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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/tropical/arithmetic.h"
#include "polymake/linalg.h"
#include "polymake/IncidenceMatrix.h"
namespace polymake { namespace tropical {
struct CovectorDecoration : public GenericStruct<CovectorDecoration> {
DeclSTRUCT( DeclFIELD(face, Set<Int>)
DeclFIELD(rank, Int)
DeclFIELD(covector,IncidenceMatrix<>) );
CovectorDecoration() {}
CovectorDecoration(const Set<Int>& f, Int r, const IncidenceMatrix<>& cv)
: face(f)
, rank(r)
, covector(cv) {}
};
/*
* @brief compute the covector of a single point in tropical projective space wrt a matrix of generators
*
*/
template <typename Addition, typename Scalar, typename Vector1, typename Vector2>
Set<Int> single_covector(const GenericVector<Vector1, TropicalNumber<Addition, Scalar>>& point,
const GenericVector<Vector2, TropicalNumber<Addition,Scalar>>& apex)
{
typedef TropicalNumber<Addition, Scalar> TNumber;
Set<Int> pt_covector = sequence(0, point.dim()) - support(point);
Vector<TNumber> tdiff = rel_coord(apex, point);
TNumber extremum = accumulate(tdiff, operations::add());
Int td_index = 0;
// determine the extremal entries
for (auto td : tdiff) {
if (td == extremum)
pt_covector += td_index;
++td_index;
}
return pt_covector;
}
/*
* @brief compute the covector of a single point in tropical projective space wrt a matrix of generators
*/
template <typename Addition, typename Scalar, typename VectorTop, typename MatrixTop>
IncidenceMatrix<> single_covector(const GenericVector<VectorTop, TropicalNumber<Addition,Scalar>>& point,
const GenericMatrix<MatrixTop, TropicalNumber<Addition, Scalar>>& generators)
{
typedef TropicalNumber<Addition, Scalar> TNumber;
const Int dimension = generators.cols();
Set<Int> non_support = sequence(0, point.dim()) - support(point);
Array<Set<Int>> pt_covector(dimension);
Int gn_index = 0;
for (auto gn : rows(generators)) {
Vector<TNumber> tdiff = rel_coord(gn, point);
TNumber extremum = accumulate(tdiff, operations::add());
Set<Int> extremal_entries = non_support;
Int td_index = 0;
// determine the extremal entries
for (auto td : tdiff) {
if (td == extremum)
extremal_entries += td_index;
++td_index;
}
// add the containing sectors to the covector of pt
for (auto ext_it : extremal_entries) {
pt_covector[ext_it] += gn_index;
}
++gn_index;
}
return IncidenceMatrix<>(pt_covector);
}
/*
* @brief determine the covector of a 0-1-ray wrt a matrix of generators
* for this only the index set of the 1 entries and the supports of the generators are taken into account
*/
template <typename Addition, typename Scalar>
IncidenceMatrix<> artificial_ray_covector(const Set<Int>& one_entries,
const Matrix<TropicalNumber<Addition, Scalar>>& generators)
{
const Int dimension = generators.cols();
RestrictedIncidenceMatrix<> pt_covector(dimension);
Int gn_index = 0;
for (auto gn = entire(rows(generators)); !gn.at_end(); ++gn, ++gn_index) {
if (incl(one_entries, sequence(0, dimension) - support(*gn)) <= 0) {
for (Int r = 0; r < dimension; ++r)
pt_covector(r, gn_index)=true;
} else {
for (Int covector_index : one_entries) {
pt_covector(covector_index, gn_index) = true;
}
}
}
return IncidenceMatrix<>(std::move(pt_covector));
}
// Documentation see perl wrapper
template <typename Addition, typename Scalar, typename Matrix1, typename Matrix2>
Array<IncidenceMatrix<>> covectors(const GenericMatrix<Matrix1, TropicalNumber<Addition, Scalar>>& points,
const GenericMatrix<Matrix2, TropicalNumber<Addition, Scalar>>& generators)
{
const Int n = points.rows();
Array<IncidenceMatrix<>> result(n);
Int pt_index = 0;
for (auto pt : rows(points)) {
// call the computation of the covector for every single point
result[pt_index] = single_covector(pt, generators);
++pt_index;
}//END iterate points
return result;
}
// Versions for scalar matrices.
template <typename Addition, typename Scalar>
Array<IncidenceMatrix<>> covectors_of_scalar_vertices(const Matrix<Scalar>& points,
const Matrix<TropicalNumber<Addition, Scalar>>& generators)
{
const Int dimension = generators.cols();
Array<IncidenceMatrix<>> result(points.rows());
Int pt_index = 0;
for (auto pt = entire(rows(points)); !pt.at_end(); ++pt, ++pt_index) {
if ((*pt)[0] == 1) {
result[pt_index] = single_covector(Vector<TropicalNumber<Addition, Scalar>>(pt->slice(range_from(1))), generators);
} else {
Set<Int> one_entries = support(pt->slice(range_from(1))); //the indices of the 1-entries of the 0/1-ray
if ((*pt)[one_entries.front()+1] * Addition::orientation() < 0)
one_entries = sequence(0, dimension) - one_entries;
result[pt_index] = artificial_ray_covector (one_entries, generators);
}
}
return result;
}
/*
* @brief compute the generalized covector of a single point w.r.t. apices defining inequalities
*
*/
template <typename Addition, typename Scalar, typename VectorTop, typename MatrixTop>
IncidenceMatrix<> generalized_apex_covector(const GenericVector<VectorTop, TropicalNumber<Addition, Scalar>>& point,
const GenericMatrix<MatrixTop, TropicalNumber<Addition, Scalar>>& apices)
{
typedef TropicalNumber<Addition, Scalar> TNumber;
IncidenceMatrix<> pt_covector(apices.rows(),apices.cols());
for (auto apex = entire<indexed>(rows(apices)); !apex.at_end(); ++apex) {
TNumber extremum = *apex*point;
if (!is_zero(extremum)) {
Vector<TNumber> hadaprod(attach_operation(*apex, point.top(), operations::mul()));
Set<Int> extremal_entries = indices(attach_selector(hadaprod, operations::fix2<TNumber,operations::eq>(extremum)));
// add the containing sectors to the covector of pt
pt_covector[apex.index()] = extremal_entries;
}
}
return pt_covector;
}
} }
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
// vim: shiftwidth=3:softtabstop=3:
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