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/* 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_POLYTOPE_SEPARATING_HYPERPLANE_H
#define POLYMAKE_POLYTOPE_SEPARATING_HYPERPLANE_H
#include "polymake/Vector.h"
#include "polymake/Matrix.h"
#include "polymake/linalg.h"
#include "polymake/polytope/solve_LP.h"
namespace polymake { namespace polytope {
template <typename Scalar, typename VectorType, typename MatrixType>
Vector<Scalar> separating_hyperplane(const GenericVector<VectorType, Scalar>& q,
const GenericMatrix<MatrixType, Scalar>& points)
{
/*
construction of LP according to cdd redundancy check for points, see
http://www.ifor.math.ethz.ch/~fukuda/polyfaq/node22.html#polytope:Vredundancy
*/
const Matrix<Scalar>
ineqs( (zero_vector<Scalar>() | (ones_vector<Scalar>() | -points.minor(All, range(1,points.cols()-1))))
// z^t p_i - z_0 <= 0; CAUTION: p_i is affine part of i-th point!
/ (ones_vector<Scalar>(2) | -q.slice(range_from(1))) ),
// z^t q - z_0 <= 1, prevents unboundedness
affine_hull(null_space(points/q)),
extension2(affine_hull.rows(), 2);
Matrix<Scalar>
affine_hull_minor(affine_hull.rows(), affine_hull.cols()-1);
if (affine_hull.cols() > 1) {
affine_hull_minor = affine_hull.minor(All, range(1, affine_hull.cols()-1));
}
const Matrix<Scalar> eqs(extension2 | -affine_hull_minor);
const Vector<Scalar> obj(zero_vector<Scalar>(1) | -ones_vector<Scalar>(1) | q.slice(range_from(1))); // z^t q - z_0
const auto S = solve_LP(ineqs, eqs, obj, true);
if (S.status != LP_status::valid || S.objective_value <= 0) //q non-red. <=> obj_val > 0
throw infeasible();
// H: z^t x = z_0, i.e., z_0 - z^t x = 0
return S.solution[1] | -S.solution.slice(range_from(2));
}
}}
#endif
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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