Gimpl>
class VariableWilsonGaugeAction : public Action<typename Gimpl::GaugeField> {
 public:
  INHERIT_GIMPL_TYPES(Gimpl);

 private:
  std::vector<RealD> b_bulk;  // bulk couplings
  std::vector<RealD> b_xdim;  // extra dimension couplings
  GridBase *grid;
  LatticeComplex beta_xdim;
  LatticeComplex beta_xdim_shifted;
  LatticeComplex beta_bulk;

  int bulk_volume;

 public:
  VariableWilsonGaugeAction(std::vector<RealD> bulk, std::vector<RealD> xdim,
                            GridBase *_grid)
      : b_bulk(bulk),
        b_xdim(xdim),
        grid(_grid),
        beta_xdim(grid),
        beta_xdim_shifted(grid),
        beta_bulk(grid) {
    // check that the grid is ok
    // todo
    int Ndim = Nd;  // change later

    std::vector<int> FullDim = grid->GlobalDimensions();
    bulk_volume = 1;
    for (int s = 0; s < Ndim - 1; s++) bulk_volume *= FullDim[s];

    LatticeComplex temp(grid);

    Lattice<iScalar<vInteger> > coor(grid);

    LatticeCoordinate(coor, Ndim - 1);

    int Nex = FullDim[Ndim - 1];
    assert(b_bulk.size() == Nex);
    assert(b_xdim.size() == Nex);

    beta_xdim = zero;
    for (int tau = 0; tau < Nex - 1; tau++) {
      temp = b_xdim[tau];
      beta_xdim = where(coor == tau, temp, beta_xdim);
    }

    beta_xdim_shifted = Cshift(beta_xdim, Ndim - 1, -1);

    beta_bulk = zero;
    for (int tau = 0; tau < Nex; tau++) {
      temp = b_bulk[tau];
      beta_bulk = where(coor == tau, temp, beta_bulk);
    }


  };

  virtual void refresh(const GaugeField &U,
                       GridParallelRNG &pRNG){};  // noop as no pseudoferms

  virtual RealD S(const GaugeField &Umu) {
    int Ndim = Nd;  // change later for generality
    conformable(grid, Umu._grid);

    std::vector<GaugeLinkField> U(Ndim, grid);

    for (int mu = 0; mu < Ndim; mu++) {
      U[mu] = PeekIndex<LorentzIndex>(Umu, mu);
    }

    LatticeComplex dirPlaq(grid);
    LatticeComplex Plaq(grid);

    LatticeComplex SumdirPlaq(grid);

    RealD OneOnNc = 1.0 / Real(Nc);

    /////////////
    // Lower dim plaquettes
    /////////////
    Plaq = zero;
    SumdirPlaq = zero;
    for (int mu = 1; mu < Ndim - 1; mu++) {
      for (int nu = 0; nu < mu; nu++) {
        WilsonLoops<Gimpl>::traceDirPlaquette(dirPlaq, U, mu, nu);
        SumdirPlaq += dirPlaq;
        Plaq = Plaq + (1.0 - dirPlaq * OneOnNc) * beta_bulk;
      }
    }

    
    double faces = (1.0 * (Nd - 1) * (Nd - 2)) / 2.0;
    SumdirPlaq *= OneOnNc / (RealD(bulk_volume) * faces);

    // print slices in the extra dimension
    int Nex = grid->_fdimensions[Ndim - 1];
    std::vector<TComplex> plaq_ex(Nex);
    sliceSum(SumdirPlaq, plaq_ex, Ndim - 1);
    for (int ex = 0; ex < Nex; ex++)
      std::cout << GridLogMessage << "Bulk plaq[" << ex
                << "] = " << TensorRemove(plaq_ex[ex]).real() << std::endl;

    /////////////
    // Extra dimension
    /////////////
    {
      int mu = Ndim - 1;
      for (int nu = 0; nu < mu; nu++) {
        WilsonLoops<Gimpl>::traceDirPlaquette(dirPlaq, U, mu, nu);
        Plaq = Plaq + (1.0 - dirPlaq * OneOnNc) * beta_xdim;
      }
    }

    TComplex Tp = sum(Plaq);
    Complex p = TensorRemove(Tp);
    RealD action = p.real();
    return action;
  };

  virtual void deriv(const GaugeField &U, GaugeField &dSdU) {
    // not optimal implementation FIXME
    // extend Ta to include Lorentz indexes

    // for the higher dimension plaquettes take the upper plaq of the
    // 4d slice and multiply by beta[s] and the lower and multiply by beta[s-1]
    // derivative of links mu = 0, ... Nd-1 inside plaq (mu,5)
    // for these I need upper and lower staples separated
    // each multiplied with their own beta
    // derivative of links mu = 5
    // living on the same slice, share the same beta

    conformable(grid, U._grid);
    int Ndim = Nd;  // change later
    RealD factor = 0.5 / RealD(Nc);

    GaugeLinkField Umu(grid);
    GaugeLinkField dSdU_mu(grid);
    GaugeLinkField staple(grid);

    for (int mu = 0; mu < Ndim; mu++) {
      Umu = PeekIndex<LorentzIndex>(U, mu);
      dSdU_mu = zero;

      for (int nu = 0; nu < Ndim; nu++) {
        if (nu != mu) {
          if ((mu < (Ndim - 1)) && (nu < (Ndim - 1))) {
            // Spacelike case apply beta space
            WilsonLoops<Gimpl>::Staple(staple, U, mu, nu);
            staple = staple * beta_bulk;
            dSdU_mu += staple;

          } else if (mu == (Ndim - 1)) {
            // nu space; mu time link
            assert(nu < (Ndim - 1));
            assert(mu == (Ndim - 1));

            // mu==tau dir link deriv, nu spatial
            WilsonLoops<Gimpl>::Staple(staple, U, mu, nu);
            staple = staple * beta_xdim;
            dSdU_mu += staple;

          } else {
            assert(mu < (Ndim - 1));
            assert(nu == (Ndim - 1));

            // nu time; mu space link

            // staple forwards in tau
            WilsonLoops<Gimpl>::StapleUpper(staple, U, mu, nu);
            staple = staple * beta_xdim;
            dSdU_mu += staple;

            // staple backwards in tau
            WilsonLoops<Gimpl>::StapleLower(staple, U, mu, nu);
            staple = staple * beta_xdim_shifted;
            dSdU_mu += staple;
          }
        }
      }

      dSdU_mu = Ta(Umu * dSdU_mu) * factor;
      PokeIndex<LorentzIndex>(dSdU, dSdU_mu, mu);
    }
  };
};
}
}

#endif