/* Copyright (c) 1997-2021
   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.
--------------------------------------------------------------------------------
*/

#pragma once

#include "polymake/Matrix.h"
#include "polymake/Vector.h"
#include "polymake/linalg.h"

#include "polymake/Set.h"
#include "polymake/list"
#include "polymake/graph/Decoration.h"

namespace polymake { namespace fan {

// Excludes all faces contained in a list of "boundary faces"
class NoBoundaryCut {
protected:
  const std::list<Set<Int>>& max_boundary_faces;
  const IncidenceMatrix<>& maximal_cones;
public:
  NoBoundaryCut(const std::list<Set<Int>>& mbf, const IncidenceMatrix<>& mc) :
    max_boundary_faces(mbf), maximal_cones(mc) {}

  bool operator()(const graph::lattice::BasicDecoration& data) const
  {
    if (data.face.size() == 0) return true;
    auto face = accumulate(rows(maximal_cones.minor(data.face,All)), operations::mul());
    for (auto mf_it : max_boundary_faces)
      if (incl(face, mf_it) < 1) return false;
    return true;
  }
};

template <typename Scalar, typename MTop, typename VTop, typename MatrixTop>
Matrix<Scalar> tight_span_vertices(const GenericMatrix<MTop, Scalar>& points, const GenericIncidenceMatrix<MatrixTop>& VIF, const GenericVector<VTop, Scalar>& lift)
{
  const bool full_dim = rank(points)==points.cols();
  const Int dim = full_dim ? points.cols()+1 : points.cols();
  Matrix<Scalar> vertices(VIF.rows(), dim);
  Matrix<Scalar> eq(points.rows(), dim);
  eq.minor(All,sequence(0,points.cols())) = points;
  eq.col(0) = lift;
  if (full_dim) {
    eq.col(dim-1) = ones_vector<Scalar>(points.rows())-points.minor(All,sequence(1,points.cols()-1))*ones_vector<Scalar>(points.cols()-1);
  }

  Int i = 0;
  for (auto it= entire(rows(VIF)); !it.at_end(); ++it, ++i) {
    vertices.row(i) = null_space(eq.minor(*it,All)).row(0);
    if (vertices(i, 0)<0)
      vertices.row(i).negate();
  }
  return vertices;
}

} }

