/* 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/Set.h"
#include "polymake/Graph.h"
#include "polymake/Array.h"
#include "polymake/Matrix.h"
#include "polymake/linalg.h"
#include "polymake/TropicalNumber.h"
#include "polymake/tropical/covectors.h"

namespace polymake { namespace tropical {

Matrix<Int> coarse_covector_from_fine(const Array<IncidenceMatrix<>>& cov)
{
   if (cov.empty()) return Matrix<Int>();
   Matrix<Int> result(cov.size(), cov[0].rows());
   Int c_index = 0;
   for (auto c = entire(cov); !c.at_end(); ++c) {
      for (auto row_it = entire(rows(*c)); !row_it.at_end(); ++row_it) {
         result(c_index, row_it.index()) = row_it->size();
      }
      ++c_index;
   }
   return result;
}

template <typename Addition, typename Scalar>
Matrix<Int> coarse_covectors(const Matrix<TropicalNumber<Addition, Scalar>>& points,
                             const Matrix<TropicalNumber<Addition, Scalar>>& generators)
{
   return coarse_covector_from_fine(covectors(points, generators));
}

template <typename Addition, typename Scalar>
Matrix<Int> coarse_covectors_of_scalar_vertices(const Matrix<Scalar>& points,
                                                const Matrix<TropicalNumber<Addition,Scalar>>& generators)
{
   return coarse_covector_from_fine(covectors_of_scalar_vertices(points, generators));
}

UserFunctionTemplate4perl("# @category Tropical covector decomposition"
                          "# This computes the (fine) covector of a list of points relative to a list of"
                          "# generators."
                          "# @param Matrix<TropicalNumber<Addition,Scalar>> points"
                          "# @param Matrix<TropicalNumber<Addition,Scalar>> generators"
                          "# @return Array<IncidenceMatrix>. Each IncidenceMatrix corresponds to a point."
                          "# Rows of a matrix correspond to coordinates and columns to generators."
                          "# Each row indicates which generators contain the point in the"
                          "# sector corresponding to the coordinate."
                          "# @example"
                          "# > $generators = new Matrix<TropicalNumber<Max>>([[0,1,0],[0,0,1],[0,\"-inf\",2]]);"
                          "# > $points = new Matrix<TropicalNumber<Max>>([[0,1,1]]);"
                          "# > print covectors($points, $generators);"
                          "# | <{0 1}"
                          "# | {0}"
                          "# | {1 2}"
                          "# | >",
                          "covectors<Addition,Scalar>(Matrix<TropicalNumber<Addition,Scalar> >, Matrix<TropicalNumber<Addition,Scalar> >)");

UserFunctionTemplate4perl("# @category Tropical covector decomposition"
                          "# This computes the (fine) covector of a list of points relative to a list of"
                          "# generators."
                          "# The points are scalar points and they are supposed to be normalized in the following sense:"
                          "# - All bounded vertices have a leading 1"
                          "# - All unbounded vertices have a leading 0 and all nonzero entries are either +1 or -1."
                          "# (but not both)"
                          "# Furthermore, the points make up a polyhedral complex - in particular, every maximal cell "
                          "# has a bounded vertex."
                          "# For the bounded vertices, covectors are computed as usual. For unbounded vertices, the"
                          "# nonzero entries are replaced by tropical zero, the complementary entries"
                          "# are copied from a bounded vertex sharing a cell and then the covector is computed."
                          "# @param Matrix<Scalar> points"
                          "# @param Matrix<TropicalNumber<Addition,Scalar>> generators"
                          "# @return Array<IncidenceMatrix>. Each IncidenceMatrix corresponds to a point."
                          "# Rows of a matrix correspond to coordinates and columns to generators."
                          "# Each row indicates which generators contain the point in the"
                          "# sector corresponding to the coordinate."
                          "# @example"
                          "# > $generators = new Matrix<TropicalNumber<Max>>([[0,1,0],[0,0,1],[0,\"-inf\",2]]);"
                          "# > $points = new Matrix([[1,0,1,1]]);"
                          "# > print covectors_of_scalar_vertices($points, $generators);"
                          "# | <{0 1}"
                          "# | {0}"
                          "# | {1 2}"
                          "# | >",
                          "covectors_of_scalar_vertices<Addition,Scalar>(Matrix<Scalar>,Matrix<TropicalNumber<Addition,Scalar> >)");

UserFunctionTemplate4perl("# @category Tropical covector decomposition"
                          "# This computes the coarse covector of a list of points relative to a list of"
                          "# generators."
                          "# @param Matrix<TropicalNumber<Addition,Scalar>> points"
                          "# @param Matrix<TropicalNumber<Addition,Scalar>> generators"
                          "# @return Matrix<Int>. Rows correspond to points, columns to coordinates. Each entry "
                          "# encodes, how many generators contain a given point in a certain coordinate."
                          "# @example"
                          "# > $generators = new Matrix<TropicalNumber<Max>>([[0,1,0],[0,0,1],[0,\"-inf\",2]]);"
                          "# > $points = new Matrix<TropicalNumber<Max>>([[0,1,1]]);"
                          "# > print coarse_covectors($points, $generators);"
                          "# | 2 1 2",
                          "coarse_covectors<Addition,Scalar>(Matrix<TropicalNumber<Addition,Scalar> >, Matrix<TropicalNumber<Addition,Scalar> >)");

UserFunctionTemplate4perl("# @category Tropical covector decomposition"
                          "# Computes the coarse covectors of a list of scalar points, as described in "
                          "# [[covectors_of_scalar_vertices]]"
                          "# @param Matrix<Scalar> points"
                          "# @param Matrix<TropicalNumber<Addition,Scalar> > generators"
                          "# @return Matrix<Int>. Rows correspond to points, columns to coordinates. Each entry "
                          "# encodes, how many generators contain a given point in a certain coordinate."
                          "# @example"
                          "# > $generators = new Matrix<TropicalNumber<Max>>([[0,1,0],[0,0,1],[0,\"-inf\",2]]);"
                          "# > $points = new Matrix([[1,0,1,1]]);"
                          "# > print coarse_covectors_of_scalar_vertices($points, $generators);"
                          "# | 2 1 2",
                          "coarse_covectors_of_scalar_vertices<Addition,Scalar>(Matrix<Scalar>,Matrix<TropicalNumber<Addition,Scalar> >)");


FunctionTemplate4perl("artificial_ray_covector<Addition,Scalar>(Set<Int>, Matrix<TropicalNumber<Addition, Scalar> >)");

FunctionTemplate4perl("generalized_apex_covector<Addition, Scalar>(Vector<TropicalNumber<Addition,Scalar> >,Matrix<TropicalNumber<Addition,Scalar> >)");

FunctionTemplate4perl("single_covector(Vector, Vector)");
FunctionTemplate4perl("single_covector(Vector, Matrix)");

} }

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