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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
#include "polymake/Matrix.h"
#include "polymake/PowerSet.h"
#include "polymake/linalg.h"
namespace pm {
// A matrix is totally unimodular if the determinant of each square submatrix equals 0, 1, or -1.
// This is the naive test (exponential in the size of the matrix).
// For polynomial time algorithms see
// Schrijver: Theory of Linear and Integer Programming, section 20.3.
template <typename Matrix, typename E>
bool totally_unimodular(const GenericMatrix<Matrix, E>& M)
{
const Int m = M.rows();
const Int n = M.cols();
const Int r = std::min(m, n);
for (Int k = 1; k <= r; ++k)
for (auto ri = entire(all_subsets_of_k(sequence(0,m),k)); !ri.at_end(); ++ri)
for (auto ci = entire(all_subsets_of_k(sequence(0,n),k)); !ci.at_end(); ++ci) {
const E d = det(M.minor(*ri, *ci));
if (!is_zero(d) && !abs_equal(d, one_value<E>())) return false;
}
return true;
}
} // end namespace pm
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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