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

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

Source file: ./lib/qcd/hmc/integrators/Integrator.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 */
//--------------------------------------------------------------------
/*! @file Integrator.h
 * @brief Classes for the Molecular Dynamics integrator
 *
 * @author Guido Cossu
 * Time-stamp: <2015-07-30 16:21:29 neo>
 */
//--------------------------------------------------------------------

#ifndef INTEGRATOR_INCLUDED
#define INTEGRATOR_INCLUDED

// class Observer;

#include <memory>

namespace Grid {
namespace QCD {

struct IntegratorParameters {
  int Nexp;
  int MDsteps;  // number of outer steps
  RealD trajL;  // trajectory length
  RealD stepsize;

  IntegratorParameters(int MDsteps_, RealD trajL_ = 1.0, int Nexp_ = 12)
      : Nexp(Nexp_),
        MDsteps(MDsteps_),
        trajL(trajL_),
        stepsize(trajL / MDsteps){
            // empty body constructor
        };
};

/*! @brief Class for Molecular Dynamics management */
template <class GaugeField, class SmearingPolicy, class RepresentationPolicy>
class Integrator {
 protected:
  typedef IntegratorParameters ParameterType;

  IntegratorParameters Params;

  const ActionSetHirep<GaugeField, RepresentationPolicy> as;

  int levels;  //
  double t_U;  // Track time passing on each level and for U and for P
  std::vector<double> t_P;  //

  GaugeField P;

  SmearingPolicy& Smearer;

  RepresentationPolicy Representations;

  // Should match any legal (SU(n)) gauge field
  // Need to use this template to match Ncol to pass to SU<N> class
  template <int Ncol, class vec>
  void generate_momenta(Lattice<iVector<iScalar<iMatrix<vec, Ncol> >, Nd> >& P,
                        GridParallelRNG& pRNG) {
    typedef Lattice<iScalar<iScalar<iMatrix<vec, Ncol> > > > GaugeLinkField;
    GaugeLinkField Pmu(P._grid);
    Pmu = zero;
    for (int mu = 0; mu < Nd; mu++) {
      SU<Ncol>::GaussianFundamentalLieAlgebraMatrix(pRNG, Pmu);
      PokeIndex<LorentzIndex>(P, Pmu, mu);
    }
  }

  // ObserverList observers; // not yet
  //      typedef std::vector<Observer*> ObserverList;
  //      void register_observers();
  //      void notify_observers();

  void update_P(GaugeField& U, int level, double ep) {
    t_P[level] += ep;
    update_P(P, U, level, ep);

    std::cout << GridLogIntegrator << "[" << level << "] P "
              << " dt " << ep << " : t_P " << t_P[level] << std::endl;
  }

  // to be used by the actionlevel class to iterate
  // over the representations
  struct _updateP {
    template <class FieldType, class GF, class Repr>
    void operator()(std::vector<Action<FieldType>*> repr_set, Repr& Rep,
                    GF& Mom, GF& U, double ep) {
      for (int a = 0; a < repr_set.size(); ++a) {
        FieldType forceR(U._grid);
        // Implement smearing only for the fundamental representation now
        repr_set.at(a)->deriv(Rep.U, forceR);
        GF force =
            Rep.RtoFundamentalProject(forceR);  // Ta for the fundamental rep
        std::cout << GridLogIntegrator << "Hirep Force average: "
                  << norm2(force) / (U._grid->gSites()) << std::endl;
        Mom -= force * ep;
      }
    }
  } update_P_hireps{};

  void update_P(GaugeField& Mom, GaugeField& U, int level, double ep) {
    // input U actually not used in the fundamental case
    // Fundamental updates, include smearing
    for (int a = 0; a < as[level].actions.size(); ++a) {
      GaugeField force(U._grid);
      GaugeField& Us = Smearer.get_U(as[level].actions.at(a)->is_smeared);
      as[level].actions.at(a)->deriv(Us, force);  // deriv should NOT include Ta

      std::cout << GridLogIntegrator
                << "Smearing (on/off): " << as[level].actions.at(a)->is_smeared
                << std::endl;
      if (as[level].actions.at(a)->is_smeared) Smearer.smeared_force(force);
      force = Ta(force);
      std::cout << GridLogIntegrator
                << "Force average: " << norm2(force) / (U._grid->gSites())
                << std::endl;
      Mom -= force * ep;
    }

    // Force from the other representations
    as[level].apply(update_P_hireps, Representations, Mom, U, ep);
  }

  void update_U(GaugeField& U, double ep) {
    update_U(P, U, ep);

    t_U += ep;
    int fl = levels - 1;
    std::cout << GridLogIntegrator << "   "
              << "[" << fl << "] U "
              << " dt " << ep << " : t_U " << t_U << std::endl;
  }
  void update_U(GaugeField& Mom, GaugeField& U, double ep) {
    // rewrite exponential to deal automatically  with the lorentz index?
    for (int mu = 0; mu < Nd; mu++) {
      auto Umu = PeekIndex<LorentzIndex>(U, mu);
      auto Pmu = PeekIndex<LorentzIndex>(Mom, mu);
      Umu = expMat(Pmu, ep, Params.Nexp) * Umu;
      PokeIndex<LorentzIndex>(U, ProjectOnGroup(Umu), mu);
    }
    // Update the smeared fields, can be implemented as observer
    Smearer.set_GaugeField(U);
    // Update the higher representations fields
    Representations.update(U);  // void functions if fundamental representation
  }

  virtual void step(GaugeField& U, int level, int first, int last) = 0;

 public:
  Integrator(GridBase* grid, IntegratorParameters Par,
             ActionSetHirep<GaugeField, RepresentationPolicy>& Aset,
             SmearingPolicy& Sm)
      : Params(Par),
        as(Aset),
        P(grid),
        levels(Aset.size()),
        Smearer(Sm),
        Representations(grid) {
    t_P.resize(levels, 0.0);
    t_U = 0.0;
    // initialization of smearer delegated outside of Integrator
  };

  virtual ~Integrator() {}

  // to be used by the actionlevel class to iterate
  // over the representations
  struct _refresh {
    template <class FieldType, class Repr>
    void operator()(std::vector<Action<FieldType>*> repr_set, Repr& Rep,
                    GridParallelRNG& pRNG) {
      for (int a = 0; a < repr_set.size(); ++a)
        repr_set.at(a)->refresh(Rep.U, pRNG);
      std::cout << GridLogDebug << "Hirep refreshing pseudofermions" << std::endl;
    }
  } refresh_hireps{};

  // Initialization of momenta and actions
  void refresh(GaugeField& U, GridParallelRNG& pRNG) {
    std::cout << GridLogIntegrator << "Integrator refresh\n";
    generate_momenta(P, pRNG);

    // Update the smeared fields, can be implemented as observer
    // necessary to keep the fields updated even after a reject
    // of the Metropolis
    Smearer.set_GaugeField(U);
    // Set the (eventual) representations gauge fields
    Representations.update(U);

    // The Smearer is attached to a pointer of the gauge field
    // automatically gets the correct field
    // whether or not has been accepted in the previous sweep
    for (int level = 0; level < as.size(); ++level) {
      for (int actionID = 0; actionID < as[level].actions.size(); ++actionID) {
        // get gauge field from the SmearingPolicy and
        // based on the boolean is_smeared in actionID
        GaugeField& Us =
            Smearer.get_U(as[level].actions.at(actionID)->is_smeared);
        as[level].actions.at(actionID)->refresh(Us, pRNG);
      }

      // Refresh the higher representation actions
      as[level].apply(refresh_hireps, Representations, pRNG);
    }
  }

  // to be used by the actionlevel class to iterate
  // over the representations
  struct _S {
    template <class FieldType, class Repr>
    void operator()(std::vector<Action<FieldType>*> repr_set, Repr& Rep,
                    int level, RealD& H) {
      
      for (int a = 0; a < repr_set.size(); ++a) {
        RealD Hterm = repr_set.at(a)->S(Rep.U);
        std::cout << GridLogMessage << "S Level " << level << " term " << a
                  << " H Hirep = " << Hterm << std::endl;
        H += Hterm;

      }
    }
  } S_hireps{};

  // Calculate action
  RealD S(GaugeField& U) {  // here also U not used

    LatticeComplex Hloc(U._grid);
    Hloc = zero;
    // Momenta
    for (int mu = 0; mu < Nd; mu++) {
      auto Pmu = PeekIndex<LorentzIndex>(P, mu);
      Hloc -= trace(Pmu * Pmu);
    }
    Complex Hsum = sum(Hloc);

    RealD H = Hsum.real();
    RealD Hterm;
    std::cout << GridLogMessage << "Momentum action H_p = " << H << "\n";

    // Actions
    for (int level = 0; level < as.size(); ++level) {
      for (int actionID = 0; actionID < as[level].actions.size(); ++actionID) {
        // get gauge field from the SmearingPolicy and
        // based on the boolean is_smeared in actionID
        GaugeField& Us =
            Smearer.get_U(as[level].actions.at(actionID)->is_smeared);
        Hterm = as[level].actions.at(actionID)->S(Us);
        std::cout << GridLogMessage << "S Level " << level << " term "
                  << actionID << " H = " << Hterm << std::endl;
        H += Hterm;
      }
      as[level].apply(S_hireps, Representations, level, H);
    }

    return H;
  }

  void integrate(GaugeField& U) {
    // reset the clocks
    t_U = 0;
    for (int level = 0; level < as.size(); ++level) {
      t_P[level] = 0;
    }

    for (int step = 0; step < Params.MDsteps; ++step) {  // MD step
      int first_step = (step == 0);
      int last_step = (step == Params.MDsteps - 1);
      this->step(U, 0, first_step, last_step);
    }

    // Check the clocks all match on all levels
    for (int level = 0; level < as.size(); ++level) {
      assert(fabs(t_U - t_P[level]) < 1.0e-6);  // must be the same
      std::cout << GridLogIntegrator << " times[" << level
                << "]= " << t_P[level] << " " << t_U << std::endl;
    }

    // and that we indeed got to the end of the trajectory
    assert(fabs(t_U - Params.trajL) < 1.0e-6);
  }
};
}
}
#endif  // INTEGRATOR_INCLUDED