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

#include "polymake/client.h"
#include "polymake/Matrix.h"
#include "polymake/PowerSet.h"
#include "polymake/Graph.h"
#include "polymake/linalg.h"

namespace polymake { namespace polytope {

template<typename Scalar>
Matrix<Scalar> splits(const Matrix<Scalar>& vert, const Graph<>& graph, const Matrix<Scalar>& facets, const Int d, OptionSet options)
{
   Set<Int> coords;
   options["Coordinates"]>>coords;
   const Int n = vert.rows();
   const Int a_dim = vert.cols()-1;

   ListMatrix<Vector<Scalar>> splits;
   // test for each d vertices if they lie in a splitting hyperplane
   for (auto i=entire(all_subsets_of_k(sequence(0,n),d)); !i.at_end(); ++i) {
      const Matrix<Scalar> h=vert.minor(*i,All);

      // they must have full rank
      if (rank(h)==d) {
         bool is_new=true;

         //exclude facets and sets that are already in a split
         for (auto j=entire(rows(splits)); is_new && !j.at_end(); ++j)
            if (is_zero(h*(*j))) is_new=false;
         for (auto j=entire(rows(facets)); is_new && !j.at_end(); ++j)
            if (is_zero(h*(*j))) is_new=false;

         if (is_new) {
            Int pos = 0;
            Matrix<Scalar> o(a_dim-d,a_dim+1);
            for (auto k=entire(coords); !k.at_end(); ++k)
               o(pos++,*k)=1;
            for (; pos<a_dim-d; ++pos) o(pos,pos)=1;
            Vector<Scalar> a=null_space(h/o).row(0);

            bool is_split=true;

            //test for each edge of it is cut by the hyperplane, which means that it does not define a split.
            for (auto e=entire(edges(graph)); is_split && !e.at_end(); ++e)
               if ((a*vert.row(e.from_node()))*(a*vert.row(e.to_node()))<0) is_split=false;

            if (is_split) {
               //normalizes the split, i.e. divides by the first non-zero entry
               Scalar fac;
               for (Int k = 0; is_zero(fac = a[k]); ++k);
               a /= fac;
               splits /= a;
            }
         }
      }
   }

   return splits;
}

UserFunctionTemplate4perl("# @category Triangulations, subdivisions and volume"
                          "# Computes the [[Polytope::SPLITS|SPLITS]] of a polytope."
                          "# The splits are normalized by dividing by the first non-zero entry."
                          "# If the polytope is not fulldimensional the first entries are set to zero unless //coords//"
                          "# are specified."
                          "# @param Matrix V vertices of the polytope"
                          "# @param Graph G graph of the polytope"
                          "# @param Matrix F facets of the polytope"
                          "# @param Int dimension of the polytope"
                          "# @option Set<Int> coords entries that should be set to zero"
                          "# @return Matrix",
                          "splits<Scalar>(Matrix<type_upgrade<Scalar>> $ Matrix<type_upgrade<Scalar>> $;{ coords => undef })");
} }

// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
