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

#ifndef POLYMAKE_TROPICAL_COVECTORS_H
#define POLYMAKE_TROPICAL_COVECTORS_H

#include "polymake/tropical/arithmetic.h"
#include "polymake/linalg.h"
#include "polymake/IncidenceMatrix.h"

namespace polymake { namespace tropical {

struct CovectorDecoration : public GenericStruct<CovectorDecoration> {
  DeclSTRUCT( DeclFIELD(face, Set<Int>)
              DeclFIELD(rank, Int)
              DeclFIELD(covector,IncidenceMatrix<>) );

  CovectorDecoration() {}
  CovectorDecoration(const Set<Int>& f, Int r, const IncidenceMatrix<>& cv)
    : face(f)
    , rank(r)
    , covector(cv) {}
};

/*
 * @brief compute the covector of a single point in tropical projective space wrt a matrix of generators
 *
 */
template <typename Addition, typename Scalar, typename Vector1, typename Vector2>
Set<Int> single_covector(const GenericVector<Vector1, TropicalNumber<Addition, Scalar>>& point,
                         const GenericVector<Vector2, TropicalNumber<Addition,Scalar>>& apex)
{
  typedef TropicalNumber<Addition, Scalar> TNumber;
  Set<Int> pt_covector = sequence(0, point.dim()) - support(point);
  Vector<TNumber> tdiff = rel_coord(apex, point);
  TNumber extremum = accumulate(tdiff, operations::add());
  Int td_index = 0;
  // determine the extremal entries
  for (auto td : tdiff) {
    if (td == extremum)
      pt_covector += td_index;
    ++td_index;
  }
  return pt_covector;
}

/*
 * @brief compute the covector of a single point in tropical projective space wrt a matrix of generators
 */

template <typename Addition, typename Scalar, typename VectorTop, typename MatrixTop>
IncidenceMatrix<> single_covector(const GenericVector<VectorTop, TropicalNumber<Addition,Scalar>>& point,
                                  const GenericMatrix<MatrixTop, TropicalNumber<Addition, Scalar>>& generators)
{
  typedef TropicalNumber<Addition, Scalar> TNumber;
  const Int dimension = generators.cols();
  Set<Int> non_support = sequence(0, point.dim()) - support(point);
  Array<Set<Int>> pt_covector(dimension);

  Int gn_index = 0;
  for (auto gn : rows(generators)) {
    Vector<TNumber> tdiff = rel_coord(gn, point);
    TNumber extremum = accumulate(tdiff, operations::add());
    Set<Int> extremal_entries = non_support;
    Int td_index = 0;
    // determine the extremal entries
    for (auto td : tdiff) {
      if (td == extremum)
        extremal_entries += td_index;
      ++td_index;
    }
    // add the containing sectors to the covector of pt
    for (auto ext_it : extremal_entries) {
      pt_covector[ext_it] += gn_index;
    }
    ++gn_index;
  }
  return IncidenceMatrix<>(pt_covector);
}

/*
 * @brief determine the covector of a 0-1-ray wrt a matrix of generators
 * for this only the index set of the 1 entries and the supports of the generators are taken into account
 */
template <typename Addition, typename Scalar>
IncidenceMatrix<> artificial_ray_covector(const Set<Int>& one_entries,
                                          const Matrix<TropicalNumber<Addition, Scalar>>& generators)
{
  const Int dimension = generators.cols();
  RestrictedIncidenceMatrix<> pt_covector(dimension);
  Int gn_index = 0;
  for (auto gn = entire(rows(generators)); !gn.at_end(); ++gn, ++gn_index) {
    if (incl(one_entries, sequence(0, dimension) - support(*gn)) <= 0) {
      for (Int r = 0; r < dimension; ++r)
        pt_covector(r, gn_index)=true;
    } else {
      for (Int covector_index : one_entries) {
        pt_covector(covector_index, gn_index) = true;
      }
    }
  }
  return IncidenceMatrix<>(std::move(pt_covector));
}

// Documentation see perl wrapper
template <typename Addition, typename Scalar, typename Matrix1, typename Matrix2>
Array<IncidenceMatrix<>> covectors(const GenericMatrix<Matrix1, TropicalNumber<Addition, Scalar>>& points,
                                   const GenericMatrix<Matrix2, TropicalNumber<Addition, Scalar>>& generators)
{
  const Int n = points.rows();
  Array<IncidenceMatrix<>> result(n);
  Int pt_index = 0;
  for (auto pt : rows(points)) {
    // call the computation of the covector for every single point
    result[pt_index] = single_covector(pt, generators);
    ++pt_index;
  }//END iterate points
  return result;
}

// Versions for scalar matrices.

template <typename Addition, typename Scalar>
Array<IncidenceMatrix<>> covectors_of_scalar_vertices(const Matrix<Scalar>& points,
                                                      const Matrix<TropicalNumber<Addition, Scalar>>& generators)
{
  const Int dimension = generators.cols();
  Array<IncidenceMatrix<>> result(points.rows());
  Int pt_index = 0;
  for (auto pt = entire(rows(points)); !pt.at_end(); ++pt, ++pt_index) {
    if ((*pt)[0] == 1) {
      result[pt_index] = single_covector(Vector<TropicalNumber<Addition, Scalar>>(pt->slice(range_from(1))), generators);
    } else {
      Set<Int> one_entries = support(pt->slice(range_from(1))); //the indices of the 1-entries of the 0/1-ray
      if ((*pt)[one_entries.front()+1] * Addition::orientation() < 0)
        one_entries = sequence(0, dimension) - one_entries;

      result[pt_index] = artificial_ray_covector (one_entries, generators);
    }
  }
  return result;
}

/*
 * @brief compute the generalized covector of a single point w.r.t. apices defining inequalities
 *
 */
template <typename Addition, typename Scalar, typename VectorTop, typename MatrixTop>
IncidenceMatrix<> generalized_apex_covector(const GenericVector<VectorTop, TropicalNumber<Addition, Scalar>>& point,
                                            const GenericMatrix<MatrixTop, TropicalNumber<Addition, Scalar>>& apices)
{
  typedef TropicalNumber<Addition, Scalar> TNumber;

  IncidenceMatrix<> pt_covector(apices.rows(),apices.cols());

  for (auto apex = entire<indexed>(rows(apices)); !apex.at_end(); ++apex) {
    TNumber extremum = *apex*point;
    if (!is_zero(extremum)) {
      Vector<TNumber> hadaprod(attach_operation(*apex, point.top(), operations::mul()));
      Set<Int> extremal_entries = indices(attach_selector(hadaprod, operations::fix2<TNumber,operations::eq>(extremum)));

      // add the containing sectors to the covector of pt
      pt_covector[apex.index()] = extremal_entries;
    }
  }
  return pt_covector;
}

} }

#endif

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