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/* 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_POLYTOPE_TO_INTERFACE_IMPL_H
#define POLYMAKE_POLYTOPE_TO_INTERFACE_IMPL_H
#include "polymake/polytope/to_interface.h"
#if POLYMAKE_DEBUG
# include "polymake/client.h"
# include "polymake/vector"
#endif
#define TO_WITHOUT_DOUBLE
#define TO_DISABLE_OUTPUT
#include "TOSimplex/TOSimplex.h"
namespace polymake {
namespace {
template <typename Coord>
void to_dual_fill_data(const Matrix<Coord>& A1, const Matrix<Coord>& A2, const std::vector<Coord>& MinObjective,
std::vector<Coord>& to_coefficients, std::vector<int>& to_colinds, std::vector<int>& to_rowbegininds,
std::vector<TOSimplex::TORationalInf<Coord> >& to_rowlowerbounds, std::vector<TOSimplex::TORationalInf<Coord> >& to_rowupperbounds,
std::vector<TOSimplex::TORationalInf<Coord> >& to_varlowerbounds, std::vector<TOSimplex::TORationalInf<Coord> >& to_varupperbounds,
std::vector<Coord>& to_objective) {
unsigned int nnz = 0;
for (int i=0; i<A1.rows(); ++i) {
for (int j=1; j<A1.cols(); ++j) {
if (!is_zero(A1(i,j))){
++nnz;
}
}
}
for (int i=0; i<A2.rows(); ++i) {
for (int j=1; j<A2.cols(); ++j) {
if (!is_zero(A2(i,j))){
++nnz;
}
}
}
to_coefficients.reserve(nnz);
to_colinds.reserve(nnz);
/*
note: polymake input with rows [c_i, a_i] and [c_j, a_j] with a_i=-a_j
could be reduced to one column with 'to_rowupperbounds' and 'to_rowlowerbounds'.
*/
const unsigned int m = A1.cols() - 1;
const unsigned int n1 = A1.rows();
const unsigned int n2 = A2.rows();
const unsigned int n = n1 + n2;
assert( (A2.cols() == 0) || (m == (unsigned int)( A2.cols() - 1 )) );
to_rowbegininds.reserve(m+1);
for (unsigned int i=1; i<=m; ++i){
to_rowbegininds.push_back(to_coefficients.size());
for (unsigned int j=0; j<n1; ++j){
if (!is_zero(A1(j,i))){
to_coefficients.push_back(A1(j,i));
to_colinds.push_back(j);
}
}
for (unsigned int j=0; j<n2; ++j){
if (!is_zero(A2(j,i))){
to_coefficients.push_back(A2(j,i));
to_colinds.push_back(n1+j);
}
}
}
to_rowbegininds.push_back(to_coefficients.size());
to_rowupperbounds.reserve(m);
for (unsigned int i=0; i<m; ++i){
to_rowupperbounds.push_back(MinObjective[i]); // A'u + E'v =< c
}
to_rowlowerbounds = to_rowupperbounds; // A'u + E'v >= c
to_objective.reserve(n);
to_varlowerbounds.reserve(n);
to_varupperbounds.reserve(n);
for (unsigned int i=0; i<n1; ++i){
to_objective.push_back(A1(i,0)); // = b_i
to_varlowerbounds.push_back(Coord(0)); // u_i >= 0
to_varupperbounds.push_back(true); // true = no restriction
}
for (unsigned int i=0; i<n2; ++i){
to_objective.push_back(A2(i,0)); // = d_i
to_varlowerbounds.push_back(true);
to_varupperbounds.push_back(true);
}
}
} // end anonymous namespace
namespace polytope { namespace to_interface {
template <typename Coord>
solver<Coord>::solver()
{
#if POLYMAKE_DEBUG
debug_print = perl::get_debug_level() > 1;
#endif
}
/* This method uses the TOSimplex-LP-solver to solve the LP.
* TOSimplex is a dual LP solver, so it cannot decide whether a given LP is infeasible or unbounded.
* To avoid this problem, the LP is implicitly dualized:
*
* min c'x - min -b'u -d'v
* s.t. Ax >= b <==> s.t. A'u + E'v = c
* Ex == d u >= 0
*
* After solving, the dual variables are obtained, if the problem is feasible.
* note: restrictions on variables (in this case u >= 0) are handeld
* via 'to_varupperbounds' and 'to_varlowerbounds'.
*/
template <typename Coord>
typename solver<Coord>::lp_solution
solver<Coord>::solve_lp(const Matrix<Coord>& Inequalities, const Matrix<Coord>& Equations,
const Vector<Coord>& Objective, bool maximize)
{
typedef TOSimplex::TOSolver<Coord> to_solver;
const int n(Inequalities.cols()-1); // beware of leading constant term
#if POLYMAKE_DEBUG
if (debug_print) {
const int m(Inequalities.rows()+Equations.rows());
cout << "to_solve_lp(m=" << m << " n=" << n << ")" << endl;
}
#endif
// translate inequality constraints into sparse description
std::vector<Coord> to_coefficients;
std::vector<int> to_colinds, to_rowbegininds;
std::vector<TOSimplex::TORationalInf<Coord> > to_rowlowerbounds, to_rowupperbounds, to_varlowerbounds, to_varupperbounds;
std::vector<Coord> to_objective;
// translate objective function into dense description, take direction into account
std::vector<Coord> to_obj(n);
if (maximize) {
for (int j=1; j<=n; ++j) to_obj[j-1]=-Objective[j];
} else {
for (int j=1; j<=n; ++j) to_obj[j-1]=Objective[j];
}
// Fill the vectors with the dual problem
to_dual_fill_data(Inequalities, Equations, to_obj, to_coefficients, to_colinds, to_rowbegininds, to_rowlowerbounds, to_rowupperbounds, to_varlowerbounds, to_varupperbounds, to_objective );
#if POLYMAKE_DEBUG
if (debug_print)
cout << "to_coefficients:" << to_coefficients <<"\n"
"to_colinds:" << to_colinds << "\n"
"to_rowbegininds:" << to_rowbegininds << "\n"
"to_obj:" << to_obj << "\n"
"to_objective:" << to_objective << endl;
#endif
to_solver solver( to_coefficients, to_colinds, to_rowbegininds, to_objective, to_rowlowerbounds, to_rowupperbounds, to_varlowerbounds, to_varupperbounds );
//add start basis:
if(!initial_basis.empty()){
int m(Inequalities.rows()+Equations.rows());
std::vector<int> b1(m);
std::vector<int> b2(n); //slack variables
/*
interpretation of the entries
0 : the value is between the bounds (non strict)
1 : the lower bound is attained
2 : the upper bound is attained
*/
int count=0;
for(Entire< Set<int> >::const_iterator it=entire(initial_basis); !it.at_end(); ++it){
b1[*it]=1;
if( ++count >= Inequalities.cols()-1 ) break;
}
solver.setBase(b1,b2);
}
const int result (solver.opt());
if (result==0) { // solved to optimality
Coord val(solver.getObj());
if (!maximize) val=-val;
const std::vector<Coord>& tox(solver.getY());
Vector<Coord> x(1+n);
x[0]=Coord(1); for (int j=1; j<=n; ++j) x[j]=-tox[j-1]; // It seems that the duals have an unexpected sign, so let's negate them
return lp_solution(val,x);
} else if (result==1) {
throw unbounded();
} else {
throw infeasible();
}
}
template <typename Coord>
void solver<Coord>::set_basis(const Set<int>& basis){
initial_basis=basis;
}
} } }
#endif // POLYMAKE_POLYTOPE_TO_INTERFACE_IMPL_H
// Local Variables:
// mode:C++
// c-basic-offset:3
// indent-tabs-mode:nil
// End:
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