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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/Vector.h"
#include "polymake/Matrix.h"
#include "polymake/linalg.h"
#include "polymake/TropicalNumber.h"
#include "polymake/polytope/canonicalize.h"
namespace polymake { namespace tropical {
// The following all canonicalize a matrix/vector of tropical numbers such that the first entry
// is zero.
template <typename TVector, typename Addition, typename Scalar>
void canonicalize_to_leading_zero(GenericVector<TVector, TropicalNumber<Addition, Scalar>>& V)
{
if (!is_leading_zero(V)) {
const auto first = *V.top().begin();
V /= first;
}
}
template <typename TVector, typename Addition, typename Scalar>
void canonicalize_to_leading_zero(GenericVector<TVector, TropicalNumber<Addition, Scalar>>&& V)
{
canonicalize_to_leading_zero(V);
}
template <typename TMatrix, typename Addition, typename Scalar>
void canonicalize_to_leading_zero(GenericMatrix<TMatrix, TropicalNumber<Addition,Scalar>>& M)
{
if (M.rows() == 0)
throw std::runtime_error("point matrix may not be empty");
for (auto r=entire(rows(M)); !r.at_end(); ++r)
canonicalize_to_leading_zero(*r);
}
template <typename TMatrix, typename Addition, typename Scalar>
void canonicalize_to_leading_zero(GenericMatrix<TMatrix, TropicalNumber<Addition,Scalar>>&& M)
{
canonicalize_to_leading_zero(M);
}
// Does the same as canonicalize_to_leading_zero, and checks and complains if there is a zero column
template <typename TMatrix, typename Addition, typename Scalar>
void canonicalize_to_leading_zero_and_check_columns(GenericMatrix<TMatrix, TropicalNumber<Addition, Scalar>>& M)
{
for (auto c = entire(rows(T(M))); !c.at_end(); ++c) {
if (support(*c).empty())
throw std::runtime_error("The points can't all lie in the same boundary stratum of projective space. Maybe use a projection?");
}
return canonicalize_to_leading_zero(M);
}
template <typename TMatrix, typename Addition, typename Scalar>
void canonicalize_to_leading_zero_and_check_columns(GenericMatrix<TMatrix, TropicalNumber<Addition, Scalar>>&& M)
{
canonicalize_to_leading_zero_and_check_columns(M);
}
// The following canonicalize matrices/vectors of scalars, but representing (finite)
// tropical homogeneous coordinates.
template <typename TVector, typename Scalar>
void canonicalize_scalar_to_leading_zero(GenericVector<TVector, Scalar>& V)
{
if (!is_leading_zero(V)) {
const auto first = *V.top().begin();
V -= same_element_vector(first, V.dim());
}
}
template <typename TVector, typename Scalar>
void canonicalize_scalar_to_leading_zero(GenericVector<TVector, Scalar>&& V)
{
canonicalize_scalar_to_leading_zero(V);
}
template <typename TMatrix, typename Scalar>
void canonicalize_scalar_to_leading_zero(GenericMatrix<TMatrix, Scalar>& M)
{
if (M.rows() == 0)
throw std::runtime_error("point matrix may not be empty");
for (auto r=entire(rows(M)); !r.at_end(); ++r)
canonicalize_scalar_to_leading_zero(*r);
}
template <typename TMatrix, typename Scalar>
void canonicalize_scalar_to_leading_zero(GenericMatrix<TMatrix, Scalar>&& M)
{
canonicalize_scalar_to_leading_zero(M);
}
// FIXME Should this be swapped for min/max, i.e. should there be a nonpositive - or rather,
// a templated version of this?
template <typename TVector, typename Scalar>
void canonicalize_scalar_to_nonnegative(GenericVector<TVector, Scalar>& V)
{
const auto x_min = accumulate(V.top(), operations::min());
if (pm::check_container_feature<TVector, pm::sparse>::value
? x_min<0 || V.top().size()==V.dim()
: !is_zero(x_min))
V -= same_element_vector(x_min, V.dim());
}
template <typename TVector, typename Scalar>
void canonicalize_scalar_to_nonnegative(GenericVector<TVector, Scalar>&& V)
{
canonicalize_scalar_to_nonnegative(V);
}
template <typename TMatrix, typename Scalar>
void canonicalize_scalar_to_nonnegative(GenericMatrix<TMatrix, Scalar>& M)
{
if (M.rows() == 0)
throw std::runtime_error("point matrix may not be empty");
for (auto r=entire(rows(M)); !r.at_end(); ++r)
canonicalize_scalar_to_nonnegative(*r);
}
template <typename TMatrix, typename Scalar>
void canonicalize_scalar_to_nonnegative(GenericMatrix<TMatrix, Scalar>&& M)
{
canonicalize_scalar_to_nonnegative(M);
}
// Assumes as input a matrix of tropically homogeneous vectors with a leading 1/0 indicating
// vertex or far vertex. Will canonicalize M.minor(All,~[0]) to have first coordinate 0.
// Then will canonicalize the full matrix as a usual vertex matrix.
template <typename TMatrix, typename Scalar>
void canonicalize_vertices_to_leading_zero(GenericMatrix<TMatrix, Scalar>& M)
{
canonicalize_scalar_to_leading_zero(M.minor(All, range_from(1)));
for (auto r = entire(rows(M)); !r.at_end(); ++r) {
polytope::canonicalize_oriented( find_in_range_if(entire(*r), operations::non_zero()) );
}
}
template <typename TMatrix, typename Scalar>
void canonicalize_vertices_to_leading_zero(GenericMatrix<TMatrix, Scalar>&& M)
{
canonicalize_vertices_to_leading_zero(M);
}
template <typename TVector, typename Scalar>
void canonicalize_vertex_to_leading_zero(GenericVector<TVector,Scalar>& V)
{
canonicalize_scalar_to_leading_zero(V.slice(1));
polytope::canonicalize_oriented( find_in_range_if(entire(V.top()), operations::non_zero()) );
}
template <typename TVector, typename Scalar>
void canonicalize_vertex_to_leading_zero(GenericVector<TVector,Scalar>&& V)
{
canonicalize_vertex_to_leading_zero(V);
}
} }
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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