/* Copyright (c) 1997-2020
   Ewgenij Gawrilow, Michael Joswig, and the polymake team
   Technische Universität Berlin, Germany
   https://polymake.org

   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, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   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.
--------------------------------------------------------------------------------
*/

#include "polymake/client.h"
#include "polymake/Rational.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Matrix.h"
#include "polymake/Vector.h"
#include "polymake/Set.h"
#include "polymake/graph/GraphIso.h"
#include "polymake/linalg.h"
#include "polymake/TropicalNumber.h"
#include "polymake/graph/lattice_builder.h"
#include "polymake/fan/hasse_diagram.h"
#include "polymake/tropical/covectors.h"

namespace polymake { namespace tropical {

using namespace graph;
using namespace graph::lattice;

// Keep only cells lying in the tropical span, i.e. whose covector has no empty entries
class CovectorCut {
public:
  bool operator()(const CovectorDecoration& data) const
  {
    for (auto r_it = entire(rows(data.covector)); !r_it.at_end(); ++r_it)
      if (r_it->empty())
        return false;
    return true;
  }
};

// Computes face and rank as normal and the covector from the face
template <typename Addition, typename Scalar>
class CovectorDecorator {
protected:
  const Array<IncidenceMatrix<>>& pseudovertex_covectors;
  const Matrix<TropicalNumber<Addition,Scalar>> points;
  const Set<Int> artificial_set;
public:
  using FaceData = graph::lattice::BasicClosureOperator<CovectorDecoration>::ClosureData;

  CovectorDecorator(const Matrix<TropicalNumber<Addition,Scalar>>& p_arg,
                    const Array<IncidenceMatrix<>>& p_cov,
                    const Set<Int>& artificial_set_)
    : pseudovertex_covectors(p_cov)
    , points(p_arg)
    , artificial_set(artificial_set_) {}

  /*
   * @brief Takes a list of covectors and returns the intersection of those elements specified by s
   */
  IncidenceMatrix<> covector_from_atoms(const Set<Int>& s) const
  {
    return accumulate( select( pseudovertex_covectors, s), operations::mul());
  }

  CovectorDecoration compute_initial_decoration(const FaceData& face) const
  {
    IncidenceMatrix<> initial_covector(points.cols(), points.rows());
    for (auto p_it = entire<indexed>(rows(points)); !p_it.at_end(); ++p_it) {
      initial_covector.col(p_it.index()) = support(*p_it);
    }
    return CovectorDecoration(Set<Int>{}, 0, initial_covector);
  }

  CovectorDecoration compute_decoration(const FaceData& face,
                                        const CovectorDecoration& predecessor_data) const
  {
    if (face.get_dual_face().empty()) {
      // This can only occur in the torus case, where this represents the artificial top node
      return CovectorDecoration( artificial_set, predecessor_data.rank+1,
                                 IncidenceMatrix<>( points.cols(), points.rows()));
    }
    IncidenceMatrix<> face_covector = covector_from_atoms( face.get_face() );
    return CovectorDecoration( face.get_face(), predecessor_data.rank+1, face_covector);
  }

  CovectorDecoration compute_artificial_decoration(const NodeMap<Directed, CovectorDecoration>& decor,
                                                   const std::list<Int>& max_nodes) const
  {
    IncidenceMatrix<> artificial_covector(points.cols(), points.rows());
    auto max_list = attach_member_accessor( select(decor, max_nodes),
                                            ptr2type<CovectorDecoration, Int, &CovectorDecoration::rank>()
                                            );
    const Int top_rank = accumulate(max_list, operations::max())+1;
    return CovectorDecoration( artificial_set, top_rank, artificial_covector);
  }
};


/*
 * @brief Computes the covector decomposition of the tropical span or the tropical
 * torus induced by a list of tropical points.
 * @param BigObject cone. A tropical::Polytope
 * @option Bool compute_only_tropical_span If true, only the covector decomposition of the tropical span is
 * computed. If false, the covector decomposition of the torus is also computed.
 *
 * Sets the properties [[POLYTOPE_COVECTOR_DECOMPOSITION]], [[POLYTOPE_MAXIMAL_COVECTOR_CELLS]]
 * and [[POLYTOPE_MAXIMAL_COVECTORS]] if compute_only_tropical_span is true, otherwise it sets
 * [[TORUS_COVECTOR_DECOMPOSITION]] and [[MAXIMAL_COVECTORS]].
 */
template <typename Addition, typename Scalar>
void compute_covector_decomposition(BigObject cone, OptionSet options) {
  const bool compute_only_tropical_span = options["compute_only_tropical_span"];

  const Array<IncidenceMatrix<> >& pseudovertex_covectors = cone.give("PSEUDOVERTEX_COVECTORS");
  const IncidenceMatrix<>& max_covector_cells = cone.give("MAXIMAL_COVECTOR_CELLS");
  const Matrix< TropicalNumber<Addition,Scalar> >& points = cone.give("POINTS");

  Lattice<CovectorDecoration> init_lattice;
  Set<Int> queuing_nodes;
  if (!compute_only_tropical_span) {
    BigObject cone_cov_obj = cone.give("POLYTOPE_COVECTOR_DECOMPOSITION");
    Graph<Directed> cone_cov_graph = cone_cov_obj.give("ADJACENCY");
    Int top_node = cone_cov_obj.give("TOP_NODE");
    const Int bottom_node = cone_cov_obj.give("BOTTOM_NODE");
    // We need to queue all maximal faces and all atoms
    for (auto max_node : cone_cov_graph.in_adjacent_nodes(top_node)) {
      queuing_nodes += ( max_node > top_node? max_node-1 : max_node);
    }
    for (auto atom : cone_cov_graph.out_adjacent_nodes(bottom_node)) {
      queuing_nodes += ( atom > top_node? atom-1 : atom);
    }
    init_lattice = copy_all_but_top_node(Lattice<CovectorDecoration>(cone_cov_obj));
  }

  fan::lattice::ComplexPrimalClosure<CovectorDecoration> cop(max_covector_cells);
  TrivialCut<CovectorDecoration> trivial_cut;
  CovectorCut covector_cut;
  CovectorDecorator<Addition, Scalar> dec = CovectorDecorator<Addition,Scalar>( points, pseudovertex_covectors, scalar2set(-1));

  // Note: The additional top node is always attained through closure in the torus decomposition,
  // as we always have at least two cells
  // For cones, such a closure is cut, so we always need an artificial top node
  Lattice<CovectorDecoration> result = compute_only_tropical_span?
    lattice_builder::compute_lattice_from_closure<CovectorDecoration>(cop, covector_cut, dec, 1, lattice_builder::Primal()) :
    lattice_builder::compute_lattice_from_closure<CovectorDecoration>(cop, trivial_cut, dec, 0, lattice_builder::Primal(), init_lattice, queuing_nodes);

  const Int n_max_nodes = result.in_degree(result.top_node());
  auto max_nodes = select(result.decoration(), result.in_adjacent_nodes(result.top_node()));
  Array<IncidenceMatrix<>> max_covectors( n_max_nodes, entire(attach_member_accessor(max_nodes,
                     ptr2type<CovectorDecoration, IncidenceMatrix<>, &CovectorDecoration::covector>())));
  Array<Set<Int>> cone_max_cells( n_max_nodes, entire(attach_member_accessor(max_nodes,
                     ptr2type<CovectorDecoration, Set<Int>, &CovectorDecoration::face>())));
  if (compute_only_tropical_span) {
    cone.take("POLYTOPE_MAXIMAL_COVECTOR_CELLS") << cone_max_cells;
    cone.take("POLYTOPE_MAXIMAL_COVECTORS") << max_covectors;
    cone.take("POLYTOPE_COVECTOR_DECOMPOSITION") << result;
  } else {
    // Torus cells might be in a different order
    Array<Int> cell_perm = find_permutation( cone_max_cells, rows(max_covector_cells)).value();
    cone.take("MAXIMAL_COVECTORS") << permuted(max_covectors, cell_perm);
    cone.take("TORUS_COVECTOR_DECOMPOSITION") << result;
  }
}

FunctionTemplate4perl("compute_covector_decomposition<Addition,Scalar>(Polytope<Addition,Scalar> {compute_only_tropical_span => 0})");

} }
