mirror of
https://github.com/Z3Prover/z3
synced 2025-11-03 21:09:11 +00:00
debug dio
This commit is contained in:
Lev Nachmanson
Lev Nachmanson
parent
cd13890650
commit
df18885f97
5 changed files with 206 additions and 110 deletions
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@ -23,20 +23,16 @@ namespace lp {
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const mpq& c() const { return m_c; }
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mpq& c() { return m_c; }
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term_o():m_c(0) {}
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term_o& operator*=(mpq const& k) {
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for (auto & t : m_coeffs)
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t.m_value *= k;
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return *this;
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}
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void substitute(const term_o& t, unsigned term_column) {
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SASSERT(!t.contains(term_column));
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auto it = this->m_coeffs.find_core(term_column);
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if (it == nullptr) return;
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mpq a = it->get_data().m_value;
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this->m_coeffs.erase(term_column);
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const mpq& a = it->get_data().m_value;
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for (auto p : t) {
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this->add_monomial(a * p.coeff(), p.j());
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}
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this->c() += a * t.c();
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this->m_coeffs.erase(term_column);
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}
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};
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@ -114,39 +110,38 @@ namespace lp {
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imp(int_solver& lia, lar_solver& lra): lia(lia), lra(lra) {}
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void init() {
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unsigned n_of_rows = static_cast<unsigned>(lra.r_basis().size());
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unsigned n_of_rows = lra.A_r().row_count();
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unsigned skipped = 0;
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unsigned fn = 0;
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auto all_vars_are_int = [this](const auto& row) {
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for (const auto& p : row) {
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if (!lia.column_is_int(p.var())) {
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return false;
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}
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}
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return true;
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};
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for (unsigned i = 0; i < n_of_rows; i++) {
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auto & row = lra.get_row(i);
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if (!all_vars_are_int(row)) continue;
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const auto lcm = get_denominators_lcm(row);
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term_o t;
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bool all_vars_are_int = true;
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for (const auto & p : row) {
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if (!lia.column_is_int(p.var())){
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all_vars_are_int = false;
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break;
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}
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for (const auto & p: row)
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if (lia.is_fixed(p.var()))
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t.c() += lia.lower_bound(p.var()).x;
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else
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t.add_monomial(lcm * p.coeff(), p.var());
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t.j() = i; //highjack this field to point to the original tableau row, TODO - is it used?
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TRACE("dioph_eq", tout << "row = ";
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lra.print_row(row, tout) << std::endl;
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tout << "t:"; print_term_o(t, tout) << std::endl;);
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}
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if (all_vars_are_int) {
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term_o t;
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const auto lcm = get_denominators_lcm(row);
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for (const auto & p: row)
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if (lia.is_fixed(p.var()))
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t.c() += lia.lower_bound(p.var()).x;
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else
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t.add_monomial(lcm * p.coeff(), p.var());
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t.j() = i; //hijach this field to point to the original tableau row
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unsigned lvar = static_cast<unsigned>(m_f.size());
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lar_term lt = lar_term(lvar);
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eprime_pair pair = {t, lt};
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m_eprime.push_back(pair);
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m_f.push_back(lvar);
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}
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unsigned lvar = static_cast<unsigned>(m_f.size());
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lar_term lt = lar_term(lvar);
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eprime_pair pair = {t, lt};
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m_eprime.push_back(pair);
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m_f.push_back(lvar);
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}
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}
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@ -169,9 +164,9 @@ namespace lp {
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}
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if (g.is_one())
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return true;
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TRACE("dioph_eq", tout << "g:" << g << std::endl;);
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mpq new_c = ep.m_e.c() / g;
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if (new_c.is_int() == false) {
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// conlict: todo - collect the conflict
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TRACE("dioph_eq",
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print_term_o(ep.m_e, tout << "conflict m_e:") << std::endl;
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tout << "g:" << g << std::endl;
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@ -192,6 +187,10 @@ namespace lp {
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}
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ep.m_e.c() = new_c;
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ep.m_l *= (1/g);
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TRACE("dioph_eq",
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tout << "ep_m_e:"; print_term_o(ep.m_e, tout) << std::endl;
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tout << "ep.ml:";
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print_lar_term_L(ep.m_l, tout ) << std::endl;);
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}
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return true;
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@ -221,14 +220,14 @@ namespace lp {
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}
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void substitute_var_on_f(unsigned k, int k_sign, const term_o& k_subst, const lar_term& l_term) {
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TRACE("dioph_eq", print_term_o(k_subst, tout<< k<< "->") << std::endl;);
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TRACE("dioph_eq", print_term_o(k_subst, tout<< "x" << k<< " -> ") << std::endl;);
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for (unsigned e_index: m_f) {
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term_o& e = m_eprime[e_index].m_e;
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if (!e.contains(k)) continue;
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const mpq& k_coeff = e.get_coeff(k);
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TRACE("dioph_eq", print_term_o(e, tout << "before:") << std::endl;
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tout << "k_coeff:" << k_coeff << std::endl;);
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m_eprime[e_index].m_l = k_sign*k_coeff*l_term + lar_term(e_index); // m_l is set to k_sign*e + e_sub
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m_eprime[e_index].m_l += mpq(k_sign)*k_coeff*l_term;
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e.substitute(k_subst, k);
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TRACE("dioph_eq", print_term_o(e, tout << "after :") << std::endl;
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print_lar_term_L(m_eprime[e_index].m_l, tout) << std::endl;);
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@ -261,10 +260,56 @@ namespace lp {
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if (p.j() == k) continue;
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t.add_monomial(-k_sign*p.coeff(), p.j());
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}
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t.c() = eh.c();
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t.c() = -k_sign*eh.c();
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TRACE("dioph_eq", tout << "subst_term:"; print_term_o(t, tout) << std::endl;);
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return t;
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}
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void eliminate_var(eprime_pair& e_pair, unsigned k, int k_sign) {
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term_o t = get_term_to_subst(e_pair.m_e, k, k_sign);
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substitute_var_on_f(k, k_sign, t, e_pair.m_l) ;
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}
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void fresh_var_step(eprime_pair & e_pair, mpq& ahk, unsigned k) {
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// step 7 from the paper
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auto & eh = e_pair.m_e;
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// xt is the fresh variable
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unsigned xt = m_last_fresh_x_var--;
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TRACE("dioph_eq", tout << "introduce fresh xt:" << "~x"<< fresh_index(xt) << std::endl;
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tout << "eh:"; print_term_o(eh,tout) << std::endl;);
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/* Let eh = sum (a_i*x_i) + c = 0.
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For each i != k, let a_i = a_qi*ahk + a_ri, and let c = c_q * ahk + c_r
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eh = ahk * (x_k + sum {a_qi*x_i) + c_q | i != k }) + sum {a_ri*x_i | i != k} + c_r = 0
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x_t = x_k + sum {a_qi*x_i) + c_q | i != k }, it will be xt_term
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Then x_k -> - sum {a_qi*x_i) + c_q | i != k } + x_t, it will be subs_k
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eh = ahk*x_t + ...
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*/
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term_o xt_term;
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term_o k_subs;
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mpq r, q = machine_div_rem(eh.c(), ahk, r);
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xt_term.add_var(k);
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xt_term.c() = q;
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xt_term.add_monomial(mpq(-1), xt);
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k_subs.add_var(xt);
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k_subs.c() = - q;
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for (const auto & p: eh) {
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if (p.j() == k) continue;
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q = machine_div_rem(p.coeff(), ahk, r);
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xt_term.add_monomial(q, p.j());
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k_subs.add_monomial(-q, p.j());
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}
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TRACE("dioph_eq", tout << "xt_term:"; print_term_o(xt_term, tout) << std::endl;
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tout << "k_subs:"; print_term_o(k_subs, tout) << std::endl;);
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eprime_pair x_t_entry = {xt_term, lar_term()}; // 0 for m_l field
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m_eprime.push_back(x_t_entry);
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substitute_var_on_f(k, 1, k_subs, e_pair.m_l);
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// the term to eliminate the fresh variable
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term_o xt_subs = xt_term.clone();
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xt_subs.add_monomial(mpq(1), xt);
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TRACE("dioph_eq", tout << "xt_subs: x~"<< fresh_index(xt) << " -> "; print_term_o(xt_subs, tout) << std::endl;);
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m_sigma.insert(xt, xt_subs);
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}
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// this is the step 6 or 7 of the algorithm
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void rewrite_eqs() {
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auto eh_it = pick_eh();
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@ -273,61 +318,19 @@ namespace lp {
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print_term_o(m_eprime[*eh_it].m_e, tout << "\tm_e:") << "," << std::endl;
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print_lar_term_L(m_eprime[*eh_it].m_l, tout<< "\tm_l:") << "\n}"<< std::endl;);
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term_o& eh = m_eprime[*eh_it].m_e;
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term_o& eh = eprime_entry.m_e;
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auto [ahk, k, k_sign] = find_minimal_abs_coeff(eh);
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TRACE("dioph_eq", tout << "ahk:" << ahk << ", k:" << k << ", k_sign:" << k_sign << std::endl;);
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if (ahk.is_one()) {
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// step 6
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m_s.push_back(*eh_it);
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m_f.erase(eh_it);
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term_o t = get_term_to_subst(eh, k, k_sign);
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m_sigma.insert(k, t);
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substitute_var_on_f(k, k_sign, t, eprime_entry.m_l) ;
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eliminate_var(eprime_entry, k , k_sign);
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} else {
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// step 7
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// the fresh variable
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unsigned xt = m_last_fresh_x_var--; // xt is a fresh variable
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ahk *= k_sign; // get the original value of ahk
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TRACE("dioph_eq", tout << "introduce fresh xt:" << "~x"<< UINT_MAX -xt << std::endl;
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tout << "eh:"; print_term_o(eh,tout) << std::endl;);
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/* Let eh = sum (a_i*x_i) + c = 0.
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For each i != k, let a_i = a_qi*ahk + a_ri, and let c = c_q * ahk + c_r
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eh = ahk * (x_k + sum {a_qi*x_i) + c_q | i != k }) + sum {a_ri*x_i | i != k} + c_r = 0
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x_t = x_k + sum {a_qi*x_i) + c_q | i != k }, it will be x_t_term
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Then x_k -> - sum {a_qi*x_i) + c_q | i != k } + x_t, it will be subs_k
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eh = ahk*x_t + ...
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*/
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term_o x_t_term;
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term_o k_subs;
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mpq c_r;
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mpq c_q = machine_div_rem(eh.c(), ahk, c_r);
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x_t_term.add_var(k);
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x_t_term.c() = c_q;
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x_t_term.add_monomial(mpq(-1), xt);
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k_subs.add_var(xt);
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k_subs.c() = - c_q;
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for (const auto & p: eh) {
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mpq a_q, a_r;
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if (p.j() == k) continue;
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a_q = machine_div_rem(p.coeff(), ahk, a_r);
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x_t_term.add_monomial(a_q, p.j());
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k_subs.add_monomial(-a_q, p.j());
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}
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TRACE("dioph_eq", tout << "x_t_term:"; print_term_o(x_t_term, tout) << std::endl;
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tout << "k_subs:"; print_term_o(k_subs, tout) << std::endl;);
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eprime_pair x_t_entry = {x_t_term, lar_term()}; // 0 for m_l field
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m_eprime.push_back(x_t_entry);
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substitute_var_on_f(k, 1, k_subs, eprime_entry.m_l);
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term_o x_t_subs = x_t_term.clone();
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x_t_subs.add_monomial(mpq(1), xt);
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TRACE("dioph_eq", tout << "x_t_subs:"; print_term_o(x_t_subs, tout) << std::endl;);
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m_sigma.insert(xt, x_t_subs);
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ahk *= k_sign; // restore the original coefficient
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fresh_var_step(eprime_entry, ahk, k);
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}
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}
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void explain(lp::explanation& ex) {
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SASSERT(ex.empty());
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auto & ep = m_eprime[m_conflict_index];
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@ -342,28 +345,40 @@ namespace lp {
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}
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TRACE("dioph_eq", lra.print_expl(tout, ex););
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}
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unsigned fresh_index(unsigned j) const {return UINT_MAX - j;}
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struct fresh_lt {
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bool operator()(unsigned v1, unsigned v2) const { return v1 > v2; }
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};
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typedef heap<fresh_lt> fresh_queue;
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void remove_fresh_variables(term_o& t) {
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std::set<unsigned> seen_fresh_vars;
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fresh_queue q(fresh_index(m_last_fresh_x_var)+1);
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std::set<unsigned> processed;
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for (auto p : t) {
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auto j = p.j();
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if (is_fresh_var(j))
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seen_fresh_vars.insert(j);
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if (is_fresh_var(j)) {
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q.insert(fresh_index(j));
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processed.insert(j);
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}
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}
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CTRACE("dioph_eq_sub_terms", seen_fresh_vars.empty() == false, print_term_o(t, tout)<< std::endl);
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while (!seen_fresh_vars.empty()) {
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unsigned j = *seen_fresh_vars.begin();
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seen_fresh_vars.erase(j);
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const term_o& ot = m_sigma.find(j);
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TRACE("dioph_eq_sub_terms", tout << "ot:"; print_term_o(ot, tout) << std::endl;);
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for (auto p : ot)
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if (is_fresh_var(p.j()))
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seen_fresh_vars.insert(p.j());
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t.substitute(ot, j);
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TRACE("dioph_eq_sub_terms", tout << "ot:"; print_term_o(ot, tout) << std::endl;
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tout << "after sub:";print_term_o(t, tout) << std::endl;);
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CTRACE("dioph_eq_fresh", q.empty() == false, print_term_o(t, tout)<< std::endl);
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while (!q.empty()) {
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unsigned j = q.erase_min();
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j = fresh_index(j);
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const term_o& sub_t = m_sigma.find(j);
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TRACE("dioph_eq_fresh", tout << "x~" << fresh_index(j) << "; sub_t:"; print_term_o(sub_t, tout) << std::endl;);
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t.substitute(sub_t, j);
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TRACE("dioph_eq_fresh", tout << "sub_t:"; print_term_o(sub_t, tout) << std::endl;
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tout << "after sub:";print_term_o(t, tout) << std::endl;);
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for (auto p : sub_t)
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if (is_fresh_var(p.j())) {
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if (processed.find(p.j()) != processed.end()) continue;
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q.insert(fresh_index(p.j()));
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processed.insert(j);
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}
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}
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}
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bool is_fresh_var(unsigned j) const {
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return j > lra.column_count();
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}
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@ -379,6 +394,7 @@ namespace lp {
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lia_move dioph_eq::check() {
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return m_imp->check();
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}
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void dioph_eq::explain(lp::explanation& ex) {
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m_imp->explain(ex);
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}
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@ -228,9 +228,9 @@ namespace lp {
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return lia_move::undef;
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++m_number_of_calls;
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if (r == lia_move::undef) r = patch_basic_columns();
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if (r == lia_move::undef && should_find_cube()) r = int_cube(lia)();
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if (r == lia_move::undef && should_solve_dioph_eq()) r = solve_dioph_eq();
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// if (r == lia_move::undef) r = patch_basic_columns();
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// if (r == lia_move::undef && should_find_cube()) r = int_cube(lia)();
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if (r == lia_move::undef && (true||should_solve_dioph_eq())) r = solve_dioph_eq();
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if (r == lia_move::undef) lra.move_non_basic_columns_to_bounds();
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if (r == lia_move::undef && should_hnf_cut()) r = hnf_cut();
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@ -879,6 +879,7 @@ namespace lp {
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bool int_solver::is_upper() const { return m_imp->m_upper; }
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bool& int_solver::is_upper() { return m_imp->m_upper; }
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explanation* int_solver::expl() { return m_imp->m_ex; }
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void int_solver::set_expl(lp::explanation * ex) { m_imp->m_ex = ex; }
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bool int_solver::column_is_int_inf(unsigned j) const {
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return m_imp->column_is_int_inf(j);
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}
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@ -895,5 +896,7 @@ namespace lp {
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bool int_solver::current_solution_is_inf_on_cut() const { return m_imp->current_solution_is_inf_on_cut(); }
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const impq & int_solver::lower_bound(unsigned j) const { return m_imp->lower_bound(j);}
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const impq & int_solver::upper_bound(unsigned j) const { return m_imp->upper_bound(j);}
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#if Z3DEBUG
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lia_move int_solver::dio_test() {return m_imp->solve_dioph_eq();}
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#endif
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}
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@ -93,6 +93,10 @@ public:
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bool is_term(unsigned j) const;
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unsigned column_count() const;
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int select_int_infeasible_var();
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void set_expl(lp::explanation * ex);
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explanation * expl();
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#if Z3DEBUG
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||||
lia_move dio_test();
|
||||
#endif
|
||||
};
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||||
}
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||||
|
|
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|||
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|
@ -171,12 +171,19 @@ public:
|
|||
|
||||
|
||||
friend lar_term operator*(const mpq& k, const lar_term& term) {
|
||||
lar_term result;
|
||||
for (const auto& p : term) {
|
||||
result.add_monomial(p.coeff()*k, p.j());
|
||||
}
|
||||
return result;
|
||||
lar_term r;
|
||||
for (const auto& p : term) {
|
||||
r.add_monomial(p.coeff()*k, p.j());
|
||||
}
|
||||
return r;
|
||||
}
|
||||
|
||||
lar_term& operator+=(const lar_term& a) {
|
||||
for (const auto& p : a) {
|
||||
add_monomial(p.coeff(), p.j());
|
||||
}
|
||||
return *this;
|
||||
}
|
||||
|
||||
lar_term& operator*=(mpq const& k) {
|
||||
for (auto & t : m_coeffs)
|
||||
|
|
|
|||
|
|
@ -491,6 +491,7 @@ void setup_args_parser(argument_parser &parser) {
|
|||
"-nla_blnt_fm",
|
||||
"test_basic_lemma_for_mon_neutral_from_factors_to_monomial");
|
||||
parser.add_option_with_help_string("-hnf", "test hermite normal form");
|
||||
parser.add_option_with_help_string("-dio", "dioph equalities");
|
||||
parser.add_option_with_help_string("-gomory", "gomory");
|
||||
parser.add_option_with_help_string("-intd", "test integer_domain");
|
||||
parser.add_option_with_help_string("-xyz_sample",
|
||||
|
|
@ -1605,6 +1606,7 @@ void test_larger_generated_hnf() {
|
|||
std::cout << "test_larger_generated_rank_hnf passed" << std::endl;
|
||||
}
|
||||
#endif
|
||||
|
||||
void test_maximize_term() {
|
||||
std::cout << "test_maximize_term\n";
|
||||
lar_solver solver;
|
||||
|
|
@ -1646,6 +1648,64 @@ void test_maximize_term() {
|
|||
std::cout << "v[" << p.first << "] = " << p.second << std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
void test_dio() {
|
||||
std::cout << "test dio\n";
|
||||
lar_solver solver;
|
||||
int_solver i_solver(solver);
|
||||
lp::explanation exp;
|
||||
i_solver.set_expl(&exp);
|
||||
unsigned _x1 = 0;
|
||||
unsigned _x2 = 1;
|
||||
unsigned _x3 = 2;
|
||||
unsigned _fx_7 = 3;
|
||||
unsigned _fx_17 = 4;
|
||||
/*
|
||||
3x1 + 3x2 + 14x3 − 7 = 0
|
||||
7x1 + 12x2 + 31x3 − 17 = 0
|
||||
*/
|
||||
lpvar x1 = solver.add_var(_x1, true);
|
||||
lpvar x2 = solver.add_var(_x2, true);
|
||||
lpvar x3 = solver.add_var(_x3, true);
|
||||
lpvar fx_7 = solver.add_var(_fx_7, true);
|
||||
lpvar fx_17 = solver.add_var(_fx_17, true);
|
||||
vector<std::pair<mpq, lpvar>> term_ls;
|
||||
/* 3x1 + 3x2 + 14x3 − 7 */
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(3), x1));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(3), x2));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(14), x3));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(-1), fx_7));
|
||||
for (auto & p: term_ls) {
|
||||
p.first = -p.first;
|
||||
}
|
||||
unsigned t0 = solver.add_term(term_ls, 10);
|
||||
term_ls.clear();
|
||||
/* 7x1 + 12x2 + 31x3 − 17 = 0*/
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(7), x1));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(12), x2));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(31), x3));
|
||||
term_ls.push_back(std::pair<mpq, lpvar>(mpq(-1), fx_17));
|
||||
|
||||
for (auto & p: term_ls) {
|
||||
p.first = -p.first;
|
||||
}
|
||||
unsigned t1 = solver.add_term(term_ls, 11);
|
||||
|
||||
solver.add_var_bound(fx_7, LE, mpq(-7));
|
||||
solver.add_var_bound(fx_7, GE, mpq(-7));
|
||||
solver.add_var_bound(fx_17, LE, mpq(-17));
|
||||
solver.add_var_bound(fx_17, GE, mpq(-17));
|
||||
solver.add_var_bound(t0, LE, mpq(0));
|
||||
solver.add_var_bound(t0, GE, mpq(0));
|
||||
solver.add_var_bound(t1, LE, mpq(0));
|
||||
solver.add_var_bound(t1, GE, mpq(0));
|
||||
// solver.find_feasible_solution();
|
||||
//lp_assert(solver.get_status() == lp_status::OPTIMAL);
|
||||
enable_trace("dioph_eq");
|
||||
enable_trace("dioph_eq_fresh");
|
||||
auto r = i_solver.dio_test();
|
||||
|
||||
}
|
||||
#ifdef Z3DEBUG
|
||||
void test_hnf() {
|
||||
test_larger_generated_hnf();
|
||||
|
|
@ -1782,6 +1842,12 @@ void test_lp_local(int argn, char **argv) {
|
|||
return finalize(0);
|
||||
}
|
||||
|
||||
if (args_parser.option_is_used("-dio")) {
|
||||
test_dio();
|
||||
return finalize(0);
|
||||
}
|
||||
|
||||
|
||||
if (args_parser.option_is_used("-gomory")) {
|
||||
test_gomory_cut();
|
||||
return finalize(0);
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue