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#ifndef COSMOINTERFACE_EVOLVERS_KERNELS_SU2KERNELS_H
#define COSMOINTERFACE_EVOLVERS_KERNELS_SU2KERNELS_H

/* This file is part of CosmoLattice, available at www.cosmolattice.net .
   Copyright Daniel G. Figueroa, Adrien Florio, Francisco Torrenti and Wessel Valkenburg.
   Released under the MIT license, see LICENSE.md. */

// File info: Main contributor(s): Daniel G. Figueroa, Adrien Florio, Francisco Torrenti,  Year: 2020

#include "CosmoInterface/definitions/gaugederivatives.h"
#include "CosmoInterface/definitions/mattercurrents.h"
#include "CosmoInterface/definitions/potential.h"
#include "TempLat/lattice/algebra/gaugealgebra/plaquetteback.h"
#include "CosmoInterface/evolvers/kernels/kernelstypes.h"

namespace TempLat
{
  class SU2Kernels
  {
  public:
    // Put public methods here. These should change very little over time.
    SU2Kernels() = delete;

    // Equations of motion:
    template <class Model, int N> static auto get(Model &model, Tag<N> n, KernelsTypes::EoM<Model> kt)
    {
      // Computes different terms in the SU(2) gauge kernels:

      // SU(2) gauge current
      auto SU2Source = MatterCurrents::SU2Current(model, n);

      // Gradient (forward contribution)
      auto GradSU2 = MakeVector(
          i, 1, Model::NDim, Total(j, 1, Model::NDim, IfElse(!IsEqual(i, j), plaq(model.fldSU2(n), i, j), ZeroType())));

      // Gradient (backward contribution)
      auto GradSU2Back =
          MakeVector(i, 1, Model::NDim,
                     Total(j, 1, Model::NDim, IfElse(!IsEqual(i, j), plaqBack(model.fldSU2(n), i, j), ZeroType())));

      auto normSU2Source = (1 / model.dx) * pow(model.aI, 1 + model.alpha); // Rescaling for SU2Source
      auto normGrad = pow<3>(1 / model.dx) / model.gQ_SU2DblSU2(0_c, n) *
                      pow(model.aI, -1 + model.alpha); // Rescaling for GradSU2 and GradSU2Back
      // --> Note: the 0_c in normGrad is correct. In our convention, the link is defined with the coupling of the 0th
      // doublet.

      // Returns kernel for the SU(2) gauge fields' EOM:
      return -normGrad * (GradSU2 - GradSU2Back) - normSU2Source * SU2Source;
    }

    template <class Model, int N> static auto get_momentum(Model &model, Tag<N> n, KernelsTypes::EoM<Model> kt)
    {
      // Returns ''momentum'' for the SU(2) gauge fields' EOM (a bit different because evolving the links). Also note
      // that our algebra variables are antihermitean, so we are really saving i E.
      return pow(model.aI, model.alpha - 1) * model.gQ_SU2DblSU2(0_c, n) * model.dx * model.piSU2(n);
    }

    // Default function returns EoM kernels, for backward compatibility.
    template <class Model, int N> static auto get(Model &model, Tag<N> a)
    {
      return SU2Kernels::get(model, a, KernelsTypes::EoM<Model>());
    }
  };
} // namespace TempLat

#endif