/usr/include/polymake/totally_unimodular.h is in libpolymake-dev-common 3.2r2-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | /* Copyright (c) 1997-2018
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.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_TOTALLY_UNIMODULAR_H
#define POLYMAKE_TOTALLY_UNIMODULAR_H
#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 (Entire< Subsets_of_k<const sequence &> >::const_iterator ri = entire(all_subsets_of_k(sequence(0,m),k)); !ri.at_end(); ++ri)
for (Entire< Subsets_of_k<const sequence &> >::const_iterator 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
#endif // POLYMAKE_TOTALLY_UNIMODULAR_H
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