/* Copyright (c) 1997-2024
   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/Integer.h"
#include "polymake/Rational.h"
#include "polymake/QuadraticExtension.h"
#include "polymake/Matrix.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Vector.h"
#include "polymake/Array.h"
#include "polymake/Set.h"
#include "polymake/vector"
#include "polymake/PowerSet.h"
#include "polymake/common/lattice_tools.h"
#include "polymake/polytope/canonicalize.h"

namespace polymake { namespace polytope {
namespace {

template <typename Scalar>
class Face {
public:
   Vector<Scalar> projFace;
   Set<Int> vertices;

   Face(Int coord, const Set<Int>& vert, const Face<Scalar>& lower, const Face<Scalar>& upper)
   {
      vertices = vert;
      projFace = lower.projFace;
      if (projFace[coord] != 0)
         projFace -= (projFace[coord]/upper.projFace[coord]) * (upper.projFace);
      canonicalize_oriented(find_in_range_if(entire(projFace), operations::non_zero()));
   }

   Face(Set<Int>& vert, Vector<Scalar>& proj)
   {
      vertices = vert;
      projFace = proj;
   }
};

template <typename Scalar>
void updateListOfChildren(std::vector<Face<Scalar>>& childList, const Face<Scalar>& childFace, const Set<Int>& child) {
   bool add = true;
   for (typename std::vector<Face<Scalar>>::iterator childIt = childList.begin(); childIt != childList.end(); ++childIt) {
      if (childFace.projFace == childIt->projFace) {
         childIt->vertices += child;
            add = false;
            break;
         }
      }
      if (add)
         childList.push_back(childFace);
}

template <typename Scalar>
void createChildren(const Matrix<Scalar>& vertices, std::vector<Face<Scalar>>& lowerFaces, 
                    std::vector<Face<Scalar>>& upperFaces, Int faceDim, Int coord,
                    std::vector<Face<Scalar>>& lowerChildren, std::vector<Face<Scalar>>& upperChildren, Int verbose)
{
   if (verbose)
      cout << "creating faces of dim " << faceDim << " from " << lowerFaces.size()<<"+"
           <<upperFaces.size() << " faces of dim " << faceDim+1 << " using coord " << coord << " ... ";
   if (lowerFaces.size() < 1 || upperFaces.size() < 1)
      throw std::runtime_error("lattice_points_via_projection: too few faces!");

   // search through all pairs of faces of lower and upper hull to find pairs
   // which intersect in a lower dimensional face
   for (typename std::vector<Face<Scalar>>::iterator lowerFaceIt=lowerFaces.begin();
        lowerFaceIt!=lowerFaces.end(); ++lowerFaceIt) {
      for (typename std::vector<Face<Scalar>>::iterator upperFaceIt=upperFaces.begin();
           upperFaceIt!=upperFaces.end(); ++upperFaceIt) {
         Set<Int> child = (lowerFaceIt->vertices)*(upperFaceIt->vertices);
         if (child.size() >= faceDim+1 && pm::rank(vertices.minor(child,range(0,coord-1))) >= faceDim+1) {
            Face<Scalar> childFace(coord, child, *lowerFaceIt, *upperFaceIt);

            // we want to have each face only once
            // if we have this vector (projFace) already, add the vertices defining this face to the existing one
            (childFace.projFace[coord-1] < 0) ? updateListOfChildren(upperChildren, childFace, child) : updateListOfChildren(lowerChildren, childFace, child);
         }
      }
   }
   if (verbose)
      cout << "done creating " << lowerChildren.size() <<"+" << upperChildren.size() << " new faces."<< endl;
}

// try to find a row R in affine hull that has a nonzero value at the current coordinate
// if found reduce all other rows at this coordinate using R and return R
template <typename Scalar>
bool tryAffineHull(Matrix<Scalar>& affineHull, Vector<Scalar>& affineHullRow, Int coord, Int verbose)
{
   if (verbose)
      cout << "trying to find affine hull row for coord "<< coord << " ... ";
   for (Int row = 0; row < affineHull.rows(); ++row) {
      if (((affineHull.row(row))[coord]) != 0) {
         affineHullRow = affineHull.row(row);
         affineHull = affineHull.minor(~scalar2set(row),All);
         for (auto r = entire(rows(affineHull)); !r.at_end(); ++r) {
            if (!is_zero((*r)[coord])) {
               (*r) -= ((*r)[coord] / affineHullRow[coord]) * affineHullRow;
            }
         }
         if (verbose)
            cout << "using row " << row << ", done updating matrix." << endl;
         return true;
      }
   }
   if (verbose)
      cout << "none found" << endl;
   return false;
}

// reduce all faces using the affine hull row and resort them according to the next coordinate
template <typename Scalar>
void affineProjection(const std::vector<Face<Scalar>>& Faces, Vector<Scalar>& affineHullRow, Int coord,
                      std::vector<Face<Scalar>>& lowerChildren, std::vector<Face<Scalar>>& upperChildren, Int verbose)
{
   for (Face<Scalar> f : Faces) {
      if (f.projFace[coord] != 0) {
         f.projFace -= (f.projFace[coord] / affineHullRow[coord] ) * affineHullRow;
      }
      if (f.projFace[coord-1] >= 0) 
         lowerChildren.push_back(f);
      else
         upperChildren.push_back(f);
   }
}

// find upper and lower bound in the next coordinate for all projected points
// then create matrix of all lifted points
template <typename Scalar>
Matrix<Integer> liftPoints(const Matrix<Integer>& projPoints, 
                           std::vector<Face<Scalar>>& lowerFaces, std::vector<Face<Scalar>>& upperFaces, 
                           Int coord, Int verbose)
{
   Int npoints = projPoints.rows();
   if (verbose)
      cout << "lifting " << npoints << " points using coord " << coord << " ... ";
    
   // first compute where all faces intersect the lines above all projected lattice points
   Matrix<Scalar> lowerBoundMatrix(lowerFaces.size(),npoints);
   Matrix<Scalar> upperBoundMatrix(upperFaces.size(),npoints);
    
   Int nlower = 0;
   for (const auto& lowerF : lowerFaces) {
      if (lowerF.projFace[coord] > 0) {
         lowerBoundMatrix[nlower] = -projPoints*lowerF.projFace / lowerF.projFace[coord];
         ++nlower;
      }
   }
   lowerBoundMatrix = lowerBoundMatrix.minor(sequence(0,nlower),All);
   Int nupper = 0;
   for (const auto& upperF : upperFaces) {
      upperBoundMatrix[nupper] = -projPoints*upperF.projFace / upperF.projFace[coord];
      ++nupper;
   }
    
   if (verbose >= 2)
      cout << "[nlower=" << nlower << ",nupper=" << nupper << "] ";
   // find the bounds for each lattice point
   Vector<Integer> lowerBounds(lowerBoundMatrix.cols(), std::numeric_limits<Integer>::min());
   Vector<Integer>::iterator lowerBound = lowerBounds.begin();

   for (auto LBcol = entire(cols(lowerBoundMatrix)); !LBcol.at_end(); ++LBcol, ++lowerBound) {
      for (auto LBcolentry = entire(*LBcol); !LBcolentry.at_end(); ++LBcolentry) {
         if (*lowerBound < *LBcolentry)
            *lowerBound = ceil(*LBcolentry);
      }
   }
    
   if (verbose >= 2)
      cout << "[apply] ";
   Vector<Integer> upperBounds(upperBoundMatrix.cols(), std::numeric_limits<Integer>::max());
   Vector<Integer>::iterator upperBound = upperBounds.begin();

   for (auto UBcol=entire(cols(upperBoundMatrix)); !UBcol.at_end(); ++UBcol, ++upperBound) {
      for (auto UBcolentry = entire(*UBcol); !UBcolentry.at_end(); ++UBcolentry) {
         if (*upperBound > *UBcolentry)
            *upperBound = floor(*UBcolentry);
      }
   }
    
   if (verbose >= 2)
      cout << "[matrix] ";
   // generate matrix containing all lifted lattice points, using the projected lattice point with all valid values in the (coord) coordinate
   const Int count = Int(accumulate(upperBounds - lowerBounds, operations::add())) + npoints;
   Matrix<Integer> points(count, projPoints.cols());
   auto point = rows(points).begin();
   for (Int i = 0; i < npoints; ++i) {
      for (Integer j = lowerBounds[i]; j <= upperBounds[i]; ++j, ++point) {
         *point = projPoints.row(i);
         (*point)[coord] = j;
      }
   }
   if (verbose)
      cout << "created " << points.rows() << " points." << endl;
   return points;
}

// calculate the next coordinate using an affine hull row
template <typename Scalar>
Matrix<Integer> liftPointsAffine(Matrix<Integer>& projPoints, Vector<Scalar>& affineHullRow, Int coord, Int verbose)
{
   if (verbose)
      cout << "calculating coord "<< coord << " for "<< projPoints.rows() <<" points using affine hull row ... " ;
   Set<Int> noninteger;
   for (Int i = 0; i < projPoints.rows(); ++i) {
      Scalar entry = projPoints[i] * affineHullRow / affineHullRow[coord];
      if (entry != 0) {
         if (entry.is_integral())
            projPoints[i][coord] = -numerator(static_cast<Rational>(entry));
         else 
            noninteger += i;
      }
   }
   if (noninteger.size() > 0) {
      if (verbose)
         cout << "done, removed " << noninteger.size() << " non-integer points." << endl;
      return projPoints.minor(~noninteger,All);
   } else {
      if (verbose)
         cout << "done." << endl;
      return projPoints;
   }
}

// main recursion calling the projection and lifting functions
template <typename Scalar>
Matrix<Integer> points(const Matrix<Scalar>& vertices, 
                        std::vector<Face<Scalar>>& lowerFaces, std::vector<Face<Scalar>>& upperFaces, 
                        Matrix<Scalar>& affineHull, Int faceDim, Int coord, Int totalDim, Int verbose) 
{
   Matrix<Integer> projPoints;
   Vector<Scalar> affineHullRow;
   bool doAffineHullProjection = false;
   if (coord > 1) {
      // create lists of upper and lower hull in one dimension lower
      std::vector<Face<Scalar>> lowerChildren;
      std::vector<Face<Scalar>> upperChildren;
      
      doAffineHullProjection = tryAffineHull(affineHull,affineHullRow,coord,verbose);
      if (doAffineHullProjection) {
         if(verbose)
            cout << "reducing coord "<< coord << " using affine hull ... ";
         affineProjection(lowerFaces,affineHullRow,coord,lowerChildren,upperChildren,verbose);
         affineProjection(upperFaces,affineHullRow,coord,lowerChildren,upperChildren,verbose);
         if(verbose)
            cout << "done." << endl;
      } else {
         faceDim--;
         createChildren(vertices,lowerFaces,upperFaces,faceDim,coord,lowerChildren,upperChildren, verbose);
      }
      
      // main recursion
      projPoints = points(vertices,lowerChildren,upperChildren,affineHull,faceDim,coord-1,totalDim,verbose);
   } else {
      if (verbose) 
         cout << "*** projecting done ***" << endl << endl << "*** lifting points now ***" << endl;
      // create one lattice point for the zero dimensional projection
      projPoints.resize(1,totalDim+1);
      projPoints(0,0)=1;
      if (faceDim == -1) {
         doAffineHullProjection = true;
         affineHullRow = affineHull.row(0);
      }
   }
    
   // lift points up one dimension
   Matrix<Integer> liftedPoints;
   if (doAffineHullProjection) {
      liftedPoints = liftPointsAffine(projPoints,affineHullRow,coord,verbose);
   } else {
      liftedPoints = liftPoints(projPoints, lowerFaces, upperFaces, coord, verbose);
   }
    
   return liftedPoints;
}
  
} // end anonymous namespace

template<typename Scalar>
Matrix<Integer> integer_points_projection(BigObject p, Int verbose)
{
   const Int ambient = p.call_method("AMBIENT_DIM");
   const Int dim = p.call_method("DIM");

   if (dim == -1)
      return Matrix<Integer>();

   if (ambient == 0) {
      Matrix<Integer> LP = unit_matrix<Integer>(1);
      return LP;
   }

   const Matrix<Scalar> facets = p.give("FACETS");
   // global vertices
   Matrix<Scalar> vertices = p.give("VERTICES");
   Matrix<Scalar> affineHull = p.give("AFFINE_HULL");
   const IncidenceMatrix<> VIF = p.give("VERTICES_IN_FACETS");

   // create first faces = facets
   std::vector<Face<Scalar>> lowerFaces;
   std::vector<Face<Scalar>> upperFaces;
   for (Int i = 0; i < facets.rows(); ++i) {
      Vector<Scalar> facet(facets[i]);
      Set<Int> vif(VIF[i]);
      if(facet[ambient] >= 0)
         lowerFaces.push_back(Face<Scalar>(vif,facet));
      else
         upperFaces.push_back(Face<Scalar>(vif,facet));
   }

   if (verbose)
      cout << "*** projecting faces ***" << endl;
   // start recursion (repeated projection of the faces and lifting of the lattice points of the projected polytope)
   Matrix<Integer> latticePoints = points(vertices,lowerFaces,upperFaces,affineHull,dim-1,ambient,ambient,verbose);
   if (verbose)
      cout << "*** done lifting ***" << endl;

   return latticePoints;
}

FunctionTemplate4perl("integer_points_projection<Scalar>(Polytope<Scalar>; $=0)");

} }

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