mirror of
https://github.com/Z3Prover/z3
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2394 lines
90 KiB
C++
2394 lines
90 KiB
C++
/*
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Copyright (c) 2017 Microsoft Corporation
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Author: Nikolaj Bjorner, Lev Nachmanson
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*/
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#include "math/lp/lar_solver.h"
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#include "smt/params/smt_params_helper.hpp"
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namespace lp {
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lp_settings& lar_solver::settings() { return m_settings; }
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lp_settings const& lar_solver::settings() const { return m_settings; }
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statistics& lar_solver::stats() { return m_settings.stats(); }
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void lar_solver::updt_params(params_ref const& _p) {
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smt_params_helper p(_p);
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track_touched_rows(p.arith_bprop_on_pivoted_rows());
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set_cut_strategy(p.arith_branch_cut_ratio());
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m_settings.updt_params(_p);
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}
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lar_solver::lar_solver() :
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m_crossed_bounds_column(null_lpvar),
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m_crossed_bounds_deps(nullptr),
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m_mpq_lar_core_solver(m_settings, *this),
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m_var_register(false),
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m_term_register(true),
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m_constraints(m_dependencies, *this) {}
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// start or ends tracking the rows that were changed by solve()
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void lar_solver::track_touched_rows(bool v) {
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m_mpq_lar_core_solver.m_r_solver.m_touched_rows = v ? (&m_touched_rows) : nullptr;
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}
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// returns true iff the solver tracks the rows that were changed by solve()
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bool lar_solver::touched_rows_are_tracked() const {
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return m_mpq_lar_core_solver.m_r_solver.m_touched_rows != nullptr;
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}
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lar_solver::~lar_solver() {
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for (auto t : m_terms)
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delete t;
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}
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bool lar_solver::sizes_are_correct() const {
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lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size());
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lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
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lp_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_x.size());
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return true;
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}
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std::ostream& lar_solver::print_implied_bound(const implied_bound& be, std::ostream& out) const {
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out << "implied bound\n";
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unsigned v = be.m_j;
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if (tv::is_term(v)) {
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out << "it is a term number " << tv::unmask_term(be.m_j) << std::endl;
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print_term(*m_terms[tv::unmask_term(v)], out);
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}
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else {
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out << get_variable_name(v);
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}
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out << " " << lconstraint_kind_string(be.kind()) << " " << be.m_bound << std::endl;
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out << "end of implied bound" << std::endl;
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return out;
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}
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std::ostream& lar_solver::print_values(std::ostream& out) const {
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for (unsigned i = 0; i < m_mpq_lar_core_solver.m_r_x.size(); i++) {
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const numeric_pair<mpq>& rp = m_mpq_lar_core_solver.m_r_x[i];
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out << this->get_variable_name(i) << " -> " << rp << "\n";
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}
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return out;
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}
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bool lar_solver::implied_bound_is_correctly_explained(implied_bound const& be, const vector<std::pair<mpq, unsigned>>& explanation) const {
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std::unordered_map<unsigned, mpq> coeff_map;
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auto rs_of_evidence = zero_of_type<mpq>();
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unsigned n_of_G = 0, n_of_L = 0;
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bool strict = false;
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for (auto& it : explanation) {
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mpq coeff = it.first;
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constraint_index con_ind = it.second;
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const auto& constr = m_constraints[con_ind];
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lconstraint_kind kind = coeff.is_pos() ? constr.kind() : flip_kind(constr.kind());
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register_in_map(coeff_map, constr, coeff);
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if (kind == GT || kind == LT)
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strict = true;
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if (kind == GE || kind == GT) n_of_G++;
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else if (kind == LE || kind == LT) n_of_L++;
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rs_of_evidence += coeff * constr.rhs();
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}
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lp_assert(n_of_G == 0 || n_of_L == 0);
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lconstraint_kind kind = n_of_G ? GE : (n_of_L ? LE : EQ);
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if (strict)
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kind = static_cast<lconstraint_kind>((static_cast<int>(kind) / 2));
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if (!tv::is_term(be.m_j)) {
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if (coeff_map.size() != 1)
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return false;
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auto it = coeff_map.find(be.m_j);
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if (it == coeff_map.end()) return false;
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mpq ratio = it->second;
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if (ratio < zero_of_type<mpq>()) {
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kind = static_cast<lconstraint_kind>(-kind);
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}
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rs_of_evidence /= ratio;
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}
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else {
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lar_term const& t = get_term(be.m_j);
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auto first_coeff = t.begin();
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unsigned j = (*first_coeff).column();
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auto it = coeff_map.find(j);
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if (it == coeff_map.end())
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return false;
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mpq ratio = it->second / (*first_coeff).coeff();
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for (auto p : t) {
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it = coeff_map.find(p.column());
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if (it == coeff_map.end())
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return false;
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if (p.coeff() * ratio != it->second)
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return false;
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}
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if (ratio < zero_of_type<mpq>()) {
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kind = static_cast<lconstraint_kind>(-kind);
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}
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rs_of_evidence /= ratio;
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// rs_of_evidence += t->m_v * ratio;
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}
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return kind == be.kind() && rs_of_evidence == be.m_bound;
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}
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bool lar_solver::row_has_a_big_num(unsigned i) const {
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for (const auto& c : A_r().m_rows[i])
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if (c.coeff().is_big())
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return true;
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return false;
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}
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void lar_solver::substitute_basis_var_in_terms_for_row(unsigned i) {
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// todo : create a map from term basic vars to the rows where they are used
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unsigned basis_j = m_mpq_lar_core_solver.m_r_solver.m_basis[i];
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for (unsigned k = 0; k < m_terms.size(); k++) {
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if (term_is_used_as_row(k))
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continue;
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if (!m_terms[k]->contains(basis_j))
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continue;
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m_terms[k]->subst_in_row(basis_j, m_mpq_lar_core_solver.m_r_solver.m_pivot_row);
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}
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}
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// Returns the column index without changes,
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// but in the case the column was created as
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// the slack variable to a term return the term index.
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// It is the same index that was returned by add_var(), or
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// by add_term()
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unsigned lar_solver::column_to_reported_index(unsigned j) const {
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if (tv::is_term(j))
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return j;
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unsigned ext_var_or_term = m_var_register.local_to_external(j);
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if (tv::is_term(ext_var_or_term)) {
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j = ext_var_or_term;
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}
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return j;
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}
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unsigned lar_solver::map_term_index_to_column_index(unsigned j) const {
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SASSERT(tv::is_term(j));
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return m_var_register.external_to_local(j);
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}
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// here i is just the term index
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bool lar_solver::term_is_used_as_row(unsigned i) const {
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SASSERT(i < m_terms.size());
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return m_var_register.external_is_used(tv::mask_term(i));
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}
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lp_status lar_solver::get_status() const { return m_status; }
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void lar_solver::set_status(lp_status s) {
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TRACE("lar_solver", tout << "setting status to " << s << "\n";);
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m_status = s;
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}
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lp_status lar_solver::find_feasible_solution() {
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stats().m_make_feasible++;
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if (A_r().column_count() > stats().m_max_cols)
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stats().m_max_cols = A_r().column_count();
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if (A_r().row_count() > stats().m_max_rows)
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stats().m_max_rows = A_r().row_count();
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if (strategy_is_undecided())
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decide_on_strategy_and_adjust_initial_state();
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auto strategy_was = settings().simplex_strategy();
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settings().set_simplex_strategy(simplex_strategy_enum::tableau_rows);
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m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = true;
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auto ret = solve();
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settings().set_simplex_strategy(strategy_was);
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return ret;
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}
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lp_status lar_solver::solve() {
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if (m_status == lp_status::INFEASIBLE)
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return m_status;
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solve_with_core_solver();
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if (m_status != lp_status::INFEASIBLE) {
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if (m_settings.bound_propagation())
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detect_rows_with_changed_bounds();
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}
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clear_columns_with_changed_bounds();
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return m_status;
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}
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void lar_solver::fill_explanation_from_crossed_bounds_column(explanation& evidence) const {
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// this is the case when the lower bound is in conflict with the upper one
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svector<constraint_index> deps;
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SASSERT(m_crossed_bounds_deps != nullptr);
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m_dependencies.linearize(m_crossed_bounds_deps, deps);
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for (auto d : deps)
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evidence.add_pair(d, -numeric_traits<mpq>::one());
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}
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void lar_solver::push() {
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m_simplex_strategy = m_settings.simplex_strategy();
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m_simplex_strategy.push();
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m_columns_to_ul_pairs.push();
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m_crossed_bounds_column = null_lpvar;
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m_crossed_bounds_deps = nullptr;
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m_mpq_lar_core_solver.push();
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m_term_count = m_terms.size();
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m_term_count.push();
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m_constraints.push();
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m_usage_in_terms.push();
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m_dependencies.push_scope();
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}
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void lar_solver::clean_popped_elements(unsigned n, indexed_uint_set& set) {
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vector<int> to_remove;
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for (unsigned j : set)
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if (j >= n)
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to_remove.push_back(j);
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for (unsigned j : to_remove)
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set.remove(j);
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}
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void lar_solver::clean_popped_elements_for_heap(unsigned n, lpvar_heap& heap) {
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vector<int> to_remove;
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for (unsigned j : heap)
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if (j >= n)
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to_remove.push_back(j);
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for (unsigned j : to_remove)
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heap.erase(j);
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}
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void lar_solver::pop(unsigned k) {
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TRACE("lar_solver", tout << "k = " << k << std::endl;);
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m_crossed_bounds_column = null_lpvar;
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m_crossed_bounds_deps = nullptr;
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unsigned n = m_columns_to_ul_pairs.peek_size(k);
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m_var_register.shrink(n);
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pop_tableau(n);
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lp_assert(A_r().column_count() == n);
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TRACE("lar_solver_details",
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for (unsigned j = 0; j < n; j++) {
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print_column_info(j, tout) << "\n";
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}
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);
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m_columns_to_ul_pairs.pop(k);
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m_mpq_lar_core_solver.pop(k);
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remove_non_fixed_from_fixed_var_table();
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clean_popped_elements(n, m_columns_with_changed_bounds);
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clean_popped_elements(n, m_incorrect_columns);
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for (auto rid : m_row_bounds_to_replay)
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add_touched_row(rid);
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m_row_bounds_to_replay.reset();
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unsigned m = A_r().row_count();
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clean_popped_elements(m, m_touched_rows);
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clean_inf_heap_of_r_solver_after_pop();
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lp_assert(
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m_settings.simplex_strategy() == simplex_strategy_enum::undecided ||
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m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
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m_constraints.pop(k);
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m_term_count.pop(k);
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for (unsigned i = m_term_count; i < m_terms.size(); i++) {
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if (m_need_register_terms)
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deregister_normalized_term(*m_terms[i]);
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delete m_terms[i];
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}
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m_term_register.shrink(m_term_count);
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m_terms.resize(m_term_count);
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m_simplex_strategy.pop(k);
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m_settings.set_simplex_strategy(m_simplex_strategy);
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lp_assert(sizes_are_correct());
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lp_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau());
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m_usage_in_terms.pop(k);
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m_dependencies.pop_scope(k);
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set_status(lp_status::UNKNOWN);
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}
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bool lar_solver::maximize_term_on_tableau(const lar_term& term,
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impq& term_max) {
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if (settings().simplex_strategy() == simplex_strategy_enum::undecided)
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decide_on_strategy_and_adjust_initial_state();
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m_mpq_lar_core_solver.m_r_solver.set_status(lp_status::FEASIBLE);
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m_mpq_lar_core_solver.solve();
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lp_status st = m_mpq_lar_core_solver.m_r_solver.get_status();
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TRACE("lar_solver", tout << st << "\n";);
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SASSERT(m_mpq_lar_core_solver.m_r_solver.calc_current_x_is_feasible_include_non_basis());
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if (st == lp_status::UNBOUNDED) {
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return false;
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}
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else {
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term_max = term.apply(m_mpq_lar_core_solver.m_r_x);
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return true;
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}
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}
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bool lar_solver::improve_bound(lpvar j, bool improve_lower_bound) {
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lar_term term = get_term_to_maximize(j);
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if (improve_lower_bound)
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term.negate();
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impq bound;
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if (!maximize_term_on_corrected_r_solver(term, bound))
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return false;
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return false;
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// TODO
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if (improve_lower_bound) {
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bound.neg();
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if (column_has_lower_bound(j) && bound.x == column_lower_bound(j).x)
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return false;
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SASSERT(!column_has_lower_bound(j) || column_lower_bound(j).x < bound.x);
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// TODO - explain new lower bound.
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// Seems the relevant information is in the "costs" that are used when
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// setting the optimization objecive. The costs are cleared after a call so
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// maybe have some way of extracting bound dependencies from the costs.
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u_dependency* dep = nullptr;
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update_column_type_and_bound(j, bound.y > 0 ? lconstraint_kind::GT : lconstraint_kind::GE, bound.x, dep);
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}
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else {
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if (column_has_upper_bound(j) && bound.x == column_upper_bound(j).x)
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return false;
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SASSERT(!column_has_upper_bound(j) || column_upper_bound(j).x > bound.x);
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// similar for upper bounds
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u_dependency* dep = nullptr;
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update_column_type_and_bound(j, bound.y < 0 ? lconstraint_kind::LT : lconstraint_kind::LE, bound.x, dep);
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}
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return true;
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}
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bool lar_solver::costs_are_zeros_for_r_solver() const {
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for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_costs.size(); j++) {
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lp_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_costs[j]));
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}
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return true;
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}
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bool lar_solver::reduced_costs_are_zeroes_for_r_solver() const {
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for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_d.size(); j++) {
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lp_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_d[j]));
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}
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return true;
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}
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void lar_solver::set_costs_to_zero(const lar_term& term) {
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auto& rslv = m_mpq_lar_core_solver.m_r_solver;
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auto& jset = m_mpq_lar_core_solver.m_r_solver.inf_heap(); // hijack this set that should be empty right now
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lp_assert(jset.empty());
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for (lar_term::ival p : term) {
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unsigned j = p.column();
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rslv.m_costs[j] = zero_of_type<mpq>();
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int i = rslv.m_basis_heading[j];
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if (i < 0)
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jset.insert(j);
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else {
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for (const auto& rc : A_r().m_rows[i])
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jset.insert(rc.var());
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}
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}
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for (unsigned j : jset)
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rslv.m_d[j] = zero_of_type<mpq>();
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jset.clear();
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lp_assert(reduced_costs_are_zeroes_for_r_solver());
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lp_assert(costs_are_zeros_for_r_solver());
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}
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void lar_solver::prepare_costs_for_r_solver(const lar_term& term) {
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TRACE("lar_solver", print_term(term, tout << "prepare: ") << "\n";);
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move_non_basic_columns_to_bounds(false);
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auto& rslv = m_mpq_lar_core_solver.m_r_solver;
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lp_assert(costs_are_zeros_for_r_solver());
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lp_assert(reduced_costs_are_zeroes_for_r_solver());
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rslv.m_costs.resize(A_r().column_count(), zero_of_type<mpq>());
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for (lar_term::ival p : term) {
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unsigned j = p.column();
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rslv.m_costs[j] = p.coeff();
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if (rslv.m_basis_heading[j] < 0)
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rslv.m_d[j] += p.coeff();
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else
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rslv.update_reduced_cost_for_basic_column_cost_change(-p.coeff(), j);
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}
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rslv.m_costs_backup = rslv.m_costs;
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lp_assert(rslv.reduced_costs_are_correct_tableau());
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}
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void lar_solver::move_non_basic_columns_to_bounds(bool shift_randomly) {
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auto& lcs = m_mpq_lar_core_solver;
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bool change = false;
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for (unsigned j : lcs.m_r_nbasis) {
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if (move_non_basic_column_to_bounds(j, shift_randomly))
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change = true;
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}
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if (!change)
|
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return;
|
|
if (settings().simplex_strategy() == simplex_strategy_enum::tableau_costs)
|
|
update_x_and_inf_costs_for_columns_with_changed_bounds_tableau();
|
|
|
|
find_feasible_solution();
|
|
}
|
|
|
|
bool lar_solver::move_non_basic_column_to_bounds(unsigned j, bool force_change) {
|
|
auto& lcs = m_mpq_lar_core_solver;
|
|
auto& val = lcs.m_r_x[j];
|
|
switch (lcs.m_column_types()[j]) {
|
|
case column_type::boxed: {
|
|
bool at_l = val == lcs.m_r_lower_bounds()[j];
|
|
bool at_u = (!at_l && (val == lcs.m_r_upper_bounds()[j]));
|
|
if (!at_l && !at_u) {
|
|
if (m_settings.random_next() % 2)
|
|
set_value_for_nbasic_column(j, lcs.m_r_lower_bounds()[j]);
|
|
else
|
|
set_value_for_nbasic_column(j, lcs.m_r_upper_bounds()[j]);
|
|
return true;
|
|
}
|
|
else if (force_change && m_settings.random_next() % 3 == 0) {
|
|
set_value_for_nbasic_column(j,
|
|
at_l ? lcs.m_r_upper_bounds()[j] : lcs.m_r_lower_bounds()[j]);
|
|
return true;
|
|
}
|
|
break;
|
|
}
|
|
case column_type::lower_bound:
|
|
if (val != lcs.m_r_lower_bounds()[j]) {
|
|
set_value_for_nbasic_column(j, lcs.m_r_lower_bounds()[j]);
|
|
return true;
|
|
}
|
|
break;
|
|
case column_type::fixed:
|
|
case column_type::upper_bound:
|
|
if (val != lcs.m_r_upper_bounds()[j]) {
|
|
set_value_for_nbasic_column(j, lcs.m_r_upper_bounds()[j]);
|
|
return true;
|
|
}
|
|
break;
|
|
case column_type::free_column:
|
|
if (column_is_int(j) && !val.is_int()) {
|
|
set_value_for_nbasic_column(j, impq(floor(val)));
|
|
return true;
|
|
}
|
|
break;
|
|
default:
|
|
SASSERT(false);
|
|
}
|
|
return false;
|
|
}
|
|
|
|
void lar_solver::set_value_for_nbasic_column(unsigned j, const impq& new_val) {
|
|
lp_assert(!is_base(j));
|
|
auto& x = m_mpq_lar_core_solver.m_r_x[j];
|
|
auto delta = new_val - x;
|
|
x = new_val;
|
|
TRACE("lar_solver_feas", tout << "setting " << j << " to "
|
|
<< new_val << (column_is_feasible(j)?"feas":"non-feas") << "\n";);
|
|
change_basic_columns_dependend_on_a_given_nb_column(j, delta);
|
|
}
|
|
|
|
|
|
bool lar_solver::maximize_term_on_corrected_r_solver(lar_term& term,
|
|
impq& term_max) {
|
|
settings().backup_costs = false;
|
|
bool ret = false;
|
|
TRACE("lar_solver", print_term(term, tout << "maximize: ") << "\n" << constraints() << ", strategy = " << (int)settings().simplex_strategy() << "\n";);
|
|
switch (settings().simplex_strategy()) {
|
|
|
|
case simplex_strategy_enum::tableau_rows:
|
|
settings().set_simplex_strategy(simplex_strategy_enum::tableau_costs);
|
|
prepare_costs_for_r_solver(term);
|
|
ret = maximize_term_on_tableau(term, term_max);
|
|
settings().set_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);
|
|
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;
|
|
|
|
|
|
default:
|
|
UNREACHABLE(); // wrong mode
|
|
}
|
|
return false;
|
|
}
|
|
// returns true iff the row of j has a non-fixed column different from j
|
|
bool lar_solver::remove_from_basis(unsigned j) {
|
|
lp_assert(is_base(j));
|
|
unsigned i = row_of_basic_column(j);
|
|
for (const auto & c : A_r().m_rows[i])
|
|
if (j != c.var() && !is_fixed(c.var()))
|
|
return m_mpq_lar_core_solver.m_r_solver.remove_from_basis_core(c.var(), j);
|
|
return false;
|
|
}
|
|
|
|
lar_term lar_solver::get_term_to_maximize(unsigned j_or_term) const {
|
|
if (tv::is_term(j_or_term)) {
|
|
return get_term(j_or_term);
|
|
}
|
|
if (j_or_term < m_mpq_lar_core_solver.m_r_x.size()) {
|
|
lar_term r;
|
|
r.add_monomial(one_of_type<mpq>(), j_or_term);
|
|
return r;
|
|
}
|
|
return lar_term(); // return an empty term
|
|
}
|
|
|
|
lp_status lar_solver::maximize_term(unsigned j_or_term,
|
|
impq& term_max) {
|
|
TRACE("lar_solver", print_values(tout););
|
|
|
|
lar_term term = get_term_to_maximize(j_or_term);
|
|
if (term.is_empty()) {
|
|
return lp_status::UNBOUNDED;
|
|
}
|
|
impq prev_value;
|
|
auto backup = m_mpq_lar_core_solver.m_r_x;
|
|
if (m_mpq_lar_core_solver.m_r_solver.calc_current_x_is_feasible_include_non_basis()) {
|
|
prev_value = term.apply(m_mpq_lar_core_solver.m_r_x);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = false;
|
|
if (solve() != lp_status::OPTIMAL)
|
|
return lp_status::UNBOUNDED;
|
|
}
|
|
|
|
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
|
|
}
|
|
}
|
|
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 (term_max < prev_value) {
|
|
term_max = prev_value;
|
|
m_mpq_lar_core_solver.m_r_x = backup;
|
|
}
|
|
TRACE("lar_solver", print_values(tout););
|
|
if (term_max == opt_val) {
|
|
set_status(lp_status::OPTIMAL);
|
|
return lp_status::OPTIMAL;
|
|
}
|
|
return lp_status::FEASIBLE;
|
|
}
|
|
|
|
|
|
|
|
const lar_term& lar_solver::get_term(unsigned j) const {
|
|
lp_assert(tv::is_term(j));
|
|
return *m_terms[tv::unmask_term(j)];
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
|
|
void lar_solver::set_upper_bound_witness(var_index j, u_dependency* dep) {
|
|
ul_pair ul = m_columns_to_ul_pairs[j];
|
|
ul.upper_bound_witness() = dep;
|
|
m_columns_to_ul_pairs[j] = ul;
|
|
}
|
|
|
|
void lar_solver::set_lower_bound_witness(var_index j, u_dependency* dep) {
|
|
ul_pair ul = m_columns_to_ul_pairs[j];
|
|
ul.lower_bound_witness() = dep;
|
|
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) const {
|
|
std::unordered_map<var_index, mpq> coeffs;
|
|
for (auto& t : left_side_with_terms) {
|
|
unsigned j = t.second;
|
|
if (!tv::is_term(j)) {
|
|
register_monoid_in_map(coeffs, t.first, j);
|
|
}
|
|
else {
|
|
const lar_term& term = *m_terms[tv::unmask_term(t.second)];
|
|
|
|
for (auto p : term)
|
|
register_monoid_in_map(coeffs, t.first * p.coeff(), p.column());
|
|
}
|
|
}
|
|
|
|
for (auto& [v, c] : coeffs)
|
|
if (!is_zero(c))
|
|
left_side.push_back(std::make_pair(c, v));
|
|
}
|
|
|
|
void lar_solver::add_touched_row(unsigned rid) {
|
|
if (m_settings.bound_propagation())
|
|
m_touched_rows.insert(rid);
|
|
}
|
|
|
|
void lar_solver::remove_fixed_vars_from_base() {
|
|
// this will allow to disable and restore the tracking of the touched rows
|
|
flet<indexed_uint_set*> f(m_mpq_lar_core_solver.m_r_solver.m_touched_rows, nullptr);
|
|
unsigned num = A_r().column_count();
|
|
unsigned_vector to_remove;
|
|
for (unsigned j : m_fixed_base_var_set) {
|
|
if (j >= num || !is_base(j) || !is_fixed(j)) {
|
|
to_remove.push_back(j);
|
|
continue;
|
|
}
|
|
|
|
lp_assert(is_base(j) && is_fixed(j));
|
|
auto const& r = basic2row(j);
|
|
for (auto const& c : r) {
|
|
unsigned j_entering = c.var();
|
|
if (!is_fixed(j_entering)) {
|
|
pivot(j_entering, j);
|
|
to_remove.push_back(j);
|
|
lp_assert(is_base(j_entering));
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
for (unsigned j : to_remove) {
|
|
m_fixed_base_var_set.remove(j);
|
|
}
|
|
lp_assert(fixed_base_removed_correctly());
|
|
}
|
|
#ifdef Z3DEBUG
|
|
bool lar_solver::fixed_base_removed_correctly() const {
|
|
for (unsigned i = 0; i < A_r().row_count(); i++) {
|
|
unsigned j = get_base_column_in_row(i);
|
|
if (column_is_fixed(j)) {
|
|
for (const auto & c : A_r().m_rows[i] ) {
|
|
if (!column_is_fixed(c.var())) {
|
|
TRACE("lar_solver", print_row(A_r().m_rows[i], tout) << "\n";
|
|
for(const auto & c : A_r().m_rows[i]) {
|
|
print_column_info(c.var(), tout) << "\n";
|
|
});
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
#endif
|
|
|
|
bool lar_solver::use_tableau_costs() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs;
|
|
}
|
|
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()];
|
|
}
|
|
CTRACE("lar_solver", !is_zero(r), tout << "row = " << i << ", j = " << m_mpq_lar_core_solver.m_r_basis[i] << "\n";
|
|
print_row(A_r().m_rows[i], tout); tout << " = " << r << "\n");
|
|
return is_zero(r);
|
|
}
|
|
|
|
unsigned lar_solver::row_of_basic_column(unsigned j) const {
|
|
return m_mpq_lar_core_solver.m_r_heading[j];
|
|
}
|
|
|
|
|
|
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) {
|
|
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.add_delta_to_x_and_track_feasibility(bj, -A_r().get_val(c) * delta);
|
|
TRACE("change_x_del",
|
|
tout << "changed basis column " << bj << ", it is " <<
|
|
(column_is_feasible(bj) ? "feas" : "inf") << std::endl;);
|
|
}
|
|
}
|
|
|
|
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.inf_heap_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.inf_heap_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)
|
|
add_touched_row(m_mpq_lar_core_solver.m_r_heading[j]);
|
|
else
|
|
add_column_rows_to_touched_rows(j);
|
|
}
|
|
|
|
void lar_solver::detect_rows_with_changed_bounds() {
|
|
for (auto j : m_columns_with_changed_bounds)
|
|
detect_rows_with_changed_bounds_for_column(j);
|
|
if (m_find_monics_with_changed_bounds_func)
|
|
m_find_monics_with_changed_bounds_func(m_columns_with_changed_bounds);
|
|
}
|
|
|
|
void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds_tableau() {
|
|
for (auto j : m_columns_with_changed_bounds)
|
|
update_x_and_inf_costs_for_column_with_changed_bounds(j);
|
|
}
|
|
|
|
|
|
void lar_solver::solve_with_core_solver() {
|
|
m_mpq_lar_core_solver.prefix_r();
|
|
update_x_and_inf_costs_for_columns_with_changed_bounds_tableau();
|
|
m_mpq_lar_core_solver.solve();
|
|
set_status(m_mpq_lar_core_solver.m_r_solver.get_status());
|
|
lp_assert(((stats().m_make_feasible% 100) != 0) || m_status != lp_status::OPTIMAL || all_constraints_hold());
|
|
}
|
|
|
|
|
|
// this function just looks at the status
|
|
bool lar_solver::is_feasible() const {
|
|
switch (this->get_status()) {
|
|
case lp_status::OPTIMAL:
|
|
case lp_status::FEASIBLE:
|
|
case lp_status::UNBOUNDED:
|
|
return true;
|
|
default:
|
|
return false;
|
|
}
|
|
}
|
|
|
|
numeric_pair<mpq> lar_solver::get_basic_var_value_from_row(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;
|
|
}
|
|
|
|
bool lar_solver::var_is_registered(var_index vj) const {
|
|
if (tv::is_term(vj)) {
|
|
return tv::unmask_term(vj) < m_terms.size();
|
|
}
|
|
return vj < A_r().column_count();
|
|
}
|
|
|
|
|
|
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 (auto const& c : m_constraints.active()) {
|
|
if (!constraint_holds(c, var_map)) {
|
|
TRACE("lar_solver",
|
|
m_constraints.display(tout, c) << "\n";
|
|
for (auto p : c.coeffs()) {
|
|
m_mpq_lar_core_solver.m_r_solver.print_column_info(p.second, tout);
|
|
});
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::constraint_holds(const lar_base_constraint& constr, std::unordered_map<var_index, mpq>& var_map) const {
|
|
mpq left_side_val = get_left_side_val(constr, var_map);
|
|
switch (constr.kind()) {
|
|
case LE: return left_side_val <= constr.rhs();
|
|
case LT: return left_side_val < constr.rhs();
|
|
case GE: return left_side_val >= constr.rhs();
|
|
case GT: return left_side_val > constr.rhs();
|
|
case EQ: return left_side_val == constr.rhs();
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
return false; // it is unreachable
|
|
}
|
|
|
|
|
|
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.coeffs()) {
|
|
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 const & [coeff, con_ind] : evidence) {
|
|
lp_assert(m_constraints.valid_index(con_ind));
|
|
register_in_map(coeff_map, m_constraints[con_ind], coeff);
|
|
}
|
|
|
|
if (!coeff_map.empty()) {
|
|
return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
|
|
bool lar_solver::explanation_is_correct(explanation& 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:
|
|
UNREACHABLE();
|
|
return false;
|
|
}
|
|
#endif
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::inf_explanation_is_correct() const {
|
|
#ifdef Z3DEBUG
|
|
explanation exp;
|
|
get_infeasibility_explanation(exp);
|
|
return explanation_is_correct(exp);
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
mpq lar_solver::sum_of_right_sides_of_explanation(explanation& exp) const {
|
|
mpq ret = numeric_traits<mpq>::zero();
|
|
for (auto it : exp) {
|
|
mpq coeff = it.coeff();
|
|
constraint_index con_ind = it.ci();
|
|
lp_assert(m_constraints.valid_index(con_ind));
|
|
ret += (m_constraints[con_ind].rhs() - m_constraints[con_ind].get_free_coeff_of_left_side()) * coeff;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
bool lar_solver::has_lower_bound(var_index var, u_dependency*& 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 != nullptr) {
|
|
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, u_dependency*& 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 != nullptr) {
|
|
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 (tv::is_term(var)) {
|
|
lar_term const& t = get_term(var);
|
|
value = 0;
|
|
for (lar_term::ival cv : t) {
|
|
impq const& r = get_column_value(cv.column());
|
|
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(explanation& exp) const {
|
|
exp.clear();
|
|
if (m_crossed_bounds_column != null_lpvar) {
|
|
fill_explanation_from_crossed_bounds_column(exp);
|
|
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(exp, inf_row, inf_sign);
|
|
lp_assert(explanation_is_correct(exp));
|
|
}
|
|
|
|
void lar_solver::get_infeasibility_explanation_for_inf_sign(
|
|
explanation& exp,
|
|
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];
|
|
|
|
u_dependency* bound_constr_i = adj_sign < 0 ? ul.upper_bound_witness() : ul.lower_bound_witness();
|
|
svector<constraint_index> deps;
|
|
m_dependencies.linearize(bound_constr_i, deps);
|
|
for (auto d : deps) {
|
|
lp_assert(m_constraints.valid_index(d));
|
|
exp.add_pair(d, coeff);
|
|
}
|
|
}
|
|
}
|
|
|
|
// (x, y) != (x', y') => (x + delta*y) != (x' + delta*y')
|
|
void lar_solver::get_model(std::unordered_map<var_index, mpq>& variable_values) const {
|
|
variable_values.clear();
|
|
if (!init_model())
|
|
return;
|
|
|
|
unsigned n = m_mpq_lar_core_solver.m_r_x.size();
|
|
|
|
for (unsigned j = 0; j < n; j++)
|
|
variable_values[j] = get_value(column_index(j));
|
|
|
|
TRACE("lar_solver_model", tout << "delta = " << m_delta << "\nmodel:\n";
|
|
for (auto p : variable_values) tout << this->get_variable_name(p.first) << " = " << p.second << "\n";);
|
|
}
|
|
|
|
bool lar_solver::init_model() const {
|
|
CTRACE("lar_solver_model",!m_columns_with_changed_bounds.empty(), tout << "non-empty changed bounds\n");
|
|
TRACE("lar_solver_model", tout << get_status() << "\n");
|
|
auto status = get_status();
|
|
SASSERT((status != lp_status::OPTIMAL && status != lp_status::FEASIBLE)
|
|
|| m_mpq_lar_core_solver.m_r_solver.calc_current_x_is_feasible_include_non_basis());
|
|
if (status != lp_status::OPTIMAL && status != lp_status::FEASIBLE)
|
|
return false;
|
|
if (!m_columns_with_changed_bounds.empty())
|
|
return false;
|
|
|
|
m_delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(mpq(1));
|
|
unsigned j;
|
|
unsigned n = m_mpq_lar_core_solver.m_r_x.size();
|
|
do {
|
|
m_set_of_different_pairs.clear();
|
|
m_set_of_different_singles.clear();
|
|
for (j = 0; j < n; j++) {
|
|
const numeric_pair<mpq>& rp = m_mpq_lar_core_solver.m_r_x[j];
|
|
mpq x = rp.x + m_delta * rp.y;
|
|
m_set_of_different_pairs.insert(rp);
|
|
m_set_of_different_singles.insert(x);
|
|
if (m_set_of_different_pairs.size() != m_set_of_different_singles.size()) {
|
|
m_delta /= mpq(2);
|
|
break;
|
|
}
|
|
}
|
|
} while (j != n);
|
|
TRACE("lar_solver_model", tout << "delta = " << m_delta << "\nmodel:\n";);
|
|
return true;
|
|
}
|
|
|
|
void lar_solver::get_model_do_not_care_about_diff_vars(std::unordered_map<var_index, mpq>& variable_values) const {
|
|
mpq delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(mpq(1));
|
|
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;
|
|
}
|
|
}
|
|
|
|
mpq lar_solver::get_value(column_index const& j) const {
|
|
SASSERT(get_status() == lp_status::OPTIMAL || get_status() == lp_status::FEASIBLE);
|
|
SASSERT(m_columns_with_changed_bounds.empty());
|
|
numeric_pair<mpq> const& rp = get_column_value(j);
|
|
return from_model_in_impq_to_mpq(rp);
|
|
}
|
|
|
|
mpq lar_solver::get_tv_value(tv const& t) const {
|
|
if (t.is_var())
|
|
return get_value(t.column());
|
|
#if 0
|
|
unsigned term_j = 0;
|
|
if (m_var_register.term_is_used(t.id(), term_j))
|
|
return get_value(column_index(term_j));
|
|
#endif
|
|
mpq r(0);
|
|
for (lar_term::ival p : get_term(t))
|
|
r += p.coeff() * get_value(p.column());
|
|
return r;
|
|
}
|
|
//fetches the cached value of the term or the variable by the given index
|
|
const impq& lar_solver::get_tv_ivalue(tv const& t) const {
|
|
unsigned j = t.is_var()? (unsigned)t.column(): this->map_term_index_to_column_index(t.index());
|
|
return this->get_column_value(j);
|
|
}
|
|
|
|
void lar_solver::get_rid_of_inf_eps() {
|
|
bool y_is_zero = true;
|
|
for (unsigned j = 0; j < number_of_vars(); j++) {
|
|
if (!m_mpq_lar_core_solver.m_r_x[j].y.is_zero()) {
|
|
y_is_zero = false;
|
|
break;
|
|
}
|
|
}
|
|
if (y_is_zero)
|
|
return;
|
|
mpq delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(mpq(1));
|
|
for (unsigned j = 0; j < number_of_vars(); j++) {
|
|
auto& r = m_mpq_lar_core_solver.m_r_x[j];
|
|
if (!r.y.is_zero())
|
|
r = impq(r.x + delta * r.y);
|
|
}
|
|
}
|
|
|
|
void lar_solver::set_variable_name(var_index vi, std::string name) {
|
|
m_var_register.set_name(vi, name);
|
|
}
|
|
|
|
std::string lar_solver::get_variable_name(var_index j) const {
|
|
if (tv::is_term(j))
|
|
return std::string("_t") + T_to_string(tv::unmask_term(j));
|
|
if (j >= m_var_register.size())
|
|
return std::string("_s") + T_to_string(j);
|
|
|
|
std::string s = m_var_register.get_name(j);
|
|
if (!s.empty()) {
|
|
return s;
|
|
}
|
|
if (m_settings.print_external_var_name()) {
|
|
return std::string("j") + T_to_string(m_var_register.local_to_external(j));
|
|
}
|
|
else {
|
|
std::string s = column_corresponds_to_term(j) ? "t" : "j";
|
|
return s + T_to_string(j);
|
|
}
|
|
}
|
|
|
|
// ********** print region start
|
|
|
|
std::ostream& lar_solver::display(std::ostream& out) const {
|
|
out << constraints();
|
|
print_terms(out);
|
|
pp(out).print();
|
|
for (unsigned j = 0; j < number_of_vars(); j++)
|
|
print_column_info(j, out);
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_terms(std::ostream& out) const {
|
|
for (auto it : m_terms) {
|
|
print_term(*it, out) << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_term(lar_term const& term, std::ostream& out) const {
|
|
if (term.size() == 0) {
|
|
out << "0";
|
|
return out;
|
|
}
|
|
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_variable_name(p.column());
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& lar_solver::print_term_as_indices(lar_term const& term, std::ostream& out) {
|
|
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.coeffs()) {
|
|
var_index j = it.second;
|
|
auto vi = var_map.find(j);
|
|
lp_assert(vi != var_map.end());
|
|
ret += it.first * vi->second;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
|
|
void lar_solver::fill_var_set_for_random_update(unsigned sz, var_index const* vars, vector<unsigned>& column_list) {
|
|
TRACE("lar_solver_rand", tout << "sz = " << sz << "\n";);
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
var_index var = vars[i];
|
|
if (tv::is_term(var)) {
|
|
if (term_is_used_as_row(tv::unmask_term(var))) {
|
|
column_list.push_back(map_term_index_to_column_index(var));
|
|
}
|
|
}
|
|
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::add_column_rows_to_touched_rows(lpvar j) {
|
|
const auto& column = A_r().m_columns[j];
|
|
for (auto const& r : column)
|
|
add_touched_row(r.var());
|
|
}
|
|
|
|
void lar_solver::pop() {
|
|
pop(1);
|
|
}
|
|
|
|
bool lar_solver::column_represents_row_in_tableau(unsigned j) {
|
|
return m_columns_to_ul_pairs()[j].associated_with_row();
|
|
}
|
|
|
|
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.coeff();
|
|
}
|
|
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());
|
|
}
|
|
|
|
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(unsigned old_size) {
|
|
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
|
|
|
|
while (A_r().column_count() > old_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_heap_of_r_solver_after_pop() {
|
|
vector<unsigned> became_feas;
|
|
clean_popped_elements_for_heap(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.inf_heap());
|
|
std::unordered_set<unsigned> basic_columns_with_changed_cost;
|
|
m_inf_index_copy.reset();
|
|
for (auto j : m_mpq_lar_core_solver.m_r_solver.inf_heap())
|
|
m_inf_index_copy.push_back(j);
|
|
for (auto j : m_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.remove_column_from_inf_heap(j);
|
|
}
|
|
became_feas.clear();
|
|
for (unsigned j : m_mpq_lar_core_solver.m_r_solver.inf_heap()) {
|
|
lp_assert(m_mpq_lar_core_solver.m_r_heading[j] >= 0);
|
|
if (column_is_feasible(j))
|
|
became_feas.push_back(j);
|
|
}
|
|
for (unsigned j : became_feas)
|
|
m_mpq_lar_core_solver.m_r_solver.remove_column_from_inf_heap(j);
|
|
|
|
}
|
|
|
|
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)
|
|
if (!(column_is_int(p.column()) && p.coeff().is_int()))
|
|
return false;
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::term_is_int(const vector<std::pair<mpq, unsigned int>>& coeffs) const {
|
|
for (auto const& [coeff, v] : coeffs)
|
|
if (!(column_is_int(v) && coeff.is_int()))
|
|
return false;
|
|
return true;
|
|
}
|
|
|
|
bool lar_solver::var_is_int(var_index v) const {
|
|
if (tv::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);
|
|
}
|
|
|
|
bool lar_solver::column_is_free(unsigned j) const {
|
|
return m_mpq_lar_core_solver.column_is_free(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_named_var(unsigned ext_j, bool is_int, const std::string& name) {
|
|
var_index j = add_var(ext_j, is_int);
|
|
m_var_register.set_name(j, name);
|
|
return j;
|
|
}
|
|
|
|
unsigned lar_solver::external_to_column_index(unsigned ext_j) const {
|
|
unsigned j = external_to_local(ext_j);
|
|
if (j == null_lpvar)
|
|
return j;
|
|
|
|
if (tv::is_term(j))
|
|
return map_term_index_to_column_index(j);
|
|
|
|
return j;
|
|
}
|
|
|
|
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;
|
|
SASSERT(!m_term_register.external_is_used(ext_j));
|
|
lp_assert(!tv::is_term(ext_j));
|
|
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(false)); // not associated with a row
|
|
while (m_usage_in_terms.size() <= ext_j) {
|
|
m_usage_in_terms.push_back(0);
|
|
}
|
|
add_non_basic_var_to_core_fields(ext_j, is_int);
|
|
lp_assert(sizes_are_correct());
|
|
return local_j;
|
|
}
|
|
|
|
bool lar_solver::has_int_var() const {
|
|
return m_var_register.has_int_var();
|
|
}
|
|
|
|
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);
|
|
}
|
|
|
|
bool lar_solver::external_is_used(unsigned v) const {
|
|
return m_var_register.external_is_used(v) || m_term_register.external_is_used(v);
|
|
}
|
|
|
|
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);
|
|
add_new_var_to_core_fields_for_mpq(false); // false for not adding a row
|
|
}
|
|
|
|
void lar_solver::add_new_var_to_core_fields_for_mpq(bool register_in_basis) {
|
|
unsigned j = A_r().column_count();
|
|
TRACE("add_var", tout << "j = " << j << std::endl;);
|
|
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.inf_heap_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);
|
|
add_touched_row(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) {
|
|
push_term(new lar_term(coeffs));
|
|
return tv::mask_term(m_terms.size() - 1);
|
|
}
|
|
|
|
#if Z3DEBUG_CHECK_UNIQUE_TERMS
|
|
bool lar_solver::term_coeffs_are_ok(const vector<std::pair<mpq, var_index>>& coeffs) {
|
|
|
|
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_term(lar_term* t) {
|
|
m_terms.push_back(t);
|
|
}
|
|
|
|
// terms
|
|
bool lar_solver::all_vars_are_registered(const vector<std::pair<mpq, var_index>>& coeffs) {
|
|
return all_of(coeffs, [&](const auto& p) { return p.second < m_var_register.size(); });
|
|
}
|
|
|
|
void lar_solver::subst_known_terms(lar_term* t) {
|
|
std::set<unsigned> seen_terms;
|
|
for (auto p : *t) {
|
|
auto j = p.column();
|
|
if (this->column_corresponds_to_term(j))
|
|
seen_terms.insert(j);
|
|
}
|
|
while (!seen_terms.empty()) {
|
|
unsigned j = *seen_terms.begin();
|
|
seen_terms.erase(j);
|
|
auto tj = this->m_var_register.local_to_external(j);
|
|
auto& ot = this->get_term(tj);
|
|
for (auto p : ot)
|
|
if (this->column_corresponds_to_term(p.column()))
|
|
seen_terms.insert(p.column());
|
|
t->subst_by_term(ot, j);
|
|
}
|
|
}
|
|
// do not register in m_var_register this term if ext_i == UINT_MAX
|
|
var_index lar_solver::add_term(const vector<std::pair<mpq, var_index>>& coeffs, unsigned ext_i) {
|
|
TRACE("lar_solver_terms", print_linear_combination_of_column_indices_only(coeffs, tout) << ", ext_i =" << ext_i << "\n";);
|
|
SASSERT(!m_var_register.external_is_used(ext_i));
|
|
m_term_register.add_var(ext_i, term_is_int(coeffs));
|
|
lp_assert(all_vars_are_registered(coeffs));
|
|
if (strategy_is_undecided())
|
|
return add_term_undecided(coeffs);
|
|
lar_term* t = new lar_term(coeffs);
|
|
subst_known_terms(t);
|
|
push_term(t);
|
|
SASSERT(m_terms.size() == m_term_register.size());
|
|
unsigned adjusted_term_index = m_terms.size() - 1;
|
|
var_index ret = tv::mask_term(adjusted_term_index);
|
|
if (!coeffs.empty())
|
|
add_row_from_term_no_constraint(m_terms.back(), ret);
|
|
|
|
lp_assert(m_var_register.size() == A_r().column_count());
|
|
if (m_need_register_terms)
|
|
register_normalized_term(*t, A_r().column_count() - 1);
|
|
return ret;
|
|
}
|
|
|
|
/**
|
|
* \brief ensure there is a column index corresponding to vi
|
|
* If vi is already a column, just return vi
|
|
* If vi is for a term, then create a row that uses the term.
|
|
*/
|
|
var_index lar_solver::ensure_column(var_index vi) {
|
|
if (lp::tv::is_term(vi))
|
|
return to_column(vi);
|
|
else
|
|
return vi;
|
|
}
|
|
|
|
|
|
void lar_solver::add_row_from_term_no_constraint(const lar_term* term, unsigned term_ext_index) {
|
|
TRACE("dump_terms", print_term(*term, 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(true); // to mark this column as associated_with_row
|
|
m_columns_to_ul_pairs.push_back(ul);
|
|
add_basic_var_to_core_fields();
|
|
|
|
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.update_x(j, get_basic_var_value_from_row(A_r().row_count() - 1));
|
|
for (lar_term::ival c : *term) {
|
|
unsigned j = c.column();
|
|
while (m_usage_in_terms.size() <= j)
|
|
m_usage_in_terms.push_back(0);
|
|
m_usage_in_terms[j] = m_usage_in_terms[j] + 1;
|
|
}
|
|
}
|
|
|
|
void lar_solver::add_basic_var_to_core_fields() {
|
|
m_mpq_lar_core_solver.m_column_types.push_back(column_type::free_column);
|
|
add_new_var_to_core_fields_for_mpq(true);
|
|
}
|
|
|
|
bool lar_solver::bound_is_integer_for_integer_column(unsigned j, const mpq& right_side) const {
|
|
return !column_is_int(j) || right_side.is_int();
|
|
}
|
|
|
|
constraint_index lar_solver::add_var_bound_check_on_equal(var_index j, lconstraint_kind kind, const mpq& right_side, var_index& equal_var) {
|
|
constraint_index ci = mk_var_bound(j, kind, right_side);
|
|
activate_check_on_equal(ci, equal_var);
|
|
return ci;
|
|
}
|
|
|
|
constraint_index lar_solver::add_var_bound(var_index j, lconstraint_kind kind, const mpq& right_side) {
|
|
constraint_index ci = mk_var_bound(j, kind, right_side);
|
|
activate(ci);
|
|
return ci;
|
|
}
|
|
|
|
template <typename T>
|
|
void lar_solver::remove_non_fixed_from_table(T& table) {
|
|
vector<mpq> to_remove;
|
|
for (const auto& p : table) {
|
|
unsigned j = p.m_value;
|
|
if (j >= column_count() || !column_is_fixed(j))
|
|
to_remove.push_back(p.m_key);
|
|
}
|
|
for (const auto& p : to_remove)
|
|
table.erase(p);
|
|
}
|
|
|
|
void lar_solver::remove_non_fixed_from_fixed_var_table() {
|
|
remove_non_fixed_from_table(m_fixed_var_table_int);
|
|
remove_non_fixed_from_table(m_fixed_var_table_real);
|
|
}
|
|
|
|
void lar_solver::register_in_fixed_var_table(unsigned j, unsigned& equal_to_j) {
|
|
SASSERT(column_is_fixed(j));
|
|
equal_to_j = null_lpvar;
|
|
const impq& bound = get_lower_bound(j);
|
|
if (!bound.y.is_zero())
|
|
return;
|
|
|
|
const mpq& key = bound.x;
|
|
unsigned k;
|
|
bool j_is_int = column_is_int(j);
|
|
if (j_is_int) {
|
|
if (!m_fixed_var_table_int.find(key, k)) {
|
|
m_fixed_var_table_int.insert(key, j);
|
|
return;
|
|
}
|
|
}
|
|
else { // j is not integral column
|
|
if (!m_fixed_var_table_real.find(key, k)) {
|
|
m_fixed_var_table_real.insert(key, j);
|
|
return;
|
|
}
|
|
}
|
|
|
|
CTRACE("arith", !column_is_fixed(k), print_terms(tout););
|
|
// SASSERT(column_is_fixed(k));
|
|
if (j != k && column_is_fixed(k)) {
|
|
SASSERT(column_is_int(j) == column_is_int(k));
|
|
equal_to_j = column_to_reported_index(k);
|
|
TRACE("lar_solver", tout << "found equal column k = " << k <<
|
|
", external = " << equal_to_j << "\n";);
|
|
}
|
|
}
|
|
|
|
void lar_solver::activate_check_on_equal(constraint_index ci, unsigned& equal_column) {
|
|
auto const& c = m_constraints[ci];
|
|
update_column_type_and_bound_check_on_equal(c.column(), c.rhs(), ci, equal_column);
|
|
}
|
|
|
|
void lar_solver::activate(constraint_index ci) {
|
|
auto const& c = m_constraints[ci];
|
|
update_column_type_and_bound(c.column(), c.rhs(), ci);
|
|
}
|
|
|
|
mpq lar_solver::adjust_bound_for_int(lpvar j, lconstraint_kind& k, const mpq& bound) {
|
|
if (!column_is_int(j))
|
|
return bound;
|
|
if (bound.is_int())
|
|
return bound;
|
|
switch (k) {
|
|
case LT:
|
|
k = LE;
|
|
case LE:
|
|
return floor(bound);
|
|
case GT:
|
|
k = GE;
|
|
case GE:
|
|
return ceil(bound);
|
|
case EQ:
|
|
return bound;
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
|
|
return bound;
|
|
|
|
}
|
|
|
|
constraint_index lar_solver::mk_var_bound(var_index j, lconstraint_kind kind, const mpq& right_side) {
|
|
TRACE("lar_solver", tout << "j = " << get_variable_name(j) << " " << lconstraint_kind_string(kind) << " " << right_side << std::endl;);
|
|
constraint_index ci;
|
|
if (!tv::is_term(j)) { // j is a var
|
|
mpq rs = adjust_bound_for_int(j, kind, right_side);
|
|
lp_assert(bound_is_integer_for_integer_column(j, rs));
|
|
ci = m_constraints.add_var_constraint(j, kind, rs);
|
|
}
|
|
else {
|
|
ci = add_var_bound_on_constraint_for_term(j, kind, right_side);
|
|
}
|
|
lp_assert(sizes_are_correct());
|
|
return ci;
|
|
}
|
|
|
|
bool lar_solver::compare_values(var_index j, lconstraint_kind k, const mpq& rhs) {
|
|
if (tv::is_term(j))
|
|
j = to_column(j);
|
|
return compare_values(get_column_value(j), k, rhs);
|
|
}
|
|
|
|
bool lar_solver::compare_values(impq const& lhs, lconstraint_kind k, const mpq& rhs) {
|
|
switch (k) {
|
|
case LT: return lhs < rhs;
|
|
case LE: return lhs <= rhs;
|
|
case GT: return lhs > rhs;
|
|
case GE: return lhs >= rhs;
|
|
case EQ: return lhs == rhs;
|
|
default:
|
|
UNREACHABLE();
|
|
return true;
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_column_type_and_bound(unsigned j,
|
|
const mpq& right_side,
|
|
constraint_index constr_index) {
|
|
TRACE("lar_solver_feas", tout << "j = " << j << " was " << (this->column_is_feasible(j)?"feas":"non-feas") << std::endl;);
|
|
m_constraints.activate(constr_index);
|
|
lconstraint_kind kind = m_constraints[constr_index].kind();
|
|
u_dependency* dep = m_constraints[constr_index].dep();
|
|
update_column_type_and_bound(j, kind, right_side, dep);
|
|
}
|
|
|
|
void lar_solver::update_column_type_and_bound(unsigned j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
if (column_has_upper_bound(j))
|
|
update_column_type_and_bound_with_ub(j, kind, right_side, dep);
|
|
else
|
|
update_column_type_and_bound_with_no_ub(j, kind, right_side, dep);
|
|
|
|
if (is_base(j) && column_is_fixed(j))
|
|
m_fixed_base_var_set.insert(j);
|
|
TRACE("lar_solver_feas", tout << "j = " << j << " became " << (this->column_is_feasible(j) ? "feas" : "non-feas") << ", and " << (this->column_is_bounded(j) ? "bounded" : "non-bounded") << std::endl;);
|
|
}
|
|
|
|
void lar_solver::insert_to_columns_with_changed_bounds(unsigned j) {
|
|
m_columns_with_changed_bounds.insert(j);
|
|
TRACE("lar_solver", tout << "column " << j << (column_is_feasible(j) ? " feas" : " non-feas") << "\n";);
|
|
}
|
|
|
|
void lar_solver::update_column_type_and_bound_check_on_equal(unsigned j,
|
|
const mpq& right_side,
|
|
constraint_index constr_index,
|
|
unsigned& equal_to_j) {
|
|
update_column_type_and_bound(j, right_side, constr_index);
|
|
equal_to_j = null_lpvar;
|
|
if (column_is_fixed(j)) {
|
|
register_in_fixed_var_table(j, equal_to_j);
|
|
}
|
|
}
|
|
|
|
constraint_index lar_solver::add_var_bound_on_constraint_for_term(var_index j, lconstraint_kind kind, const mpq& right_side) {
|
|
lp_assert(tv::is_term(j));
|
|
unsigned adjusted_term_index = tv::unmask_term(j);
|
|
// lp_assert(!term_is_int(m_terms[adjusted_term_index]) || right_side.is_int());
|
|
unsigned term_j;
|
|
lar_term const* term = m_terms[adjusted_term_index];
|
|
if (m_var_register.external_is_used(j, term_j)) {
|
|
mpq rs = adjust_bound_for_int(term_j, kind, right_side);
|
|
lp_assert(bound_is_integer_for_integer_column(term_j, rs));
|
|
return m_constraints.add_term_constraint(term_j, term, kind, rs);
|
|
}
|
|
else {
|
|
return add_constraint_from_term_and_create_new_column_row(j, term, kind, right_side);
|
|
}
|
|
}
|
|
|
|
constraint_index 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;
|
|
mpq rs = adjust_bound_for_int(j, kind, right_side);
|
|
lp_assert(bound_is_integer_for_integer_column(j, rs));
|
|
return m_constraints.add_term_constraint(j, term, kind, rs);
|
|
}
|
|
|
|
void lar_solver::decide_on_strategy_and_adjust_initial_state() {
|
|
lp_assert(strategy_is_undecided());
|
|
|
|
m_settings.set_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::tableau_rows:
|
|
adjust_initial_state_for_tableau_rows();
|
|
break;
|
|
case simplex_strategy_enum::tableau_costs:
|
|
UNREACHABLE(); // not implemented
|
|
case simplex_strategy_enum::undecided:
|
|
adjust_initial_state_for_tableau_rows();
|
|
break;
|
|
}
|
|
}
|
|
|
|
|
|
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(tv::mask_term(i)))
|
|
continue;
|
|
add_row_from_term_no_constraint(m_terms[i], tv::mask_term(i));
|
|
}
|
|
}
|
|
|
|
|
|
void lar_solver::update_column_type_and_bound_with_ub(unsigned j, lp::lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
SASSERT(column_has_upper_bound(j));
|
|
if (column_has_lower_bound(j)) {
|
|
update_bound_with_ub_lb(j, kind, right_side, dep);
|
|
}
|
|
else {
|
|
update_bound_with_ub_no_lb(j, kind, right_side, dep);
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_column_type_and_bound_with_no_ub(unsigned j, lp::lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
SASSERT(!column_has_upper_bound(j));
|
|
if (column_has_lower_bound(j)) {
|
|
update_bound_with_no_ub_lb(j, kind, right_side, dep);
|
|
}
|
|
else {
|
|
update_bound_with_no_ub_no_lb(j, kind, right_side, dep);
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_bound_with_ub_lb(var_index j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
lp_assert(column_has_lower_bound(j) && column_has_upper_bound(j));
|
|
lp_assert(m_mpq_lar_core_solver.m_column_types[j] == column_type::boxed ||
|
|
m_mpq_lar_core_solver.m_column_types[j] == column_type::fixed);
|
|
|
|
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_lower_bounds[j]) {
|
|
set_crossed_bounds_column_and_deps(j, true, dep);
|
|
}
|
|
else {
|
|
if (up >= m_mpq_lar_core_solver.m_r_upper_bounds[j]) return;
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, dep);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
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_upper_bounds[j]) {
|
|
set_crossed_bounds_column_and_deps(j, false, dep);
|
|
} else {
|
|
if (low < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
return;
|
|
}
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_column_types[j] = (low == m_mpq_lar_core_solver.m_r_upper_bounds[j] ? column_type::fixed : column_type::boxed);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
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]){
|
|
set_crossed_bounds_column_and_deps(j, false, dep);
|
|
}
|
|
else if (v < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
set_crossed_bounds_column_and_deps(j, true, dep);
|
|
}
|
|
else {
|
|
set_upper_bound_witness(j, dep);
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = m_mpq_lar_core_solver.m_r_lower_bounds[j] = v;
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
break;
|
|
}
|
|
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
if (m_mpq_lar_core_solver.m_r_upper_bounds[j] == m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
}
|
|
}
|
|
|
|
void lar_solver::update_bound_with_no_ub_lb(var_index j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
lp_assert(column_has_lower_bound(j) && !column_has_upper_bound(j));
|
|
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);
|
|
if (up < m_mpq_lar_core_solver.m_r_lower_bounds[j]) {
|
|
set_crossed_bounds_column_and_deps(j, true, dep);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_column_types[j] = (up == m_mpq_lar_core_solver.m_r_lower_bounds[j] ? column_type::fixed : column_type::boxed);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
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]) {
|
|
return;
|
|
}
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
set_lower_bound_witness(j, dep);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
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]) {
|
|
set_crossed_bounds_column_and_deps(j, true, dep);
|
|
}
|
|
else {
|
|
set_upper_bound_witness(j, dep);
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = m_mpq_lar_core_solver.m_r_lower_bounds[j] = v;
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
break;
|
|
}
|
|
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
}
|
|
// clang-format off
|
|
void lar_solver::update_bound_with_ub_no_lb(var_index j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
lp_assert(!column_has_lower_bound(j) && column_has_upper_bound(j));
|
|
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]) return;
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, dep);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
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_upper_bounds[j]) {
|
|
set_crossed_bounds_column_and_deps(j, false, dep);
|
|
}
|
|
else {
|
|
m_mpq_lar_core_solver.m_r_lower_bounds[j] = low;
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_column_types[j] = (low == m_mpq_lar_core_solver.m_r_upper_bounds[j] ? column_type::fixed : column_type::boxed);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
}
|
|
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]) {
|
|
set_crossed_bounds_column_and_deps(j, false, dep);
|
|
}
|
|
else {
|
|
set_upper_bound_witness(j, dep);
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = m_mpq_lar_core_solver.m_r_lower_bounds[j] = v;
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
break;
|
|
}
|
|
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
}
|
|
// clang-format on
|
|
void lar_solver::update_bound_with_no_ub_no_lb(var_index j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep) {
|
|
lp_assert(!column_has_lower_bound(j) && !column_has_upper_bound(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);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = up;
|
|
set_upper_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::upper_bound;
|
|
} break;
|
|
case GT:
|
|
y_of_bound = 1;
|
|
case GE: {
|
|
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, dep);
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::lower_bound;
|
|
|
|
} break;
|
|
case EQ: {
|
|
auto v = numeric_pair<mpq>(right_side, zero_of_type<mpq>());
|
|
set_upper_bound_witness(j, dep);
|
|
set_lower_bound_witness(j, dep);
|
|
m_mpq_lar_core_solver.m_r_upper_bounds[j] = m_mpq_lar_core_solver.m_r_lower_bounds[j] = v;
|
|
m_mpq_lar_core_solver.m_column_types[j] = column_type::fixed;
|
|
break;
|
|
}
|
|
|
|
default:
|
|
UNREACHABLE();
|
|
}
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
// clang-format off
|
|
bool lar_solver::column_corresponds_to_term(unsigned j) const {
|
|
return tv::is_term(m_var_register.local_to_external(j));
|
|
}
|
|
|
|
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(tv const& t, const impq& delta) {
|
|
SASSERT(t.is_term());
|
|
unsigned tj = t.index();
|
|
unsigned j;
|
|
if (!m_var_register.external_is_used(tj, j))
|
|
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) || !is_zero(slv.m_upper_bounds[j].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) || !is_zero(slv.m_lower_bounds[j].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;
|
|
impq& v = m_mpq_lar_core_solver.m_r_x[j];
|
|
if (v.is_int())
|
|
continue;
|
|
TRACE("cube", m_int_solver->display_column(tout, j););
|
|
impq flv = impq(floor(v));
|
|
auto del = flv - v; // del is negative
|
|
if (del < -impq(mpq(1, 2))) {
|
|
del = impq(one_of_type<mpq>()) + del;
|
|
v = impq(ceil(v));
|
|
}
|
|
else {
|
|
v = flv;
|
|
}
|
|
m_incorrect_columns.insert(j);
|
|
TRACE("cube", tout << "new val = " << v << " column: " << j << "\n";);
|
|
}
|
|
if (!m_incorrect_columns.empty()) {
|
|
fix_terms_with_rounded_columns();
|
|
m_incorrect_columns.reset();
|
|
}
|
|
}
|
|
|
|
void lar_solver::fix_terms_with_rounded_columns() {
|
|
|
|
for (unsigned i = 0; i < m_terms.size(); i++) {
|
|
if (!term_is_used_as_row(i))
|
|
continue;
|
|
bool need_to_fix = false;
|
|
const lar_term& t = *m_terms[i];
|
|
for (lar_term::ival p : t) {
|
|
if (m_incorrect_columns.contains(p.column())) {
|
|
need_to_fix = true;
|
|
break;
|
|
}
|
|
}
|
|
if (need_to_fix) {
|
|
lpvar j = m_var_register.external_to_local(tv::mask_term(i));
|
|
impq v = t.apply(m_mpq_lar_core_solver.m_r_x);
|
|
m_mpq_lar_core_solver.m_r_solver.update_x(j, v);
|
|
}
|
|
}
|
|
|
|
SASSERT(ax_is_correct());
|
|
}
|
|
|
|
// 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 (lar_term::ival c : t) {
|
|
const auto& x = m_mpq_lar_core_solver.m_r_x[c.column()];
|
|
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(tv const& t, mpq& rs, u_dependency*& ci, bool& upper_bound) const {
|
|
lp_assert(t.is_term());
|
|
unsigned j;
|
|
bool is_int;
|
|
if (!m_var_register.external_is_used(t.index(), j, is_int))
|
|
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& term = get_term(t);
|
|
if (has_upper_bound(j, ci, b, is_strict) && !is_strict) {
|
|
lp_assert(b.is_int());
|
|
if (!sum_first_coords(term, 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(term, 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::register_normalized_term(const lar_term& t, lpvar j) {
|
|
mpq a;
|
|
lar_term normalized_t = t.get_normalized_by_min_var(a);
|
|
TRACE("lar_solver_terms", tout << "t="; print_term_as_indices(t, tout);
|
|
tout << ", normalized_t="; print_term_as_indices(normalized_t, tout) << "\n";);
|
|
if (m_normalized_terms_to_columns.find(normalized_t) == m_normalized_terms_to_columns.end()) {
|
|
m_normalized_terms_to_columns[normalized_t] = std::make_pair(a, j);
|
|
}
|
|
else {
|
|
TRACE("lar_solver_terms", tout << "the term has been seen already\n";);
|
|
}
|
|
}
|
|
|
|
void lar_solver::deregister_normalized_term(const lar_term& t) {
|
|
TRACE("lar_solver_terms", tout << "deregister term ";
|
|
print_term_as_indices(t, tout) << "\n";);
|
|
mpq a;
|
|
lar_term normalized_t = t.get_normalized_by_min_var(a);
|
|
m_normalized_terms_to_columns.erase(normalized_t);
|
|
}
|
|
|
|
void lar_solver::register_existing_terms() {
|
|
if (!m_need_register_terms) {
|
|
TRACE("nla_solver", tout << "registering " << m_terms.size() << " terms\n";);
|
|
for (unsigned k = 0; k < m_terms.size(); k++) {
|
|
lpvar j = m_var_register.external_to_local(tv::mask_term(k));
|
|
register_normalized_term(*m_terms[k], j);
|
|
}
|
|
}
|
|
m_need_register_terms = true;
|
|
}
|
|
// a_j.first gives the normalised coefficient,
|
|
// a_j.second givis the column
|
|
bool lar_solver::fetch_normalized_term_column(const lar_term& c, std::pair<mpq, lpvar>& a_j) const {
|
|
TRACE("lar_solver_terms", tout << "looking for term ";
|
|
print_term_as_indices(c, tout) << "\n";);
|
|
lp_assert(c.is_normalized());
|
|
auto it = m_normalized_terms_to_columns.find(c);
|
|
if (it != m_normalized_terms_to_columns.end()) {
|
|
TRACE("lar_solver_terms", tout << "got " << it->second << "\n";);
|
|
a_j = it->second;
|
|
return true;
|
|
}
|
|
TRACE("lar_solver_terms", tout << "have not found\n";);
|
|
return false;
|
|
}
|
|
|
|
std::pair<constraint_index, constraint_index> lar_solver::add_equality(lpvar j, lpvar k) {
|
|
vector<std::pair<mpq, var_index>> coeffs;
|
|
if (tv::is_term(j))
|
|
j = map_term_index_to_column_index(j);
|
|
|
|
if (tv::is_term(k))
|
|
k = map_term_index_to_column_index(k);
|
|
|
|
coeffs.push_back(std::make_pair(mpq(1), j));
|
|
coeffs.push_back(std::make_pair(mpq(-1), k));
|
|
unsigned term_index = add_term(coeffs, UINT_MAX); // UINT_MAX is the external null var
|
|
|
|
if (get_column_value(j) != get_column_value(k))
|
|
set_status(lp_status::UNKNOWN);
|
|
|
|
return std::pair<constraint_index, constraint_index>(
|
|
add_var_bound(term_index, lconstraint_kind::LE, mpq(0)),
|
|
add_var_bound(term_index, lconstraint_kind::GE, mpq(0)));
|
|
}
|
|
|
|
bool lar_solver::inside_bounds(lpvar j, const impq& val) const {
|
|
if (column_has_upper_bound(j) && val > get_upper_bound(j))
|
|
return false;
|
|
if (column_has_lower_bound(j) && val < get_lower_bound(j))
|
|
return false;
|
|
return true;
|
|
}
|
|
// If lower_bound is true than the new asserted upper bound is less than the existing lower bound.
|
|
// Otherwise the new asserted lower bound is is greater than the existing upper bound.
|
|
// dep is the reason for the new bound
|
|
|
|
void lar_solver::set_crossed_bounds_column_and_deps(unsigned j, bool lower_bound, u_dependency* dep) {
|
|
if (m_crossed_bounds_column != null_lpvar) return; // already set
|
|
SASSERT(m_crossed_bounds_deps == nullptr);
|
|
set_status(lp_status::INFEASIBLE);
|
|
m_crossed_bounds_column = j;
|
|
const auto& ul = this->m_columns_to_ul_pairs()[j];
|
|
u_dependency* bdep = lower_bound? ul.lower_bound_witness() : ul.upper_bound_witness();
|
|
SASSERT(bdep != nullptr);
|
|
m_crossed_bounds_deps = m_dependencies.mk_join(bdep, dep);
|
|
insert_to_columns_with_changed_bounds(j);
|
|
}
|
|
|
|
void lar_solver::collect_more_rows_for_lp_propagation(){
|
|
for (auto j : m_columns_with_changed_bounds)
|
|
detect_rows_with_changed_bounds_for_column(j);
|
|
}
|
|
|
|
|
|
} // namespace lp
|
|
|
|
|