mirror of
https://github.com/Z3Prover/z3
synced 2025-04-15 05:18:44 +00:00
2282 lines
81 KiB
C++
2282 lines
81 KiB
C++
#include "util/lp/lar_solver.h"
|
|
/*
|
|
Copyright (c) 2017 Microsoft Corporation
|
|
Author: Nikolaj Bjorner, Lev Nachmanson
|
|
*/
|
|
|
|
namespace lp {
|
|
|
|
unsigned lar_solver::constraint_count() const {
|
|
return m_constraints.size();
|
|
}
|
|
const lar_base_constraint& lar_solver::get_constraint(unsigned ci) const {
|
|
return *(m_constraints[ci]);
|
|
}
|
|
|
|
////////////////// methods ////////////////////////////////
|
|
static_matrix<mpq, numeric_pair<mpq>> & lar_solver::A_r() { return m_mpq_lar_core_solver.m_r_A;}
|
|
static_matrix<mpq, numeric_pair<mpq>> const & lar_solver::A_r() const { return m_mpq_lar_core_solver.m_r_A;}
|
|
static_matrix<double, double> & lar_solver::A_d() { return m_mpq_lar_core_solver.m_d_A;}
|
|
static_matrix<double, double > const & lar_solver::A_d() const { return m_mpq_lar_core_solver.m_d_A;}
|
|
|
|
lp_settings & lar_solver::settings() { return m_settings;}
|
|
|
|
lp_settings const & lar_solver::settings() const { return m_settings;}
|
|
|
|
void clear() {lp_assert(false); // not implemented
|
|
}
|
|
|
|
|
|
lar_solver::lar_solver() : m_status(lp_status::OPTIMAL),
|
|
m_infeasible_column_index(-1),
|
|
m_terms_start_index(1000000),
|
|
m_mpq_lar_core_solver(m_settings, *this),
|
|
m_int_solver(nullptr)
|
|
{}
|
|
|
|
void lar_solver::set_track_pivoted_rows(bool v) {
|
|
m_mpq_lar_core_solver.m_r_solver.m_pivoted_rows = v? (& m_rows_with_changed_bounds) : nullptr;
|
|
}
|
|
|
|
bool lar_solver::get_track_pivoted_rows() const {
|
|
return m_mpq_lar_core_solver.m_r_solver.m_pivoted_rows != nullptr;
|
|
}
|
|
|
|
|
|
lar_solver::~lar_solver(){
|
|
for (auto c : m_constraints)
|
|
delete c;
|
|
for (auto t : m_terms)
|
|
delete t;
|
|
}
|
|
|
|
bool lar_solver::is_term(var_index j) const {
|
|
return j >= m_terms_start_index && j - m_terms_start_index < m_terms.size();
|
|
}
|
|
|
|
unsigned lar_solver::adjust_term_index(unsigned j) const {
|
|
lp_assert(is_term(j));
|
|
return j - m_terms_start_index;
|
|
}
|
|
|
|
|
|
bool lar_solver::use_lu() const { return m_settings.simplex_strategy() == simplex_strategy_enum::lu; }
|
|
|
|
bool lar_solver::sizes_are_correct() const {
|
|
lp_assert(strategy_is_undecided() || !m_mpq_lar_core_solver.need_to_presolve_with_double_solver() || A_r().column_count() == A_d().column_count());
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size());
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_x.size());
|
|
return true;
|
|
}
|
|
|
|
|
|
std::ostream& lar_solver::print_implied_bound(const implied_bound& be, std::ostream & out) const {
|
|
out << "implied bound\n";
|
|
unsigned v = be.m_j;
|
|
if (is_term(v)) {
|
|
out << "it is a term number " << be.m_j << std::endl;
|
|
print_term(*m_terms[be.m_j - m_terms_start_index], out);
|
|
}
|
|
else {
|
|
out << get_column_name(v);
|
|
}
|
|
out << " " << lconstraint_kind_string(be.kind()) << " " << be.m_bound << std::endl;
|
|
out << "end of implied bound" << std::endl;
|
|
return out;
|
|
}
|
|
|
|
bool lar_solver::implied_bound_is_correctly_explained(implied_bound const & be, const vector<std::pair<mpq, unsigned>> & explanation) const {
|
|
std::unordered_map<unsigned, mpq> coeff_map;
|
|
auto rs_of_evidence = zero_of_type<mpq>();
|
|
unsigned n_of_G = 0, n_of_L = 0;
|
|
bool strict = false;
|
|
for (auto & it : explanation) {
|
|
mpq coeff = it.first;
|
|
constraint_index con_ind = it.second;
|
|
const auto & constr = *m_constraints[con_ind];
|
|
lconstraint_kind kind = coeff.is_pos() ? constr.m_kind : flip_kind(constr.m_kind);
|
|
register_in_map(coeff_map, constr, coeff);
|
|
if (kind == GT || kind == LT)
|
|
strict = true;
|
|
if (kind == GE || kind == GT) n_of_G++;
|
|
else if (kind == LE || kind == LT) n_of_L++;
|
|
rs_of_evidence += coeff*constr.m_right_side;
|
|
}
|
|
lp_assert(n_of_G == 0 || n_of_L == 0);
|
|
lconstraint_kind kind = n_of_G ? GE : (n_of_L ? LE : EQ);
|
|
if (strict)
|
|
kind = static_cast<lconstraint_kind>((static_cast<int>(kind) / 2));
|
|
|
|
if (!is_term(be.m_j)) {
|
|
if (coeff_map.size() != 1)
|
|
return false;
|
|
auto it = coeff_map.find(be.m_j);
|
|
if (it == coeff_map.end()) return false;
|
|
mpq ratio = it->second;
|
|
if (ratio < zero_of_type<mpq>()) {
|
|
kind = static_cast<lconstraint_kind>(-kind);
|
|
}
|
|
rs_of_evidence /= ratio;
|
|
} else {
|
|
const lar_term * t = m_terms[adjust_term_index(be.m_j)];
|
|
const auto first_coeff = *t->m_coeffs.begin();
|
|
unsigned j = first_coeff.first;
|
|
auto it = coeff_map.find(j);
|
|
if (it == coeff_map.end())
|
|
return false;
|
|
mpq ratio = it->second / first_coeff.second;
|
|
for (auto & p : t->m_coeffs) {
|
|
it = coeff_map.find(p.first);
|
|
if (it == coeff_map.end())
|
|
return false;
|
|
if (p.second * ratio != it->second)
|
|
return false;
|
|
}
|
|
if (ratio < zero_of_type<mpq>()) {
|
|
kind = static_cast<lconstraint_kind>(-kind);
|
|
}
|
|
rs_of_evidence /= ratio;
|
|
rs_of_evidence += t->m_v * ratio;
|
|
}
|
|
|
|
return kind == be.kind() && rs_of_evidence == be.m_bound;
|
|
}
|
|
|
|
|
|
void lar_solver::analyze_new_bounds_on_row(
|
|
unsigned row_index,
|
|
bound_propagator & bp) {
|
|
lp_assert(!use_tableau());
|
|
unsigned j = m_mpq_lar_core_solver.m_r_basis[row_index]; // basis column for the row
|
|
bound_analyzer_on_row<indexed_vector<mpq>>
|
|
ra_pos(m_mpq_lar_core_solver.get_pivot_row(),
|
|
j,
|
|
zero_of_type<numeric_pair<mpq>>(),
|
|
row_index,
|
|
bp
|
|
);
|
|
ra_pos.analyze();
|
|
}
|
|
|
|
void lar_solver::analyze_new_bounds_on_row_tableau(
|
|
unsigned row_index,
|
|
bound_propagator & bp ) {
|
|
|
|
if (A_r().m_rows[row_index].size() > settings().max_row_length_for_bound_propagation)
|
|
return;
|
|
lp_assert(use_tableau());
|
|
bound_analyzer_on_row<row_strip<mpq>>::analyze_row(A_r().m_rows[row_index],
|
|
static_cast<unsigned>(-1),
|
|
zero_of_type<numeric_pair<mpq>>(),
|
|
row_index,
|
|
bp
|
|
);
|
|
}
|
|
|
|
|
|
void lar_solver::substitute_basis_var_in_terms_for_row(unsigned i) {
|
|
// todo : create a map from term basic vars to the rows where they are used
|
|
unsigned basis_j = m_mpq_lar_core_solver.m_r_solver.m_basis[i];
|
|
for (unsigned k = 0; k < m_terms.size(); k++) {
|
|
if (term_is_used_as_row(k))
|
|
continue;
|
|
if (!m_terms[k]->contains(basis_j))
|
|
continue;
|
|
m_terms[k]->subst(basis_j, m_mpq_lar_core_solver.m_r_solver.m_pivot_row);
|
|
}
|
|
}
|
|
|
|
void lar_solver::calculate_implied_bounds_for_row(unsigned i, bound_propagator & bp) {
|
|
if(use_tableau()) {
|
|
analyze_new_bounds_on_row_tableau(i, bp);
|
|
} else {
|
|
m_mpq_lar_core_solver.calculate_pivot_row(i);
|
|
substitute_basis_var_in_terms_for_row(i);
|
|
analyze_new_bounds_on_row(i, bp);
|
|
}
|
|
}
|
|
|
|
unsigned lar_solver::adjust_column_index_to_term_index(unsigned j) const {
|
|
unsigned ext_var_or_term = m_var_register.local_to_external(j);
|
|
return ext_var_or_term < m_terms_start_index ? j : ext_var_or_term;
|
|
}
|
|
|
|
void lar_solver::propagate_bounds_on_a_term(const lar_term& t, bound_propagator & bp, unsigned term_offset) {
|
|
lp_assert(false); // not implemented
|
|
}
|
|
|
|
|
|
void lar_solver::explain_implied_bound(implied_bound & ib, bound_propagator & bp) {
|
|
unsigned i = ib.m_row_or_term_index;
|
|
int bound_sign = ib.m_is_lower_bound? 1: -1;
|
|
int j_sign = (ib.m_coeff_before_j_is_pos ? 1 :-1) * bound_sign;
|
|
unsigned bound_j = ib.m_j;
|
|
if (is_term(bound_j)) {
|
|
bound_j = m_var_register.external_to_local(bound_j);
|
|
}
|
|
for (auto const& r : A_r().m_rows[i]) {
|
|
unsigned j = r.var();
|
|
if (j == bound_j) continue;
|
|
mpq const& a = r.get_val();
|
|
int a_sign = is_pos(a)? 1: -1;
|
|
int sign = j_sign * a_sign;
|
|
const ul_pair & ul = m_columns_to_ul_pairs[j];
|
|
auto witness = sign > 0? ul.upper_bound_witness(): ul.lower_bound_witness();
|
|
lp_assert(is_valid(witness));
|
|
bp.consume(a, witness);
|
|
}
|
|
// lp_assert(implied_bound_is_correctly_explained(ib, explanation));
|
|
}
|
|
|
|
|
|
bool lar_solver::term_is_used_as_row(unsigned term) const {
|
|
lp_assert(is_term(term));
|
|
return m_var_register.external_is_used(term);
|
|
}
|
|
|
|
void lar_solver::propagate_bounds_on_terms(bound_propagator & bp) {
|
|
for (unsigned i = 0; i < m_terms.size(); i++) {
|
|
if (term_is_used_as_row(i + m_terms_start_index))
|
|
continue; // this term is used a left side of a constraint,
|
|
// it was processed as a touched row if needed
|
|
propagate_bounds_on_a_term(*m_terms[i], bp, i);
|
|
}
|
|
}
|
|
|
|
|
|
// goes over touched rows and tries to induce bounds
|
|
void lar_solver::propagate_bounds_for_touched_rows(bound_propagator & bp) {
|
|
if (!use_tableau())
|
|
return; // todo: consider to remove the restriction
|
|
|
|
for (unsigned i : m_rows_with_changed_bounds.m_index) {
|
|
calculate_implied_bounds_for_row(i, bp);
|
|
if (settings().get_cancel_flag())
|
|
return;
|
|
}
|
|
m_rows_with_changed_bounds.clear();
|
|
if (!use_tableau()) {
|
|
propagate_bounds_on_terms(bp);
|
|
}
|
|
}
|
|
|
|
lp_status lar_solver::get_status() const { return m_status;}
|
|
|
|
void lar_solver::set_status(lp_status s) {m_status = s;}
|
|
|
|
lp_status lar_solver::find_feasible_solution() {
|
|
m_settings.st().m_make_feasible++;
|
|
if (A_r().column_count() > m_settings.st().m_max_cols)
|
|
m_settings.st().m_max_cols = A_r().column_count();
|
|
if (A_r().row_count() > m_settings.st().m_max_rows)
|
|
m_settings.st().m_max_rows = A_r().row_count();
|
|
if (strategy_is_undecided())
|
|
decide_on_strategy_and_adjust_initial_state();
|
|
|
|
m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = true;
|
|
auto ret = solve();
|
|
return ret;
|
|
}
|
|
|
|
lp_status lar_solver::solve() {
|
|
if (m_status == lp_status::INFEASIBLE) {
|
|
return m_status;
|
|
}
|
|
solve_with_core_solver();
|
|
if (m_status != lp_status::INFEASIBLE) {
|
|
if (m_settings.bound_propagation())
|
|
detect_rows_with_changed_bounds();
|
|
}
|
|
|
|
m_columns_with_changed_bound.clear();
|
|
return m_status;
|
|
}
|
|
|
|
void lar_solver::fill_explanation_from_infeasible_column(vector<std::pair<mpq, constraint_index>> & evidence) const{
|
|
|
|
// this is the case when the lower bound is in conflict with the upper one
|
|
const ul_pair & ul = m_columns_to_ul_pairs[m_infeasible_column_index];
|
|
evidence.push_back(std::make_pair(numeric_traits<mpq>::one(), ul.upper_bound_witness()));
|
|
evidence.push_back(std::make_pair(-numeric_traits<mpq>::one(), ul.lower_bound_witness()));
|
|
}
|
|
|
|
|
|
unsigned lar_solver::get_total_iterations() const { return m_mpq_lar_core_solver.m_r_solver.total_iterations(); }
|
|
vector<unsigned> lar_solver::get_list_of_all_var_indices() const {
|
|
vector<unsigned> ret;
|
|
for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_heading.size(); j++)
|
|
ret.push_back(j);
|
|
return ret;
|
|
}
|
|
void lar_solver::push() {
|
|
m_simplex_strategy = m_settings.simplex_strategy();
|
|
m_simplex_strategy.push();
|
|
m_columns_to_ul_pairs.push();
|
|
m_infeasible_column_index.push();
|
|
m_mpq_lar_core_solver.push();
|
|
m_term_count = m_terms.size();
|
|
m_term_count.push();
|
|
m_constraint_count = m_constraints.size();
|
|
m_constraint_count.push();
|
|
}
|
|
|
|
void lar_solver::clean_popped_elements(unsigned n, int_set& set) {
|
|
vector<int> to_remove;
|
|
for (unsigned j: set.m_index)
|
|
if (j >= n)
|
|
to_remove.push_back(j);
|
|
for (unsigned j : to_remove)
|
|
set.erase(j);
|
|
}
|
|
|
|
void lar_solver::shrink_inf_set_after_pop(unsigned n, int_set & set) {
|
|
clean_popped_elements(n, set);
|
|
set.resize(n);
|
|
}
|
|
|
|
|
|
void lar_solver::pop(unsigned k) {
|
|
TRACE("arith_int", tout << "pop" << std::endl;);
|
|
TRACE("lar_solver", tout << "k = " << k << std::endl;);
|
|
|
|
m_infeasible_column_index.pop(k);
|
|
unsigned n = m_columns_to_ul_pairs.peek_size(k);
|
|
m_var_register.shrink(n);
|
|
TRACE("arith_int", tout << "pop" << std::endl;);
|
|
if (m_settings.use_tableau()) {
|
|
pop_tableau();
|
|
}
|
|
lp_assert(A_r().column_count() == n);
|
|
m_columns_to_ul_pairs.pop(k);
|
|
|
|
m_mpq_lar_core_solver.pop(k);
|
|
clean_popped_elements(n, m_columns_with_changed_bound);
|
|
unsigned m = A_r().row_count();
|
|
clean_popped_elements(m, m_rows_with_changed_bounds);
|
|
clean_inf_set_of_r_solver_after_pop();
|
|
lp_assert(m_settings.simplex_strategy() == simplex_strategy_enum::undecided ||
|
|
(!use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
|
|
|
|
|
|
lp_assert(ax_is_correct());
|
|
m_constraint_count.pop(k);
|
|
for (unsigned i = m_constraint_count; i < m_constraints.size(); i++)
|
|
delete m_constraints[i];
|
|
|
|
m_constraints.resize(m_constraint_count);
|
|
m_term_count.pop(k);
|
|
for (unsigned i = m_term_count; i < m_terms.size(); i++) {
|
|
#if Z3DEBUG_CHECK_UNIQUE_TERMS
|
|
m_set_of_terms.erase(m_terms[i]);
|
|
#endif
|
|
delete m_terms[i];
|
|
}
|
|
m_terms.resize(m_term_count);
|
|
m_simplex_strategy.pop(k);
|
|
m_settings.simplex_strategy() = m_simplex_strategy;
|
|
lp_assert(sizes_are_correct());
|
|
lp_assert((!m_settings.use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
|
|
m_status = m_mpq_lar_core_solver.m_r_solver.current_x_is_feasible()? lp_status::OPTIMAL: lp_status::UNKNOWN;
|
|
}
|
|
|
|
vector<constraint_index> lar_solver::get_all_constraint_indices() const {
|
|
vector<constraint_index> ret;
|
|
constraint_index i = 0;
|
|
while ( i < m_constraints.size())
|
|
ret.push_back(i++);
|
|
return ret;
|
|
}
|
|
|
|
bool lar_solver::maximize_term_on_tableau(const lar_term & term,
|
|
impq &term_max) {
|
|
if (settings().simplex_strategy() == simplex_strategy_enum::undecided)
|
|
decide_on_strategy_and_adjust_initial_state();
|
|
|
|
m_mpq_lar_core_solver.m_r_solver.set_status(lp_status::FEASIBLE);
|
|
m_mpq_lar_core_solver.solve();
|
|
if (m_mpq_lar_core_solver.m_r_solver.get_status() == lp_status::UNBOUNDED)
|
|
return false;
|
|
|
|
term_max = term.apply(m_mpq_lar_core_solver.m_r_x);
|
|
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::costs_are_zeros_for_r_solver() const {
|
|
for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_costs.size(); j++) {
|
|
lp_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_costs[j]));
|
|
}
|
|
return true;
|
|
}
|
|
bool lar_solver::reduced_costs_are_zeroes_for_r_solver() const {
|
|
for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_d.size(); j++) {
|
|
lp_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_d[j]));
|
|
}
|
|
return true;
|
|
}
|
|
|
|
void lar_solver::set_costs_to_zero(const lar_term& term) {
|
|
auto & rslv = m_mpq_lar_core_solver.m_r_solver;
|
|
auto & jset = m_mpq_lar_core_solver.m_r_solver.m_inf_set; // hijack this set that should be empty right now
|
|
lp_assert(jset.m_index.size()==0);
|
|
|
|
for (const auto & p : term) {
|
|
unsigned j = p.var();
|
|
rslv.m_costs[j] = zero_of_type<mpq>();
|
|
int i = rslv.m_basis_heading[j];
|
|
if (i < 0)
|
|
jset.insert(j);
|
|
else {
|
|
for (const auto & rc : A_r().m_rows[i])
|
|
jset.insert(rc.var());
|
|
}
|
|
}
|
|
|
|
for (unsigned j : jset.m_index)
|
|
rslv.m_d[j] = zero_of_type<mpq>();
|
|
|
|
jset.clear();
|
|
|
|
lp_assert(reduced_costs_are_zeroes_for_r_solver());
|
|
lp_assert(costs_are_zeros_for_r_solver());
|
|
}
|
|
|
|
void lar_solver::prepare_costs_for_r_solver(const lar_term & term) {
|
|
|
|
auto & rslv = m_mpq_lar_core_solver.m_r_solver;
|
|
rslv.m_using_infeas_costs = false;
|
|
lp_assert(costs_are_zeros_for_r_solver());
|
|
lp_assert(reduced_costs_are_zeroes_for_r_solver());
|
|
rslv.m_costs.resize(A_r().column_count(), zero_of_type<mpq>());
|
|
for (const auto & p : term) {
|
|
unsigned j = p.var();
|
|
rslv.m_costs[j] = p.coeff();
|
|
if (rslv.m_basis_heading[j] < 0)
|
|
rslv.m_d[j] += p.coeff();
|
|
else
|
|
rslv.update_reduced_cost_for_basic_column_cost_change(- p.coeff(), j);
|
|
}
|
|
lp_assert(rslv.reduced_costs_are_correct_tableau());
|
|
}
|
|
|
|
bool lar_solver::maximize_term_on_corrected_r_solver(lar_term & term,
|
|
impq &term_max) {
|
|
settings().backup_costs = false;
|
|
switch (settings().simplex_strategy()) {
|
|
case simplex_strategy_enum::tableau_rows:
|
|
prepare_costs_for_r_solver(term);
|
|
settings().simplex_strategy() = simplex_strategy_enum::tableau_costs;
|
|
{
|
|
bool ret = maximize_term_on_tableau(term, term_max);
|
|
settings().simplex_strategy() = simplex_strategy_enum::tableau_rows;
|
|
set_costs_to_zero(term);
|
|
m_mpq_lar_core_solver.m_r_solver.set_status(lp_status::OPTIMAL);
|
|
return ret;
|
|
}
|
|
case simplex_strategy_enum::tableau_costs:
|
|
prepare_costs_for_r_solver(term);
|
|
{
|
|
bool ret = maximize_term_on_tableau(term, term_max);
|
|
set_costs_to_zero(term);
|
|
m_mpq_lar_core_solver.m_r_solver.set_status(lp_status::OPTIMAL);
|
|
return ret;
|
|
}
|
|
|
|
case simplex_strategy_enum::lu:
|
|
lp_assert(false); // not implemented
|
|
return false;
|
|
default:
|
|
lp_unreachable(); // wrong mode
|
|
}
|
|
return false;
|
|
}
|
|
|
|
|
|
bool lar_solver::remove_from_basis(unsigned j) {
|
|
return m_mpq_lar_core_solver.m_r_solver.remove_from_basis(j);
|
|
}
|
|
|
|
lar_term lar_solver::get_term_to_maximize(unsigned ext_j) const {
|
|
unsigned local_j;
|
|
if (m_var_register.external_is_used(ext_j, local_j)) {
|
|
lar_term r;
|
|
r. add_monomial(one_of_type<mpq>(), local_j);
|
|
return r;
|
|
}
|
|
if (!is_term(ext_j) || adjust_term_index(ext_j) >= m_terms.size())
|
|
return lar_term(); // return an empty term
|
|
return get_term(ext_j);
|
|
}
|
|
|
|
lp_status lar_solver::maximize_term(unsigned ext_j,
|
|
impq &term_max) {
|
|
bool was_feasible = m_mpq_lar_core_solver.m_r_solver.calc_current_x_is_feasible_include_non_basis();
|
|
impq prev_value;
|
|
lar_term term = get_term_to_maximize(ext_j);
|
|
if (term.is_empty()) {
|
|
return lp_status::UNBOUNDED;
|
|
}
|
|
|
|
auto backup = m_mpq_lar_core_solver.m_r_x;
|
|
if (was_feasible) {
|
|
prev_value = term.apply(m_mpq_lar_core_solver.m_r_x);
|
|
}
|
|
|
|
m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = false;
|
|
if (!maximize_term_on_corrected_r_solver(term, term_max)) {
|
|
m_mpq_lar_core_solver.m_r_x = backup;
|
|
return lp_status::UNBOUNDED;
|
|
}
|
|
|
|
impq opt_val = term_max;
|
|
|
|
bool change = false;
|
|
for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_x.size(); j++) {
|
|
if (!column_is_int(j))
|
|
continue;
|
|
if (column_value_is_integer(j))
|
|
continue;
|
|
if (m_int_solver->is_base(j)) {
|
|
if (!remove_from_basis(j)) { // consider a special version of remove_from_basis that would not remove inf_int columns
|
|
m_mpq_lar_core_solver.m_r_x = backup;
|
|
term_max = prev_value;
|
|
return lp_status::FEASIBLE; // it should not happen
|
|
}
|
|
}
|
|
m_int_solver->patch_nbasic_column(j, false);
|
|
if (!column_value_is_integer(j)) {
|
|
term_max = prev_value;
|
|
m_mpq_lar_core_solver.m_r_x = backup;
|
|
return lp_status::FEASIBLE;
|
|
}
|
|
change = true;
|
|
}
|
|
if (change) {
|
|
term_max = term.apply(m_mpq_lar_core_solver.m_r_x);
|
|
}
|
|
if (was_feasible && term_max < prev_value) {
|
|
term_max = prev_value;
|
|
m_mpq_lar_core_solver.m_r_x = backup;
|
|
}
|
|
return term_max == opt_val? lp_status::OPTIMAL :lp_status::FEASIBLE;
|
|
}
|
|
|
|
|
|
|
|
const lar_term & lar_solver::get_term(unsigned j) const {
|
|
lp_assert(j >= m_terms_start_index);
|
|
return *m_terms[j - m_terms_start_index];
|
|
}
|
|
|
|
void lar_solver::pop_core_solver_params() {
|
|
pop_core_solver_params(1);
|
|
}
|
|
|
|
void lar_solver::pop_core_solver_params(unsigned k) {
|
|
A_r().pop(k);
|
|
A_d().pop(k);
|
|
}
|
|
|
|
|
|
void lar_solver::set_upper_bound_witness(var_index j, constraint_index ci) {
|
|
ul_pair ul = m_columns_to_ul_pairs[j];
|
|
ul.upper_bound_witness() = ci;
|
|
m_columns_to_ul_pairs[j] = ul;
|
|
}
|
|
|
|
void lar_solver::set_lower_bound_witness(var_index j, constraint_index ci) {
|
|
ul_pair ul = m_columns_to_ul_pairs[j];
|
|
ul.lower_bound_witness() = ci;
|
|
m_columns_to_ul_pairs[j] = ul;
|
|
}
|
|
|
|
void lar_solver::register_monoid_in_map(std::unordered_map<var_index, mpq> & coeffs, const mpq & a, unsigned j) {
|
|
auto it = coeffs.find(j);
|
|
if (it == coeffs.end()) {
|
|
coeffs[j] = a;
|
|
} else {
|
|
it->second += a;
|
|
}
|
|
}
|
|
|
|
|
|
void lar_solver::substitute_terms_in_linear_expression(const vector<std::pair<mpq, var_index>>& left_side_with_terms,
|
|
vector<std::pair<mpq, var_index>> &left_side, mpq & free_coeff) const {
|
|
std::unordered_map<var_index, mpq> coeffs;
|
|
for (auto & t : left_side_with_terms) {
|
|
unsigned j = t.second;
|
|
if (!is_term(j)) {
|
|
register_monoid_in_map(coeffs, t.first, j);
|
|
} else {
|
|
const lar_term & term = * m_terms[adjust_term_index(t.second)];
|
|
for (auto & p : term.coeffs()){
|
|
register_monoid_in_map(coeffs, t.first * p.second , p.first);
|
|
}
|
|
free_coeff += t.first * term.m_v;
|
|
}
|
|
}
|
|
|
|
for (auto & p : coeffs)
|
|
if (!is_zero(p.second))
|
|
left_side.push_back(std::make_pair(p.second, p.first));
|
|
}
|
|
|
|
|
|
void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column(unsigned j) {
|
|
if (A_r().row_count() != m_column_buffer.data_size())
|
|
m_column_buffer.resize(A_r().row_count());
|
|
else
|
|
m_column_buffer.clear();
|
|
lp_assert(m_column_buffer.size() == 0 && m_column_buffer.is_OK());
|
|
|
|
m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer);
|
|
for (unsigned i : m_column_buffer.m_index)
|
|
m_rows_with_changed_bounds.insert(i);
|
|
}
|
|
|
|
|
|
|
|
void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column_tableau(unsigned j) {
|
|
for (auto & rc : m_mpq_lar_core_solver.m_r_A.m_columns[j])
|
|
m_rows_with_changed_bounds.insert(rc.var());
|
|
}
|
|
|
|
bool lar_solver::use_tableau() const { return m_settings.use_tableau(); }
|
|
|
|
bool lar_solver::use_tableau_costs() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs;
|
|
}
|
|
|
|
void lar_solver::detect_rows_of_column_with_bound_change(unsigned j) {
|
|
if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { // it is a basic column
|
|
// just mark the row at touched and exit
|
|
m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]);
|
|
return;
|
|
}
|
|
|
|
if (use_tableau())
|
|
detect_rows_of_bound_change_column_for_nbasic_column_tableau(j);
|
|
else
|
|
detect_rows_of_bound_change_column_for_nbasic_column(j);
|
|
}
|
|
|
|
void lar_solver::adjust_x_of_column(unsigned j) {
|
|
lp_assert(false);
|
|
}
|
|
|
|
bool lar_solver::row_is_correct(unsigned i) const {
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
for (const auto & c : A_r().m_rows[i]) {
|
|
r += c.coeff() * m_mpq_lar_core_solver.m_r_x[c.var()];
|
|
}
|
|
return is_zero(r);
|
|
}
|
|
|
|
bool lar_solver::ax_is_correct() const {
|
|
for (unsigned i = 0; i < A_r().row_count(); i++) {
|
|
if (!row_is_correct(i))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::tableau_with_costs() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs;
|
|
}
|
|
|
|
bool lar_solver::costs_are_used() const {
|
|
return m_settings.simplex_strategy() != simplex_strategy_enum::tableau_rows;
|
|
}
|
|
|
|
void lar_solver::change_basic_columns_dependend_on_a_given_nb_column(unsigned j, const numeric_pair<mpq> & delta) {
|
|
if (use_tableau()) {
|
|
for (const auto & c : A_r().m_columns[j]) {
|
|
unsigned bj = m_mpq_lar_core_solver.m_r_basis[c.var()];
|
|
if (tableau_with_costs()) {
|
|
m_basic_columns_with_changed_cost.insert(bj);
|
|
}
|
|
m_mpq_lar_core_solver.m_r_solver.update_x_with_delta_and_track_feasibility(bj, - A_r().get_val(c) * delta);
|
|
TRACE("change_x_del",
|
|
tout << "changed basis column " << bj << ", it is " <<
|
|
( m_mpq_lar_core_solver.m_r_solver.column_is_feasible(bj)? "feas":"inf") << std::endl;);
|
|
|
|
}
|
|
} else {
|
|
m_column_buffer.clear();
|
|
m_column_buffer.resize(A_r().row_count());
|
|
m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer);
|
|
for (unsigned i : m_column_buffer.m_index) {
|
|
unsigned bj = m_mpq_lar_core_solver.m_r_basis[i];
|
|
m_mpq_lar_core_solver.m_r_solver.update_x_with_delta_and_track_feasibility(bj, -m_column_buffer[i] * delta);
|
|
}
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j) {
|
|
if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
|
|
if (costs_are_used()) {
|
|
bool was_infeas = m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j);
|
|
m_mpq_lar_core_solver.m_r_solver.track_column_feasibility(j);
|
|
if (was_infeas != m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j))
|
|
m_basic_columns_with_changed_cost.insert(j);
|
|
} else {
|
|
m_mpq_lar_core_solver.m_r_solver.track_column_feasibility(j);
|
|
}
|
|
} else {
|
|
numeric_pair<mpq> delta;
|
|
if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta))
|
|
change_basic_columns_dependend_on_a_given_nb_column(j, delta);
|
|
}
|
|
}
|
|
|
|
|
|
void lar_solver::detect_rows_with_changed_bounds_for_column(unsigned j) {
|
|
if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
|
|
m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]);
|
|
return;
|
|
}
|
|
|
|
if (use_tableau())
|
|
detect_rows_of_bound_change_column_for_nbasic_column_tableau(j);
|
|
else
|
|
detect_rows_of_bound_change_column_for_nbasic_column(j);
|
|
}
|
|
|
|
void lar_solver::detect_rows_with_changed_bounds() {
|
|
for (auto j : m_columns_with_changed_bound.m_index)
|
|
detect_rows_with_changed_bounds_for_column(j);
|
|
}
|
|
|
|
void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds() {
|
|
for (auto j : m_columns_with_changed_bound.m_index)
|
|
update_x_and_inf_costs_for_column_with_changed_bounds(j);
|
|
}
|
|
|
|
void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds_tableau() {
|
|
for (auto j : m_columns_with_changed_bound.m_index)
|
|
update_x_and_inf_costs_for_column_with_changed_bounds(j);
|
|
|
|
if (tableau_with_costs()) {
|
|
for (unsigned j : m_basic_columns_with_changed_cost.m_index)
|
|
m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j);
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
|
|
}
|
|
}
|
|
|
|
|
|
void lar_solver::solve_with_core_solver() {
|
|
if (!use_tableau())
|
|
add_last_rows_to_lu(m_mpq_lar_core_solver.m_r_solver);
|
|
if (m_mpq_lar_core_solver.need_to_presolve_with_double_solver()) {
|
|
add_last_rows_to_lu(m_mpq_lar_core_solver.m_d_solver);
|
|
}
|
|
m_mpq_lar_core_solver.prefix_r();
|
|
if (costs_are_used()) {
|
|
m_basic_columns_with_changed_cost.clear();
|
|
m_basic_columns_with_changed_cost.resize(m_mpq_lar_core_solver.m_r_x.size());
|
|
}
|
|
if (use_tableau())
|
|
update_x_and_inf_costs_for_columns_with_changed_bounds_tableau();
|
|
else
|
|
update_x_and_inf_costs_for_columns_with_changed_bounds();
|
|
m_mpq_lar_core_solver.solve();
|
|
set_status(m_mpq_lar_core_solver.m_r_solver.get_status());
|
|
lp_assert(m_status != lp_status::OPTIMAL || all_constraints_hold());
|
|
}
|
|
|
|
|
|
numeric_pair<mpq> lar_solver::get_basic_var_value_from_row_directly(unsigned i) {
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
|
|
unsigned bj = m_mpq_lar_core_solver.m_r_solver.m_basis[i];
|
|
for (const auto & c: A_r().m_rows[i]) {
|
|
if (c.var() == bj) continue;
|
|
const auto & x = m_mpq_lar_core_solver.m_r_x[c.var()];
|
|
if (!is_zero(x))
|
|
r -= c.coeff() * x;
|
|
}
|
|
return r;
|
|
}
|
|
|
|
numeric_pair<mpq> lar_solver::get_basic_var_value_from_row(unsigned i) {
|
|
if (settings().use_tableau()) {
|
|
return get_basic_var_value_from_row_directly(i);
|
|
}
|
|
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
m_mpq_lar_core_solver.calculate_pivot_row(i);
|
|
for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_index) {
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis_heading[j] < 0);
|
|
r -= m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_data[j] * m_mpq_lar_core_solver.m_r_x[j];
|
|
}
|
|
return r;
|
|
}
|
|
|
|
template <typename K, typename L>
|
|
void lar_solver::add_last_rows_to_lu(lp_primal_core_solver<K,L> & s) {
|
|
auto & f = s.m_factorization;
|
|
if (f != nullptr) {
|
|
auto columns_to_replace = f->get_set_of_columns_to_replace_for_add_last_rows(s.m_basis_heading);
|
|
if (f->m_refactor_counter + columns_to_replace.size() >= 200 || f->has_dense_submatrix()) {
|
|
delete f;
|
|
f = nullptr;
|
|
} else {
|
|
f->add_last_rows_to_B(s.m_basis_heading, columns_to_replace);
|
|
}
|
|
}
|
|
if (f == nullptr) {
|
|
init_factorization(f, s.m_A, s.m_basis, m_settings);
|
|
if (f->get_status() != LU_status::OK) {
|
|
delete f;
|
|
f = nullptr;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
bool lar_solver::x_is_correct() const {
|
|
if (m_mpq_lar_core_solver.m_r_x.size() != A_r().column_count()) {
|
|
return false;
|
|
}
|
|
for (unsigned i = 0; i < A_r().row_count(); i++) {
|
|
numeric_pair<mpq> delta = A_r().dot_product_with_row(i, m_mpq_lar_core_solver.m_r_x);
|
|
if (!delta.is_zero()) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;;
|
|
|
|
}
|
|
|
|
bool lar_solver::var_is_registered(var_index vj) const {
|
|
if (vj >= m_terms_start_index) {
|
|
if (vj - m_terms_start_index >= m_terms.size())
|
|
return false;
|
|
} else if ( vj >= A_r().column_count()) {
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
unsigned lar_solver::constraint_stack_size() const {
|
|
return m_constraint_count.stack_size();
|
|
}
|
|
|
|
void lar_solver::fill_last_row_of_A_r(static_matrix<mpq, numeric_pair<mpq>> & A, const lar_term * ls) {
|
|
lp_assert(A.row_count() > 0);
|
|
lp_assert(A.column_count() > 0);
|
|
unsigned last_row = A.row_count() - 1;
|
|
lp_assert(A.m_rows[last_row].size() == 0);
|
|
for (auto & t : ls->m_coeffs) {
|
|
lp_assert(!is_zero(t.second));
|
|
var_index j = t.first;
|
|
A.set(last_row, j, - t.second);
|
|
}
|
|
unsigned basis_j = A.column_count() - 1;
|
|
A.set(last_row, basis_j, mpq(1));
|
|
}
|
|
|
|
template <typename U, typename V>
|
|
void lar_solver::create_matrix_A(static_matrix<U, V> & matr) {
|
|
lp_assert(false); // not implemented
|
|
/*
|
|
unsigned m = number_or_nontrivial_left_sides();
|
|
unsigned n = m_vec_of_canonic_left_sides.size();
|
|
if (matr.row_count() == m && matr.column_count() == n)
|
|
return;
|
|
matr.init_empty_matrix(m, n);
|
|
copy_from_mpq_matrix(matr);
|
|
*/
|
|
}
|
|
|
|
template <typename U, typename V>
|
|
void lar_solver::copy_from_mpq_matrix(static_matrix<U, V> & matr) {
|
|
matr.m_rows.resize(A_r().row_count());
|
|
matr.m_columns.resize(A_r().column_count());
|
|
for (unsigned i = 0; i < matr.row_count(); i++) {
|
|
for (auto & it : A_r().m_rows[i]) {
|
|
matr.set(i, it.var(), convert_struct<U, mpq>::convert(it.get_val()));
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
bool lar_solver::try_to_set_fixed(column_info<mpq> & ci) {
|
|
if (ci.upper_bound_is_set() && ci.lower_bound_is_set() && ci.get_upper_bound() == ci.get_lower_bound() && !ci.is_fixed()) {
|
|
ci.set_fixed_value(ci.get_upper_bound());
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
column_type lar_solver::get_column_type(const column_info<mpq> & ci) {
|
|
auto ret = ci.get_column_type_no_flipping();
|
|
if (ret == column_type::boxed) { // changing boxed to fixed because of the no span
|
|
if (ci.get_lower_bound() == ci.get_upper_bound())
|
|
ret = column_type::fixed;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
std::string lar_solver::get_column_name(unsigned j) const {
|
|
if (j >= m_terms_start_index)
|
|
return std::string("_t") + T_to_string(j);
|
|
if (j >= m_var_register.size())
|
|
return std::string("_s") + T_to_string(j);
|
|
|
|
return std::string("v") + T_to_string(m_var_register.local_to_external(j));
|
|
}
|
|
|
|
bool lar_solver::all_constrained_variables_are_registered(const vector<std::pair<mpq, var_index>>& left_side) {
|
|
for (auto it : left_side) {
|
|
if (! var_is_registered(it.second))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::all_constraints_hold() const {
|
|
if (m_settings.get_cancel_flag())
|
|
return true;
|
|
std::unordered_map<var_index, mpq> var_map;
|
|
get_model_do_not_care_about_diff_vars(var_map);
|
|
|
|
for (unsigned i = 0; i < m_constraints.size(); i++) {
|
|
if (!constraint_holds(*m_constraints[i], var_map)) {
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::constraint_holds(const lar_base_constraint & constr, std::unordered_map<var_index, mpq> & var_map) const {
|
|
return true;
|
|
mpq left_side_val = get_left_side_val(constr, var_map);
|
|
switch (constr.m_kind) {
|
|
case LE: return left_side_val <= constr.m_right_side;
|
|
case LT: return left_side_val < constr.m_right_side;
|
|
case GE: return left_side_val >= constr.m_right_side;
|
|
case GT: return left_side_val > constr.m_right_side;
|
|
case EQ: return left_side_val == constr.m_right_side;
|
|
default:
|
|
lp_unreachable();
|
|
}
|
|
return false; // it is unreachable
|
|
}
|
|
|
|
bool lar_solver::the_relations_are_of_same_type(const vector<std::pair<mpq, unsigned>> & evidence, lconstraint_kind & the_kind_of_sum) const {
|
|
unsigned n_of_G = 0, n_of_L = 0;
|
|
bool strict = false;
|
|
for (auto & it : evidence) {
|
|
mpq coeff = it.first;
|
|
constraint_index con_ind = it.second;
|
|
lconstraint_kind kind = coeff.is_pos() ?
|
|
m_constraints[con_ind]->m_kind :
|
|
flip_kind(m_constraints[con_ind]->m_kind);
|
|
if (kind == GT || kind == LT)
|
|
strict = true;
|
|
if (kind == GE || kind == GT) n_of_G++;
|
|
else if (kind == LE || kind == LT) n_of_L++;
|
|
}
|
|
the_kind_of_sum = n_of_G ? GE : (n_of_L ? LE : EQ);
|
|
if (strict)
|
|
the_kind_of_sum = static_cast<lconstraint_kind>((static_cast<int>(the_kind_of_sum) / 2));
|
|
|
|
return n_of_G == 0 || n_of_L == 0;
|
|
}
|
|
|
|
void lar_solver::register_in_map(std::unordered_map<var_index, mpq> & coeffs, const lar_base_constraint & cn, const mpq & a) {
|
|
for (auto & it : cn.get_left_side_coefficients()) {
|
|
unsigned j = it.second;
|
|
auto p = coeffs.find(j);
|
|
if (p == coeffs.end())
|
|
coeffs[j] = it.first * a;
|
|
else {
|
|
p->second += it.first * a;
|
|
if (p->second.is_zero())
|
|
coeffs.erase(p);
|
|
}
|
|
}
|
|
}
|
|
|
|
bool lar_solver::the_left_sides_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence) const {
|
|
std::unordered_map<var_index, mpq> coeff_map;
|
|
for (auto & it : evidence) {
|
|
mpq coeff = it.first;
|
|
constraint_index con_ind = it.second;
|
|
lp_assert(con_ind < m_constraints.size());
|
|
register_in_map(coeff_map, *m_constraints[con_ind], coeff);
|
|
}
|
|
|
|
if (!coeff_map.empty()) {
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::the_right_sides_do_not_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence) {
|
|
mpq ret = numeric_traits<mpq>::zero();
|
|
for (auto & it : evidence) {
|
|
mpq coeff = it.first;
|
|
constraint_index con_ind = it.second;
|
|
lp_assert(con_ind < m_constraints.size());
|
|
const lar_constraint & constr = *m_constraints[con_ind];
|
|
ret += constr.m_right_side * coeff;
|
|
}
|
|
return !numeric_traits<mpq>::is_zero(ret);
|
|
}
|
|
|
|
bool lar_solver::explanation_is_correct(const vector<std::pair<mpq, unsigned>>& explanation) const {
|
|
return true;
|
|
#if 0
|
|
// disabled: kind is uninitialized
|
|
#ifdef Z3DEBUG
|
|
lconstraint_kind kind;
|
|
lp_assert(the_left_sides_sum_to_zero(explanation));
|
|
mpq rs = sum_of_right_sides_of_explanation(explanation);
|
|
switch (kind) {
|
|
case LE: lp_assert(rs < zero_of_type<mpq>());
|
|
break;
|
|
case LT: lp_assert(rs <= zero_of_type<mpq>());
|
|
break;
|
|
case GE: lp_assert(rs > zero_of_type<mpq>());
|
|
break;
|
|
case GT: lp_assert(rs >= zero_of_type<mpq>());
|
|
break;
|
|
case EQ: lp_assert(rs != zero_of_type<mpq>());
|
|
break;
|
|
default:
|
|
lp_assert(false);
|
|
return false;
|
|
}
|
|
#endif
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::inf_explanation_is_correct() const {
|
|
#ifdef Z3DEBUG
|
|
vector<std::pair<mpq, unsigned>> explanation;
|
|
get_infeasibility_explanation(explanation);
|
|
return explanation_is_correct(explanation);
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
mpq lar_solver::sum_of_right_sides_of_explanation(const vector<std::pair<mpq, unsigned>> & explanation) const {
|
|
mpq ret = numeric_traits<mpq>::zero();
|
|
for (auto & it : explanation) {
|
|
mpq coeff = it.first;
|
|
constraint_index con_ind = it.second;
|
|
lp_assert(con_ind < m_constraints.size());
|
|
ret += (m_constraints[con_ind]->m_right_side - m_constraints[con_ind]->get_free_coeff_of_left_side()) * coeff;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
bool lar_solver::has_lower_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) const {
|
|
|
|
if (var >= m_columns_to_ul_pairs.size()) {
|
|
// TBD: bounds on terms could also be used, caller may have to track these.
|
|
return false;
|
|
}
|
|
const ul_pair & ul = m_columns_to_ul_pairs[var];
|
|
ci = ul.lower_bound_witness();
|
|
if (ci != static_cast<constraint_index>(-1)) {
|
|
auto& p = m_mpq_lar_core_solver.m_r_lower_bounds()[var];
|
|
value = p.x;
|
|
is_strict = p.y.is_pos();
|
|
return true;
|
|
}
|
|
else {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool lar_solver::has_upper_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) const {
|
|
|
|
if (var >= m_columns_to_ul_pairs.size()) {
|
|
// TBD: bounds on terms could also be used, caller may have to track these.
|
|
return false;
|
|
}
|
|
const ul_pair & ul = m_columns_to_ul_pairs[var];
|
|
ci = ul.upper_bound_witness();
|
|
if (ci != static_cast<constraint_index>(-1)) {
|
|
auto& p = m_mpq_lar_core_solver.m_r_upper_bounds()[var];
|
|
value = p.x;
|
|
is_strict = p.y.is_neg();
|
|
return true;
|
|
}
|
|
else {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool lar_solver::has_value(var_index var, mpq& value) const {
|
|
if (is_term(var)) {
|
|
lar_term const& t = get_term(var);
|
|
value = t.m_v;
|
|
for (auto const& cv : t) {
|
|
impq const& r = get_column_value(cv.var());
|
|
if (!numeric_traits<mpq>::is_zero(r.y)) return false;
|
|
value += r.x * cv.coeff();
|
|
}
|
|
return true;
|
|
}
|
|
else {
|
|
impq const& r = get_column_value(var);
|
|
value = r.x;
|
|
return numeric_traits<mpq>::is_zero(r.y);
|
|
}
|
|
}
|
|
|
|
|
|
void lar_solver::get_infeasibility_explanation(vector<std::pair<mpq, constraint_index>> & explanation) const {
|
|
explanation.clear();
|
|
if (m_infeasible_column_index != -1) {
|
|
fill_explanation_from_infeasible_column(explanation);
|
|
return;
|
|
}
|
|
if (m_mpq_lar_core_solver.get_infeasible_sum_sign() == 0) {
|
|
return;
|
|
}
|
|
// the infeasibility sign
|
|
int inf_sign;
|
|
auto inf_row = m_mpq_lar_core_solver.get_infeasibility_info(inf_sign);
|
|
get_infeasibility_explanation_for_inf_sign(explanation, inf_row, inf_sign);
|
|
lp_assert(explanation_is_correct(explanation));
|
|
}
|
|
|
|
|
|
|
|
void lar_solver::get_infeasibility_explanation_for_inf_sign(
|
|
vector<std::pair<mpq, constraint_index>> & explanation,
|
|
const vector<std::pair<mpq, unsigned>> & inf_row,
|
|
int inf_sign) const {
|
|
|
|
for (auto & it : inf_row) {
|
|
mpq coeff = it.first;
|
|
unsigned j = it.second;
|
|
|
|
int adj_sign = coeff.is_pos() ? inf_sign : -inf_sign;
|
|
const ul_pair & ul = m_columns_to_ul_pairs[j];
|
|
|
|
constraint_index bound_constr_i = adj_sign < 0 ? ul.upper_bound_witness() : ul.lower_bound_witness();
|
|
lp_assert(bound_constr_i < m_constraints.size());
|
|
explanation.push_back(std::make_pair(coeff, bound_constr_i));
|
|
}
|
|
}
|
|
|
|
void lar_solver::get_model(std::unordered_map<var_index, mpq> & variable_values) const {
|
|
lp_assert(m_status == lp_status::OPTIMAL);
|
|
mpq delta = mpq(1, 2); // start from 0.5 to have less clashes
|
|
unsigned i;
|
|
do {
|
|
// different pairs have to produce different singleton values
|
|
std::unordered_set<impq> set_of_different_pairs;
|
|
std::unordered_set<mpq> set_of_different_singles;
|
|
delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(delta);
|
|
for (i = 0; i < m_mpq_lar_core_solver.m_r_x.size(); i++ ) {
|
|
const numeric_pair<mpq> & rp = m_mpq_lar_core_solver.m_r_x[i];
|
|
set_of_different_pairs.insert(rp);
|
|
mpq x = rp.x + delta * rp.y;
|
|
set_of_different_singles.insert(x);
|
|
if (set_of_different_pairs.size()
|
|
!= set_of_different_singles.size()) {
|
|
delta /= mpq(2);
|
|
break;
|
|
}
|
|
|
|
variable_values[i] = x;
|
|
}
|
|
} while (i != m_mpq_lar_core_solver.m_r_x.size());
|
|
}
|
|
|
|
void lar_solver::get_model_do_not_care_about_diff_vars(std::unordered_map<var_index, mpq> & variable_values) const {
|
|
mpq delta = mpq(1);
|
|
delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(delta);
|
|
for (unsigned i = 0; i < m_mpq_lar_core_solver.m_r_x.size(); i++ ) {
|
|
const impq & rp = m_mpq_lar_core_solver.m_r_x[i];
|
|
variable_values[i] = rp.x + delta * rp.y;
|
|
}
|
|
}
|
|
|
|
|
|
std::string lar_solver::get_variable_name(var_index vi) const {
|
|
return get_column_name(vi);
|
|
}
|
|
|
|
// ********** print region start
|
|
std::ostream& lar_solver::print_constraint(constraint_index ci, std::ostream & out) const {
|
|
if (ci >= m_constraints.size()) {
|
|
out << "constraint " << T_to_string(ci) << " is not found";
|
|
out << std::endl;
|
|
return out;
|
|
}
|
|
|
|
return print_constraint(m_constraints[ci], out);
|
|
}
|
|
|
|
std::ostream& lar_solver::print_constraints(std::ostream& out) const {
|
|
out << "number of constraints = " << m_constraints.size() << std::endl;
|
|
for (auto c : m_constraints) {
|
|
print_constraint(c, out);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_terms(std::ostream& out) const {
|
|
for (auto it : m_terms) {
|
|
print_term(*it, out);
|
|
out << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_left_side_of_constraint(const lar_base_constraint * c, std::ostream & out) const {
|
|
print_linear_combination_of_column_indices(c->get_left_side_coefficients(), out);
|
|
mpq free_coeff = c->get_free_coeff_of_left_side();
|
|
if (!is_zero(free_coeff))
|
|
out << " + " << free_coeff;
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_term(lar_term const& term, std::ostream & out) const {
|
|
if (!numeric_traits<mpq>::is_zero(term.m_v)) {
|
|
out << term.m_v << " + ";
|
|
}
|
|
bool first = true;
|
|
for (const auto p : term) {
|
|
mpq val = p.coeff();
|
|
if (first) {
|
|
first = false;
|
|
} else {
|
|
if (is_pos(val)) {
|
|
out << " + ";
|
|
} else {
|
|
out << " - ";
|
|
val = -val;
|
|
}
|
|
}
|
|
if (val == -numeric_traits<mpq>::one())
|
|
out << " - ";
|
|
else if (val != numeric_traits<mpq>::one())
|
|
out << T_to_string(val);
|
|
out << this->get_column_name(p.var());
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_term_as_indices(lar_term const& term, std::ostream & out) const {
|
|
if (!numeric_traits<mpq>::is_zero(term.m_v)) {
|
|
out << term.m_v << " + ";
|
|
}
|
|
print_linear_combination_of_column_indices_only(term.coeffs_as_vector(), out);
|
|
return out;
|
|
}
|
|
|
|
mpq lar_solver::get_left_side_val(const lar_base_constraint & cns, const std::unordered_map<var_index, mpq> & var_map) const {
|
|
mpq ret = cns.get_free_coeff_of_left_side();
|
|
for (auto & it : cns.get_left_side_coefficients()) {
|
|
var_index j = it.second;
|
|
auto vi = var_map.find(j);
|
|
lp_assert(vi != var_map.end());
|
|
ret += it.first * vi->second;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_constraint(const lar_base_constraint * c, std::ostream & out) const {
|
|
print_left_side_of_constraint(c, out);
|
|
out << " " << lconstraint_kind_string(c->m_kind) << " " << c->m_right_side << std::endl;
|
|
return out;
|
|
}
|
|
|
|
void lar_solver::fill_var_set_for_random_update(unsigned sz, var_index const * vars, vector<unsigned>& column_list) {
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
var_index var = vars[i];
|
|
if (var >= m_terms_start_index) { // handle the term
|
|
for (auto & it : m_terms[var - m_terms_start_index]->m_coeffs) {
|
|
column_list.push_back(it.first);
|
|
}
|
|
} else {
|
|
column_list.push_back(var);
|
|
}
|
|
}
|
|
}
|
|
|
|
void lar_solver::random_update(unsigned sz, var_index const * vars) {
|
|
vector<unsigned> column_list;
|
|
fill_var_set_for_random_update(sz, vars, column_list);
|
|
random_updater ru(*this, column_list);
|
|
ru.update();
|
|
}
|
|
|
|
|
|
void lar_solver::pivot_fixed_vars_from_basis() {
|
|
m_mpq_lar_core_solver.m_r_solver.pivot_fixed_vars_from_basis();
|
|
}
|
|
|
|
void lar_solver::pop() {
|
|
pop(1);
|
|
}
|
|
|
|
bool lar_solver::column_represents_row_in_tableau(unsigned j) {
|
|
return m_columns_to_ul_pairs()[j].m_i != static_cast<row_index>(-1);
|
|
}
|
|
|
|
void lar_solver::make_sure_that_the_bottom_right_elem_not_zero_in_tableau(unsigned i, unsigned j) {
|
|
// i, j - is the indices of the bottom-right element of the tableau
|
|
lp_assert(A_r().row_count() == i + 1 && A_r().column_count() == j + 1);
|
|
auto & last_column = A_r().m_columns[j];
|
|
int non_zero_column_cell_index = -1;
|
|
for (unsigned k = last_column.size(); k-- > 0;){
|
|
auto & cc = last_column[k];
|
|
if (cc.var() == i)
|
|
return;
|
|
non_zero_column_cell_index = k;
|
|
}
|
|
|
|
lp_assert(non_zero_column_cell_index != -1);
|
|
lp_assert(static_cast<unsigned>(non_zero_column_cell_index) != i);
|
|
m_mpq_lar_core_solver.m_r_solver.transpose_rows_tableau(last_column[non_zero_column_cell_index].var(), i);
|
|
}
|
|
|
|
void lar_solver::remove_last_row_and_column_from_tableau(unsigned j) {
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
|
|
auto & slv = m_mpq_lar_core_solver.m_r_solver;
|
|
unsigned i = A_r().row_count() - 1; //last row index
|
|
make_sure_that_the_bottom_right_elem_not_zero_in_tableau(i, j);
|
|
if (slv.m_basis_heading[j] < 0) {
|
|
slv.pivot_column_tableau(j, i);
|
|
}
|
|
|
|
auto & last_row = A_r().m_rows[i];
|
|
mpq &cost_j = m_mpq_lar_core_solver.m_r_solver.m_costs[j];
|
|
bool cost_is_nz = !is_zero(cost_j);
|
|
for (unsigned k = last_row.size(); k-- > 0;) {
|
|
auto &rc = last_row[k];
|
|
if (cost_is_nz) {
|
|
m_mpq_lar_core_solver.m_r_solver.m_d[rc.var()] += cost_j*rc.get_val();
|
|
}
|
|
A_r().remove_element(last_row, rc);
|
|
}
|
|
lp_assert(last_row.size() == 0);
|
|
lp_assert(A_r().m_columns[j].size() == 0);
|
|
A_r().m_rows.pop_back();
|
|
A_r().m_columns.pop_back();
|
|
CASSERT("check_static_matrix", A_r().is_correct());
|
|
slv.m_b.pop_back();
|
|
}
|
|
|
|
void lar_solver::remove_last_column_from_A() {
|
|
// the last column has to be empty
|
|
lp_assert(A_r().m_columns.back().size() == 0);
|
|
A_r().m_columns.pop_back();
|
|
}
|
|
|
|
void lar_solver::remove_last_column_from_basis_tableau(unsigned j) {
|
|
auto& rslv = m_mpq_lar_core_solver.m_r_solver;
|
|
int i = rslv.m_basis_heading[j];
|
|
if (i >= 0) { // j is a basic var
|
|
int last_pos = static_cast<int>(rslv.m_basis.size()) - 1;
|
|
lp_assert(last_pos >= 0);
|
|
if (i != last_pos) {
|
|
unsigned j_at_last_pos = rslv.m_basis[last_pos];
|
|
rslv.m_basis[i] = j_at_last_pos;
|
|
rslv.m_basis_heading[j_at_last_pos] = i;
|
|
}
|
|
rslv.m_basis.pop_back(); // remove j from the basis
|
|
} else {
|
|
int last_pos = static_cast<int>(rslv.m_nbasis.size()) - 1;
|
|
lp_assert(last_pos >= 0);
|
|
i = - 1 - i;
|
|
if (i != last_pos) {
|
|
unsigned j_at_last_pos = rslv.m_nbasis[last_pos];
|
|
rslv.m_nbasis[i] = j_at_last_pos;
|
|
rslv.m_basis_heading[j_at_last_pos] = - i - 1;
|
|
}
|
|
rslv.m_nbasis.pop_back(); // remove j from the basis
|
|
}
|
|
rslv.m_basis_heading.pop_back();
|
|
lp_assert(rslv.m_basis.size() == A_r().row_count());
|
|
lp_assert(rslv.basis_heading_is_correct());
|
|
}
|
|
|
|
void lar_solver::remove_last_column_from_tableau() {
|
|
auto& rslv = m_mpq_lar_core_solver.m_r_solver;
|
|
unsigned j = A_r().column_count() - 1;
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
|
|
if (column_represents_row_in_tableau(j)) {
|
|
remove_last_row_and_column_from_tableau(j);
|
|
if (rslv.m_basis_heading[j] < 0)
|
|
rslv.change_basis_unconditionally(j, rslv.m_basis[A_r().row_count()]); // A_r().row_count() is the index of the last row in the basis still
|
|
}
|
|
else {
|
|
remove_last_column_from_A();
|
|
}
|
|
rslv.m_x.pop_back();
|
|
rslv.m_d.pop_back();
|
|
rslv.m_costs.pop_back();
|
|
|
|
remove_last_column_from_basis_tableau(j);
|
|
lp_assert(m_mpq_lar_core_solver.r_basis_is_OK());
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
|
|
}
|
|
|
|
void lar_solver::pop_tableau() {
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count());
|
|
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count());
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
|
|
// We remove last variables starting from m_column_names.size() to m_vec_of_canonic_left_sides.size().
|
|
// At this moment m_column_names is already popped
|
|
unsigned size = m_var_register.size();
|
|
while (A_r().column_count() > size)
|
|
remove_last_column_from_tableau();
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count());
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count());
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct());
|
|
}
|
|
|
|
void lar_solver::clean_inf_set_of_r_solver_after_pop() {
|
|
vector<unsigned> became_feas;
|
|
clean_popped_elements(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.m_inf_set);
|
|
std::unordered_set<unsigned> basic_columns_with_changed_cost;
|
|
auto inf_index_copy = m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index;
|
|
for (auto j: inf_index_copy) {
|
|
if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) {
|
|
continue;
|
|
}
|
|
// some basic columns might become non-basic - these columns need to be made feasible
|
|
numeric_pair<mpq> delta;
|
|
if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta)) {
|
|
|
|
change_basic_columns_dependend_on_a_given_nb_column(j, delta);
|
|
}
|
|
became_feas.push_back(j);
|
|
}
|
|
|
|
for (unsigned j : became_feas) {
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.m_basis_heading[j] < 0);
|
|
m_mpq_lar_core_solver.m_r_solver.m_d[j] -= m_mpq_lar_core_solver.m_r_solver.m_costs[j];
|
|
m_mpq_lar_core_solver.m_r_solver.m_costs[j] = zero_of_type<mpq>();
|
|
m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j);
|
|
}
|
|
became_feas.clear();
|
|
for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index) {
|
|
lp_assert(m_mpq_lar_core_solver.m_r_heading[j] >= 0);
|
|
if (m_mpq_lar_core_solver.m_r_solver.column_is_feasible(j))
|
|
became_feas.push_back(j);
|
|
}
|
|
for (unsigned j : became_feas)
|
|
m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j);
|
|
|
|
|
|
if (use_tableau_costs()) {
|
|
for (unsigned j : became_feas)
|
|
m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j);
|
|
for (unsigned j : basic_columns_with_changed_cost)
|
|
m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j);
|
|
lp_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
|
|
}
|
|
}
|
|
|
|
bool lar_solver::model_is_int_feasible() const {
|
|
unsigned n = A_r().column_count();
|
|
for (unsigned j = 0; j < n; j++) {
|
|
if (column_is_int(j) && !column_value_is_integer(j))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::term_is_int(const lar_term * t) const {
|
|
for (auto const & p : t->m_coeffs)
|
|
if (! (column_is_int(p.first) && p.second.is_int()))
|
|
return false;
|
|
return t->m_v.is_int();
|
|
}
|
|
|
|
bool lar_solver::var_is_int(var_index v) const {
|
|
if (is_term(v)) {
|
|
lar_term const& t = get_term(v);
|
|
return term_is_int(&t);
|
|
}
|
|
else {
|
|
return column_is_int(v);
|
|
}
|
|
}
|
|
|
|
bool lar_solver::column_is_int(unsigned j) const {
|
|
return m_var_register.local_is_int(j);
|
|
}
|
|
|
|
bool lar_solver::column_is_fixed(unsigned j) const {
|
|
return m_mpq_lar_core_solver.column_is_fixed(j);
|
|
}
|
|
|
|
// below is the initialization functionality of lar_solver
|
|
|
|
bool lar_solver::strategy_is_undecided() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::undecided;
|
|
}
|
|
|
|
var_index lar_solver::add_var(unsigned ext_j, bool is_int) {
|
|
TRACE("add_var", tout << "adding var " << ext_j << (is_int? " int" : " nonint") << std::endl;);
|
|
var_index local_j;
|
|
lp_assert(ext_j < m_terms_start_index);
|
|
if (m_var_register.external_is_used(ext_j, local_j))
|
|
return local_j;
|
|
lp_assert(m_columns_to_ul_pairs.size() == A_r().column_count());
|
|
local_j = A_r().column_count();
|
|
m_columns_to_ul_pairs.push_back(ul_pair(static_cast<unsigned>(-1)));
|
|
add_non_basic_var_to_core_fields(ext_j, is_int);
|
|
lp_assert(sizes_are_correct());
|
|
return local_j;
|
|
}
|
|
|
|
void lar_solver::register_new_ext_var_index(unsigned ext_v, bool is_int) {
|
|
lp_assert(!m_var_register.external_is_used(ext_v));
|
|
m_var_register.add_var(ext_v, is_int);
|
|
}
|
|
|
|
void lar_solver::add_non_basic_var_to_core_fields(unsigned ext_j, bool is_int) {
|
|
register_new_ext_var_index(ext_j, is_int);
|
|
m_mpq_lar_core_solver.m_column_types.push_back(column_type::free_column);
|
|
m_columns_with_changed_bound.increase_size_by_one();
|
|
add_new_var_to_core_fields_for_mpq(false);
|
|
if (use_lu())
|
|
add_new_var_to_core_fields_for_doubles(false);
|
|
}
|
|
|
|
void lar_solver::add_new_var_to_core_fields_for_doubles(bool register_in_basis) {
|
|
unsigned j = A_d().column_count();
|
|
A_d().add_column();
|
|
lp_assert(m_mpq_lar_core_solver.m_d_x.size() == j);
|
|
// lp_assert(m_mpq_lar_core_solver.m_d_lower_bounds.size() == j && m_mpq_lar_core_solver.m_d_upper_bounds.size() == j); // restore later
|
|
m_mpq_lar_core_solver.m_d_x.resize(j + 1);
|
|
m_mpq_lar_core_solver.m_d_lower_bounds.resize(j + 1);
|
|
m_mpq_lar_core_solver.m_d_upper_bounds.resize(j + 1);
|
|
lp_assert(m_mpq_lar_core_solver.m_d_heading.size() == j); // as A().column_count() on the entry to the method
|
|
if (register_in_basis) {
|
|
A_d().add_row();
|
|
m_mpq_lar_core_solver.m_d_heading.push_back(m_mpq_lar_core_solver.m_d_basis.size());
|
|
m_mpq_lar_core_solver.m_d_basis.push_back(j);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_d_heading.push_back(-static_cast<int>(m_mpq_lar_core_solver.m_d_nbasis.size()) - 1);
|
|
m_mpq_lar_core_solver.m_d_nbasis.push_back(j);
|
|
}
|
|
}
|
|
|
|
void lar_solver::add_new_var_to_core_fields_for_mpq(bool register_in_basis) {
|
|
unsigned j = A_r().column_count();
|
|
A_r().add_column();
|
|
lp_assert(m_mpq_lar_core_solver.m_r_x.size() == j);
|
|
// lp_assert(m_mpq_lar_core_solver.m_r_lower_bounds.size() == j && m_mpq_lar_core_solver.m_r_upper_bounds.size() == j); // restore later
|
|
m_mpq_lar_core_solver.m_r_x.resize(j + 1);
|
|
m_mpq_lar_core_solver.m_r_lower_bounds.increase_size_by_one();
|
|
m_mpq_lar_core_solver.m_r_upper_bounds.increase_size_by_one();
|
|
m_mpq_lar_core_solver.m_r_solver.m_inf_set.increase_size_by_one();
|
|
m_mpq_lar_core_solver.m_r_solver.m_costs.resize(j + 1);
|
|
m_mpq_lar_core_solver.m_r_solver.m_d.resize(j + 1);
|
|
lp_assert(m_mpq_lar_core_solver.m_r_heading.size() == j); // as A().column_count() on the entry to the method
|
|
if (register_in_basis) {
|
|
A_r().add_row();
|
|
m_mpq_lar_core_solver.m_r_heading.push_back(m_mpq_lar_core_solver.m_r_basis.size());
|
|
m_mpq_lar_core_solver.m_r_basis.push_back(j);
|
|
if (m_settings.bound_propagation())
|
|
m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_heading.push_back(-static_cast<int>(m_mpq_lar_core_solver.m_r_nbasis.size()) - 1);
|
|
m_mpq_lar_core_solver.m_r_nbasis.push_back(j);
|
|
}
|
|
}
|
|
|
|
|
|
var_index lar_solver::add_term_undecided(const vector<std::pair<mpq, var_index>> & coeffs,
|
|
const mpq &m_v) {
|
|
push_and_register_term(new lar_term(coeffs, m_v));
|
|
return m_terms_start_index + m_terms.size() - 1;
|
|
}
|
|
|
|
#if Z3DEBUG_CHECK_UNIQUE_TERMS
|
|
bool lar_solver::term_coeffs_are_ok(const vector<std::pair<mpq, var_index>> & coeffs, const mpq& v) {
|
|
if (coeffs.empty()) {
|
|
return is_zero(v);
|
|
}
|
|
|
|
for (const auto & p : coeffs) {
|
|
if (column_is_real(p.second))
|
|
return true;
|
|
}
|
|
|
|
mpq g;
|
|
bool g_is_set = false;
|
|
for (const auto & p : coeffs) {
|
|
if (!p.first.is_int()) {
|
|
return false;
|
|
}
|
|
if (!g_is_set) {
|
|
g_is_set = true;
|
|
g = p.first;
|
|
} else {
|
|
g = gcd(g, p.first);
|
|
}
|
|
}
|
|
if (g == one_of_type<mpq>())
|
|
return true;
|
|
|
|
return false;
|
|
}
|
|
#endif
|
|
void lar_solver::push_and_register_term(lar_term* t) {
|
|
#if Z3DEBUG_CHECK_UNIQUE_TERMS
|
|
lp_assert(m_set_of_terms.find(t) == m_set_of_terms.end());
|
|
m_set_of_terms.insert(t);
|
|
#endif
|
|
m_terms.push_back(t);
|
|
}
|
|
|
|
// terms
|
|
var_index lar_solver::add_term(const vector<std::pair<mpq, var_index>> & coeffs,
|
|
const mpq &m_v) {
|
|
if (strategy_is_undecided())
|
|
return add_term_undecided(coeffs, m_v);
|
|
|
|
push_and_register_term(new lar_term(coeffs, m_v));
|
|
unsigned adjusted_term_index = m_terms.size() - 1;
|
|
var_index ret = m_terms_start_index + adjusted_term_index;
|
|
if (use_tableau() && !coeffs.empty()) {
|
|
add_row_from_term_no_constraint(m_terms.back(), ret);
|
|
if (m_settings.bound_propagation())
|
|
m_rows_with_changed_bounds.insert(A_r().row_count() - 1);
|
|
}
|
|
CTRACE("add_term_lar_solver", !m_v.is_zero(), print_term(*m_terms.back(), tout););
|
|
lp_assert(m_var_register.size() == A_r().column_count());
|
|
return ret;
|
|
}
|
|
|
|
void lar_solver::add_row_from_term_no_constraint(const lar_term * term, unsigned term_ext_index) {
|
|
TRACE("dump_terms", print_term(*term, tout); tout << std::endl;);
|
|
register_new_ext_var_index(term_ext_index, term_is_int(term));
|
|
// j will be a new variable
|
|
unsigned j = A_r().column_count();
|
|
ul_pair ul(j);
|
|
m_columns_to_ul_pairs.push_back(ul);
|
|
add_basic_var_to_core_fields();
|
|
if (use_tableau()) {
|
|
A_r().fill_last_row_with_pivoting(*term,
|
|
j,
|
|
m_mpq_lar_core_solver.m_r_solver.m_basis_heading);
|
|
m_mpq_lar_core_solver.m_r_solver.m_b.resize(A_r().column_count(), zero_of_type<mpq>());
|
|
}
|
|
else {
|
|
fill_last_row_of_A_r(A_r(), term);
|
|
}
|
|
m_mpq_lar_core_solver.m_r_solver.update_x_and_call_tracker(j, get_basic_var_value_from_row_directly(A_r().row_count() - 1));
|
|
if (use_lu())
|
|
fill_last_row_of_A_d(A_d(), term);
|
|
}
|
|
|
|
void lar_solver::add_basic_var_to_core_fields() {
|
|
bool use_lu = m_mpq_lar_core_solver.need_to_presolve_with_double_solver();
|
|
lp_assert(!use_lu || A_r().column_count() == A_d().column_count());
|
|
m_mpq_lar_core_solver.m_column_types.push_back(column_type::free_column);
|
|
m_columns_with_changed_bound.increase_size_by_one();
|
|
m_rows_with_changed_bounds.increase_size_by_one();
|
|
add_new_var_to_core_fields_for_mpq(true);
|
|
if (use_lu)
|
|
add_new_var_to_core_fields_for_doubles(true);
|
|
}
|
|
|
|
bool lar_solver::bound_is_integer_for_integer_column(unsigned j, const mpq & right_side) const {
|
|
if (!column_is_int(j))
|
|
return true;
|
|
return right_side.is_int();
|
|
}
|
|
|
|
constraint_index lar_solver::add_var_bound(var_index j, lconstraint_kind kind, const mpq & right_side) {
|
|
TRACE("lar_solver", tout << "j = " << j << std::endl;);
|
|
constraint_index ci = m_constraints.size();
|
|
if (!is_term(j)) { // j is a var
|
|
lp_assert(bound_is_integer_for_integer_column(j, right_side));
|
|
auto vc = new lar_var_constraint(j, kind, right_side);
|
|
m_constraints.push_back(vc);
|
|
update_column_type_and_bound(j, kind, right_side, ci);
|
|
}
|
|
else {
|
|
add_var_bound_on_constraint_for_term(j, kind, right_side, ci);
|
|
}
|
|
lp_assert(sizes_are_correct());
|
|
return ci;
|
|
}
|
|
|
|
void lar_solver::update_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index) {
|
|
switch (m_mpq_lar_core_solver.m_column_types[j]) {
|
|
case column_type::free_column:
|
|
update_free_column_type_and_bound(j, kind, right_side, constr_index);
|
|
break;
|
|
case column_type::boxed:
|
|
update_boxed_column_type_and_bound(j, kind, right_side, constr_index);
|
|
break;
|
|
case column_type::lower_bound:
|
|
update_lower_bound_column_type_and_bound(j, kind, right_side, constr_index);
|
|
break;
|
|
case column_type::upper_bound:
|
|
update_upper_bound_column_type_and_bound(j, kind, right_side, constr_index);
|
|
break;
|
|
case column_type::fixed:
|
|
update_fixed_column_type_and_bound(j, kind, right_side, constr_index);
|
|
break;
|
|
default:
|
|
lp_assert(false); // cannot be here
|
|
}
|
|
}
|
|
|
|
void lar_solver::add_var_bound_on_constraint_for_term(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
|
|
lp_assert(is_term(j));
|
|
unsigned adjusted_term_index = adjust_term_index(j);
|
|
// lp_assert(!term_is_int(m_terms[adjusted_term_index]) || right_side.is_int());
|
|
unsigned term_j;
|
|
if (m_var_register.external_is_used(j, term_j)) {
|
|
mpq rs = right_side - m_terms[adjusted_term_index]->m_v;
|
|
m_constraints.push_back(new lar_term_constraint(m_terms[adjusted_term_index], kind, right_side));
|
|
update_column_type_and_bound(term_j, kind, rs, ci);
|
|
}
|
|
else {
|
|
add_constraint_from_term_and_create_new_column_row(j, m_terms[adjusted_term_index], kind, right_side);
|
|
}
|
|
}
|
|
|
|
constraint_index lar_solver::add_constraint(const vector<std::pair<mpq, var_index>>& left_side_with_terms, lconstraint_kind kind_par, const mpq& right_side_parm) {
|
|
vector<std::pair<mpq, var_index>> left_side;
|
|
mpq rs = -right_side_parm;
|
|
substitute_terms_in_linear_expression(left_side_with_terms, left_side, rs);
|
|
unsigned term_index = add_term(left_side, zero_of_type<mpq>());
|
|
constraint_index ci = m_constraints.size();
|
|
add_var_bound_on_constraint_for_term(term_index, kind_par, -rs, ci);
|
|
return ci;
|
|
}
|
|
|
|
void lar_solver::add_constraint_from_term_and_create_new_column_row(unsigned term_j, const lar_term* term,
|
|
lconstraint_kind kind, const mpq & right_side) {
|
|
|
|
add_row_from_term_no_constraint(term, term_j);
|
|
unsigned j = A_r().column_count() - 1;
|
|
update_column_type_and_bound(j, kind, right_side - term->m_v, m_constraints.size());
|
|
m_constraints.push_back(new lar_term_constraint(term, kind, right_side));
|
|
lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
|
|
}
|
|
|
|
void lar_solver::decide_on_strategy_and_adjust_initial_state() {
|
|
lp_assert(strategy_is_undecided());
|
|
if (m_columns_to_ul_pairs.size() > m_settings.column_number_threshold_for_using_lu_in_lar_solver) {
|
|
m_settings.simplex_strategy() = simplex_strategy_enum::lu;
|
|
}
|
|
else {
|
|
m_settings.simplex_strategy() = simplex_strategy_enum::tableau_rows; // todo: when to switch to tableau_costs?
|
|
}
|
|
adjust_initial_state();
|
|
}
|
|
|
|
void lar_solver::adjust_initial_state() {
|
|
switch (m_settings.simplex_strategy()) {
|
|
case simplex_strategy_enum::lu:
|
|
adjust_initial_state_for_lu();
|
|
break;
|
|
case simplex_strategy_enum::tableau_rows:
|
|
adjust_initial_state_for_tableau_rows();
|
|
break;
|
|
case simplex_strategy_enum::tableau_costs:
|
|
lp_assert(false); // not implemented
|
|
case simplex_strategy_enum::undecided:
|
|
adjust_initial_state_for_tableau_rows();
|
|
break;
|
|
}
|
|
}
|
|
|
|
void lar_solver::adjust_initial_state_for_lu() {
|
|
copy_from_mpq_matrix(A_d());
|
|
unsigned n = A_d().column_count();
|
|
m_mpq_lar_core_solver.m_d_x.resize(n);
|
|
m_mpq_lar_core_solver.m_d_lower_bounds.resize(n);
|
|
m_mpq_lar_core_solver.m_d_upper_bounds.resize(n);
|
|
m_mpq_lar_core_solver.m_d_heading = m_mpq_lar_core_solver.m_r_heading;
|
|
m_mpq_lar_core_solver.m_d_basis = m_mpq_lar_core_solver.m_r_basis;
|
|
|
|
/*
|
|
unsigned j = A_d().column_count();
|
|
A_d().add_column();
|
|
lp_assert(m_mpq_lar_core_solver.m_d_x.size() == j);
|
|
// lp_assert(m_mpq_lar_core_solver.m_d_lower_bounds.size() == j && m_mpq_lar_core_solver.m_d_upper_bounds.size() == j); // restore later
|
|
m_mpq_lar_core_solver.m_d_x.resize(j + 1 );
|
|
m_mpq_lar_core_solver.m_d_lower_bounds.resize(j + 1);
|
|
m_mpq_lar_core_solver.m_d_upper_bounds.resize(j + 1);
|
|
lp_assert(m_mpq_lar_core_solver.m_d_heading.size() == j); // as A().column_count() on the entry to the method
|
|
if (register_in_basis) {
|
|
A_d().add_row();
|
|
m_mpq_lar_core_solver.m_d_heading.push_back(m_mpq_lar_core_solver.m_d_basis.size());
|
|
m_mpq_lar_core_solver.m_d_basis.push_back(j);
|
|
}else {
|
|
m_mpq_lar_core_solver.m_d_heading.push_back(- static_cast<int>(m_mpq_lar_core_solver.m_d_nbasis.size()) - 1);
|
|
m_mpq_lar_core_solver.m_d_nbasis.push_back(j);
|
|
}*/
|
|
}
|
|
|
|
void lar_solver::adjust_initial_state_for_tableau_rows() {
|
|
for (unsigned i = 0; i < m_terms.size(); i++) {
|
|
if (m_var_register.external_is_used(i + m_terms_start_index))
|
|
continue;
|
|
add_row_from_term_no_constraint(m_terms[i], i + m_terms_start_index);
|
|
}
|
|
}
|
|
|
|
// this fills the last row of A_d and sets the basis column: -1 in the last column of the row
|
|
void lar_solver::fill_last_row_of_A_d(static_matrix<double, double> & A, const lar_term* ls) {
|
|
lp_assert(A.row_count() > 0);
|
|
lp_assert(A.column_count() > 0);
|
|
unsigned last_row = A.row_count() - 1;
|
|
lp_assert(A.m_rows[last_row].empty());
|
|
|
|
for (auto & t : ls->m_coeffs) {
|
|
lp_assert(!is_zero(t.second));
|
|
var_index j = t.first;
|
|
A.set(last_row, j, -t.second.get_double());
|
|
}
|
|
|
|
unsigned basis_j = A.column_count() - 1;
|
|
A.set(last_row, basis_j, -1);
|
|
lp_assert(A.is_correct());
|
|
}
|
|
|
|
void lar_solver::update_free_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_ind) {
|
|
mpq y_of_bound(0);
|
|
switch (kind) {
|
|
case LT:
|
|
y_of_bound = -1;
|
|
case LE:
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::upper_bound;
|
|
lp_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::upper_bound);
|
|
lp_assert(m_mpq_lar_core_solver.m_r_upper_bounds.size() > j);
|
|
{
|
|
auto up = numeric_pair<mpq>(right_side, y_of_bound);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
}
|
|
set_upper_bound_witness(j, constr_ind);
|
|
break;
|
|
case GT:
|
|
y_of_bound = 1;
|
|
case GE:
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::lower_bound;
|
|
lp_assert(m_mpq_lar_core_solver.m_r_upper_bounds.size() > j);
|
|
{
|
|
auto low = numeric_pair<mpq>(right_side, y_of_bound);
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
}
|
|
set_lower_bound_witness(j, constr_ind);
|
|
break;
|
|
case EQ:
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
|
|
set_upper_bound_witness(j, constr_ind);
|
|
set_lower_bound_witness(j, constr_ind);
|
|
break;
|
|
|
|
default:
|
|
lp_unreachable();
|
|
|
|
}
|
|
m_columns_with_changed_bound.insert(j);
|
|
}
|
|
|
|
void lar_solver::update_upper_bound_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
|
|
lp_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::upper_bound);
|
|
mpq y_of_bound(0);
|
|
switch (kind) {
|
|
case LT:
|
|
y_of_bound = -1;
|
|
case LE:
|
|
{
|
|
auto up = numeric_pair<mpq>(right_side, y_of_bound);
|
|
if (up < m_mpq_lar_core_solver.m_r_upper_bounds()[j]) {
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, ci);
|
|
m_columns_with_changed_bound.insert(j);
|
|
}
|
|
}
|
|
break;
|
|
case GT:
|
|
y_of_bound = 1;
|
|
case GE:
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::boxed;
|
|
{
|
|
auto low = numeric_pair<mpq>(right_side, y_of_bound);
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
set_lower_bound_witness(j, ci);
|
|
m_columns_with_changed_bound.insert(j);
|
|
if (low > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_column_types[j] = m_mpq_lar_core_solver.m_r_lower_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j] ? column_type::boxed : column_type::fixed;
|
|
}
|
|
}
|
|
break;
|
|
case EQ:
|
|
{
|
|
auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
|
|
if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
set_lower_bound_witness(j, ci);
|
|
m_infeasible_column_index = j;
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
|
|
m_columns_with_changed_bound.insert(j);
|
|
set_lower_bound_witness(j, ci);
|
|
set_upper_bound_witness(j, ci);
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
}
|
|
break;
|
|
}
|
|
break;
|
|
|
|
default:
|
|
lp_unreachable();
|
|
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_boxed_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
|
|
lp_assert(m_status == lp_status::INFEASIBLE || (m_mpq_lar_core_solver.m_column_types()[j] == column_type::boxed && m_mpq_lar_core_solver.m_r_lower_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j]));
|
|
mpq y_of_bound(0);
|
|
switch (kind) {
|
|
case LT:
|
|
y_of_bound = -1;
|
|
case LE:
|
|
{
|
|
auto up = numeric_pair<mpq>(right_side, y_of_bound);
|
|
if (up < m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, ci);
|
|
m_columns_with_changed_bound.insert(j);
|
|
}
|
|
|
|
if (up < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
}
|
|
else {
|
|
if (m_mpq_lar_core_solver.m_r_lower_bounds()[j] == m_mpq_lar_core_solver.m_r_upper_bounds()[j])
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
}
|
|
}
|
|
break;
|
|
case GT:
|
|
y_of_bound = 1;
|
|
case GE:
|
|
{
|
|
auto low = numeric_pair<mpq>(right_side, y_of_bound);
|
|
if (low > m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
m_columns_with_changed_bound.insert(j);
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
if (low > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
}
|
|
else if (low == m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
}
|
|
}
|
|
break;
|
|
case EQ:
|
|
{
|
|
auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
|
|
if (v < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_upper_bound_witness(j, ci);
|
|
}
|
|
else if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
|
|
set_lower_bound_witness(j, ci);
|
|
set_upper_bound_witness(j, ci);
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
m_columns_with_changed_bound.insert(j);
|
|
}
|
|
|
|
break;
|
|
}
|
|
|
|
default:
|
|
lp_unreachable();
|
|
|
|
}
|
|
}
|
|
void lar_solver::update_lower_bound_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
|
|
lp_assert(m_mpq_lar_core_solver.m_column_types()[j] == column_type::lower_bound);
|
|
mpq y_of_bound(0);
|
|
switch (kind) {
|
|
case LT:
|
|
y_of_bound = -1;
|
|
case LE:
|
|
{
|
|
auto up = numeric_pair<mpq>(right_side, y_of_bound);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, ci);
|
|
m_columns_with_changed_bound.insert(j);
|
|
|
|
if (up < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_column_types[j] = m_mpq_lar_core_solver.m_r_lower_bounds()[j] < m_mpq_lar_core_solver.m_r_upper_bounds()[j] ? column_type::boxed : column_type::fixed;
|
|
}
|
|
}
|
|
break;
|
|
case GT:
|
|
y_of_bound = 1;
|
|
case GE:
|
|
{
|
|
auto low = numeric_pair<mpq>(right_side, y_of_bound);
|
|
if (low > m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
m_columns_with_changed_bound.insert(j);
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
}
|
|
break;
|
|
case EQ:
|
|
{
|
|
auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
|
|
if (v < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_upper_bound_witness(j, ci);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = m_mpq_lar_core_solver.m_r_upper_bounds[j] = v;
|
|
set_lower_bound_witness(j, ci);
|
|
set_upper_bound_witness(j, ci);
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
}
|
|
m_columns_with_changed_bound.insert(j);
|
|
break;
|
|
}
|
|
|
|
default:
|
|
lp_unreachable();
|
|
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_fixed_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index ci) {
|
|
lp_assert(m_status == lp_status::INFEASIBLE || (m_mpq_lar_core_solver.m_column_types()[j] == column_type::fixed && m_mpq_lar_core_solver.m_r_lower_bounds()[j] == m_mpq_lar_core_solver.m_r_upper_bounds()[j]));
|
|
lp_assert(m_status == lp_status::INFEASIBLE || (m_mpq_lar_core_solver.m_r_lower_bounds()[j].y.is_zero() && m_mpq_lar_core_solver.m_r_upper_bounds()[j].y.is_zero()));
|
|
auto v = numeric_pair<mpq>(right_side, mpq(0));
|
|
|
|
mpq y_of_bound(0);
|
|
switch (kind) {
|
|
case LT:
|
|
if (v <= m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_upper_bound_witness(j, ci);
|
|
}
|
|
break;
|
|
case LE:
|
|
{
|
|
if (v < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_upper_bound_witness(j, ci);
|
|
}
|
|
}
|
|
break;
|
|
case GT:
|
|
{
|
|
if (v >= m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
}
|
|
break;
|
|
case GE:
|
|
{
|
|
if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
}
|
|
break;
|
|
case EQ:
|
|
{
|
|
if (v < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_upper_bound_witness(j, ci);
|
|
}
|
|
else if (v > m_mpq_lar_core_solver.m_r_upper_bounds[j]) {
|
|
m_status = lp_status::INFEASIBLE;
|
|
m_infeasible_column_index = j;
|
|
set_lower_bound_witness(j, ci);
|
|
}
|
|
break;
|
|
}
|
|
|
|
default:
|
|
lp_unreachable();
|
|
|
|
}
|
|
}
|
|
|
|
bool lar_solver::column_corresponds_to_term(unsigned j) const {
|
|
return m_var_register.local_to_external(j) >= m_terms_start_index;
|
|
}
|
|
|
|
var_index lar_solver::to_column(unsigned ext_j) const {
|
|
return m_var_register.external_to_local(ext_j);
|
|
}
|
|
|
|
bool lar_solver::tighten_term_bounds_by_delta(unsigned term_index, const impq& delta) {
|
|
unsigned tj = term_index + m_terms_start_index;
|
|
unsigned j;
|
|
if (m_var_register.external_is_used(tj, j) == false)
|
|
return true; // the term is not a column so it has no bounds
|
|
auto & slv = m_mpq_lar_core_solver.m_r_solver;
|
|
TRACE("cube", tout << "delta = " << delta << std::endl;
|
|
m_int_solver->display_column(tout, j); );
|
|
if (slv.column_has_upper_bound(j) && slv.column_has_lower_bound(j)) {
|
|
if (slv.m_upper_bounds[j] - delta < slv.m_lower_bounds[j] + delta) {
|
|
TRACE("cube", tout << "cannot tighten, delta = " << delta;);
|
|
return false;
|
|
}
|
|
}
|
|
TRACE("cube", tout << "can tighten";);
|
|
if (slv.column_has_upper_bound(j)) {
|
|
if (!is_zero(delta.y))
|
|
add_var_bound(tj, lconstraint_kind::LT, slv.m_upper_bounds[j].x - delta.x);
|
|
else
|
|
add_var_bound(tj, lconstraint_kind::LE, slv.m_upper_bounds[j].x - delta.x);
|
|
}
|
|
if (slv.column_has_lower_bound(j)) {
|
|
if (!is_zero(delta.y))
|
|
add_var_bound(tj, lconstraint_kind::GT, slv.m_lower_bounds[j].x + delta.x);
|
|
else
|
|
add_var_bound(tj, lconstraint_kind::GE, slv.m_lower_bounds[j].x + delta.x);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
void lar_solver::round_to_integer_solution() {
|
|
for (unsigned j = 0; j < column_count(); j++) {
|
|
if (!column_is_int(j)) continue;
|
|
if (column_corresponds_to_term(j)) continue;
|
|
TRACE("cube", m_int_solver->display_column(tout, j););
|
|
impq& v = m_mpq_lar_core_solver.m_r_x[j];
|
|
if (v.is_int())
|
|
continue;
|
|
impq flv = floor(v);
|
|
auto del = flv - v; // del is negative
|
|
if (del < - mpq(1, 2)) {
|
|
del = impq(one_of_type<mpq>()) + del;
|
|
v = ceil(v);
|
|
} else {
|
|
v = flv;
|
|
}
|
|
}
|
|
}
|
|
// return true if all y coords are zeroes
|
|
bool lar_solver::sum_first_coords(const lar_term& t, mpq & val) const {
|
|
val = zero_of_type<mpq>();
|
|
for (const auto & c : t) {
|
|
const auto & x = m_mpq_lar_core_solver.m_r_x[c.var()];
|
|
if (!is_zero(x.y))
|
|
return false;
|
|
val += x.x * c.coeff();
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::get_equality_and_right_side_for_term_on_current_x(unsigned term_index, mpq & rs, constraint_index& ci, bool &upper_bound) const {
|
|
unsigned tj = term_index + m_terms_start_index;
|
|
unsigned j;
|
|
bool is_int;
|
|
if (m_var_register.external_is_used(tj, j, is_int) == false)
|
|
return false; // the term does not have a bound because it does not correspond to a column
|
|
if (!is_int) // todo - allow for the next version of hnf
|
|
return false;
|
|
bool rs_is_calculated = false;
|
|
mpq b;
|
|
bool is_strict;
|
|
const lar_term& t = *terms()[term_index];
|
|
if (has_upper_bound(j, ci, b, is_strict) && !is_strict) {
|
|
lp_assert(b.is_int());
|
|
if (!sum_first_coords(t, rs))
|
|
return false;
|
|
rs_is_calculated = true;
|
|
if (rs == b) {
|
|
upper_bound = true;
|
|
return true;
|
|
}
|
|
}
|
|
if (has_lower_bound(j, ci, b, is_strict) && !is_strict) {
|
|
if (!rs_is_calculated){
|
|
if (!sum_first_coords(t, rs))
|
|
return false;
|
|
}
|
|
lp_assert(b.is_int());
|
|
|
|
if (rs == b) {
|
|
upper_bound = false;
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
void lar_solver::set_cut_strategy(unsigned cut_frequency) {
|
|
if (cut_frequency < 4) {
|
|
settings().m_int_gomory_cut_period = 2; // do it often
|
|
settings().set_hnf_cut_period(4); // also create hnf cuts
|
|
} else if (cut_frequency == 4) { // enable all cuts and cube equally
|
|
settings().m_int_gomory_cut_period = 4;
|
|
settings().set_hnf_cut_period(4);
|
|
} else {
|
|
// disable all heuristics except cube
|
|
settings().m_int_gomory_cut_period = 10000000;
|
|
settings().set_hnf_cut_period(100000000);
|
|
}
|
|
}
|
|
|
|
void lar_solver::adjust_cut_for_terms(const lar_term& t, mpq & rs) {
|
|
for (const auto& p : t) {
|
|
if (!is_term(p.var())) continue;
|
|
const lar_term & p_term = get_term(p.var());
|
|
if (p_term.m_v.is_zero()) continue;
|
|
rs -= p.coeff() * p_term.m_v;
|
|
}
|
|
}
|
|
|
|
|
|
} // namespace lp
|
|
|
|
|