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/* 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.
--------------------------------------------------------------------------------
*/
#pragma once
namespace polymake { namespace polytope {
template <typename TMatrix, typename E>
Matrix<E> balance(const GenericMatrix<TMatrix, E>& G_arg)
{
// Given a matrix of vectors in R^d (actually, R^{n-d}), we want to
// scale d of them by positive coefficients so that the entire set
// of vectors has the origin as barycenter. To do this, we
// exhaustively check all d-tuples of vectors for feasibility.
Matrix<E> G (G_arg);
const Int n = G.rows(), d = G.cols();
Vector<E> coeffs;
bool success (false);
for (auto r = entire(all_subsets_of_k(sequence(0,n), d)); !r.at_end() && !success; ++r) {
Set<Int> comp (sequence(0,n)), rset(*r);
comp -= rset;
const Vector<E> mbarycenter = - ones_vector<E>(comp.size()) * G.minor(comp,All);
try {
coeffs = lin_solve(T(G.minor(rset,All)), mbarycenter);
} catch (const linalg_error& e) {
continue;
}
success = accumulate(coeffs, operations::min()) > 0;
if (success) {
auto vit = entire(coeffs);
for (auto sit = entire(rset); !sit.at_end() && !vit.at_end(); ++sit, ++vit)
G.row(*sit) *= *vit;
}
}
if (!success)
throw std::runtime_error("Could not balance the Gale diagram. This shouldn't have happened.");
return G;
}
} } // namespaces
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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