/usr/include/polymake/tropical/misc_tools.h is in libpolymake-dev-common 3.2r2-3.
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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
of the License, or (at your option) any later version.
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.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.
---
Copyright (C) 2011 - 2015, Simon Hampe <simon.hampe@googlemail.com>
Contains some miscellaneous tools.
*/
#ifndef POLYMAKE_ATINT_MISC_TOOLS_H
#define POLYMAKE_ATINT_MISC_TOOLS_H
#include "polymake/Rational.h"
#include "polymake/Matrix.h"
#include "polymake/Set.h"
#include "polymake/IncidenceMatrix.h"
#include "polymake/Array.h"
#include "polymake/RandomGenerators.h"
#include "polymake/linalg.h"
#include "polymake/tropical/homogeneous_convex_hull.h"
namespace polymake { namespace tropical {
/**
@brief Takes a matrix and returns the row indices where the first coordinate is nonzero and where the first coordinate is zero in two different sets
@param Matrix<Rational> m The matrix whose rows we consider
@return std::pair<Set<int>, Set<int> > The first set contains the row indices of rows that start with a zero entry, the second set is the complement
*/
template <typename MType> inline
std::pair<Set<int>, Set<int> > far_and_nonfar_vertices(const GenericMatrix<MType> &m) {
const auto& first_col_supp = support(m.col(0));
return std::pair<Set<int>, Set<int> >( sequence(0, m.rows()) - first_col_supp, first_col_supp);
}
/*
* @brief Takes a polyhedral complex and returns [[CONES]] summarized into one single incidence matrix.
* @param PolyhedralComplex
* @return IncidenceMatrix<>
*/
IncidenceMatrix<> all_cones_as_incidence(perl::Object complex);
/*
* @brief Converts an incidence matrix to a Vector<Set<int> >
*/
template <typename MType> inline
Vector<Set<int> > incMatrixToVector(const GenericIncidenceMatrix<MType> &i) {
return Vector<Set<int> >(i.rows(), entire(rows(i)));
}
inline Array<Integer> randomInteger(const int& max_arg, const int &n) {
static UniformlyRandomRanged<Integer> rg(max_arg);
return Array<Integer>(n, rg.begin());
}
/**
@brief Computes all vectors of dimension n with entries +1 and -1.
They are sorted such that each vector v has the row index determined by the sum:
sum_{i: v_i = 1} 2^i (where i runs from 0 to n-1)
@param int n The column dimension of the matrix
@return Matrix<Rational> A 2^n by n matrix containing all +-1-vectors of dimension n
*/
Matrix<Rational> binaryMatrix(int n);
/**
@brief Assumes v is a vector with entries +1 and -1 only.
Returns sum_{i: v_i = 1} 2^i (where i runs from 0 to n-1
*/
template <typename VType> inline
int binaryIndex(const GenericVector<VType> &v) {
int result = 0;
for(const auto &i : indices(attach_selector( v.top(), operations::positive())))
result += pow(2,i);
return result;
}
/**
@brief Helper function for the refinement function.
Given a polyhedral cell in terms of rays and lineality space, it computes, whether a given ray
is contained in this cell (possibly modulo (1,..,1)).
@param Matrix<Rational> rays The rays of the cell
@param Matrix<Rational> lineality The lineality space of the cell
@param Vector<Rational> ray The ray to be tested
@param bool is_projective Whether coordinates are given as tropical projective coordinates.
(False means they're affine).
@param solver A convex hull solver
@returns true, if and only if ray lies in the cone
*/
template <typename ch_solver>
bool is_ray_in_cone(const Matrix<Rational> &rays, const Matrix<Rational> &lineality,
const Vector<Rational> &ray, bool is_projective, ch_solver& sv) {
std::pair<Matrix<Rational>, Matrix<Rational> > facets =
is_projective ? enumerate_homogeneous_facets(rays, lineality, sv) :
sv.enumerate_facets(rays,lineality, false,false);
//Check equations
for(auto l = entire(rows(facets.second)); !l.at_end(); ++l) {
if(*l * ray != 0) return false;
}
//Check facets
for(auto f = entire(rows(facets.first)); !f.at_end(); ++f) {
if(*f * ray < 0) return false;
}
return true;
}//END is_ray_in_cone
}}
#endif
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