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https://github.com/Z3Prover/z3
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split nla_grobner to separate file
This commit is contained in:
Nikolaj Bjorner
parent
7d0c789af0
commit
b81f70f6fc
4 changed files with 398 additions and 363 deletions
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@ -34,6 +34,7 @@ z3_add_component(lp
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nla_basics_lemmas.cpp
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nla_common.cpp
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nla_core.cpp
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nla_grobner.cpp
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nla_intervals.cpp
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nla_monotone_lemmas.cpp
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nla_order_lemmas.cpp
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@ -1636,362 +1636,6 @@ std::ostream& core::print_term( const lp::lar_term& t, std::ostream& out) const
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}
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void core::run_grobner() {
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unsigned& quota = m_nla_settings.grobner_quota;
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if (quota == 1) {
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return;
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}
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clear_and_resize_active_var_set();
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find_nl_cluster();
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lp_settings().stats().m_grobner_calls++;
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configure_grobner();
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m_pdd_grobner.saturate();
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bool conflict = false;
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unsigned n = m_pdd_grobner.number_of_conflicts_to_report();
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SASSERT(n > 0);
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for (auto eq : m_pdd_grobner.equations()) {
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if (check_pdd_eq(eq)) {
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conflict = true;
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if (--n == 0)
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break;
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}
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}
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TRACE("grobner", m_pdd_grobner.display(tout));
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if (conflict) {
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IF_VERBOSE(2, verbose_stream() << "grobner conflict\n");
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return;
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}
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#if 0
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vector<dd::pdd> eqs;
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for (auto eq : m_pdd_grobner.equations())
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eqs.push_back(eq->poly());
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m_nra.check(eqs);
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#endif
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#if 0
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bool propagated = false;
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for (auto eq : m_pdd_grobner.equations()) {
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auto const& p = eq->poly();
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if (p.is_offset()) {
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lpvar v = p.var();
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if (m_lar_solver.column_has_lower_bound(v) &&
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m_lar_solver.column_has_upper_bound(v))
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continue;
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rational fixed_val = -p.lo().val();
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lp::explanation ex;
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u_dependency_manager dm;
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vector<unsigned, false> lv;
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dm.linearize(eq->dep(), lv);
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for (unsigned ci : lv)
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ex.push_back(ci);
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new_lemma lemma(*this, "pdd-eq");
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lemma &= ex;
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lemma |= ineq(v, llc::EQ, fixed_val);
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propagated = true;
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}
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}
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if (propagated)
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return;
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#endif
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if (quota > 1)
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quota--;
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IF_VERBOSE(2, verbose_stream() << "grobner miss, quota " << quota << "\n");
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IF_VERBOSE(4, diagnose_pdd_miss(verbose_stream()));
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}
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void core::configure_grobner() {
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m_pdd_grobner.reset();
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try {
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set_level2var_for_grobner();
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TRACE("grobner",
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tout << "base vars: ";
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for (lpvar j : active_var_set())
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if (m_lar_solver.is_base(j))
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tout << "j" << j << " ";
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tout << "\n");
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for (lpvar j : active_var_set()) {
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if (m_lar_solver.is_base(j))
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add_row_to_grobner(m_lar_solver.basic2row(j));
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if (is_monic_var(j) && var_is_fixed(j)) {
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u_dependency* dep = nullptr;
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dd::pdd r = m_pdd_manager.mk_val(rational(1));
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for (lpvar k : emons()[j].vars())
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r *= pdd_expr(rational::one(), k, dep);
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r -= val_of_fixed_var_with_deps(j, dep);
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add_eq_to_grobner(r, dep);
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}
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}
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}
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catch (...) {
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IF_VERBOSE(2, verbose_stream() << "pdd throw\n");
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return;
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}
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TRACE("grobner", m_pdd_grobner.display(tout));
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#if 0
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IF_VERBOSE(2, m_pdd_grobner.display(verbose_stream()));
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dd::pdd_eval eval(m_pdd_manager);
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eval.var2val() = [&](unsigned j){ return val(j); };
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for (auto* e : m_pdd_grobner.equations()) {
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dd::pdd p = e->poly();
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rational v = eval(p);
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if (p.is_linear() && !eval(p).is_zero()) {
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IF_VERBOSE(0, verbose_stream() << "violated linear constraint " << p << "\n");
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}
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}
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#endif
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struct dd::solver::config cfg;
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cfg.m_max_steps = m_pdd_grobner.equations().size();
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cfg.m_max_simplified = m_nla_settings.grobner_max_simplified;
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cfg.m_eqs_growth = m_nla_settings.grobner_eqs_growth;
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cfg.m_expr_size_growth = m_nla_settings.grobner_expr_size_growth;
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cfg.m_expr_degree_growth = m_nla_settings.grobner_expr_degree_growth;
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cfg.m_number_of_conflicts_to_report = m_nla_settings.grobner_number_of_conflicts_to_report;
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m_pdd_grobner.set(cfg);
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m_pdd_grobner.adjust_cfg();
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m_pdd_manager.set_max_num_nodes(10000); // or something proportional to the number of initial nodes.
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}
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std::ostream& core::diagnose_pdd_miss(std::ostream& out) {
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// m_pdd_grobner.display(out);
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dd::pdd_eval eval;
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eval.var2val() = [&](unsigned j){ return val(j); };
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for (auto* e : m_pdd_grobner.equations()) {
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dd::pdd p = e->poly();
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rational v = eval(p);
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if (!v.is_zero()) {
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out << p << " := " << v << "\n";
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}
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}
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for (unsigned j = 0; j < m_lar_solver.number_of_vars(); ++j) {
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if (m_lar_solver.column_has_lower_bound(j) || m_lar_solver.column_has_upper_bound(j)) {
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out << j << ": [";
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if (m_lar_solver.column_has_lower_bound(j)) out << m_lar_solver.get_lower_bound(j);
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out << "..";
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if (m_lar_solver.column_has_upper_bound(j)) out << m_lar_solver.get_upper_bound(j);
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out << "]\n";
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}
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}
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return out;
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}
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bool core::check_pdd_eq(const dd::solver::equation* e) {
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auto& di = m_intervals.get_dep_intervals();
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dd::pdd_interval eval(di);
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eval.var2interval() = [this](lpvar j, bool deps, scoped_dep_interval& a) {
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if (deps) m_intervals.set_var_interval<dd::w_dep::with_deps>(j, a);
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else m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
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};
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scoped_dep_interval i(di), i_wd(di);
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eval.get_interval<dd::w_dep::without_deps>(e->poly(), i);
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if (!di.separated_from_zero(i)) {
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TRACE("grobner", m_pdd_grobner.display(tout << "not separated from 0 ", *e) << "\n";
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eval.get_interval_distributed<dd::w_dep::without_deps>(e->poly(), i);
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tout << "separated from 0: " << di.separated_from_zero(i) << "\n";
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for (auto j : e->poly().free_vars()) {
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scoped_dep_interval a(di);
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m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
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m_intervals.display(tout << "j" << j << " ", a); tout << " ";
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}
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tout << "\n");
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return false;
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}
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eval.get_interval<dd::w_dep::with_deps>(e->poly(), i_wd);
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std::function<void (const lp::explanation&)> f = [this](const lp::explanation& e) {
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new_lemma lemma(*this, "pdd");
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lemma &= e;
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};
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if (di.check_interval_for_conflict_on_zero(i_wd, e->dep(), f)) {
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TRACE("grobner", m_pdd_grobner.display(tout << "conflict ", *e) << "\n");
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lp_settings().stats().m_grobner_conflicts++;
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return true;
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}
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else {
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TRACE("grobner", m_pdd_grobner.display(tout << "no conflict ", *e) << "\n");
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return false;
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}
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}
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void core::add_var_and_its_factors_to_q_and_collect_new_rows(lpvar j, svector<lpvar> & q) {
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if (active_var_set_contains(j))
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return;
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insert_to_active_var_set(j);
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if (is_monic_var(j)) {
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const monic& m = emons()[j];
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for (auto fcn : factorization_factory_imp(m, *this))
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for (const factor& fc: fcn)
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q.push_back(var(fc));
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}
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if (var_is_fixed(j))
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return;
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const auto& matrix = m_lar_solver.A_r();
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for (auto & s : matrix.m_columns[j]) {
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unsigned row = s.var();
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if (m_rows.contains(row))
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continue;
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m_rows.insert(row);
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unsigned k = m_lar_solver.get_base_column_in_row(row);
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if (m_lar_solver.column_is_free(k) && k != j)
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continue;
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CTRACE("grobner", matrix.m_rows[row].size() > m_nla_settings.grobner_row_length_limit,
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tout << "ignore the row " << row << " with the size " << matrix.m_rows[row].size() << "\n";);
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if (matrix.m_rows[row].size() > m_nla_settings.grobner_row_length_limit)
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continue;
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for (auto& rc : matrix.m_rows[row])
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add_var_and_its_factors_to_q_and_collect_new_rows(rc.var(), q);
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}
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}
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const rational& core::val_of_fixed_var_with_deps(lpvar j, u_dependency*& dep) {
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unsigned lc, uc;
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m_lar_solver.get_bound_constraint_witnesses_for_column(j, lc, uc);
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dep = m_intervals.mk_join(dep, m_intervals.mk_leaf(lc));
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dep = m_intervals.mk_join(dep, m_intervals.mk_leaf(uc));
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return m_lar_solver.column_lower_bound(j).x;
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}
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dd::pdd core::pdd_expr(const rational& c, lpvar j, u_dependency*& dep) {
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dd::pdd r = m_pdd_manager.mk_val(c);
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sbuffer<lpvar> vars;
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vars.push_back(j);
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u_dependency* zero_dep = dep;
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while (!vars.empty()) {
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j = vars.back();
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vars.pop_back();
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if (m_nla_settings.grobner_subs_fixed > 0 && var_is_fixed_to_zero(j)) {
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r = m_pdd_manager.mk_val(val_of_fixed_var_with_deps(j, zero_dep));
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dep = zero_dep;
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return r;
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}
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if (m_nla_settings.grobner_subs_fixed == 1 && var_is_fixed(j))
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r *= val_of_fixed_var_with_deps(j, dep);
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else if (!is_monic_var(j))
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r *= m_pdd_manager.mk_var(j);
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else
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for (lpvar k : emons()[j].vars())
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vars.push_back(k);
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}
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return r;
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}
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/**
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\brief convert p == 0 into a solved form v == r, such that
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v has bounds [lo, oo) iff r has bounds [lo', oo)
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v has bounds (oo,hi] iff r has bounds (oo,hi']
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The solved form allows the Grobner solver identify more bounds conflicts.
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A bad leading term can miss bounds conflicts.
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For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
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we prefer to solve z == -x - y instead of x == -z - y
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because the solution -z - y has neither an upper, nor a lower bound.
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*/
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bool core::is_solved(dd::pdd const& p, unsigned& v, dd::pdd& r) {
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if (!p.is_linear())
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return false;
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r = p;
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unsigned num_lo = 0, num_hi = 0;
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unsigned lo = 0, hi = 0;
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rational lc, hc, c;
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while (!r.is_val()) {
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SASSERT(r.hi().is_val());
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v = r.var();
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rational val = r.hi().val();
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switch (m_lar_solver.get_column_type(v)) {
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case lp::column_type::lower_bound:
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if (val > 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
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break;
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case lp::column_type::upper_bound:
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if (val < 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
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break;
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case lp::column_type::fixed:
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case lp::column_type::boxed:
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break;
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default:
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return false;
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}
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if (num_lo > 1 && num_hi > 1)
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return false;
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r = r.lo();
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}
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if (num_lo == 1 && num_hi > 1) {
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v = lo;
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c = lc;
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}
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else if (num_hi == 1 && num_lo > 1) {
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v = hi;
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c = hc;
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}
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else
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return false;
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r = c*m_pdd_manager.mk_var(v) - p;
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if (c != 1)
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r = r * (1/c);
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return true;
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}
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/**
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\brief add an equality to grobner solver, convert it to solved form if available.
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*/
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void core::add_eq_to_grobner(dd::pdd& p, u_dependency* dep) {
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unsigned v;
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dd::pdd q(m_pdd_manager);
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m_pdd_grobner.simplify(p, dep);
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if (is_solved(p, v, q))
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m_pdd_grobner.add_subst(v, q, dep);
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else
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m_pdd_grobner.add(p, dep);
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}
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void core::add_row_to_grobner(const vector<lp::row_cell<rational>> & row) {
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u_dependency *dep = nullptr;
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rational val;
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dd::pdd sum = m_pdd_manager.mk_val(rational(0));
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for (const auto &p : row)
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sum += pdd_expr(p.coeff(), p.var(), dep);
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TRACE("grobner", print_row(row, tout) << " " << sum << "\n");
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add_eq_to_grobner(sum, dep);
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}
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void core::find_nl_cluster() {
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prepare_rows_and_active_vars();
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svector<lpvar> q;
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TRACE("grobner", for (lpvar j : m_to_refine) print_monic(emons()[j], tout) << "\n";);
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for (lpvar j : m_to_refine)
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q.push_back(j);
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while (!q.empty()) {
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lpvar j = q.back();
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q.pop_back();
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add_var_and_its_factors_to_q_and_collect_new_rows(j, q);
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}
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TRACE("grobner", tout << "vars in cluster: ";
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for (lpvar j : active_var_set()) tout << "j" << j << " "; tout << "\n";
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display_matrix_of_m_rows(tout);
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);
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}
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void core::prepare_rows_and_active_vars() {
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m_rows.clear();
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m_rows.resize(m_lar_solver.row_count());
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clear_and_resize_active_var_set();
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}
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std::unordered_set<lpvar> core::get_vars_of_expr_with_opening_terms(const nex *e ) {
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@ -2016,13 +1660,6 @@ std::unordered_set<lpvar> core::get_vars_of_expr_with_opening_terms(const nex *e
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return ret;
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}
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void core::display_matrix_of_m_rows(std::ostream & out) const {
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const auto& matrix = m_lar_solver.A_r();
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out << m_rows.size() << " rows" << "\n";
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out << "the matrix\n";
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for (const auto & r : matrix.m_rows)
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print_row(r, out) << std::endl;
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}
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void core::set_active_vars_weights(nex_creator& nc) {
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nc.set_number_of_vars(m_lar_solver.column_count());
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@ -458,6 +458,8 @@ public:
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}
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return lp::print_linear_combination_customized(v, [this](lpvar j) { return var_str(j); }, out);
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}
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void run_grobner();
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void find_nl_cluster();
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void prepare_rows_and_active_vars();
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@ -467,6 +469,7 @@ public:
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void set_active_vars_weights(nex_creator&);
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unsigned get_var_weight(lpvar) const;
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void add_row_to_grobner(const vector<lp::row_cell<rational>> & row);
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void add_fixed_monic_to_grobner(unsigned j);
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bool is_solved(dd::pdd const& p, unsigned& v, dd::pdd& r);
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void add_eq_to_grobner(dd::pdd& p, u_dependency* dep);
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bool check_pdd_eq(const dd::solver::equation*);
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@ -476,6 +479,7 @@ public:
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void configure_grobner();
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bool influences_nl_var(lpvar) const;
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bool is_nl_var(lpvar) const;
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bool is_used_in_monic(lpvar) const;
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void patch_monomials();
|
||||
void patch_monomials_on_to_refine();
|
||||
|
|
|
|||
393
src/math/lp/nla_grobner.cpp
Normal file
393
src/math/lp/nla_grobner.cpp
Normal file
|
|
@ -0,0 +1,393 @@
|
|||
/*++
|
||||
Copyright (c) 2017 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
nla_grobner.cpp
|
||||
|
||||
Author:
|
||||
Lev Nachmanson (levnach)
|
||||
Nikolaj Bjorner (nbjorner)
|
||||
|
||||
--*/
|
||||
#include "util/uint_set.h"
|
||||
#include "math/lp/nla_core.h"
|
||||
#include "math/lp/factorization_factory_imp.h"
|
||||
#include "math/lp/nex.h"
|
||||
#include "math/grobner/pdd_solver.h"
|
||||
#include "math/dd/pdd_interval.h"
|
||||
#include "math/dd/pdd_eval.h"
|
||||
|
||||
namespace nla {
|
||||
|
||||
void core::run_grobner() {
|
||||
unsigned& quota = m_nla_settings.grobner_quota;
|
||||
if (quota == 1) {
|
||||
return;
|
||||
}
|
||||
clear_and_resize_active_var_set();
|
||||
find_nl_cluster();
|
||||
|
||||
lp_settings().stats().m_grobner_calls++;
|
||||
configure_grobner();
|
||||
m_pdd_grobner.saturate();
|
||||
bool conflict = false;
|
||||
unsigned n = m_pdd_grobner.number_of_conflicts_to_report();
|
||||
SASSERT(n > 0);
|
||||
for (auto eq : m_pdd_grobner.equations()) {
|
||||
if (check_pdd_eq(eq)) {
|
||||
conflict = true;
|
||||
if (--n == 0)
|
||||
break;
|
||||
}
|
||||
}
|
||||
TRACE("grobner", m_pdd_grobner.display(tout));
|
||||
if (conflict) {
|
||||
IF_VERBOSE(2, verbose_stream() << "grobner conflict\n");
|
||||
return;
|
||||
}
|
||||
|
||||
#if 0
|
||||
// diagnostics: did we miss something
|
||||
vector<dd::pdd> eqs;
|
||||
for (auto eq : m_pdd_grobner.equations())
|
||||
eqs.push_back(eq->poly());
|
||||
m_nra.check(eqs);
|
||||
#endif
|
||||
|
||||
#if 0
|
||||
bool propagated = false;
|
||||
for (auto eq : m_pdd_grobner.equations()) {
|
||||
auto const& p = eq->poly();
|
||||
if (p.is_offset()) {
|
||||
lpvar v = p.var();
|
||||
if (m_lar_solver.column_has_lower_bound(v) &&
|
||||
m_lar_solver.column_has_upper_bound(v))
|
||||
continue;
|
||||
rational fixed_val = -p.lo().val();
|
||||
lp::explanation ex;
|
||||
u_dependency_manager dm;
|
||||
vector<unsigned, false> lv;
|
||||
dm.linearize(eq->dep(), lv);
|
||||
for (unsigned ci : lv)
|
||||
ex.push_back(ci);
|
||||
new_lemma lemma(*this, "pdd-eq");
|
||||
lemma &= ex;
|
||||
lemma |= ineq(v, llc::EQ, fixed_val);
|
||||
propagated = true;
|
||||
}
|
||||
}
|
||||
if (propagated)
|
||||
return;
|
||||
#endif
|
||||
|
||||
if (quota > 1)
|
||||
quota--;
|
||||
IF_VERBOSE(2, verbose_stream() << "grobner miss, quota " << quota << "\n");
|
||||
IF_VERBOSE(4, diagnose_pdd_miss(verbose_stream()));
|
||||
|
||||
}
|
||||
|
||||
void core::configure_grobner() {
|
||||
m_pdd_grobner.reset();
|
||||
try {
|
||||
set_level2var_for_grobner();
|
||||
TRACE("grobner",
|
||||
tout << "base vars: ";
|
||||
for (lpvar j : active_var_set())
|
||||
if (m_lar_solver.is_base(j))
|
||||
tout << "j" << j << " ";
|
||||
tout << "\n");
|
||||
for (lpvar j : active_var_set()) {
|
||||
if (m_lar_solver.is_base(j))
|
||||
add_row_to_grobner(m_lar_solver.basic2row(j));
|
||||
|
||||
if (is_monic_var(j) && var_is_fixed(j))
|
||||
add_fixed_monic_to_grobner(j);
|
||||
}
|
||||
}
|
||||
catch (...) {
|
||||
IF_VERBOSE(2, verbose_stream() << "pdd throw\n");
|
||||
return;
|
||||
}
|
||||
TRACE("grobner", m_pdd_grobner.display(tout));
|
||||
|
||||
#if 0
|
||||
IF_VERBOSE(2, m_pdd_grobner.display(verbose_stream()));
|
||||
dd::pdd_eval eval(m_pdd_manager);
|
||||
eval.var2val() = [&](unsigned j){ return val(j); };
|
||||
for (auto* e : m_pdd_grobner.equations()) {
|
||||
dd::pdd p = e->poly();
|
||||
rational v = eval(p);
|
||||
if (p.is_linear() && !eval(p).is_zero()) {
|
||||
IF_VERBOSE(0, verbose_stream() << "violated linear constraint " << p << "\n");
|
||||
}
|
||||
}
|
||||
#endif
|
||||
|
||||
struct dd::solver::config cfg;
|
||||
cfg.m_max_steps = m_pdd_grobner.equations().size();
|
||||
cfg.m_max_simplified = m_nla_settings.grobner_max_simplified;
|
||||
cfg.m_eqs_growth = m_nla_settings.grobner_eqs_growth;
|
||||
cfg.m_expr_size_growth = m_nla_settings.grobner_expr_size_growth;
|
||||
cfg.m_expr_degree_growth = m_nla_settings.grobner_expr_degree_growth;
|
||||
cfg.m_number_of_conflicts_to_report = m_nla_settings.grobner_number_of_conflicts_to_report;
|
||||
m_pdd_grobner.set(cfg);
|
||||
m_pdd_grobner.adjust_cfg();
|
||||
m_pdd_manager.set_max_num_nodes(10000); // or something proportional to the number of initial nodes.
|
||||
}
|
||||
|
||||
std::ostream& core::diagnose_pdd_miss(std::ostream& out) {
|
||||
|
||||
// m_pdd_grobner.display(out);
|
||||
|
||||
dd::pdd_eval eval;
|
||||
eval.var2val() = [&](unsigned j){ return val(j); };
|
||||
for (auto* e : m_pdd_grobner.equations()) {
|
||||
dd::pdd p = e->poly();
|
||||
rational v = eval(p);
|
||||
if (!v.is_zero()) {
|
||||
out << p << " := " << v << "\n";
|
||||
}
|
||||
}
|
||||
|
||||
for (unsigned j = 0; j < m_lar_solver.number_of_vars(); ++j) {
|
||||
if (m_lar_solver.column_has_lower_bound(j) || m_lar_solver.column_has_upper_bound(j)) {
|
||||
out << j << ": [";
|
||||
if (m_lar_solver.column_has_lower_bound(j)) out << m_lar_solver.get_lower_bound(j);
|
||||
out << "..";
|
||||
if (m_lar_solver.column_has_upper_bound(j)) out << m_lar_solver.get_upper_bound(j);
|
||||
out << "]\n";
|
||||
}
|
||||
}
|
||||
return out;
|
||||
}
|
||||
|
||||
bool core::check_pdd_eq(const dd::solver::equation* e) {
|
||||
auto& di = m_intervals.get_dep_intervals();
|
||||
dd::pdd_interval eval(di);
|
||||
eval.var2interval() = [this](lpvar j, bool deps, scoped_dep_interval& a) {
|
||||
if (deps) m_intervals.set_var_interval<dd::w_dep::with_deps>(j, a);
|
||||
else m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
|
||||
};
|
||||
scoped_dep_interval i(di), i_wd(di);
|
||||
eval.get_interval<dd::w_dep::without_deps>(e->poly(), i);
|
||||
if (!di.separated_from_zero(i)) {
|
||||
TRACE("grobner", m_pdd_grobner.display(tout << "not separated from 0 ", *e) << "\n";
|
||||
eval.get_interval_distributed<dd::w_dep::without_deps>(e->poly(), i);
|
||||
tout << "separated from 0: " << di.separated_from_zero(i) << "\n";
|
||||
for (auto j : e->poly().free_vars()) {
|
||||
scoped_dep_interval a(di);
|
||||
m_intervals.set_var_interval<dd::w_dep::without_deps>(j, a);
|
||||
m_intervals.display(tout << "j" << j << " ", a); tout << " ";
|
||||
}
|
||||
tout << "\n");
|
||||
|
||||
return false;
|
||||
}
|
||||
eval.get_interval<dd::w_dep::with_deps>(e->poly(), i_wd);
|
||||
std::function<void (const lp::explanation&)> f = [this](const lp::explanation& e) {
|
||||
new_lemma lemma(*this, "pdd");
|
||||
lemma &= e;
|
||||
};
|
||||
if (di.check_interval_for_conflict_on_zero(i_wd, e->dep(), f)) {
|
||||
TRACE("grobner", m_pdd_grobner.display(tout << "conflict ", *e) << "\n");
|
||||
lp_settings().stats().m_grobner_conflicts++;
|
||||
return true;
|
||||
}
|
||||
else {
|
||||
TRACE("grobner", m_pdd_grobner.display(tout << "no conflict ", *e) << "\n");
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
void core::add_var_and_its_factors_to_q_and_collect_new_rows(lpvar j, svector<lpvar> & q) {
|
||||
if (active_var_set_contains(j))
|
||||
return;
|
||||
insert_to_active_var_set(j);
|
||||
if (is_monic_var(j)) {
|
||||
const monic& m = emons()[j];
|
||||
for (auto fcn : factorization_factory_imp(m, *this))
|
||||
for (const factor& fc: fcn)
|
||||
q.push_back(var(fc));
|
||||
}
|
||||
|
||||
if (var_is_fixed(j))
|
||||
return;
|
||||
const auto& matrix = m_lar_solver.A_r();
|
||||
for (auto & s : matrix.m_columns[j]) {
|
||||
unsigned row = s.var();
|
||||
if (m_rows.contains(row))
|
||||
continue;
|
||||
m_rows.insert(row);
|
||||
unsigned k = m_lar_solver.get_base_column_in_row(row);
|
||||
if (m_lar_solver.column_is_free(k) && k != j)
|
||||
continue;
|
||||
CTRACE("grobner", matrix.m_rows[row].size() > m_nla_settings.grobner_row_length_limit,
|
||||
tout << "ignore the row " << row << " with the size " << matrix.m_rows[row].size() << "\n";);
|
||||
if (matrix.m_rows[row].size() > m_nla_settings.grobner_row_length_limit)
|
||||
continue;
|
||||
for (auto& rc : matrix.m_rows[row])
|
||||
add_var_and_its_factors_to_q_and_collect_new_rows(rc.var(), q);
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
|
||||
const rational& core::val_of_fixed_var_with_deps(lpvar j, u_dependency*& dep) {
|
||||
unsigned lc, uc;
|
||||
m_lar_solver.get_bound_constraint_witnesses_for_column(j, lc, uc);
|
||||
dep = m_intervals.mk_join(dep, m_intervals.mk_leaf(lc));
|
||||
dep = m_intervals.mk_join(dep, m_intervals.mk_leaf(uc));
|
||||
return m_lar_solver.column_lower_bound(j).x;
|
||||
}
|
||||
|
||||
dd::pdd core::pdd_expr(const rational& c, lpvar j, u_dependency*& dep) {
|
||||
dd::pdd r = m_pdd_manager.mk_val(c);
|
||||
sbuffer<lpvar> vars;
|
||||
vars.push_back(j);
|
||||
u_dependency* zero_dep = dep;
|
||||
while (!vars.empty()) {
|
||||
j = vars.back();
|
||||
vars.pop_back();
|
||||
if (m_nla_settings.grobner_subs_fixed > 0 && var_is_fixed_to_zero(j)) {
|
||||
r = m_pdd_manager.mk_val(val_of_fixed_var_with_deps(j, zero_dep));
|
||||
dep = zero_dep;
|
||||
return r;
|
||||
}
|
||||
if (m_nla_settings.grobner_subs_fixed == 1 && var_is_fixed(j))
|
||||
r *= val_of_fixed_var_with_deps(j, dep);
|
||||
else if (!is_monic_var(j))
|
||||
r *= m_pdd_manager.mk_var(j);
|
||||
else
|
||||
for (lpvar k : emons()[j].vars())
|
||||
vars.push_back(k);
|
||||
}
|
||||
return r;
|
||||
}
|
||||
|
||||
/**
|
||||
\brief convert p == 0 into a solved form v == r, such that
|
||||
v has bounds [lo, oo) iff r has bounds [lo', oo)
|
||||
v has bounds (oo,hi] iff r has bounds (oo,hi']
|
||||
|
||||
The solved form allows the Grobner solver identify more bounds conflicts.
|
||||
A bad leading term can miss bounds conflicts.
|
||||
For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
|
||||
we prefer to solve z == -x - y instead of x == -z - y
|
||||
because the solution -z - y has neither an upper, nor a lower bound.
|
||||
*/
|
||||
bool core::is_solved(dd::pdd const& p, unsigned& v, dd::pdd& r) {
|
||||
if (!p.is_linear())
|
||||
return false;
|
||||
r = p;
|
||||
unsigned num_lo = 0, num_hi = 0;
|
||||
unsigned lo = 0, hi = 0;
|
||||
rational lc, hc, c;
|
||||
while (!r.is_val()) {
|
||||
SASSERT(r.hi().is_val());
|
||||
v = r.var();
|
||||
rational val = r.hi().val();
|
||||
switch (m_lar_solver.get_column_type(v)) {
|
||||
case lp::column_type::lower_bound:
|
||||
if (val > 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
|
||||
break;
|
||||
case lp::column_type::upper_bound:
|
||||
if (val < 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
|
||||
break;
|
||||
case lp::column_type::fixed:
|
||||
case lp::column_type::boxed:
|
||||
break;
|
||||
default:
|
||||
return false;
|
||||
}
|
||||
if (num_lo > 1 && num_hi > 1)
|
||||
return false;
|
||||
r = r.lo();
|
||||
}
|
||||
if (num_lo == 1 && num_hi > 1) {
|
||||
v = lo;
|
||||
c = lc;
|
||||
}
|
||||
else if (num_hi == 1 && num_lo > 1) {
|
||||
v = hi;
|
||||
c = hc;
|
||||
}
|
||||
else
|
||||
return false;
|
||||
|
||||
r = c*m_pdd_manager.mk_var(v) - p;
|
||||
if (c != 1)
|
||||
r = r * (1/c);
|
||||
return true;
|
||||
}
|
||||
|
||||
/**
|
||||
\brief add an equality to grobner solver, convert it to solved form if available.
|
||||
*/
|
||||
void core::add_eq_to_grobner(dd::pdd& p, u_dependency* dep) {
|
||||
unsigned v;
|
||||
dd::pdd q(m_pdd_manager);
|
||||
m_pdd_grobner.simplify(p, dep);
|
||||
if (is_solved(p, v, q))
|
||||
m_pdd_grobner.add_subst(v, q, dep);
|
||||
else
|
||||
m_pdd_grobner.add(p, dep);
|
||||
}
|
||||
|
||||
void core::add_fixed_monic_to_grobner(unsigned j) {
|
||||
u_dependency* dep = nullptr;
|
||||
dd::pdd r = m_pdd_manager.mk_val(rational(1));
|
||||
for (lpvar k : emons()[j].vars())
|
||||
r *= pdd_expr(rational::one(), k, dep);
|
||||
r -= val_of_fixed_var_with_deps(j, dep);
|
||||
add_eq_to_grobner(r, dep);
|
||||
}
|
||||
|
||||
void core::add_row_to_grobner(const vector<lp::row_cell<rational>> & row) {
|
||||
u_dependency *dep = nullptr;
|
||||
rational val;
|
||||
dd::pdd sum = m_pdd_manager.mk_val(rational(0));
|
||||
for (const auto &p : row)
|
||||
sum += pdd_expr(p.coeff(), p.var(), dep);
|
||||
TRACE("grobner", print_row(row, tout) << " " << sum << "\n");
|
||||
add_eq_to_grobner(sum, dep);
|
||||
}
|
||||
|
||||
|
||||
void core::find_nl_cluster() {
|
||||
prepare_rows_and_active_vars();
|
||||
svector<lpvar> q;
|
||||
TRACE("grobner", for (lpvar j : m_to_refine) print_monic(emons()[j], tout) << "\n";);
|
||||
|
||||
for (lpvar j : m_to_refine)
|
||||
q.push_back(j);
|
||||
|
||||
while (!q.empty()) {
|
||||
lpvar j = q.back();
|
||||
q.pop_back();
|
||||
add_var_and_its_factors_to_q_and_collect_new_rows(j, q);
|
||||
}
|
||||
TRACE("grobner", tout << "vars in cluster: ";
|
||||
for (lpvar j : active_var_set()) tout << "j" << j << " "; tout << "\n";
|
||||
display_matrix_of_m_rows(tout);
|
||||
);
|
||||
}
|
||||
|
||||
void core::prepare_rows_and_active_vars() {
|
||||
m_rows.clear();
|
||||
m_rows.resize(m_lar_solver.row_count());
|
||||
clear_and_resize_active_var_set();
|
||||
}
|
||||
|
||||
|
||||
void core::display_matrix_of_m_rows(std::ostream & out) const {
|
||||
const auto& matrix = m_lar_solver.A_r();
|
||||
out << m_rows.size() << " rows" << "\n";
|
||||
out << "the matrix\n";
|
||||
for (const auto & r : matrix.m_rows)
|
||||
print_row(r, out) << std::endl;
|
||||
}
|
||||
|
||||
|
||||
}
|
||||
Loading…
Add table
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Reference in a new issue