diff --git a/src/util/lp/init_lar_solver.cpp b/src/util/lp/init_lar_solver.cpp index 5efa24a48..58486e6ba 100644 --- a/src/util/lp/init_lar_solver.cpp +++ b/src/util/lp/init_lar_solver.cpp @@ -95,7 +95,6 @@ void lar_solver::add_new_var_to_core_fields_for_mpq(bool register_in_basis) { var_index lar_solver::add_term_undecided(const vector> & coeffs, const mpq &m_v) { m_terms.push_back(new lar_term(coeffs, m_v)); - m_orig_terms.push_back(new lar_term(coeffs, m_v)); return m_terms_start_index + m_terms.size() - 1; } @@ -106,11 +105,10 @@ var_index lar_solver::add_term(const vector> & coeffs, return add_term_undecided(coeffs, m_v); m_terms.push_back(new lar_term(coeffs, m_v)); - m_orig_terms.push_back(new lar_term(coeffs, m_v)); unsigned adjusted_term_index = m_terms.size() - 1; var_index ret = m_terms_start_index + adjusted_term_index; if (use_tableau() && !coeffs.empty()) { - add_row_for_term(m_orig_terms.back(), ret); + add_row_for_term(m_terms.back(), ret); if (m_settings.bound_propagation()) m_rows_with_changed_bounds.insert(A_r().row_count() - 1); } @@ -196,15 +194,36 @@ void lar_solver::add_var_bound_on_constraint_for_term(var_index j, lconstraint_k auto it = m_ext_vars_to_columns.find(j); if (it != m_ext_vars_to_columns.end()) { unsigned term_j = it->second.ext_j(); - mpq rs = right_side - m_orig_terms[adjusted_term_index]->m_v; - m_constraints.push_back(new lar_term_constraint(m_orig_terms[adjusted_term_index], kind, right_side)); + mpq rs = right_side - m_terms[adjusted_term_index]->m_v; + m_constraints.push_back(new lar_term_constraint(m_terms[adjusted_term_index], kind, right_side)); update_column_type_and_bound(term_j, kind, rs, ci); } else { - add_constraint_from_term_and_create_new_column_row(j, m_orig_terms[adjusted_term_index], kind, right_side); + add_constraint_from_term_and_create_new_column_row(j, m_terms[adjusted_term_index], kind, right_side); } } +constraint_index lar_solver::add_constraint(const vector>& left_side_with_terms, lconstraint_kind kind_par, const mpq& right_side_parm) { + this->print_linear_combination_of_column_indices(left_side_with_terms, std::cout); + std::cout << std::endl; + vector> left_side; + mpq rs = - right_side_parm; + std::cout << "before rs = " << rs << std::endl; + substitute_terms_in_linear_expression(left_side_with_terms, left_side, rs); + std::cout << "after rs = " << rs << std::endl; + + this->print_linear_combination_of_column_indices(left_side, std::cout); + std::cout << std::endl; + + unsigned term_index = add_term(left_side, zero_of_type()); + constraint_index ci = m_constraints.size(); + add_var_bound_on_constraint_for_term(term_index, kind_par, -rs, ci); + std::cout << "constraint = "; + print_constraint(ci, std::cout); + std::cout << std::endl; + + return ci; +} void lar_solver::add_constraint_from_term_and_create_new_column_row(unsigned term_j, const lar_term* term, lconstraint_kind kind, const mpq & right_side) { diff --git a/src/util/lp/lar_solver.cpp b/src/util/lp/lar_solver.cpp index 594abae46..78b71ecfd 100644 --- a/src/util/lp/lar_solver.cpp +++ b/src/util/lp/lar_solver.cpp @@ -13,1388 +13,1377 @@ const lar_base_constraint& lar_solver::get_constraint(unsigned ci) const { return *(m_constraints[ci]); } - ////////////////// methods //////////////////////////////// - static_matrix> & lar_solver::A_r() { return m_mpq_lar_core_solver.m_r_A;} - static_matrix> const & lar_solver::A_r() const { return m_mpq_lar_core_solver.m_r_A;} - static_matrix & lar_solver::A_d() { return m_mpq_lar_core_solver.m_d_A;} - static_matrix const & lar_solver::A_d() const { return m_mpq_lar_core_solver.m_d_A;} +////////////////// methods //////////////////////////////// +static_matrix> & lar_solver::A_r() { return m_mpq_lar_core_solver.m_r_A;} +static_matrix> const & lar_solver::A_r() const { return m_mpq_lar_core_solver.m_r_A;} +static_matrix & lar_solver::A_d() { return m_mpq_lar_core_solver.m_d_A;} +static_matrix const & lar_solver::A_d() const { return m_mpq_lar_core_solver.m_d_A;} - lp_settings & lar_solver::settings() { return m_settings;} +lp_settings & lar_solver::settings() { return m_settings;} - lp_settings const & lar_solver::settings() const { return m_settings;} +lp_settings const & lar_solver::settings() const { return m_settings;} - void clear() {lean_assert(false); // not implemented - } - - - lar_solver::lar_solver() : m_status(OPTIMAL), - m_infeasible_column_index(-1), - m_terms_start_index(1000000), - m_column_type_function ([this] (unsigned j) {return m_mpq_lar_core_solver.m_column_types()[j];}), - m_mpq_lar_core_solver(m_settings, *this) - {} - - void lar_solver::set_propagate_bounds_on_pivoted_rows_mode(bool v) { - m_mpq_lar_core_solver.m_r_solver.m_pivoted_rows = v? (& m_rows_with_changed_bounds) : nullptr; - } - - lar_solver::~lar_solver(){ - for (auto c : m_constraints) - delete c; - for (auto t : m_terms) - delete t; - for (auto t : m_orig_terms) - delete t; - } - - numeric_pair const& lar_solver::get_value(var_index vi) const { return m_mpq_lar_core_solver.m_r_x[vi]; } - - bool lar_solver::is_term(var_index j) const { - return j >= m_terms_start_index && j - m_terms_start_index < m_terms.size(); - } - - unsigned lar_solver::adjust_term_index(unsigned j) const { - lean_assert(is_term(j)); - return j - m_terms_start_index; - } - - - bool lar_solver::use_lu() const { return m_settings.simplex_strategy() == simplex_strategy_enum::lu; } - - bool lar_solver::sizes_are_correct() const { - lean_assert(strategy_is_undecided() || !m_mpq_lar_core_solver.need_to_presolve_with_double_solver() || A_r().column_count() == A_d().column_count()); - lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size()); - lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size()); - lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_x.size()); - return true; - } - - - void lar_solver::print_implied_bound(const implied_bound& be, std::ostream & out) const { - out << "implied bound\n"; - unsigned v = be.m_j; - if (is_term(v)) { - out << "it is a term number " << be.m_j << std::endl; - print_term(*m_orig_terms[be.m_j - m_terms_start_index], out); - } - else { - out << get_column_name(v); - } - out << " " << lconstraint_kind_string(be.kind()) << " " << be.m_bound << std::endl; - // for (auto & p : be.m_explanation) { - // out << p.first << " : "; - // print_constraint(p.second, out); - // } - - // m_mpq_lar_core_solver.m_r_solver.print_column_info(be.m_j< m_terms_start_index? be.m_j : adjust_term_index(be.m_j), out); - out << "end of implied bound" << std::endl; - } - - bool lar_solver::implied_bound_is_correctly_explained(implied_bound const & be, const vector> & explanation) const { - std::unordered_map coeff_map; - auto rs_of_evidence = zero_of_type(); - unsigned n_of_G = 0, n_of_L = 0; - bool strict = false; - for (auto & it : explanation) { - mpq coeff = it.first; - constraint_index con_ind = it.second; - const auto & constr = *m_constraints[con_ind]; - lconstraint_kind kind = coeff.is_pos() ? constr.m_kind : flip_kind(constr.m_kind); - register_in_map(coeff_map, constr, coeff); - if (kind == GT || kind == LT) - strict = true; - if (kind == GE || kind == GT) n_of_G++; - else if (kind == LE || kind == LT) n_of_L++; - rs_of_evidence += coeff*constr.m_right_side; - } - lean_assert(n_of_G == 0 || n_of_L == 0); - lconstraint_kind kind = n_of_G ? GE : (n_of_L ? LE : EQ); - if (strict) - kind = static_cast((static_cast(kind) / 2)); - - if (!is_term(be.m_j)) { - if (coeff_map.size() != 1) - return false; - auto it = coeff_map.find(be.m_j); - if (it == coeff_map.end()) return false; - mpq ratio = it->second; - if (ratio < zero_of_type()) { - kind = static_cast(-kind); - } - rs_of_evidence /= ratio; - } else { - const lar_term * t = m_orig_terms[adjust_term_index(be.m_j)]; - const auto first_coeff = *t->m_coeffs.begin(); - unsigned j = first_coeff.first; - auto it = coeff_map.find(j); - if (it == coeff_map.end()) - return false; - mpq ratio = it->second / first_coeff.second; - for (auto & p : t->m_coeffs) { - it = coeff_map.find(p.first); - if (it == coeff_map.end()) - return false; - if (p.second * ratio != it->second) - return false; - } - if (ratio < zero_of_type()) { - kind = static_cast(-kind); - } - rs_of_evidence /= ratio; - rs_of_evidence += t->m_v * ratio; - } - - return kind == be.kind() && rs_of_evidence == be.m_bound; - } - - - void lar_solver::analyze_new_bounds_on_row( - unsigned row_index, - bound_propagator & bp) { - lean_assert(!use_tableau()); - iterator_on_pivot_row it(m_mpq_lar_core_solver.get_pivot_row(), m_mpq_lar_core_solver.m_r_basis[row_index]); - - bound_analyzer_on_row ra_pos(it, - zero_of_type>(), - row_index, - bp - ); - ra_pos.analyze(); - } - - void lar_solver::analyze_new_bounds_on_row_tableau( - unsigned row_index, - bound_propagator & bp - ) { - - if (A_r().m_rows[row_index].size() > settings().max_row_length_for_bound_propagation) - return; - iterator_on_row it(A_r().m_rows[row_index]); - lean_assert(use_tableau()); - bound_analyzer_on_row::analyze_row(it, - zero_of_type>(), - row_index, - bp - ); - } - - - void lar_solver::substitute_basis_var_in_terms_for_row(unsigned i) { - // todo : create a map from term basic vars to the rows where they are used - unsigned basis_j = m_mpq_lar_core_solver.m_r_solver.m_basis[i]; - for (unsigned k = 0; k < m_terms.size(); k++) { - if (term_is_used_as_row(k)) - continue; - if (!m_terms[k]->contains(basis_j)) - continue; - m_terms[k]->subst(basis_j, m_mpq_lar_core_solver.m_r_solver.m_pivot_row); - } - } - - void lar_solver::calculate_implied_bounds_for_row(unsigned i, bound_propagator & bp) { - if(use_tableau()) { - analyze_new_bounds_on_row_tableau(i, bp); - } else { - m_mpq_lar_core_solver.calculate_pivot_row(i); - substitute_basis_var_in_terms_for_row(i); - analyze_new_bounds_on_row(i, bp); - } - } - - - linear_combination_iterator * lar_solver::create_new_iter_from_term(unsigned term_index) const { - lean_assert(false); // not implemented - return nullptr; - // new linear_combination_iterator_on_vector(m_terms[adjust_term_index(term_index)]->coeffs_as_vector()); - } - - unsigned lar_solver::adjust_column_index_to_term_index(unsigned j) const { - unsigned ext_var_or_term = m_columns_to_ext_vars_or_term_indices[j]; - return ext_var_or_term < m_terms_start_index ? j : ext_var_or_term; - } - - void lar_solver::propagate_bounds_on_a_term(const lar_term& t, bound_propagator & bp, unsigned term_offset) { - lean_assert(false); // not implemented - } - - - void lar_solver::explain_implied_bound(implied_bound & ib, bound_propagator & bp) { - unsigned i = ib.m_row_or_term_index; - int bound_sign = ib.m_is_low_bound? 1: -1; - int j_sign = (ib.m_coeff_before_j_is_pos ? 1 :-1) * bound_sign; - unsigned m_j = ib.m_j; - if (is_term(m_j)) { - auto it = m_ext_vars_to_columns.find(m_j); - lean_assert(it != m_ext_vars_to_columns.end()); - m_j = it->second.ext_j(); - } - for (auto const& r : A_r().m_rows[i]) { - unsigned j = r.m_j; - mpq const& a = r.get_val(); - if (j == m_j) continue; - if (is_term(j)) { - auto it = m_ext_vars_to_columns.find(j); - lean_assert(it != m_ext_vars_to_columns.end()); - j = it->second.ext_j(); - } - int a_sign = is_pos(a)? 1: -1; - int sign = j_sign * a_sign; - const ul_pair & ul = m_vars_to_ul_pairs[j]; - auto witness = sign > 0? ul.upper_bound_witness(): ul.low_bound_witness(); - lean_assert(is_valid(witness)); - bp.consume(a, witness); - } - // lean_assert(implied_bound_is_correctly_explained(ib, explanation)); - } - - - bool lar_solver::term_is_used_as_row(unsigned term) const { - lean_assert(is_term(term)); - return contains(m_ext_vars_to_columns, term); - } - - void lar_solver::propagate_bounds_on_terms(bound_propagator & bp) { - for (unsigned i = 0; i < m_terms.size(); i++) { - if (term_is_used_as_row(i + m_terms_start_index)) - continue; // this term is used a left side of a constraint, - // it was processed as a touched row if needed - propagate_bounds_on_a_term(*m_terms[i], bp, i); - } - } - - - // goes over touched rows and tries to induce bounds - void lar_solver::propagate_bounds_for_touched_rows(bound_propagator & bp) { - if (!use_tableau()) - return; // ! todo : enable bound propagaion here. The current bug is that after the pop - // the changed terms become incorrect! - - for (unsigned i : m_rows_with_changed_bounds.m_index) { - calculate_implied_bounds_for_row(i, bp); - } - m_rows_with_changed_bounds.clear(); - if (!use_tableau()) { - propagate_bounds_on_terms(bp); - } - } - - lp_status lar_solver::get_status() const { return m_status;} - - void lar_solver::set_status(lp_status s) {m_status = s;} - - lp_status lar_solver::find_feasible_solution() { - if (strategy_is_undecided()) - decide_on_strategy_and_adjust_initial_state(); - - m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = true; - return solve(); - } - - lp_status lar_solver::solve() { - if (m_status == INFEASIBLE) { - return m_status; - } - solve_with_core_solver(); - if (m_status != INFEASIBLE) { - if (m_settings.bound_propagation()) - detect_rows_with_changed_bounds(); - } - - m_columns_with_changed_bound.clear(); - return m_status; - } - - void lar_solver::fill_explanation_from_infeasible_column(vector> & evidence) const{ - - // this is the case when the lower bound is in conflict with the upper one - const ul_pair & ul = m_vars_to_ul_pairs[m_infeasible_column_index]; - evidence.push_back(std::make_pair(numeric_traits::one(), ul.upper_bound_witness())); - evidence.push_back(std::make_pair(-numeric_traits::one(), ul.low_bound_witness())); - } - - - unsigned lar_solver::get_total_iterations() const { return m_mpq_lar_core_solver.m_r_solver.total_iterations(); } - // see http://research.microsoft.com/projects/z3/smt07.pdf - // This method searches for a feasible solution with as many different values of variables, reverenced in vars, as it can find - // Attention, after a call to this method the non-basic variables don't necesserarly stick to their bounds anymore - vector lar_solver::get_list_of_all_var_indices() const { - vector ret; - for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_heading.size(); j++) - ret.push_back(j); - return ret; - } - void lar_solver::push() { - m_simplex_strategy = m_settings.simplex_strategy(); - m_simplex_strategy.push(); - m_status.push(); - m_vars_to_ul_pairs.push(); - m_infeasible_column_index.push(); - m_mpq_lar_core_solver.push(); - m_term_count = m_terms.size(); - m_term_count.push(); - m_constraint_count = m_constraints.size(); - m_constraint_count.push(); - } - - void lar_solver::clean_large_elements_after_pop(unsigned n, int_set& set) { - vector to_remove; - for (unsigned j: set.m_index) - if (j >= n) - to_remove.push_back(j); - for (unsigned j : to_remove) - set.erase(j); - } - - void lar_solver::shrink_inf_set_after_pop(unsigned n, int_set & set) { - clean_large_elements_after_pop(n, set); - set.resize(n); - } - - - void lar_solver::pop(unsigned k) { - int n_was = static_cast(m_ext_vars_to_columns.size()); - m_status.pop(k); - m_infeasible_column_index.pop(k); - unsigned n = m_vars_to_ul_pairs.peek_size(k); - for (unsigned j = n_was; j-- > n;) - m_ext_vars_to_columns.erase(m_columns_to_ext_vars_or_term_indices[j]); - m_columns_to_ext_vars_or_term_indices.resize(n); - if (m_settings.use_tableau()) { - pop_tableau(); - } - m_vars_to_ul_pairs.pop(k); - - m_mpq_lar_core_solver.pop(k); - clean_large_elements_after_pop(n, m_columns_with_changed_bound); - unsigned m = A_r().row_count(); - clean_large_elements_after_pop(m, m_rows_with_changed_bounds); - clean_inf_set_of_r_solver_after_pop(); - lean_assert(m_settings.simplex_strategy() == simplex_strategy_enum::undecided || - (!use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); - - - lean_assert(ax_is_correct()); - lean_assert(m_mpq_lar_core_solver.m_r_solver.inf_set_is_correct()); - m_constraint_count.pop(k); - for (unsigned i = m_constraint_count; i < m_constraints.size(); i++) - delete m_constraints[i]; - - m_constraints.resize(m_constraint_count); - m_term_count.pop(k); - for (unsigned i = m_term_count; i < m_terms.size(); i++) { - delete m_terms[i]; - delete m_orig_terms[i]; - } - m_terms.resize(m_term_count); - m_orig_terms.resize(m_term_count); - m_simplex_strategy.pop(k); - m_settings.simplex_strategy() = m_simplex_strategy; - lean_assert(sizes_are_correct()); - lean_assert((!m_settings.use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); - } - - vector lar_solver::get_all_constraint_indices() const { - vector ret; - constraint_index i = 0; - while ( i < m_constraints.size()) - ret.push_back(i++); - return ret; - } - - bool lar_solver::maximize_term_on_tableau(const vector> & term, - impq &term_max) { - if (settings().simplex_strategy() == simplex_strategy_enum::undecided) - decide_on_strategy_and_adjust_initial_state(); - - m_mpq_lar_core_solver.solve(); - if (m_mpq_lar_core_solver.m_r_solver.get_status() == UNBOUNDED) - return false; - - term_max = 0; - for (auto & p : term) - term_max += p.first * m_mpq_lar_core_solver.m_r_x[p.second]; - - return true; - } - - bool lar_solver::costs_are_zeros_for_r_solver() const { - for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_costs.size(); j++) { - lean_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_costs[j])); - } - return true; - } - bool lar_solver::reduced_costs_are_zeroes_for_r_solver() const { - for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_d.size(); j++) { - lean_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_d[j])); - } - return true; - } - - void lar_solver::set_costs_to_zero(const vector> & term) { - auto & rslv = m_mpq_lar_core_solver.m_r_solver; - auto & jset = m_mpq_lar_core_solver.m_r_solver.m_inf_set; // hijack this set that should be empty right now - lean_assert(jset.m_index.size()==0); - - for (auto & p : term) { - unsigned j = p.second; - rslv.m_costs[j] = zero_of_type(); - int i = rslv.m_basis_heading[j]; - if (i < 0) - jset.insert(j); - else { - for (auto & rc : A_r().m_rows[i]) - jset.insert(rc.m_j); - } - } - - for (unsigned j : jset.m_index) - rslv.m_d[j] = zero_of_type(); - - jset.clear(); - - lean_assert(reduced_costs_are_zeroes_for_r_solver()); - lean_assert(costs_are_zeros_for_r_solver()); - } - - void lar_solver::prepare_costs_for_r_solver(const vector> & term) { - - auto & rslv = m_mpq_lar_core_solver.m_r_solver; - rslv.m_using_infeas_costs = false; - lean_assert(costs_are_zeros_for_r_solver()); - lean_assert(reduced_costs_are_zeroes_for_r_solver()); - rslv.m_costs.resize(A_r().column_count(), zero_of_type()); - for (auto & p : term) { - unsigned j = p.second; - rslv.m_costs[j] = p.first; - if (rslv.m_basis_heading[j] < 0) - rslv.m_d[j] += p.first; - else - rslv.update_reduced_cost_for_basic_column_cost_change(- p.first, j); - } - lean_assert(rslv.reduced_costs_are_correct_tableau()); - } - - bool lar_solver::maximize_term_on_corrected_r_solver(const vector> & term, - impq &term_max) { - settings().backup_costs = false; - switch (settings().simplex_strategy()) { - case simplex_strategy_enum::tableau_rows: - prepare_costs_for_r_solver(term); - settings().simplex_strategy() = simplex_strategy_enum::tableau_costs; - { - bool ret = maximize_term_on_tableau(term, term_max); - settings().simplex_strategy() = simplex_strategy_enum::tableau_rows; - set_costs_to_zero(term); - m_mpq_lar_core_solver.m_r_solver.set_status(OPTIMAL); - return ret; - } - case simplex_strategy_enum::tableau_costs: - prepare_costs_for_r_solver(term); - { - bool ret = maximize_term_on_tableau(term, term_max); - set_costs_to_zero(term); - m_mpq_lar_core_solver.m_r_solver.set_status(OPTIMAL); - return ret; - } - - case simplex_strategy_enum::lu: - lean_assert(false); // not implemented - return false; - default: - lean_unreachable(); // wrong mode - } - return false; - } - // starting from a given feasible state look for the maximum of the term - // return true if found and false if unbounded - bool lar_solver::maximize_term(const vector> & term, - impq &term_max) { - lean_assert(m_mpq_lar_core_solver.m_r_solver.current_x_is_feasible()); - m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = false; - return maximize_term_on_corrected_r_solver(term, term_max); - } - - - - const lar_term & lar_solver::get_term(unsigned j) const { - lean_assert(j >= m_terms_start_index); - return *m_terms[j - m_terms_start_index]; - } - - void lar_solver::pop_core_solver_params() { - pop_core_solver_params(1); - } - - void lar_solver::pop_core_solver_params(unsigned k) { - A_r().pop(k); - A_d().pop(k); - } - - - void lar_solver::set_upper_bound_witness(var_index j, constraint_index ci) { - ul_pair ul = m_vars_to_ul_pairs[j]; - ul.upper_bound_witness() = ci; - m_vars_to_ul_pairs[j] = ul; - } - - void lar_solver::set_low_bound_witness(var_index j, constraint_index ci) { - ul_pair ul = m_vars_to_ul_pairs[j]; - ul.low_bound_witness() = ci; - m_vars_to_ul_pairs[j] = ul; - } - - - void lar_solver::substitute_terms(const mpq & mult, - const vector>& left_side_with_terms, - vector> &left_side, mpq & right_side) const { - for (auto & t : left_side_with_terms) { - if (t.second < m_terms_start_index) { - lean_assert(t.second < A_r().column_count()); - left_side.push_back(std::pair(mult * t.first, t.second)); - } else { - const lar_term & term = * m_terms[adjust_term_index(t.second)]; - substitute_terms(mult * t.first, left_side_with_terms, left_side, right_side); - right_side -= mult * term.m_v; - } - } - } - - - void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column(unsigned j) { - if (A_r().row_count() != m_column_buffer.data_size()) - m_column_buffer.resize(A_r().row_count()); - else - m_column_buffer.clear(); - lean_assert(m_column_buffer.size() == 0 && m_column_buffer.is_OK()); - - m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer); - for (unsigned i : m_column_buffer.m_index) - m_rows_with_changed_bounds.insert(i); - } - - - - void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column_tableau(unsigned j) { - for (auto & rc : m_mpq_lar_core_solver.m_r_A.m_columns[j]) - m_rows_with_changed_bounds.insert(rc.m_i); - } - - bool lar_solver::use_tableau() const { return m_settings.use_tableau(); } - - bool lar_solver::use_tableau_costs() const { - return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs; - } - - void lar_solver::detect_rows_of_column_with_bound_change(unsigned j) { - if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { // it is a basic column - // just mark the row at touched and exit - m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]); - return; - } - - if (use_tableau()) - detect_rows_of_bound_change_column_for_nbasic_column_tableau(j); - else - detect_rows_of_bound_change_column_for_nbasic_column(j); - } - - void lar_solver::adjust_x_of_column(unsigned j) { - lean_assert(false); - } - - bool lar_solver::row_is_correct(unsigned i) const { - numeric_pair r = zero_of_type>(); - for (const auto & c : A_r().m_rows[i]) - r += c.m_value * m_mpq_lar_core_solver.m_r_x[c.m_j]; - return is_zero(r); - } - - bool lar_solver::ax_is_correct() const { - for (unsigned i = 0; i < A_r().row_count(); i++) { - if (!row_is_correct(i)) - return false; - } - return true; - } - - bool lar_solver::tableau_with_costs() const { - return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs; - } - - bool lar_solver::costs_are_used() const { - return m_settings.simplex_strategy() != simplex_strategy_enum::tableau_rows; - } - - void lar_solver::change_basic_x_by_delta_on_column(unsigned j, const numeric_pair & delta) { - if (use_tableau()) { - for (const auto & c : A_r().m_columns[j]) { - unsigned bj = m_mpq_lar_core_solver.m_r_basis[c.m_i]; - m_mpq_lar_core_solver.m_r_x[bj] -= A_r().get_val(c) * delta; - if (tableau_with_costs()) { - m_basic_columns_with_changed_cost.insert(bj); - } - m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(bj); - } - } else { - m_column_buffer.clear(); - m_column_buffer.resize(A_r().row_count()); - m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer); - for (unsigned i : m_column_buffer.m_index) { - unsigned bj = m_mpq_lar_core_solver.m_r_basis[i]; - m_mpq_lar_core_solver.m_r_x[bj] -= m_column_buffer[i] * delta; - m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(bj); - } - } - } - - void lar_solver::update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j) { - if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { - if (costs_are_used()) { - bool was_infeas = m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j); - m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(j); - if (was_infeas != m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j)) - m_basic_columns_with_changed_cost.insert(j); - } else { - m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(j); - } - } else { - numeric_pair delta; - if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta)) - change_basic_x_by_delta_on_column(j, delta); - } - } - - - void lar_solver::detect_rows_with_changed_bounds_for_column(unsigned j) { - if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { - m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]); - return; - } - - if (use_tableau()) - detect_rows_of_bound_change_column_for_nbasic_column_tableau(j); - else - detect_rows_of_bound_change_column_for_nbasic_column(j); - } - - void lar_solver::detect_rows_with_changed_bounds() { - for (auto j : m_columns_with_changed_bound.m_index) - detect_rows_with_changed_bounds_for_column(j); - } - - void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds() { - for (auto j : m_columns_with_changed_bound.m_index) - update_x_and_inf_costs_for_column_with_changed_bounds(j); - } - - void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds_tableau() { - lean_assert(ax_is_correct()); - for (auto j : m_columns_with_changed_bound.m_index) - update_x_and_inf_costs_for_column_with_changed_bounds(j); - - if (tableau_with_costs()) { - for (unsigned j : m_basic_columns_with_changed_cost.m_index) - m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); - lean_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); - } - } - - - void lar_solver::solve_with_core_solver() { - if (!use_tableau()) - add_last_rows_to_lu(m_mpq_lar_core_solver.m_r_solver); - if (m_mpq_lar_core_solver.need_to_presolve_with_double_solver()) { - add_last_rows_to_lu(m_mpq_lar_core_solver.m_d_solver); - } - m_mpq_lar_core_solver.prefix_r(); - if (costs_are_used()) { - m_basic_columns_with_changed_cost.clear(); - m_basic_columns_with_changed_cost.resize(m_mpq_lar_core_solver.m_r_x.size()); - } - if (use_tableau()) - update_x_and_inf_costs_for_columns_with_changed_bounds_tableau(); - else - update_x_and_inf_costs_for_columns_with_changed_bounds(); - m_mpq_lar_core_solver.solve(); - set_status(m_mpq_lar_core_solver.m_r_solver.get_status()); - lean_assert(m_status != OPTIMAL || all_constraints_hold()); - } - - - numeric_pair lar_solver::get_basic_var_value_from_row_directly(unsigned i) { - numeric_pair r = zero_of_type>(); - - unsigned bj = m_mpq_lar_core_solver.m_r_solver.m_basis[i]; - for (const auto & c: A_r().m_rows[i]) { - if (c.m_j == bj) continue; - const auto & x = m_mpq_lar_core_solver.m_r_x[c.m_j]; - if (!is_zero(x)) - r -= c.m_value * x; - } - return r; - } - - numeric_pair lar_solver::get_basic_var_value_from_row(unsigned i) { - if (settings().use_tableau()) { - return get_basic_var_value_from_row_directly(i); - } - - numeric_pair r = zero_of_type>(); - m_mpq_lar_core_solver.calculate_pivot_row(i); - for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_index) { - lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis_heading[j] < 0); - r -= m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_data[j] * m_mpq_lar_core_solver.m_r_x[j]; - } - return r; - } - - template - void lar_solver::add_last_rows_to_lu(lp_primal_core_solver & s) { - auto & f = s.m_factorization; - if (f != nullptr) { - auto columns_to_replace = f->get_set_of_columns_to_replace_for_add_last_rows(s.m_basis_heading); - if (f->m_refactor_counter + columns_to_replace.size() >= 200 || f->has_dense_submatrix()) { - delete f; - f = nullptr; - } else { - f->add_last_rows_to_B(s.m_basis_heading, columns_to_replace); - } - } - if (f == nullptr) { - init_factorization(f, s.m_A, s.m_basis, m_settings); - if (f->get_status() != LU_status::OK) { - delete f; - f = nullptr; - } - } - - } - - bool lar_solver::x_is_correct() const { - if (m_mpq_lar_core_solver.m_r_x.size() != A_r().column_count()) { - // std::cout << "the size is off " << m_r_solver.m_x.size() << ", " << A().column_count() << std::endl; - return false; - } - for (unsigned i = 0; i < A_r().row_count(); i++) { - numeric_pair delta = A_r().dot_product_with_row(i, m_mpq_lar_core_solver.m_r_x); - if (!delta.is_zero()) { - // std::cout << "x is off ("; - // std::cout << "m_b[" << i << "] = " << m_b[i] << " "; - // std::cout << "left side = " << A().dot_product_with_row(i, m_r_solver.m_x) << ' '; - // std::cout << "delta = " << delta << ' '; - // std::cout << "iters = " << total_iterations() << ")" << std::endl; - // std::cout << "row " << i << " is off" << std::endl; - return false; - } - } - return true;; - - } - - bool lar_solver::var_is_registered(var_index vj) const { - if (vj >= m_terms_start_index) { - if (vj - m_terms_start_index >= m_terms.size()) - return false; - } else if ( vj >= A_r().column_count()) { - return false; - } - return true; - } - - unsigned lar_solver::constraint_stack_size() const { - return m_constraint_count.stack_size(); - } - - void lar_solver::fill_last_row_of_A_r(static_matrix> & A, const lar_term * ls) { - lean_assert(A.row_count() > 0); - lean_assert(A.column_count() > 0); - unsigned last_row = A.row_count() - 1; - lean_assert(A.m_rows[last_row].size() == 0); - for (auto & t : ls->m_coeffs) { - lean_assert(!is_zero(t.second)); - var_index j = t.first; - A.set(last_row, j, - t.second); - } - unsigned basis_j = A.column_count() - 1; - A.set(last_row, basis_j, mpq(1)); - } - - template - void lar_solver::create_matrix_A(static_matrix & matr) { - lean_assert(false); // not implemented - /* - unsigned m = number_or_nontrivial_left_sides(); - unsigned n = m_vec_of_canonic_left_sides.size(); - if (matr.row_count() == m && matr.column_count() == n) - return; - matr.init_empty_matrix(m, n); - copy_from_mpq_matrix(matr); - */ - } - - template - void lar_solver::copy_from_mpq_matrix(static_matrix & matr) { - matr.m_rows.resize(A_r().row_count()); - matr.m_columns.resize(A_r().column_count()); - for (unsigned i = 0; i < matr.row_count(); i++) { - for (auto & it : A_r().m_rows[i]) { - matr.set(i, it.m_j, convert_struct::convert(it.get_val())); - } - } - } - - - bool lar_solver::try_to_set_fixed(column_info & ci) { - if (ci.upper_bound_is_set() && ci.low_bound_is_set() && ci.get_upper_bound() == ci.get_low_bound() && !ci.is_fixed()) { - ci.set_fixed_value(ci.get_upper_bound()); - return true; - } - return false; - } - - column_type lar_solver::get_column_type(const column_info & ci) { - auto ret = ci.get_column_type_no_flipping(); - if (ret == column_type::boxed) { // changing boxed to fixed because of the no span - if (ci.get_low_bound() == ci.get_upper_bound()) - ret = column_type::fixed; - } - return ret; - } - - std::string lar_solver::get_column_name(unsigned j) const { - if (j >= m_terms_start_index) - return std::string("_t") + T_to_string(j); - if (j >= m_columns_to_ext_vars_or_term_indices.size()) - return std::string("_s") + T_to_string(j); - - return std::string("v") + T_to_string(m_columns_to_ext_vars_or_term_indices[j]); - } - - bool lar_solver::all_constrained_variables_are_registered(const vector>& left_side) { - for (auto it : left_side) { - if (! var_is_registered(it.second)) - return false; - } - return true; - } - - constraint_index lar_solver::add_constraint(const vector>& left_side_with_terms, lconstraint_kind kind_par, const mpq& right_side_parm) { - /* - mpq rs = right_side_parm; - vector> left_side; - substitute_terms(one_of_type(), left_side_with_terms, left_side, rs); - lean_assert(left_side.size() > 0); - lean_assert(all_constrained_variables_are_registered(left_side)); - lar_constraint original_constr(left_side, kind_par, rs); - unsigned j; // j is the index of the basic variables corresponding to the left side - canonic_left_side ls = create_or_fetch_canonic_left_side(left_side, j); - mpq ratio = find_ratio_of_original_constraint_to_normalized(ls, original_constr); - auto kind = ratio.is_neg() ? flip_kind(kind_par) : kind_par; - rs/= ratio; - lar_normalized_constraint normalized_constraint(ls, ratio, kind, rs, original_constr); - m_constraints.push_back(normalized_constraint); - constraint_index constr_ind = m_constraints.size() - 1; - update_column_type_and_bound(j, kind, rs, constr_ind); - return constr_ind; - */ - lean_assert(false); // not implemented - return 0; - } - - bool lar_solver::all_constraints_hold() const { - if (m_settings.get_cancel_flag()) - return true; - std::unordered_map var_map; - get_model(var_map); - - for (unsigned i = 0; i < m_constraints.size(); i++) { - if (!constraint_holds(*m_constraints[i], var_map)) { - print_constraint(i, std::cout); - return false; - } - } - return true; - } - - bool lar_solver::constraint_holds(const lar_base_constraint & constr, std::unordered_map & var_map) const { - mpq left_side_val = get_left_side_val(constr, var_map); - switch (constr.m_kind) { - case LE: return left_side_val <= constr.m_right_side; - case LT: return left_side_val < constr.m_right_side; - case GE: return left_side_val >= constr.m_right_side; - case GT: return left_side_val > constr.m_right_side; - case EQ: return left_side_val == constr.m_right_side; - default: - lean_unreachable(); - } - return false; // it is unreachable - } - - bool lar_solver::the_relations_are_of_same_type(const vector> & evidence, lconstraint_kind & the_kind_of_sum) const { - unsigned n_of_G = 0, n_of_L = 0; - bool strict = false; - for (auto & it : evidence) { - mpq coeff = it.first; - constraint_index con_ind = it.second; - lconstraint_kind kind = coeff.is_pos() ? - m_constraints[con_ind]->m_kind : - flip_kind(m_constraints[con_ind]->m_kind); - if (kind == GT || kind == LT) - strict = true; - if (kind == GE || kind == GT) n_of_G++; - else if (kind == LE || kind == LT) n_of_L++; - } - the_kind_of_sum = n_of_G ? GE : (n_of_L ? LE : EQ); - if (strict) - the_kind_of_sum = static_cast((static_cast(the_kind_of_sum) / 2)); - - return n_of_G == 0 || n_of_L == 0; - } - -void lar_solver::register_in_map(std::unordered_map & coeffs, const lar_base_constraint & cn, const mpq & a) { - for (auto & it : cn.get_left_side_coefficients()) { - unsigned j = it.second; - auto p = coeffs.find(j); - if (p == coeffs.end()) - coeffs[j] = it.first * a; - else { - p->second += it.first * a; - if (p->second.is_zero()) - coeffs.erase(p); - } - } - } - - bool lar_solver::the_left_sides_sum_to_zero(const vector> & evidence) const { - std::unordered_map coeff_map; - for (auto & it : evidence) { - mpq coeff = it.first; - constraint_index con_ind = it.second; - lean_assert(con_ind < m_constraints.size()); - register_in_map(coeff_map, *m_constraints[con_ind], coeff); - } - - if (!coeff_map.empty()) { - std::cout << "left side = "; - vector> t; - for (auto & it : coeff_map) { - t.push_back(std::make_pair(it.second, it.first)); - } - print_linear_combination_of_column_indices(t, std::cout); - std::cout << std::endl; - return false; - } - - return true; - } - - bool lar_solver::the_right_sides_do_not_sum_to_zero(const vector> & evidence) { - mpq ret = numeric_traits::zero(); - for (auto & it : evidence) { - mpq coeff = it.first; - constraint_index con_ind = it.second; - lean_assert(con_ind < m_constraints.size()); - const lar_constraint & constr = *m_constraints[con_ind]; - ret += constr.m_right_side * coeff; - } - return !numeric_traits::is_zero(ret); - } - - bool lar_solver::explanation_is_correct(const vector>& explanation) const { -#ifdef LEAN_DEBUG - lconstraint_kind kind; - lean_assert(the_relations_are_of_same_type(explanation, kind)); - lean_assert(the_left_sides_sum_to_zero(explanation)); - mpq rs = sum_of_right_sides_of_explanation(explanation); - switch (kind) { - case LE: lean_assert(rs < zero_of_type()); - break; - case LT: lean_assert(rs <= zero_of_type()); - break; - case GE: lean_assert(rs > zero_of_type()); - break; - case GT: lean_assert(rs >= zero_of_type()); - break; - case EQ: lean_assert(rs != zero_of_type()); - break; - default: - lean_assert(false); - return false; - } -#endif - return true; - } - - bool lar_solver::inf_explanation_is_correct() const { -#ifdef LEAN_DEBUG - vector> explanation; - get_infeasibility_explanation(explanation); - return explanation_is_correct(explanation); -#endif - return true; - } - - mpq lar_solver::sum_of_right_sides_of_explanation(const vector> & explanation) const { - mpq ret = numeric_traits::zero(); - for (auto & it : explanation) { - mpq coeff = it.first; - constraint_index con_ind = it.second; - lean_assert(con_ind < m_constraints.size()); - ret += (m_constraints[con_ind]->m_right_side - m_constraints[con_ind]->get_free_coeff_of_left_side()) * coeff; - } - return ret; - } - - bool lar_solver::has_lower_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) { - - if (var >= m_vars_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_vars_to_ul_pairs[var]; - ci = ul.low_bound_witness(); - if (ci != static_cast(-1)) { - auto& p = m_mpq_lar_core_solver.m_r_low_bounds()[var]; - value = p.x; - is_strict = p.y.is_pos(); - return true; - } - else { - return false; - } - } - - bool lar_solver::has_upper_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) { - - if (var >= m_vars_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_vars_to_ul_pairs[var]; - ci = ul.upper_bound_witness(); - if (ci != static_cast(-1)) { - auto& p = m_mpq_lar_core_solver.m_r_upper_bounds()[var]; - value = p.x; - is_strict = p.y.is_neg(); - return true; - } - else { - return false; - } - } - - void lar_solver::get_infeasibility_explanation(vector> & explanation) const { - explanation.clear(); - if (m_infeasible_column_index != -1) { - fill_explanation_from_infeasible_column(explanation); - return; - } - if (m_mpq_lar_core_solver.get_infeasible_sum_sign() == 0) { - return; - } - // the infeasibility sign - int inf_sign; - auto inf_row = m_mpq_lar_core_solver.get_infeasibility_info(inf_sign); - get_infeasibility_explanation_for_inf_sign(explanation, inf_row, inf_sign); - lean_assert(explanation_is_correct(explanation)); - } - - void lar_solver::get_infeasibility_explanation_for_inf_sign( - vector> & explanation, - const vector> & 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_vars_to_ul_pairs[j]; - - constraint_index bound_constr_i = adj_sign < 0 ? ul.upper_bound_witness() : ul.low_bound_witness(); - lean_assert(bound_constr_i < m_constraints.size()); - explanation.push_back(std::make_pair(coeff, bound_constr_i)); - } - } - - void lar_solver::get_model(std::unordered_map & variable_values) const { - mpq delta = mpq(1, 2); // start from 0.5 to have less clashes - lean_assert(m_status == OPTIMAL); - unsigned i; - do { - - // different pairs have to produce different singleton values - std::unordered_set set_of_different_pairs; - std::unordered_set set_of_different_singles; - delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(delta); - for (i = 0; i < m_mpq_lar_core_solver.m_r_x.size(); i++ ) { - const numeric_pair & rp = m_mpq_lar_core_solver.m_r_x[i]; - set_of_different_pairs.insert(rp); - mpq x = rp.x + delta * rp.y; - set_of_different_singles.insert(x); - if (set_of_different_pairs.size() - != set_of_different_singles.size()) { - delta /= mpq(2); - break; - } - - variable_values[i] = x; - } - } while (i != m_mpq_lar_core_solver.m_r_x.size()); - } - -std::string lar_solver::get_variable_name(var_index vi) const { - return get_column_name(vi); +void clear() {lean_assert(false); // not implemented } - // ********** print region start - void lar_solver::print_constraint(constraint_index ci, std::ostream & out) const { - if (ci >= m_constraints.size()) { - out << "constraint " << T_to_string(ci) << " is not found"; - out << std::endl; - return; - } - print_constraint(m_constraints[ci], out); +lar_solver::lar_solver() : m_status(OPTIMAL), + m_infeasible_column_index(-1), + m_terms_start_index(1000000), + m_column_type_function ([this] (unsigned j) {return m_mpq_lar_core_solver.m_column_types()[j];}), + m_mpq_lar_core_solver(m_settings, *this) +{} + +void lar_solver::set_propagate_bounds_on_pivoted_rows_mode(bool v) { + m_mpq_lar_core_solver.m_r_solver.m_pivoted_rows = v? (& m_rows_with_changed_bounds) : nullptr; +} + +lar_solver::~lar_solver(){ + for (auto c : m_constraints) + delete c; + for (auto t : m_terms) + delete t; +} + +numeric_pair const& lar_solver::get_value(var_index vi) const { return m_mpq_lar_core_solver.m_r_x[vi]; } + +bool lar_solver::is_term(var_index j) const { + return j >= m_terms_start_index && j - m_terms_start_index < m_terms.size(); +} + +unsigned lar_solver::adjust_term_index(unsigned j) const { + lean_assert(is_term(j)); + return j - m_terms_start_index; +} + + +bool lar_solver::use_lu() const { return m_settings.simplex_strategy() == simplex_strategy_enum::lu; } + +bool lar_solver::sizes_are_correct() const { + lean_assert(strategy_is_undecided() || !m_mpq_lar_core_solver.need_to_presolve_with_double_solver() || A_r().column_count() == A_d().column_count()); + lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size()); + lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size()); + lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_x.size()); + return true; +} + + +void lar_solver::print_implied_bound(const implied_bound& be, std::ostream & out) const { + out << "implied bound\n"; + unsigned v = be.m_j; + if (is_term(v)) { + out << "it is a term number " << be.m_j << std::endl; + print_term(*m_terms[be.m_j - m_terms_start_index], out); } - - void lar_solver::print_constraints(std::ostream& out) const { - for (auto c : m_constraints) { - print_constraint(c, out); - } + else { + out << get_column_name(v); } - - void lar_solver::print_terms(std::ostream& out) const { - for (auto it : m_terms) { - print_term(*it, out); - out << "\n"; - } - } - - void lar_solver::print_left_side_of_constraint(const lar_base_constraint * c, std::ostream & out) const { - print_linear_combination_of_column_indices(c->get_left_side_coefficients(), out); - mpq free_coeff = c->get_free_coeff_of_left_side(); - if (!is_zero(free_coeff)) - out << " + " << free_coeff; + out << " " << lconstraint_kind_string(be.kind()) << " " << be.m_bound << std::endl; + // for (auto & p : be.m_explanation) { + // out << p.first << " : "; + // print_constraint(p.second, out); + // } + // m_mpq_lar_core_solver.m_r_solver.print_column_info(be.m_j< m_terms_start_index? be.m_j : adjust_term_index(be.m_j), out); + out << "end of implied bound" << std::endl; +} + +bool lar_solver::implied_bound_is_correctly_explained(implied_bound const & be, const vector> & explanation) const { + std::unordered_map coeff_map; + auto rs_of_evidence = zero_of_type(); + unsigned n_of_G = 0, n_of_L = 0; + bool strict = false; + for (auto & it : explanation) { + mpq coeff = it.first; + constraint_index con_ind = it.second; + const auto & constr = *m_constraints[con_ind]; + lconstraint_kind kind = coeff.is_pos() ? constr.m_kind : flip_kind(constr.m_kind); + register_in_map(coeff_map, constr, coeff); + if (kind == GT || kind == LT) + strict = true; + if (kind == GE || kind == GT) n_of_G++; + else if (kind == LE || kind == LT) n_of_L++; + rs_of_evidence += coeff*constr.m_right_side; } - - void lar_solver::print_term(lar_term const& term, std::ostream & out) const { - if (!numeric_traits::is_zero(term.m_v)) { - out << term.m_v << " + "; + lean_assert(n_of_G == 0 || n_of_L == 0); + lconstraint_kind kind = n_of_G ? GE : (n_of_L ? LE : EQ); + if (strict) + kind = static_cast((static_cast(kind) / 2)); + + if (!is_term(be.m_j)) { + if (coeff_map.size() != 1) + return false; + auto it = coeff_map.find(be.m_j); + if (it == coeff_map.end()) return false; + mpq ratio = it->second; + if (ratio < zero_of_type()) { + kind = static_cast(-kind); } - print_linear_combination_of_column_indices(term.coeffs_as_vector(), out); - } - - mpq lar_solver::get_left_side_val(const lar_base_constraint & cns, const std::unordered_map & var_map) const { - mpq ret = cns.get_free_coeff_of_left_side(); - for (auto & it : cns.get_left_side_coefficients()) { - var_index j = it.second; - auto vi = var_map.find(j); - lean_assert(vi != var_map.end()); - ret += it.first * vi->second; + rs_of_evidence /= ratio; + } else { + const lar_term * t = m_terms[adjust_term_index(be.m_j)]; + const auto first_coeff = *t->m_coeffs.begin(); + unsigned j = first_coeff.first; + auto it = coeff_map.find(j); + if (it == coeff_map.end()) + return false; + mpq ratio = it->second / first_coeff.second; + for (auto & p : t->m_coeffs) { + it = coeff_map.find(p.first); + if (it == coeff_map.end()) + return false; + if (p.second * ratio != it->second) + return false; } - return ret; - } - - void lar_solver::print_constraint(const lar_base_constraint * c, std::ostream & out) const { - print_left_side_of_constraint(c, out); - out << " " << lconstraint_kind_string(c->m_kind) << " " << c->m_right_side << std::endl; - } - - void lar_solver::fill_var_set_for_random_update(unsigned sz, var_index const * vars, vector& column_list) { - for (unsigned i = 0; i < sz; i++) { - var_index var = vars[i]; - if (var >= m_terms_start_index) { // handle the term - for (auto & it : m_terms[var - m_terms_start_index]->m_coeffs) { - column_list.push_back(it.first); - } - } else { - column_list.push_back(var); - } + if (ratio < zero_of_type()) { + kind = static_cast(-kind); } + rs_of_evidence /= ratio; + rs_of_evidence += t->m_v * ratio; } - void lar_solver::random_update(unsigned sz, var_index const * vars) { - vector column_list; - fill_var_set_for_random_update(sz, vars, column_list); - random_updater ru(m_mpq_lar_core_solver, column_list); - ru.update(); + return kind == be.kind() && rs_of_evidence == be.m_bound; +} + + +void lar_solver::analyze_new_bounds_on_row( + unsigned row_index, + bound_propagator & bp) { + lean_assert(!use_tableau()); + iterator_on_pivot_row it(m_mpq_lar_core_solver.get_pivot_row(), m_mpq_lar_core_solver.m_r_basis[row_index]); + + bound_analyzer_on_row ra_pos(it, + zero_of_type>(), + row_index, + bp + ); + ra_pos.analyze(); +} + +void lar_solver::analyze_new_bounds_on_row_tableau( + unsigned row_index, + bound_propagator & bp + ) { + + if (A_r().m_rows[row_index].size() > settings().max_row_length_for_bound_propagation) + return; + iterator_on_row it(A_r().m_rows[row_index]); + lean_assert(use_tableau()); + bound_analyzer_on_row::analyze_row(it, + zero_of_type>(), + row_index, + bp + ); +} + + +void lar_solver::substitute_basis_var_in_terms_for_row(unsigned i) { + // todo : create a map from term basic vars to the rows where they are used + unsigned basis_j = m_mpq_lar_core_solver.m_r_solver.m_basis[i]; + for (unsigned k = 0; k < m_terms.size(); k++) { + if (term_is_used_as_row(k)) + continue; + if (!m_terms[k]->contains(basis_j)) + continue; + m_terms[k]->subst(basis_j, m_mpq_lar_core_solver.m_r_solver.m_pivot_row); } - - - void lar_solver::try_pivot_fixed_vars_from_basis() { - m_mpq_lar_core_solver.m_r_solver.pivot_fixed_vars_from_basis(); +} + +void lar_solver::calculate_implied_bounds_for_row(unsigned i, bound_propagator & bp) { + if(use_tableau()) { + analyze_new_bounds_on_row_tableau(i, bp); + } else { + m_mpq_lar_core_solver.calculate_pivot_row(i); + substitute_basis_var_in_terms_for_row(i); + analyze_new_bounds_on_row(i, bp); } +} - void lar_solver::pop() { - pop(1); + +linear_combination_iterator * lar_solver::create_new_iter_from_term(unsigned term_index) const { + lean_assert(false); // not implemented + return nullptr; + // new linear_combination_iterator_on_vector(m_terms[adjust_term_index(term_index)]->coeffs_as_vector()); +} + +unsigned lar_solver::adjust_column_index_to_term_index(unsigned j) const { + unsigned ext_var_or_term = m_columns_to_ext_vars_or_term_indices[j]; + return ext_var_or_term < m_terms_start_index ? j : ext_var_or_term; +} + +void lar_solver::propagate_bounds_on_a_term(const lar_term& t, bound_propagator & bp, unsigned term_offset) { + lean_assert(false); // not implemented +} + + +void lar_solver::explain_implied_bound(implied_bound & ib, bound_propagator & bp) { + unsigned i = ib.m_row_or_term_index; + int bound_sign = ib.m_is_low_bound? 1: -1; + int j_sign = (ib.m_coeff_before_j_is_pos ? 1 :-1) * bound_sign; + unsigned m_j = ib.m_j; + if (is_term(m_j)) { + auto it = m_ext_vars_to_columns.find(m_j); + lean_assert(it != m_ext_vars_to_columns.end()); + m_j = it->second.ext_j(); } - - bool lar_solver::column_represents_row_in_tableau(unsigned j) { - return m_vars_to_ul_pairs()[j].m_i != static_cast(-1); + for (auto const& r : A_r().m_rows[i]) { + unsigned j = r.m_j; + mpq const& a = r.get_val(); + if (j == m_j) continue; + if (is_term(j)) { + auto it = m_ext_vars_to_columns.find(j); + lean_assert(it != m_ext_vars_to_columns.end()); + j = it->second.ext_j(); + } + int a_sign = is_pos(a)? 1: -1; + int sign = j_sign * a_sign; + const ul_pair & ul = m_vars_to_ul_pairs[j]; + auto witness = sign > 0? ul.upper_bound_witness(): ul.low_bound_witness(); + lean_assert(is_valid(witness)); + bp.consume(a, witness); } + // lean_assert(implied_bound_is_correctly_explained(ib, explanation)); +} - 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 - lean_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.m_i == i) - return; - non_zero_column_cell_index = k; - } - lean_assert(non_zero_column_cell_index != -1); - lean_assert(static_cast(non_zero_column_cell_index) != i); - m_mpq_lar_core_solver.m_r_solver.transpose_rows_tableau(last_column[non_zero_column_cell_index].m_i, i); +bool lar_solver::term_is_used_as_row(unsigned term) const { + lean_assert(is_term(term)); + return contains(m_ext_vars_to_columns, term); +} + +void lar_solver::propagate_bounds_on_terms(bound_propagator & bp) { + for (unsigned i = 0; i < m_terms.size(); i++) { + if (term_is_used_as_row(i + m_terms_start_index)) + continue; // this term is used a left side of a constraint, + // it was processed as a touched row if needed + propagate_bounds_on_a_term(*m_terms[i], bp, i); } +} - void lar_solver::remove_last_row_and_column_from_tableau(unsigned j) { - lean_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.m_j] += cost_j*rc.get_val(); - } - - A_r().remove_element(last_row, rc); - } - lean_assert(last_row.size() == 0); - lean_assert(A_r().m_columns[j].size() == 0); - A_r().m_rows.pop_back(); - A_r().m_columns.pop_back(); - slv.m_b.pop_back(); +// goes over touched rows and tries to induce bounds +void lar_solver::propagate_bounds_for_touched_rows(bound_propagator & bp) { + if (!use_tableau()) + return; // todo: consider to remove the restriction + + for (unsigned i : m_rows_with_changed_bounds.m_index) { + calculate_implied_bounds_for_row(i, bp); } - - void lar_solver::remove_last_column_from_tableau(unsigned j) { - lean_assert(j == A_r().column_count() - 1); - // the last column has to be empty - lean_assert(A_r().m_columns[j].size() == 0); - A_r().m_columns.pop_back(); + m_rows_with_changed_bounds.clear(); + if (!use_tableau()) { + propagate_bounds_on_terms(bp); } +} - void lar_solver::remove_last_column_from_basis_tableau(unsigned j) { - auto& rslv = m_mpq_lar_core_solver.m_r_solver; +lp_status lar_solver::get_status() const { return m_status;} + +void lar_solver::set_status(lp_status s) {m_status = s;} + +lp_status lar_solver::find_feasible_solution() { + if (strategy_is_undecided()) + decide_on_strategy_and_adjust_initial_state(); + + m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = true; + return solve(); +} + +lp_status lar_solver::solve() { + if (m_status == INFEASIBLE) { + return m_status; + } + solve_with_core_solver(); + if (m_status != INFEASIBLE) { + if (m_settings.bound_propagation()) + detect_rows_with_changed_bounds(); + } + + m_columns_with_changed_bound.clear(); + return m_status; +} + +void lar_solver::fill_explanation_from_infeasible_column(vector> & evidence) const{ + + // this is the case when the lower bound is in conflict with the upper one + const ul_pair & ul = m_vars_to_ul_pairs[m_infeasible_column_index]; + evidence.push_back(std::make_pair(numeric_traits::one(), ul.upper_bound_witness())); + evidence.push_back(std::make_pair(-numeric_traits::one(), ul.low_bound_witness())); +} + + +unsigned lar_solver::get_total_iterations() const { return m_mpq_lar_core_solver.m_r_solver.total_iterations(); } +// see http://research.microsoft.com/projects/z3/smt07.pdf +// This method searches for a feasible solution with as many different values of variables, reverenced in vars, as it can find +// Attention, after a call to this method the non-basic variables don't necesserarly stick to their bounds anymore +vector lar_solver::get_list_of_all_var_indices() const { + vector ret; + for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_heading.size(); j++) + ret.push_back(j); + return ret; +} +void lar_solver::push() { + m_simplex_strategy = m_settings.simplex_strategy(); + m_simplex_strategy.push(); + m_status.push(); + m_vars_to_ul_pairs.push(); + m_infeasible_column_index.push(); + m_mpq_lar_core_solver.push(); + m_term_count = m_terms.size(); + m_term_count.push(); + m_constraint_count = m_constraints.size(); + m_constraint_count.push(); +} + +void lar_solver::clean_large_elements_after_pop(unsigned n, int_set& set) { + vector to_remove; + for (unsigned j: set.m_index) + if (j >= n) + to_remove.push_back(j); + for (unsigned j : to_remove) + set.erase(j); +} + +void lar_solver::shrink_inf_set_after_pop(unsigned n, int_set & set) { + clean_large_elements_after_pop(n, set); + set.resize(n); +} + + +void lar_solver::pop(unsigned k) { + int n_was = static_cast(m_ext_vars_to_columns.size()); + m_status.pop(k); + m_infeasible_column_index.pop(k); + unsigned n = m_vars_to_ul_pairs.peek_size(k); + for (unsigned j = n_was; j-- > n;) + m_ext_vars_to_columns.erase(m_columns_to_ext_vars_or_term_indices[j]); + m_columns_to_ext_vars_or_term_indices.resize(n); + if (m_settings.use_tableau()) { + pop_tableau(); + } + m_vars_to_ul_pairs.pop(k); + + m_mpq_lar_core_solver.pop(k); + clean_large_elements_after_pop(n, m_columns_with_changed_bound); + unsigned m = A_r().row_count(); + clean_large_elements_after_pop(m, m_rows_with_changed_bounds); + clean_inf_set_of_r_solver_after_pop(); + lean_assert(m_settings.simplex_strategy() == simplex_strategy_enum::undecided || + (!use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); + + + lean_assert(ax_is_correct()); + lean_assert(m_mpq_lar_core_solver.m_r_solver.inf_set_is_correct()); + m_constraint_count.pop(k); + for (unsigned i = m_constraint_count; i < m_constraints.size(); i++) + delete m_constraints[i]; + + m_constraints.resize(m_constraint_count); + m_term_count.pop(k); + for (unsigned i = m_term_count; i < m_terms.size(); i++) { + delete m_terms[i]; + } + m_terms.resize(m_term_count); + m_simplex_strategy.pop(k); + m_settings.simplex_strategy() = m_simplex_strategy; + lean_assert(sizes_are_correct()); + lean_assert((!m_settings.use_tableau()) || m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); +} + +vector lar_solver::get_all_constraint_indices() const { + vector ret; + constraint_index i = 0; + while ( i < m_constraints.size()) + ret.push_back(i++); + return ret; +} + +bool lar_solver::maximize_term_on_tableau(const vector> & term, + impq &term_max) { + if (settings().simplex_strategy() == simplex_strategy_enum::undecided) + decide_on_strategy_and_adjust_initial_state(); + + m_mpq_lar_core_solver.solve(); + if (m_mpq_lar_core_solver.m_r_solver.get_status() == UNBOUNDED) + return false; + + term_max = 0; + for (auto & p : term) + term_max += p.first * m_mpq_lar_core_solver.m_r_x[p.second]; + + return true; +} + +bool lar_solver::costs_are_zeros_for_r_solver() const { + for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_costs.size(); j++) { + lean_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_costs[j])); + } + return true; +} +bool lar_solver::reduced_costs_are_zeroes_for_r_solver() const { + for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_solver.m_d.size(); j++) { + lean_assert(is_zero(m_mpq_lar_core_solver.m_r_solver.m_d[j])); + } + return true; +} + +void lar_solver::set_costs_to_zero(const vector> & term) { + auto & rslv = m_mpq_lar_core_solver.m_r_solver; + auto & jset = m_mpq_lar_core_solver.m_r_solver.m_inf_set; // hijack this set that should be empty right now + lean_assert(jset.m_index.size()==0); + + for (auto & p : term) { + unsigned j = p.second; + rslv.m_costs[j] = zero_of_type(); int i = rslv.m_basis_heading[j]; - if (i >= 0) { // j is a basic var - int last_pos = static_cast(rslv.m_basis.size()) - 1; - lean_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(rslv.m_nbasis.size()) - 1; - lean_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(); - lean_assert(rslv.m_basis.size() == A_r().row_count()); - lean_assert(rslv.basis_heading_is_correct()); - } - - void lar_solver::remove_column_from_tableau(unsigned j) { - auto& rslv = m_mpq_lar_core_solver.m_r_solver; - lean_assert(j == A_r().column_count() - 1); - lean_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 - } + if (i < 0) + jset.insert(j); else { - remove_last_column_from_tableau(j); + for (auto & rc : A_r().m_rows[i]) + jset.insert(rc.m_j); } - rslv.m_x.pop_back(); - rslv.m_d.pop_back(); - rslv.m_costs.pop_back(); - - remove_last_column_from_basis_tableau(j); - lean_assert(m_mpq_lar_core_solver.r_basis_is_OK()); - lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size()); } - void lar_solver::pop_tableau() { - lean_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count()); + for (unsigned j : jset.m_index) + rslv.m_d[j] = zero_of_type(); - lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count()); - lean_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 - for (unsigned j = A_r().column_count(); j-- > m_columns_to_ext_vars_or_term_indices.size();) - remove_column_from_tableau(j); - lean_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count()); - lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count()); - lean_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct()); + jset.clear(); + + lean_assert(reduced_costs_are_zeroes_for_r_solver()); + lean_assert(costs_are_zeros_for_r_solver()); +} + +void lar_solver::prepare_costs_for_r_solver(const vector> & term) { + + auto & rslv = m_mpq_lar_core_solver.m_r_solver; + rslv.m_using_infeas_costs = false; + lean_assert(costs_are_zeros_for_r_solver()); + lean_assert(reduced_costs_are_zeroes_for_r_solver()); + rslv.m_costs.resize(A_r().column_count(), zero_of_type()); + for (auto & p : term) { + unsigned j = p.second; + rslv.m_costs[j] = p.first; + if (rslv.m_basis_heading[j] < 0) + rslv.m_d[j] += p.first; + else + rslv.update_reduced_cost_for_basic_column_cost_change(- p.first, j); } + lean_assert(rslv.reduced_costs_are_correct_tableau()); +} + +bool lar_solver::maximize_term_on_corrected_r_solver(const vector> & term, + impq &term_max) { + settings().backup_costs = false; + switch (settings().simplex_strategy()) { + case simplex_strategy_enum::tableau_rows: + prepare_costs_for_r_solver(term); + settings().simplex_strategy() = simplex_strategy_enum::tableau_costs; + { + bool ret = maximize_term_on_tableau(term, term_max); + settings().simplex_strategy() = simplex_strategy_enum::tableau_rows; + set_costs_to_zero(term); + m_mpq_lar_core_solver.m_r_solver.set_status(OPTIMAL); + return ret; + } + case simplex_strategy_enum::tableau_costs: + prepare_costs_for_r_solver(term); + { + bool ret = maximize_term_on_tableau(term, term_max); + set_costs_to_zero(term); + m_mpq_lar_core_solver.m_r_solver.set_status(OPTIMAL); + return ret; + } + + case simplex_strategy_enum::lu: + lean_assert(false); // not implemented + return false; + default: + lean_unreachable(); // wrong mode + } + return false; +} +// starting from a given feasible state look for the maximum of the term +// return true if found and false if unbounded +bool lar_solver::maximize_term(const vector> & term, + impq &term_max) { + lean_assert(m_mpq_lar_core_solver.m_r_solver.current_x_is_feasible()); + m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = false; + return maximize_term_on_corrected_r_solver(term, term_max); +} + + + +const lar_term & lar_solver::get_term(unsigned j) const { + lean_assert(j >= m_terms_start_index); + return *m_terms[j - m_terms_start_index]; +} + +void lar_solver::pop_core_solver_params() { + pop_core_solver_params(1); +} + +void lar_solver::pop_core_solver_params(unsigned k) { + A_r().pop(k); + A_d().pop(k); +} + + +void lar_solver::set_upper_bound_witness(var_index j, constraint_index ci) { + ul_pair ul = m_vars_to_ul_pairs[j]; + ul.upper_bound_witness() = ci; + m_vars_to_ul_pairs[j] = ul; +} + +void lar_solver::set_low_bound_witness(var_index j, constraint_index ci) { + ul_pair ul = m_vars_to_ul_pairs[j]; + ul.low_bound_witness() = ci; + m_vars_to_ul_pairs[j] = ul; +} + +void lar_solver::register_one_coeff_in_map(std::unordered_map & 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>& left_side_with_terms, + vector> &left_side, mpq & right_side) const { + std::unordered_map coeffs; + for (auto & t : left_side_with_terms) { + unsigned j = t.second; + if (!is_term(j)) { + register_one_coeff_in_map(coeffs, t.first, j); + } else { + const lar_term & term = * m_terms[adjust_term_index(t.second)]; + std::cout << "term = "; + print_term(term, std::cout); + std::cout << std::endl; + for (auto & p : term.coeffs()){ + register_one_coeff_in_map(coeffs, t.first * p.second , p.first); + } + right_side += t.first * term.m_v; + } + } + + for (auto & p : coeffs) + left_side.push_back(std::make_pair(p.second, p.first)); +} + + +void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column(unsigned j) { + if (A_r().row_count() != m_column_buffer.data_size()) + m_column_buffer.resize(A_r().row_count()); + else + m_column_buffer.clear(); + lean_assert(m_column_buffer.size() == 0 && m_column_buffer.is_OK()); + + m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer); + for (unsigned i : m_column_buffer.m_index) + m_rows_with_changed_bounds.insert(i); +} + + + +void lar_solver::detect_rows_of_bound_change_column_for_nbasic_column_tableau(unsigned j) { + for (auto & rc : m_mpq_lar_core_solver.m_r_A.m_columns[j]) + m_rows_with_changed_bounds.insert(rc.m_i); +} + +bool lar_solver::use_tableau() const { return m_settings.use_tableau(); } + +bool lar_solver::use_tableau_costs() const { + return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs; +} + +void lar_solver::detect_rows_of_column_with_bound_change(unsigned j) { + if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { // it is a basic column + // just mark the row at touched and exit + m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]); + return; + } + + if (use_tableau()) + detect_rows_of_bound_change_column_for_nbasic_column_tableau(j); + else + detect_rows_of_bound_change_column_for_nbasic_column(j); +} + +void lar_solver::adjust_x_of_column(unsigned j) { + lean_assert(false); +} + +bool lar_solver::row_is_correct(unsigned i) const { + numeric_pair r = zero_of_type>(); + for (const auto & c : A_r().m_rows[i]) + r += c.m_value * m_mpq_lar_core_solver.m_r_x[c.m_j]; + return is_zero(r); +} + +bool lar_solver::ax_is_correct() const { + for (unsigned i = 0; i < A_r().row_count(); i++) { + if (!row_is_correct(i)) + return false; + } + return true; +} + +bool lar_solver::tableau_with_costs() const { + return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs; +} + +bool lar_solver::costs_are_used() const { + return m_settings.simplex_strategy() != simplex_strategy_enum::tableau_rows; +} + +void lar_solver::change_basic_x_by_delta_on_column(unsigned j, const numeric_pair & delta) { + if (use_tableau()) { + for (const auto & c : A_r().m_columns[j]) { + unsigned bj = m_mpq_lar_core_solver.m_r_basis[c.m_i]; + m_mpq_lar_core_solver.m_r_x[bj] -= A_r().get_val(c) * delta; + if (tableau_with_costs()) { + m_basic_columns_with_changed_cost.insert(bj); + } + m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(bj); + } + } else { + m_column_buffer.clear(); + m_column_buffer.resize(A_r().row_count()); + m_mpq_lar_core_solver.m_r_solver.solve_Bd(j, m_column_buffer); + for (unsigned i : m_column_buffer.m_index) { + unsigned bj = m_mpq_lar_core_solver.m_r_basis[i]; + m_mpq_lar_core_solver.m_r_x[bj] -= m_column_buffer[i] * delta; + m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(bj); + } + } +} + +void lar_solver::update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j) { + if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { + if (costs_are_used()) { + bool was_infeas = m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j); + m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(j); + if (was_infeas != m_mpq_lar_core_solver.m_r_solver.m_inf_set.contains(j)) + m_basic_columns_with_changed_cost.insert(j); + } else { + m_mpq_lar_core_solver.m_r_solver.update_column_in_inf_set(j); + } + } else { + numeric_pair delta; + if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta)) + change_basic_x_by_delta_on_column(j, delta); + } +} + + +void lar_solver::detect_rows_with_changed_bounds_for_column(unsigned j) { + if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { + m_rows_with_changed_bounds.insert(m_mpq_lar_core_solver.m_r_heading[j]); + return; + } + + if (use_tableau()) + detect_rows_of_bound_change_column_for_nbasic_column_tableau(j); + else + detect_rows_of_bound_change_column_for_nbasic_column(j); +} + +void lar_solver::detect_rows_with_changed_bounds() { + for (auto j : m_columns_with_changed_bound.m_index) + detect_rows_with_changed_bounds_for_column(j); +} + +void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds() { + for (auto j : m_columns_with_changed_bound.m_index) + update_x_and_inf_costs_for_column_with_changed_bounds(j); +} + +void lar_solver::update_x_and_inf_costs_for_columns_with_changed_bounds_tableau() { + lean_assert(ax_is_correct()); + for (auto j : m_columns_with_changed_bound.m_index) + update_x_and_inf_costs_for_column_with_changed_bounds(j); + + if (tableau_with_costs()) { + for (unsigned j : m_basic_columns_with_changed_cost.m_index) + m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); + lean_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); + } +} + + +void lar_solver::solve_with_core_solver() { + if (!use_tableau()) + add_last_rows_to_lu(m_mpq_lar_core_solver.m_r_solver); + if (m_mpq_lar_core_solver.need_to_presolve_with_double_solver()) { + add_last_rows_to_lu(m_mpq_lar_core_solver.m_d_solver); + } + m_mpq_lar_core_solver.prefix_r(); + if (costs_are_used()) { + m_basic_columns_with_changed_cost.clear(); + m_basic_columns_with_changed_cost.resize(m_mpq_lar_core_solver.m_r_x.size()); + } + if (use_tableau()) + update_x_and_inf_costs_for_columns_with_changed_bounds_tableau(); + else + update_x_and_inf_costs_for_columns_with_changed_bounds(); + m_mpq_lar_core_solver.solve(); + set_status(m_mpq_lar_core_solver.m_r_solver.get_status()); + lean_assert(m_status != OPTIMAL || all_constraints_hold()); +} + + +numeric_pair lar_solver::get_basic_var_value_from_row_directly(unsigned i) { + numeric_pair r = zero_of_type>(); + + unsigned bj = m_mpq_lar_core_solver.m_r_solver.m_basis[i]; + for (const auto & c: A_r().m_rows[i]) { + if (c.m_j == bj) continue; + const auto & x = m_mpq_lar_core_solver.m_r_x[c.m_j]; + if (!is_zero(x)) + r -= c.m_value * x; + } + return r; +} + +numeric_pair lar_solver::get_basic_var_value_from_row(unsigned i) { + if (settings().use_tableau()) { + return get_basic_var_value_from_row_directly(i); + } + + numeric_pair r = zero_of_type>(); + m_mpq_lar_core_solver.calculate_pivot_row(i); + for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_index) { + lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis_heading[j] < 0); + r -= m_mpq_lar_core_solver.m_r_solver.m_pivot_row.m_data[j] * m_mpq_lar_core_solver.m_r_x[j]; + } + return r; +} + +template +void lar_solver::add_last_rows_to_lu(lp_primal_core_solver & s) { + auto & f = s.m_factorization; + if (f != nullptr) { + auto columns_to_replace = f->get_set_of_columns_to_replace_for_add_last_rows(s.m_basis_heading); + if (f->m_refactor_counter + columns_to_replace.size() >= 200 || f->has_dense_submatrix()) { + delete f; + f = nullptr; + } else { + f->add_last_rows_to_B(s.m_basis_heading, columns_to_replace); + } + } + if (f == nullptr) { + init_factorization(f, s.m_A, s.m_basis, m_settings); + if (f->get_status() != LU_status::OK) { + delete f; + f = nullptr; + } + } + +} + +bool lar_solver::x_is_correct() const { + if (m_mpq_lar_core_solver.m_r_x.size() != A_r().column_count()) { + // std::cout << "the size is off " << m_r_solver.m_x.size() << ", " << A().column_count() << std::endl; + return false; + } + for (unsigned i = 0; i < A_r().row_count(); i++) { + numeric_pair delta = A_r().dot_product_with_row(i, m_mpq_lar_core_solver.m_r_x); + if (!delta.is_zero()) { + // std::cout << "x is off ("; + // std::cout << "m_b[" << i << "] = " << m_b[i] << " "; + // std::cout << "left side = " << A().dot_product_with_row(i, m_r_solver.m_x) << ' '; + // std::cout << "delta = " << delta << ' '; + // std::cout << "iters = " << total_iterations() << ")" << std::endl; + // std::cout << "row " << i << " is off" << std::endl; + return false; + } + } + return true;; + +} + +bool lar_solver::var_is_registered(var_index vj) const { + if (vj >= m_terms_start_index) { + if (vj - m_terms_start_index >= m_terms.size()) + return false; + } else if ( vj >= A_r().column_count()) { + return false; + } + return true; +} + +unsigned lar_solver::constraint_stack_size() const { + return m_constraint_count.stack_size(); +} + +void lar_solver::fill_last_row_of_A_r(static_matrix> & A, const lar_term * ls) { + lean_assert(A.row_count() > 0); + lean_assert(A.column_count() > 0); + unsigned last_row = A.row_count() - 1; + lean_assert(A.m_rows[last_row].size() == 0); + for (auto & t : ls->m_coeffs) { + lean_assert(!is_zero(t.second)); + var_index j = t.first; + A.set(last_row, j, - t.second); + } + unsigned basis_j = A.column_count() - 1; + A.set(last_row, basis_j, mpq(1)); +} + +template +void lar_solver::create_matrix_A(static_matrix & matr) { + lean_assert(false); // not implemented + /* + unsigned m = number_or_nontrivial_left_sides(); + unsigned n = m_vec_of_canonic_left_sides.size(); + if (matr.row_count() == m && matr.column_count() == n) + return; + matr.init_empty_matrix(m, n); + copy_from_mpq_matrix(matr); + */ +} + +template +void lar_solver::copy_from_mpq_matrix(static_matrix & matr) { + matr.m_rows.resize(A_r().row_count()); + matr.m_columns.resize(A_r().column_count()); + for (unsigned i = 0; i < matr.row_count(); i++) { + for (auto & it : A_r().m_rows[i]) { + matr.set(i, it.m_j, convert_struct::convert(it.get_val())); + } + } +} + + +bool lar_solver::try_to_set_fixed(column_info & ci) { + if (ci.upper_bound_is_set() && ci.low_bound_is_set() && ci.get_upper_bound() == ci.get_low_bound() && !ci.is_fixed()) { + ci.set_fixed_value(ci.get_upper_bound()); + return true; + } + return false; +} + +column_type lar_solver::get_column_type(const column_info & ci) { + auto ret = ci.get_column_type_no_flipping(); + if (ret == column_type::boxed) { // changing boxed to fixed because of the no span + if (ci.get_low_bound() == ci.get_upper_bound()) + ret = column_type::fixed; + } + return ret; +} + +std::string lar_solver::get_column_name(unsigned j) const { + if (j >= m_terms_start_index) + return std::string("_t") + T_to_string(j); + if (j >= m_columns_to_ext_vars_or_term_indices.size()) + return std::string("_s") + T_to_string(j); + + return std::string("v") + T_to_string(m_columns_to_ext_vars_or_term_indices[j]); +} + +bool lar_solver::all_constrained_variables_are_registered(const vector>& 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_map; + get_model(var_map); + + for (unsigned i = 0; i < m_constraints.size(); i++) { + if (!constraint_holds(*m_constraints[i], var_map)) { + print_constraint(i, std::cout); + return false; + } + } + return true; +} + +bool lar_solver::constraint_holds(const lar_base_constraint & constr, std::unordered_map & var_map) const { + mpq left_side_val = get_left_side_val(constr, var_map); + switch (constr.m_kind) { + case LE: return left_side_val <= constr.m_right_side; + case LT: return left_side_val < constr.m_right_side; + case GE: return left_side_val >= constr.m_right_side; + case GT: return left_side_val > constr.m_right_side; + case EQ: return left_side_val == constr.m_right_side; + default: + lean_unreachable(); + } + return false; // it is unreachable +} + +bool lar_solver::the_relations_are_of_same_type(const vector> & evidence, lconstraint_kind & the_kind_of_sum) const { + unsigned n_of_G = 0, n_of_L = 0; + bool strict = false; + for (auto & it : evidence) { + mpq coeff = it.first; + constraint_index con_ind = it.second; + lconstraint_kind kind = coeff.is_pos() ? + m_constraints[con_ind]->m_kind : + flip_kind(m_constraints[con_ind]->m_kind); + if (kind == GT || kind == LT) + strict = true; + if (kind == GE || kind == GT) n_of_G++; + else if (kind == LE || kind == LT) n_of_L++; + } + the_kind_of_sum = n_of_G ? GE : (n_of_L ? LE : EQ); + if (strict) + the_kind_of_sum = static_cast((static_cast(the_kind_of_sum) / 2)); + + return n_of_G == 0 || n_of_L == 0; +} + +void lar_solver::register_in_map(std::unordered_map & coeffs, const lar_base_constraint & cn, const mpq & a) { + for (auto & it : cn.get_left_side_coefficients()) { + unsigned j = it.second; + auto p = coeffs.find(j); + if (p == coeffs.end()) + coeffs[j] = it.first * a; + else { + p->second += it.first * a; + if (p->second.is_zero()) + coeffs.erase(p); + } + } +} + +bool lar_solver::the_left_sides_sum_to_zero(const vector> & evidence) const { + std::unordered_map coeff_map; + for (auto & it : evidence) { + mpq coeff = it.first; + constraint_index con_ind = it.second; + lean_assert(con_ind < m_constraints.size()); + register_in_map(coeff_map, *m_constraints[con_ind], coeff); + } + + if (!coeff_map.empty()) { + std::cout << "left side = "; + vector> t; + for (auto & it : coeff_map) { + t.push_back(std::make_pair(it.second, it.first)); + } + print_linear_combination_of_column_indices(t, std::cout); + std::cout << std::endl; + return false; + } + + return true; +} + +bool lar_solver::the_right_sides_do_not_sum_to_zero(const vector> & evidence) { + mpq ret = numeric_traits::zero(); + for (auto & it : evidence) { + mpq coeff = it.first; + constraint_index con_ind = it.second; + lean_assert(con_ind < m_constraints.size()); + const lar_constraint & constr = *m_constraints[con_ind]; + ret += constr.m_right_side * coeff; + } + return !numeric_traits::is_zero(ret); +} + +bool lar_solver::explanation_is_correct(const vector>& explanation) const { +#ifdef LEAN_DEBUG + lconstraint_kind kind; + lean_assert(the_relations_are_of_same_type(explanation, kind)); + lean_assert(the_left_sides_sum_to_zero(explanation)); + mpq rs = sum_of_right_sides_of_explanation(explanation); + switch (kind) { + case LE: lean_assert(rs < zero_of_type()); + break; + case LT: lean_assert(rs <= zero_of_type()); + break; + case GE: lean_assert(rs > zero_of_type()); + break; + case GT: lean_assert(rs >= zero_of_type()); + break; + case EQ: lean_assert(rs != zero_of_type()); + break; + default: + lean_assert(false); + return false; + } +#endif + return true; +} + +bool lar_solver::inf_explanation_is_correct() const { +#ifdef LEAN_DEBUG + vector> explanation; + get_infeasibility_explanation(explanation); + return explanation_is_correct(explanation); +#endif + return true; +} + +mpq lar_solver::sum_of_right_sides_of_explanation(const vector> & explanation) const { + mpq ret = numeric_traits::zero(); + for (auto & it : explanation) { + mpq coeff = it.first; + constraint_index con_ind = it.second; + lean_assert(con_ind < m_constraints.size()); + ret += (m_constraints[con_ind]->m_right_side - m_constraints[con_ind]->get_free_coeff_of_left_side()) * coeff; + } + return ret; +} + +bool lar_solver::has_lower_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) { + + if (var >= m_vars_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_vars_to_ul_pairs[var]; + ci = ul.low_bound_witness(); + if (ci != static_cast(-1)) { + auto& p = m_mpq_lar_core_solver.m_r_low_bounds()[var]; + value = p.x; + is_strict = p.y.is_pos(); + return true; + } + else { + return false; + } +} + +bool lar_solver::has_upper_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) { + + if (var >= m_vars_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_vars_to_ul_pairs[var]; + ci = ul.upper_bound_witness(); + if (ci != static_cast(-1)) { + auto& p = m_mpq_lar_core_solver.m_r_upper_bounds()[var]; + value = p.x; + is_strict = p.y.is_neg(); + return true; + } + else { + return false; + } +} + +void lar_solver::get_infeasibility_explanation(vector> & explanation) const { + explanation.clear(); + if (m_infeasible_column_index != -1) { + fill_explanation_from_infeasible_column(explanation); + return; + } + if (m_mpq_lar_core_solver.get_infeasible_sum_sign() == 0) { + return; + } + // the infeasibility sign + int inf_sign; + auto inf_row = m_mpq_lar_core_solver.get_infeasibility_info(inf_sign); + get_infeasibility_explanation_for_inf_sign(explanation, inf_row, inf_sign); + lean_assert(explanation_is_correct(explanation)); +} + +void lar_solver::get_infeasibility_explanation_for_inf_sign( + vector> & explanation, + const vector> & 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_vars_to_ul_pairs[j]; + + constraint_index bound_constr_i = adj_sign < 0 ? ul.upper_bound_witness() : ul.low_bound_witness(); + lean_assert(bound_constr_i < m_constraints.size()); + explanation.push_back(std::make_pair(coeff, bound_constr_i)); + } +} + +void lar_solver::get_model(std::unordered_map & variable_values) const { + mpq delta = mpq(1, 2); // start from 0.5 to have less clashes + lean_assert(m_status == OPTIMAL); + unsigned i; + do { + + // different pairs have to produce different singleton values + std::unordered_set set_of_different_pairs; + std::unordered_set set_of_different_singles; + delta = m_mpq_lar_core_solver.find_delta_for_strict_bounds(delta); + for (i = 0; i < m_mpq_lar_core_solver.m_r_x.size(); i++ ) { + const numeric_pair & rp = m_mpq_lar_core_solver.m_r_x[i]; + set_of_different_pairs.insert(rp); + mpq x = rp.x + delta * rp.y; + set_of_different_singles.insert(x); + if (set_of_different_pairs.size() + != set_of_different_singles.size()) { + delta /= mpq(2); + break; + } + + variable_values[i] = x; + } + } while (i != m_mpq_lar_core_solver.m_r_x.size()); +} + +std::string lar_solver::get_variable_name(var_index vi) const { + return get_column_name(vi); +} + +// ********** print region start +void lar_solver::print_constraint(constraint_index ci, std::ostream & out) const { + if (ci >= m_constraints.size()) { + out << "constraint " << T_to_string(ci) << " is not found"; + out << std::endl; + return; + } + + print_constraint(m_constraints[ci], out); +} + +void lar_solver::print_constraints(std::ostream& out) const { + for (auto c : m_constraints) { + print_constraint(c, out); + } +} + +void lar_solver::print_terms(std::ostream& out) const { + for (auto it : m_terms) { + print_term(*it, out); + out << "\n"; + } +} + +void lar_solver::print_left_side_of_constraint(const lar_base_constraint * c, std::ostream & out) const { + print_linear_combination_of_column_indices(c->get_left_side_coefficients(), out); + mpq free_coeff = c->get_free_coeff_of_left_side(); + if (!is_zero(free_coeff)) + out << " + " << free_coeff; + +} + +void lar_solver::print_term(lar_term const& term, std::ostream & out) const { + if (!numeric_traits::is_zero(term.m_v)) { + out << term.m_v << " + "; + } + print_linear_combination_of_column_indices(term.coeffs_as_vector(), out); +} + +mpq lar_solver::get_left_side_val(const lar_base_constraint & cns, const std::unordered_map & var_map) const { + mpq ret = cns.get_free_coeff_of_left_side(); + for (auto & it : cns.get_left_side_coefficients()) { + var_index j = it.second; + auto vi = var_map.find(j); + lean_assert(vi != var_map.end()); + ret += it.first * vi->second; + } + return ret; +} + +void lar_solver::print_constraint(const lar_base_constraint * c, std::ostream & out) const { + print_left_side_of_constraint(c, out); + out << " " << lconstraint_kind_string(c->m_kind) << " " << c->m_right_side << std::endl; +} + +void lar_solver::fill_var_set_for_random_update(unsigned sz, var_index const * vars, vector& column_list) { + for (unsigned i = 0; i < sz; i++) { + var_index var = vars[i]; + if (var >= m_terms_start_index) { // handle the term + for (auto & it : m_terms[var - m_terms_start_index]->m_coeffs) { + column_list.push_back(it.first); + } + } else { + column_list.push_back(var); + } + } +} + +void lar_solver::random_update(unsigned sz, var_index const * vars) { + vector column_list; + fill_var_set_for_random_update(sz, vars, column_list); + random_updater ru(m_mpq_lar_core_solver, column_list); + ru.update(); +} + + +void lar_solver::try_pivot_fixed_vars_from_basis() { + m_mpq_lar_core_solver.m_r_solver.pivot_fixed_vars_from_basis(); +} + +void lar_solver::pop() { + pop(1); +} + +bool lar_solver::column_represents_row_in_tableau(unsigned j) { + return m_vars_to_ul_pairs()[j].m_i != static_cast(-1); +} + +void lar_solver::make_sure_that_the_bottom_right_elem_not_zero_in_tableau(unsigned i, unsigned j) { + // i, j - is the indices of the bottom-right element of the tableau + lean_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.m_i == i) + return; + non_zero_column_cell_index = k; + } + + lean_assert(non_zero_column_cell_index != -1); + lean_assert(static_cast(non_zero_column_cell_index) != i); + m_mpq_lar_core_solver.m_r_solver.transpose_rows_tableau(last_column[non_zero_column_cell_index].m_i, i); +} + +void lar_solver::remove_last_row_and_column_from_tableau(unsigned j) { + lean_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.m_j] += cost_j*rc.get_val(); + } + + A_r().remove_element(last_row, rc); + } + lean_assert(last_row.size() == 0); + lean_assert(A_r().m_columns[j].size() == 0); + A_r().m_rows.pop_back(); + A_r().m_columns.pop_back(); + slv.m_b.pop_back(); +} + +void lar_solver::remove_last_column_from_tableau(unsigned j) { + lean_assert(j == A_r().column_count() - 1); + // the last column has to be empty + lean_assert(A_r().m_columns[j].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(rslv.m_basis.size()) - 1; + lean_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(rslv.m_nbasis.size()) - 1; + lean_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(); + lean_assert(rslv.m_basis.size() == A_r().row_count()); + lean_assert(rslv.basis_heading_is_correct()); +} + +void lar_solver::remove_column_from_tableau(unsigned j) { + auto& rslv = m_mpq_lar_core_solver.m_r_solver; + lean_assert(j == A_r().column_count() - 1); + lean_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_tableau(j); + } + rslv.m_x.pop_back(); + rslv.m_d.pop_back(); + rslv.m_costs.pop_back(); + + remove_last_column_from_basis_tableau(j); + lean_assert(m_mpq_lar_core_solver.r_basis_is_OK()); + lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size()); +} + +void lar_solver::pop_tableau() { + lean_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count()); + + lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count()); + lean_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 + for (unsigned j = A_r().column_count(); j-- > m_columns_to_ext_vars_or_term_indices.size();) + remove_column_from_tableau(j); + lean_assert(m_mpq_lar_core_solver.m_r_solver.m_costs.size() == A_r().column_count()); + lean_assert(m_mpq_lar_core_solver.m_r_solver.m_basis.size() == A_r().row_count()); + lean_assert(m_mpq_lar_core_solver.m_r_solver.basis_heading_is_correct()); +} void lar_solver::clean_inf_set_of_r_solver_after_pop() { - vector became_feas; - clean_large_elements_after_pop(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.m_inf_set); - std::unordered_set basic_columns_with_changed_cost; - auto inf_index_copy = m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index; - for (auto j: inf_index_copy) { - if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { - continue; - } - // some basic columns might become non-basic - these columns need to be made feasible - numeric_pair delta; - if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta)) - change_basic_x_by_delta_on_column(j, delta); + vector became_feas; + clean_large_elements_after_pop(A_r().column_count(), m_mpq_lar_core_solver.m_r_solver.m_inf_set); + std::unordered_set basic_columns_with_changed_cost; + auto inf_index_copy = m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index; + for (auto j: inf_index_copy) { + if (m_mpq_lar_core_solver.m_r_heading[j] >= 0) { + continue; + } + // some basic columns might become non-basic - these columns need to be made feasible + numeric_pair delta; + if (m_mpq_lar_core_solver.m_r_solver.make_column_feasible(j, delta)) + change_basic_x_by_delta_on_column(j, delta); + became_feas.push_back(j); + } + + for (unsigned j : became_feas) { + lean_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(); + m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j); + } + became_feas.clear(); + for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index) { + lean_assert(m_mpq_lar_core_solver.m_r_heading[j] >= 0); + if (m_mpq_lar_core_solver.m_r_solver.column_is_feasible(j)) became_feas.push_back(j); - } - - for (unsigned j : became_feas) { - lean_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(); - m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j); - } - became_feas.clear(); - for (unsigned j : m_mpq_lar_core_solver.m_r_solver.m_inf_set.m_index) { - lean_assert(m_mpq_lar_core_solver.m_r_heading[j] >= 0); - if (m_mpq_lar_core_solver.m_r_solver.column_is_feasible(j)) - became_feas.push_back(j); - } + } + for (unsigned j : became_feas) + m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j); + + + if (use_tableau_costs()) { for (unsigned j : became_feas) - m_mpq_lar_core_solver.m_r_solver.m_inf_set.erase(j); - - - if (use_tableau_costs()) { - for (unsigned j : became_feas) - m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); - for (unsigned j : basic_columns_with_changed_cost) - m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); - lean_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); - } + m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); + for (unsigned j : basic_columns_with_changed_cost) + m_mpq_lar_core_solver.m_r_solver.update_inf_cost_for_column_tableau(j); + lean_assert(m_mpq_lar_core_solver.m_r_solver.reduced_costs_are_correct_tableau()); } +} - void lar_solver::shrink_explanation_to_minimum(vector> & explanation) const { - // implementing quickXplain - quick_xplain::run(explanation, *this); - lean_assert(this->explanation_is_correct(explanation)); - } +void lar_solver::shrink_explanation_to_minimum(vector> & explanation) const { + // implementing quickXplain + quick_xplain::run(explanation, *this); + lean_assert(this->explanation_is_correct(explanation)); +} } // namespace lean diff --git a/src/util/lp/lar_solver.h b/src/util/lp/lar_solver.h index 78795e0e4..655f307c3 100644 --- a/src/util/lp/lar_solver.h +++ b/src/util/lp/lar_solver.h @@ -60,7 +60,6 @@ class lar_solver : public column_namer { stacked_value m_infeasible_column_index; // such can be found at the initialization step stacked_value m_term_count; vector m_terms; - vector m_orig_terms; const var_index m_terms_start_index; indexed_vector m_column_buffer; std::function m_column_type_function; @@ -255,8 +254,7 @@ public: void set_low_bound_witness(var_index j, constraint_index ci); - void substitute_terms(const mpq & mult, - const vector>& left_side_with_terms, + void substitute_terms_in_linear_expression( const vector>& left_side_with_terms, vector> &left_side, mpq & right_side) const; @@ -337,6 +335,9 @@ public: bool the_relations_are_of_same_type(const vector> & evidence, lconstraint_kind & the_kind_of_sum) const; static void register_in_map(std::unordered_map & coeffs, const lar_base_constraint & cn, const mpq & a); + static void register_one_coeff_in_map(std::unordered_map & coeffs, const mpq & a, unsigned j); + + bool the_left_sides_sum_to_zero(const vector> & evidence) const; bool the_right_sides_do_not_sum_to_zero(const vector> & evidence);