#pragma once
#include <algorithm>
#include <functional>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include "math/lp/bound_analyzer_on_row.h"
#include "math/lp/implied_bound.h"
#include "math/lp/int_solver.h"
#include "math/lp/lar_constraints.h"
#include "math/lp/lar_core_solver.h"
#include "math/lp/lp_bound_propagator.h"
#include "math/lp/lp_types.h"
#include "math/lp/nra_solver.h"
#include "math/lp/numeric_pair.h"
#include "math/lp/random_updater.h"
#include "math/lp/stacked_vector.h"
#include "util/buffer.h"
#include "util/debug.h"
#include "util/stacked_value.h"
#include "util/vector.h"
#include "util/trail.h"
namespace lp {
class int_branch;
class int_solver;
class lar_solver : public column_namer {
struct imp;
imp* m_imp;
bool row_has_a_big_num(unsigned i) const;
void register_new_external_var(unsigned ext_v, bool is_int);
bool term_is_int(const lar_term* t) const;
bool term_is_int(const vector<std::pair<mpq, unsigned int>>& coeffs) const;
void add_non_basic_var_to_core_fields(unsigned ext_j, bool is_int);
void add_new_var_to_core_fields_for_mpq(bool register_in_basis);
mpq adjust_bound_for_int(lpvar j, lconstraint_kind&, const mpq&);
bool all_vars_are_registered(const vector<std::pair<mpq, lpvar>>& coeffs);
bool term_coeffs_are_ok(const vector<std::pair<mpq, lpvar>>& coeffs);
void add_row_from_term_no_constraint(lar_term* term, unsigned term_ext_index);
void add_basic_var_to_core_fields();
bool compare_values(impq const& lhs, lconstraint_kind k, const mpq& rhs);
void clear_columns_with_changed_bounds();
public:
const indexed_uint_set& columns_with_changed_bounds() const;
void insert_to_columns_with_changed_bounds(unsigned j);
const u_dependency* crossed_bounds_deps() const;
u_dependency*& crossed_bounds_deps();
lpvar crossed_bounds_column() const;
lpvar& crossed_bounds_column();
private:
bool validate_bound(lpvar j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep);
void add_dep_constraints_to_solver(lar_solver& ls, u_dependency* dep);
void add_bound_negation_to_solver(lar_solver& ls, lpvar j, lconstraint_kind kind, const mpq& right_side);
void add_constraint_to_validate(lar_solver& ls, constraint_index ci);
bool m_validate_blocker = false;
void update_column_type_and_bound_check_on_equal(unsigned j, const impq& right_side, constraint_index ci, unsigned&);
void update_column_type_and_bound(unsigned j, const impq& right_side, constraint_index ci);
public:
bool validate_blocker() const { return m_validate_blocker; }
bool & validate_blocker() { return m_validate_blocker; }
void update_column_type_and_bound(unsigned j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_column_type_and_bound(unsigned j, lconstraint_kind kind, const mpq& right_side, u_dependency* dep);
private:
void update_column_type_and_bound_with_ub(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_column_type_and_bound_with_no_ub(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_bound_with_ub_lb(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_bound_with_no_ub_lb(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_bound_with_ub_no_lb(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void update_bound_with_no_ub_no_lb(lpvar j, lconstraint_kind kind, const impq& right_side, u_dependency* dep);
void remove_non_fixed_from_fixed_var_table();
constraint_index add_var_bound_on_constraint_for_term(lpvar j, lconstraint_kind kind, const mpq& right_side);
void set_crossed_bounds_column_and_deps(unsigned j, bool lower_bound, u_dependency* dep);
unsigned row_of_basic_column(unsigned) const;
bool sizes_are_correct() const;
bool implied_bound_is_correctly_explained(implied_bound const& be, const vector<std::pair<mpq, unsigned>>& explanation) const;
template <typename T>
unsigned calculate_implied_bounds_for_row(unsigned row_index, lp_bound_propagator<T>& bp) {
if (A_r().m_rows[row_index].size() > settings().max_row_length_for_bound_propagation)
return 0;
++stats().m_bp_rows_analyzed;
return bound_analyzer_on_row<row_strip<mpq>, lp_bound_propagator<T>>::analyze_row(
A_r().m_rows[row_index],
m_zero_rs,
bp);
}
static void clean_popped_elements_for_heap(unsigned n, lpvar_heap& set);
static void clean_popped_elements(unsigned n, indexed_uint_set& set);
bool maximize_term_on_tableau(const lar_term& term, impq& term_max);
bool costs_are_zeros_for_r_solver() const;
bool reduced_costs_are_zeroes_for_r_solver() const;
void set_costs_to_zero(const lar_term& term);
void prepare_costs_for_r_solver(const lar_term& term);
bool maximize_term_on_feasible_r_solver(lar_term& term, impq& term_max, vector<std::pair<mpq,lpvar>>* max_coeffs);
u_dependency* get_dependencies_of_maximum(const vector<std::pair<mpq,lpvar>>& max_coeffs);
void set_upper_bound_witness(lpvar j, u_dependency* ci, impq const& high);
void set_lower_bound_witness(lpvar j, u_dependency* ci, impq const& low);
void substitute_terms_in_linear_expression(const vector<std::pair<mpq, lpvar>>& left_side_with_terms,
vector<std::pair<mpq, lpvar>>& left_side) const;
bool use_tableau_costs() const;
bool tableau_with_costs() const;
bool costs_are_used() const;
void change_basic_columns_dependend_on_a_given_nb_column(unsigned j, const numeric_pair<mpq>& delta);
void update_x_and_inf_costs_for_column_with_changed_bounds(unsigned j);
void add_touched_row(unsigned rid);
void detect_rows_with_changed_bounds_for_column(unsigned j);
void detect_rows_with_changed_bounds();
void update_x_and_inf_costs_for_columns_with_changed_bounds_tableau();
void solve_with_core_solver();
numeric_pair<mpq> get_basic_var_value_from_row(unsigned i);
bool all_constrained_variables_are_registered(const vector<std::pair<mpq, lpvar>>& left_side);
bool all_constraints_hold() const;
bool constraint_holds(const lar_base_constraint& constr) const;
static void register_in_map(std::unordered_map<lpvar, mpq>& coeffs, const lar_base_constraint& cn, const mpq& a);
static void register_monoid_in_map(std::unordered_map<lpvar, mpq>& coeffs, const mpq& a, unsigned j);
bool the_left_sides_sum_to_zero(const vector<std::pair<mpq, unsigned>>& evidence) const;
bool explanation_is_correct(explanation&) const;
bool inf_explanation_is_correct() const;
mpq sum_of_right_sides_of_explanation(explanation&) const;
mpq get_left_side_val(const lar_base_constraint& cns, const std::unordered_map<lpvar, mpq>& var_map) const;
void fill_var_set_for_random_update(unsigned sz, lpvar const* vars, vector<unsigned>& column_list);
bool column_represents_row_in_tableau(unsigned j);
void make_sure_that_the_bottom_right_elem_not_zero_in_tableau(unsigned i, unsigned j);
void remove_last_row_and_column_from_tableau(unsigned j);
void remove_last_column_from_A();
void remove_last_column_from_basis_tableau(unsigned j);
void remove_last_column_from_tableau();
void clean_inf_heap_of_r_solver_after_pop();
inline bool column_value_is_integer(unsigned j) const { return get_column_value(j).is_int(); }
bool model_is_int_feasible() const;
bool bound_is_integer_for_integer_column(unsigned j, const mpq& right_side) const;
const lar_core_solver& get_core_solver() const;
lar_core_solver& get_core_solver();
lpvar to_column(unsigned ext_j) const;
void fix_terms_with_rounded_columns();
bool remove_from_basis(unsigned);
lp_status adjust_integer_columns(lar_term const& term, impq const& prev_value, impq& term_max);
lar_term get_term_to_maximize(unsigned ext_j) const;
bool sum_first_coords(const lar_term& t, mpq& val) const;
void register_normalized_term(const lar_term&, lpvar);
void deregister_normalized_term(const lar_term&);
public:
u_dependency* find_improved_bound(lpvar j, bool is_lower, mpq& bound);
std::ostream& print_explanation(
std::ostream& out, const explanation& exp,
std::function<std::string(lpvar)> var_str = [](lpvar j) { return std::string("j") + T_to_string(j); }) const;
bool is_feasible() const;
const map<mpq, unsigned, obj_hash<mpq>, default_eq<mpq>>& fixed_var_table_int() const;
const map<mpq, unsigned, obj_hash<mpq>, default_eq<mpq>>& fixed_var_table_real() const;
bool find_in_fixed_tables(const rational& mpq, bool is_int, unsigned& j) const {
return is_int ? fixed_var_table_int().find(mpq, j) : fixed_var_table_real().find(mpq, j);
}
template <typename T>
void remove_non_fixed_from_table(T&);
bool inside_bounds(lpvar, const impq&) const;
void set_column_value(unsigned j, const impq& v);
inline void set_column_value_test(unsigned j, const impq& v) {
set_column_value(j, v);
}
lp_status maximize_term(unsigned j_or_term, impq& term_max, bool fix_int_cols,
u_dependency** upper_bound_dependencies = nullptr);
core_solver_pretty_printer<lp::mpq, lp::impq> pp(std::ostream& out) const;
void get_infeasibility_explanation(explanation&) const;
std::function<void(lpvar)> m_fixed_var_eh;
template <typename T>
u_dependency* explain_implied_bound(const implied_bound& ib, lp_bound_propagator<T>& bp) {
ib.explain_weighted([&](mpq const& coeff, u_dependency* dep) {
if (dep_manager().proofs_enabled()) {
explanation ex;
explain_evidence(dep, coeff, ex);
for (auto ev : ex)
bp.consume(ev.coeff(), ev.ci());
}
else
for (auto ci : flatten(dep))
bp.consume(coeff, ci);
});
return dep_manager().proofs_enabled() ? ib.explain_implied() : nullptr;
}
void set_value_for_nbasic_column(unsigned j, const impq& new_val);
void remove_fixed_vars_from_base();
struct solution {
unsigned j;
lar_term t;
};
lpvar add_named_var(unsigned ext_j, bool is_integer, const std::string&);
void solve_for(unsigned_vector const& js, vector<solution>& sol);
void check_fixed(unsigned j);
void solve_for(unsigned j, uint_set& tabu, vector<solution>& sol);
unsigned get_base_column_in_row(unsigned row_index) const;
#ifdef Z3DEBUG
bool fixed_base_removed_correctly() const;
#endif
constraint_index mk_var_bound(lpvar j, lconstraint_kind kind, const mpq& right_side);
constraint_index mk_var_bound(lpvar j, lconstraint_kind kind, const mpq& right_side, const mpq& eps);
void activate_check_on_equal(constraint_index, lpvar&);
void activate(constraint_index);
bool constraint_is_redundant(constraint_index ci) const;
void random_update(unsigned sz, lpvar const* vars);
void add_column_rows_to_touched_rows(lpvar j);
const indexed_uint_set & touched_rows() const;
indexed_uint_set & touched_rows();
unsigned_vector& row_bounds_to_replay();
template <typename T>
void propagate_bounds_for_touched_rows(lp_bound_propagator<T>& bp) {
if (settings().propagate_eqs()) {
if (settings().random_next() % 10 == 0)
remove_fixed_vars_from_base();
bp.clear_for_eq();
for (unsigned i : touched_rows()) {
unsigned offset_eqs = stats().m_offset_eqs;
bp.cheap_eq_on_nbase(i);
if (settings().get_cancel_flag())
return;
if (stats().m_offset_eqs > offset_eqs)
row_bounds_to_replay().push_back(i);
}
}
for (unsigned i : touched_rows()) {
calculate_implied_bounds_for_row(i, bp);
if (settings().get_cancel_flag())
return;
}
touched_rows().reset();
}
void collect_more_rows_for_lp_propagation();
template <typename T>
void check_missed_propagations(lp_bound_propagator<T>& bp) {
for (unsigned i = 0; i < A_r().row_count(); ++i)
if (!touched_rows().contains(i))
if (0 < calculate_implied_bounds_for_row(i, bp)) {
verbose_stream() << i << ": " << get_row(i) << "\n";
}
}
const impq m_zero_rs; public:
std::function<void (const lar_term*)> m_add_term_callback;
std::function<void (unsigned)> m_update_column_bound_callback;
bool external_is_used(unsigned) const;
void pop(unsigned k);
trail_stack& trail();
bool compare_values(lpvar j, lconstraint_kind kind, const mpq& right_side);
lpvar add_term(const vector<std::pair<mpq, lpvar>>& coeffs, unsigned ext_i);
void register_existing_terms();
class scoped_auxiliary {
lar_solver& s;
public:
scoped_auxiliary(lar_solver& s);
~scoped_auxiliary();
};
constraint_index add_var_bound(lpvar, lconstraint_kind, const mpq&);
constraint_index add_var_bound_check_on_equal(lpvar, lconstraint_kind, const mpq&, lpvar&);
lpvar add_var(unsigned ext_j, bool is_integer);
void set_cut_strategy(unsigned cut_frequency);
inline unsigned column_count() const { return A_r().column_count(); }
lpvar local_to_external(lpvar idx) const;
bool column_associated_with_row(lpvar j) const;
unsigned row_count() const { return A_r().row_count(); }
bool var_is_registered(lpvar vj) const;
void clear_inf_heap() {
get_core_solver().m_r_solver.inf_heap().clear();
}
void pivot(int entering, int leaving) {
get_core_solver().pivot(entering, leaving);
}
indexed_uint_set& basic_columns_with_changed_cost();
template <typename ChangeReport>
void change_basic_columns_dependend_on_a_given_nb_column_report(unsigned j,
const numeric_pair<mpq>& delta,
const ChangeReport& after) {
for (const auto& c : A_r().m_columns[j]) {
unsigned bj = get_core_solver().m_r_basis[c.var()];
if (tableau_with_costs())
basic_columns_with_changed_cost().insert(bj);
get_core_solver().m_r_solver.add_delta_to_x_and_track_feasibility(bj, -A_r().get_val(c) * delta);
after(bj);
TRACE(change_x_del,
tout << "changed basis column " << bj << ", it is " << (get_core_solver().m_r_solver.column_is_feasible(bj) ? "feas" : "inf") << std::endl;);
}
}
template <typename ChangeReport>
void set_value_for_nbasic_column_report(unsigned j,
const impq& new_val,
const ChangeReport& after) {
SASSERT(!is_base(j));
auto& x = get_core_solver().r_x(j);
auto delta = new_val - x;
x = new_val;
after(j);
change_basic_columns_dependend_on_a_given_nb_column_report(j, delta, after);
}
template <typename Blocker, typename ChangeReport>
bool try_to_patch(lpvar j, const mpq& val,
const Blocker& is_blocked,
const ChangeReport& change_report) {
if (is_base(j)) {
TRACE(nla_solver, get_int_solver()->display_row_info(tout, row_of_basic_column(j)) << "\n";);
if (!remove_from_basis(j))
return false;
}
impq ival(val);
if (is_blocked(j, ival))
return false;
TRACE(nla_solver, tout << "j" << j << " not blocked\n";);
impq delta = get_column_value(j) - ival;
for (auto c : A_r().column(j)) {
unsigned row_index = c.var();
const mpq& a = c.coeff();
unsigned rj = get_core_solver().m_r_basis[row_index];
impq rj_new_val = a * delta + get_column_value(rj);
if (is_blocked(rj, rj_new_val))
return false;
}
set_value_for_nbasic_column_report(j, ival, change_report);
return true;
}
inline bool column_has_upper_bound(unsigned j) const {
return get_core_solver().m_r_solver.column_has_upper_bound(j);
}
inline bool column_has_lower_bound(unsigned j) const {
return get_core_solver().m_r_solver.column_has_lower_bound(j);
}
svector<constraint_index> const& flatten(u_dependency* d);
void push_explanation(u_dependency* d, explanation& ex) {
for (auto ci : flatten(d))
ex.push_back(ci);
}
const evidence_manager& dep_manager() const;
evidence_manager& dep_manager();
void explain_evidence(u_dependency* dep, mpq const& coefficient, explanation& ex) const;
u_dependency* explain_integer_infeasibility(lar_term const& row, unsigned_vector const& boxed = {});
u_dependency* get_column_upper_bound_witness(unsigned j) const;
const impq& get_upper_bound(lpvar j) const;
const impq& get_lower_bound(lpvar j) const;
mpq bound_span_x(lpvar j) const;
bool has_lower_bound(lpvar var, u_dependency*& ci, mpq& value, bool& is_strict) const;
bool has_upper_bound(lpvar var, u_dependency*& ci, mpq& value, bool& is_strict) const;
bool has_bound_of_type(lpvar var, u_dependency*& ci, mpq& value, bool& is_strict, bool is_upper) const;
bool has_value(lpvar var, mpq& value) const;
bool fetch_normalized_term_column(const lar_term& t, std::pair<mpq, lpvar>&) const;
bool column_is_fixed(unsigned j) const;
bool column_is_free(unsigned j) const;
bool column_is_feasible(unsigned j) const;
lp_settings& settings();
lp_settings const& settings() const;
statistics& stats();
void backup_x() { get_core_solver().backup_x(); }
void restore_x() {
auto& cs = get_core_solver();
unsigned backup_sz = cs.backup_x_size();
unsigned current_sz = cs.m_n();
CTRACE(lar_solver_restore, backup_sz != current_sz,
tout << "restore_x: backup_sz=" << backup_sz
<< " current_sz=" << current_sz << "\n";);
cs.restore_x();
if (backup_sz < current_sz) {
for (unsigned i = 0; i < A_r().row_count(); i++)
set_column_value(r_basis()[i], get_basic_var_value_from_row(i));
move_non_basic_columns_to_bounds();
}
else {
SASSERT(ax_is_correct());
SASSERT(cs.m_r_solver.calc_current_x_is_feasible_include_non_basis());
}
}
void updt_params(params_ref const& p);
column_type get_column_type(unsigned j) const { return get_core_solver().m_column_types()[j]; }
const vector<column_type>& get_column_types() const { return get_core_solver().m_column_types(); }
std::ostream& print_terms(std::ostream& out) const;
std::ostream& print_term(lar_term const& term, std::ostream& out) const;
static std::ostream& print_term_as_indices(lar_term const& term, std::ostream& out);
std::ostream& print_constraint_indices_only(const lar_base_constraint* c, std::ostream& out) const;
std::ostream& print_implied_bound(const implied_bound& be, std::ostream& out) const;
std::ostream& print_values(std::ostream& out) const;
std::ostream& display(std::ostream& out) const;
std::ostream& display_constraint(std::ostream& out, constraint_index ci) const;
bool init_model() const;
mpq from_model_in_impq_to_mpq(const impq& v) const;
mpq get_value(lpvar j) const;
void get_model(std::unordered_map<lpvar, mpq>& variable_values) const;
void get_rid_of_inf_eps();
void get_model_do_not_care_about_diff_vars(std::unordered_map<lpvar, mpq>& variable_values) const;
void get_model_do_not_care_about_diff_vars(std::unordered_map<lpvar, mpq>& variable_values, const mpq& delta) const;
std::string get_variable_name(lpvar vi) const override;
void set_variable_name(lpvar vi, const std::string&);
unsigned number_of_vars() const;
inline bool is_base(unsigned j) const { return get_core_solver().m_r_heading[j] >= 0; }
inline const impq& column_lower_bound(unsigned j) const {
return get_core_solver().lower_bound(j);
}
inline const impq& column_upper_bound(unsigned j) const {
return get_core_solver().upper_bound(j);
}
inline bool column_is_bounded(unsigned j) const {
return get_core_solver().column_is_bounded(j);
}
bool check_feasible() const {
return get_core_solver().m_r_solver.calc_current_x_is_feasible_include_non_basis();
}
bool are_equal(lpvar j, lpvar k);
std::pair<constraint_index, constraint_index> add_equality(lpvar j, lpvar k);
u_dependency* get_bound_constraint_witnesses_for_column(unsigned j);
template <typename T>
u_dependency* get_bound_constraint_witnesses_for_columns(const T& collection) {
u_dependency* dep = nullptr;
for (auto j : collection) {
u_dependency* d = get_bound_constraint_witnesses_for_column(j);
dep = dep_manager().mk_join(dep, d);
}
return dep;
}
std::ostream& print_expl(std::ostream& out, const explanation& exp) const {
for (auto p : exp)
constraints().display(
out, [this](lpvar j) { return get_variable_name(j); }, p.ci());
return out;
}
void explain_fixed_column(unsigned j, explanation& ex);
void explain_fixed_in_row(unsigned row, explanation& ex);
u_dependency* join_deps(u_dependency* a, u_dependency *b) { return dep_manager().mk_join(a, b); }
const constraint_set & constraints() const;
void push();
void pop();
unsigned get_scope_level() const;
u_dependency* get_column_lower_bound_witness(unsigned j) const;
bool column_has_term(lpvar j) const;
std::ostream& print_column_info(unsigned j, std::ostream& out, bool print_expl = false) const;
std::ostream& display_column_explanation(std::ostream& out, unsigned j) const;
void subst_known_terms(lar_term*);
std::ostream& print_column_bound_info(unsigned j, std::ostream& out) const {
return get_core_solver().m_r_solver.print_column_bound_info(j, out);
}
bool has_int_var() const;
inline bool has_inf_int() const {
for (unsigned j = 0; j < column_count(); ++j) {
if (column_is_int(j) && !column_value_is_int(j))
return true;
}
return false;
}
const vector<lar_term*>& terms() const;
void set_int_solver(int_solver* int_slv);
int_solver* get_int_solver();
const int_solver* get_int_solver() const;
const lar_term& get_term(lpvar j) const;
lp_status find_feasible_solution();
void move_non_basic_columns_to_bounds();
bool move_non_basic_column_to_bounds(unsigned j);
bool move_lpvar_to_value(lpvar j, mpq const& value);
inline bool r_basis_has_inf_int() const {
for (unsigned j : r_basis()) {
if (column_is_int(j) && !column_value_is_int(j))
return true;
}
return false;
}
void round_to_integer_solution();
inline const row_strip<mpq>& get_row(unsigned i) const { return A_r().m_rows[i]; }
inline const row_strip<mpq>& basic2row(unsigned i) const { return A_r().m_rows[row_of_basic_column(i)]; }
inline const column_strip& get_column(unsigned i) const { return A_r().m_columns[i]; }
bool row_is_correct(unsigned i) const;
bool ax_is_correct() const;
bool get_equality_and_right_side_for_term_on_current_x(lpvar j, mpq& rs, u_dependency*& ci, bool& upper_bound) const;
bool var_is_int(lpvar v) const;
inline const std_vector<int>& r_heading() const { return get_core_solver().m_r_heading; }
inline const vector<unsigned>& r_basis() const { return get_core_solver().r_basis(); }
inline const vector<unsigned>& r_nbasis() const { return get_core_solver().r_nbasis(); }
inline bool column_is_real(unsigned j) const { return !column_is_int(j); }
lp_status get_status() const;
bool has_changed_columns() const;
void set_status(lp_status s);
lp_status solve();
void fill_explanation_from_crossed_bounds_column(explanation& evidence) const;
bool tighten_term_bounds_by_delta(lpvar j, const impq&);
explicit lar_solver(bool proofs = false);
void track_touched_rows(bool v);
bool touched_rows_are_tracked() const;
~lar_solver() override;
const vector<impq>& r_x() const { return get_core_solver().r_x(); }
bool column_is_int(unsigned j) const;
inline bool column_value_is_int(unsigned j) const { return get_core_solver().r_x(j).is_int(); }
inline static_matrix<mpq, impq>& A_r() { return get_core_solver().m_r_A; }
inline const static_matrix<mpq, impq>& A_r() const { return get_core_solver().m_r_A; }
const impq& get_column_value(lpvar j) const { return get_core_solver().r_x(j); }
lpvar external_to_local(unsigned j) const;
unsigned usage_in_terms(lpvar j) const;
std::string get_bounds_string(unsigned j) const;
void write_bound_lemma(unsigned j, bool is_low, const std::string & location, std::ostream & out) const;
std::function<void (const indexed_uint_set& columns_with_changed_bound)> m_find_monics_with_changed_bounds_func = nullptr;
friend int_solver;
friend int_branch;
friend imp;
};
}