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z3/src/math/lp/lar_solver.h
Nikolaj Bjorner e50082b484 add tv
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2020-03-25 19:43:55 -07:00

645 lines
23 KiB
C++

/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
<name>
Abstract:
<abstract>
Author:
Nikolaj Bjorner (nbjorner)
Lev Nachmanson (levnach)
Revision History:
--*/
#pragma once
#include "util/vector.h"
#include <utility>
#include "util/debug.h"
#include "util/buffer.h"
#include <unordered_map>
#include <unordered_set>
#include <string>
#include <algorithm>
#include <stack>
#include <functional>
#include "math/lp/lar_constraints.h"
#include "math/lp/lar_core_solver.h"
#include "math/lp/numeric_pair.h"
#include "math/lp/scaler.h"
#include "math/lp/lp_primal_core_solver.h"
#include "math/lp/random_updater.h"
#include "math/lp/stacked_value.h"
#include "math/lp/stacked_vector.h"
#include "math/lp/implied_bound.h"
#include "math/lp/bound_analyzer_on_row.h"
#include "math/lp/conversion_helper.h"
#include "math/lp/int_solver.h"
#include "math/lp/nra_solver.h"
#include "math/lp/lp_bound_propagator.h"
namespace lp {
typedef unsigned lpvar;
const lpvar null_lpvar = UINT_MAX;
const constraint_index null_ci = UINT_MAX;
class lar_solver : public column_namer {
struct term_hasher {
std::size_t operator()(const lar_term &t) const
{
using std::size_t;
using std::hash;
using std::string;
size_t seed = 0;
int i = 0;
for (const auto p : t) {
hash_combine(seed, p.var());
hash_combine(seed, p.coeff());
if (i++ > 10)
break;
}
return seed;
}
};
struct term_comparer {
bool operator()(const lar_term &a, const lar_term& b) const
{
return a == b;
}
};
//////////////////// fields //////////////////////////
lp_settings m_settings;
lp_status m_status;
stacked_value<simplex_strategy_enum> m_simplex_strategy;
stacked_value<int> m_infeasible_column; // such can be found at the initialization step
public:
lar_core_solver m_mpq_lar_core_solver;
private:
int_solver * m_int_solver;
bool m_need_register_terms;
public:
var_register m_var_register;
var_register m_term_register;
stacked_vector<ul_pair> m_columns_to_ul_pairs;
constraint_set m_constraints;
// the set of column indices j such that bounds have changed for j
int_set m_columns_with_changed_bound;
int_set m_rows_with_changed_bounds;
int_set m_basic_columns_with_changed_cost;
// these are basic columns with the value changed, so the the corresponding row in the tableau
// does not sum to zero anymore
int_set m_incorrect_columns;
stacked_value<int> m_infeasible_column_index; // such can be found at the initialization step
stacked_value<unsigned> m_term_count;
vector<lar_term*> m_terms;
indexed_vector<mpq> m_column_buffer;
std::unordered_map<lar_term, std::pair<mpq, unsigned>, term_hasher, term_comparer>
m_normalized_terms_to_columns;
// end of fields
const vector<lar_term*> & terms() const { return m_terms; }
lar_term const& term(unsigned i) const { return *m_terms[i]; }
constraint_set const& constraints() const { return m_constraints; }
void set_int_solver(int_solver * int_slv) { m_int_solver = int_slv; }
int_solver * get_int_solver() { return m_int_solver; }
////////////////// methods ////////////////////////////////
static_matrix<mpq, numeric_pair<mpq>> & A_r();
static_matrix<mpq, numeric_pair<mpq>> const & A_r() const;
static_matrix<double, double> & A_d();
static_matrix<double, double > const & A_d() const;
static bool valid_index(unsigned j){ return static_cast<int>(j) >= 0;}
bool column_is_int(unsigned j) const;
bool column_value_is_int(unsigned j) const {
return m_mpq_lar_core_solver.m_r_x[j].is_int();
}
const impq& get_column_value(unsigned j) const {
return m_mpq_lar_core_solver.m_r_x[j];
}
void set_column_value(unsigned j, const impq& v) {
m_mpq_lar_core_solver.m_r_x[j] = v;
}
const mpq& get_column_value_rational(unsigned j) const {
if (tv::is_term(j)) {
j = m_var_register.external_to_local(j);
}
return m_mpq_lar_core_solver.m_r_x[j].x;
}
bool column_is_fixed(unsigned j) const;
bool column_is_free(unsigned j) const;
public:
// init region
bool strategy_is_undecided() const;
var_index add_var(unsigned ext_j, bool is_integer);
var_index add_named_var(unsigned ext_j, bool is_integer, const std::string&);
void register_new_ext_var_index(unsigned ext_v, bool is_int);
bool external_is_used(unsigned) const;
bool term_is_int(const lar_term * t) const;
bool term_is_int(const vector<std::pair<mpq, unsigned int>> & coeffs) const;
bool var_is_int(var_index v) const;
void add_non_basic_var_to_core_fields(unsigned ext_j, bool is_int);
void add_new_var_to_core_fields_for_doubles(bool register_in_basis);
void add_new_var_to_core_fields_for_mpq(bool register_in_basis);
mpq adjust_bound_for_int(lpvar j, lconstraint_kind&, const mpq&);
// terms
bool all_vars_are_registered(const vector<std::pair<mpq, var_index>> & coeffs);
var_index add_term(const vector<std::pair<mpq, var_index>> & coeffs, unsigned ext_i);
var_index add_term_undecided(const vector<std::pair<mpq, var_index>> & coeffs);
bool term_coeffs_are_ok(const vector<std::pair<mpq, var_index>> & coeffs);
void push_term(lar_term* t);
void add_row_for_term(const lar_term * term, unsigned term_ext_index);
void add_row_from_term_no_constraint(const lar_term * term, unsigned term_ext_index);
void add_basic_var_to_core_fields();
constraint_index mk_var_bound(var_index j, lconstraint_kind kind, const mpq & right_side);
void activate(constraint_index ci);
constraint_index add_var_bound(var_index j, lconstraint_kind kind, const mpq & right_side) ;
bool compare_values(var_index j, lconstraint_kind kind, const mpq & right_side);
bool compare_values(impq const& lhs, lconstraint_kind k, const mpq & rhs);
void update_column_type_and_bound(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_column_type_and_bound_with_ub(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_column_type_and_bound_with_no_ub(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_bound_with_ub_lb(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_bound_with_no_ub_lb(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_bound_with_ub_no_lb(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
void update_bound_with_no_ub_no_lb(var_index j, lconstraint_kind kind, const mpq & right_side, constraint_index constr_index);
constraint_index add_var_bound_on_constraint_for_term(var_index j, lconstraint_kind kind, const mpq & right_side);
void set_infeasible_column(unsigned j) {
set_status(lp_status::INFEASIBLE);
m_infeasible_column = j;
}
constraint_index add_constraint_from_term_and_create_new_column_row(unsigned term_j, const lar_term* term,
lconstraint_kind kind, const mpq & right_side);
unsigned row_of_basic_column(unsigned) const;
void decide_on_strategy_and_adjust_initial_state();
void adjust_initial_state();
void adjust_initial_state_for_lu();
void adjust_initial_state_for_tableau_rows();
// this fills the last row of A_d and sets the basis column: -1 in the last column of the row
void fill_last_row_of_A_d(static_matrix<double, double> & A, const lar_term* ls);
//end of init region
lp_settings & settings();
lp_settings const & settings() const;
void clear();
lar_solver();
void set_track_pivoted_rows(bool v);
bool get_track_pivoted_rows() const;
virtual ~lar_solver();
bool use_lu() const;
bool sizes_are_correct() const;
bool implied_bound_is_correctly_explained(implied_bound const & be, const vector<std::pair<mpq, unsigned>> & explanation) const;
void analyze_new_bounds_on_row(
unsigned row_index,
lp_bound_propagator & bp);
void analyze_new_bounds_on_row_tableau(
unsigned row_index,
lp_bound_propagator & bp);
void substitute_basis_var_in_terms_for_row(unsigned i);
void calculate_implied_bounds_for_row(unsigned i, lp_bound_propagator & bp);
unsigned adjust_column_index_to_term_index(unsigned j) const;
unsigned map_term_index_to_column_index(unsigned j) const;
var_index local_to_external(var_index idx) const { return tv::is_term(idx)?
m_term_register.local_to_external(idx) : m_var_register.local_to_external(idx); }
unsigned number_of_vars() const { return m_var_register.size(); }
var_index external_to_local(unsigned j) const {
var_index local_j;
if (
m_var_register.external_is_used(j, local_j) ||
m_term_register.external_is_used(j, local_j))
{
return local_j;
}
else
return -1;
}
bool column_has_upper_bound(unsigned j) const {
return m_mpq_lar_core_solver.m_r_solver.column_has_upper_bound(j);
}
bool column_has_lower_bound(unsigned j) const {
return m_mpq_lar_core_solver.m_r_solver.column_has_lower_bound(j);
}
const impq& get_upper_bound(unsigned j) const {
return m_mpq_lar_core_solver.m_r_solver.m_upper_bounds[j];
}
const impq& get_lower_bound(unsigned j) const {
return m_mpq_lar_core_solver.m_r_solver.m_lower_bounds[j];
}
void propagate_bounds_on_a_term(const lar_term& t, lp_bound_propagator & bp, unsigned term_offset);
void explain_implied_bound(implied_bound & ib, lp_bound_propagator & bp);
bool term_is_used_as_row(unsigned term) const;
void propagate_bounds_on_terms(lp_bound_propagator & bp);
// goes over touched rows and tries to induce bounds
void propagate_bounds_for_touched_rows(lp_bound_propagator & bp);
lp_status get_status() const;
void set_status(lp_status s);
lp_status find_feasible_solution();
lp_status solve();
void fill_explanation_from_infeasible_column(explanation & evidence) const;
unsigned get_total_iterations() const;
// 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<unsigned> get_list_of_all_var_indices() const;
void push();
static void clean_popped_elements(unsigned n, int_set& set);
static void shrink_inf_set_after_pop(unsigned n, int_set & set);
void pop(unsigned k);
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_corrected_r_solver(lar_term & term, impq &term_max);
// starting from a given feasible state look for the maximum of the term
// return true if found and false if unbounded
lp_status maximize_term(unsigned j_or_term, impq &term_max);
const lar_term & get_term(unsigned j) const;
void pop_core_solver_params();
void pop_core_solver_params(unsigned k);
void set_upper_bound_witness(var_index j, constraint_index ci);
void set_lower_bound_witness(var_index j, constraint_index ci);
void substitute_terms_in_linear_expression( const vector<std::pair<mpq, var_index>>& left_side_with_terms,
vector<std::pair<mpq, var_index>> &left_side) const;
void detect_rows_of_bound_change_column_for_nbasic_column(unsigned j);
void detect_rows_of_bound_change_column_for_nbasic_column_tableau(unsigned j);
bool use_tableau() const;
bool use_tableau_costs() const;
void detect_rows_of_column_with_bound_change(unsigned j);
void adjust_x_of_column(unsigned j);
bool row_is_correct(unsigned i) const;
bool ax_is_correct() 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);
unsigned num_changed_bounds() const { return m_rows_with_changed_bounds.size(); }
void detect_rows_with_changed_bounds_for_column(unsigned j);
void detect_rows_with_changed_bounds();
inline bool is_base(unsigned j) const {
return m_mpq_lar_core_solver.m_r_heading[j] >= 0;
}
bool move_non_basic_columns_to_bounds();
bool move_non_basic_column_to_bounds(unsigned j);
void set_value_for_nbasic_column(unsigned j, const impq & new_val);
void update_x_and_inf_costs_for_columns_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);
template <typename K, typename L>
void add_last_rows_to_lu(lp_primal_core_solver<K,L> & s);
bool x_is_correct() const;
bool var_is_registered(var_index vj) const;
void fill_last_row_of_A_r(static_matrix<mpq, numeric_pair<mpq>> & A, const lar_term * ls);
template <typename U, typename V>
void create_matrix_A(static_matrix<U, V> & matr);
template <typename U, typename V>
void copy_from_mpq_matrix(static_matrix<U, V> & matr);
bool try_to_set_fixed(column_info<mpq> & ci);
column_type get_column_type(unsigned j) const;
bool all_constrained_variables_are_registered(const vector<std::pair<mpq, var_index>>& left_side);
bool all_constraints_hold() const;
bool constraint_holds(const lar_base_constraint & constr, std::unordered_map<var_index, mpq> & var_map) const;
bool the_relations_are_of_same_type(const vector<std::pair<mpq, unsigned>> & evidence, lconstraint_kind & the_kind_of_sum) const;
static void register_in_map(std::unordered_map<var_index, mpq> & coeffs, const lar_base_constraint & cn, const mpq & a);
static void register_monoid_in_map(std::unordered_map<var_index, mpq> & coeffs, const mpq & a, unsigned j);
bool the_left_sides_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence) const;
bool the_right_sides_do_not_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence);
bool explanation_is_correct(explanation&) const;
bool inf_explanation_is_correct() const;
mpq sum_of_right_sides_of_explanation(explanation &) const;
bool has_lower_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) const;
bool has_upper_bound(var_index var, constraint_index& ci, mpq& value, bool& is_strict) const;
bool has_value(var_index var, mpq& value) const;
void get_infeasibility_explanation(explanation &) const;
void get_infeasibility_explanation_for_inf_sign(
explanation & exp,
const vector<std::pair<mpq, unsigned>> & inf_row,
int inf_sign) const;
void get_model(std::unordered_map<var_index, mpq> & variable_values) const;
void get_rid_of_inf_eps();
void get_model_do_not_care_about_diff_vars(std::unordered_map<var_index, mpq> & variable_values) const;
std::string get_variable_name(var_index vi) const;
void set_variable_name(var_index vi, std::string);
// ********** print region start
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;
mpq get_left_side_val(const lar_base_constraint & cns, const std::unordered_map<var_index, mpq> & var_map) const;
void fill_var_set_for_random_update(unsigned sz, var_index const * vars, vector<unsigned>& column_list);
void random_update(unsigned sz, var_index const * vars);
void pivot_fixed_vars_from_basis();
void pop();
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 pop_tableau();
void clean_inf_set_of_r_solver_after_pop();
void shrink_explanation_to_minimum(vector<std::pair<mpq, constraint_index>> & explanation) const;
bool column_value_is_integer(unsigned j) const {
return get_column_value(j).is_int();
}
bool column_is_real(unsigned j) const {
return !column_is_int(j);
}
bool model_is_int_feasible() const;
const impq & column_lower_bound(unsigned j) const {
return m_mpq_lar_core_solver.lower_bound(j);
}
const impq & column_upper_bound(unsigned j) const {
return m_mpq_lar_core_solver.upper_bound(j);
}
bool column_is_bounded(unsigned j) const {
return m_mpq_lar_core_solver.column_is_bounded(j);
}
std::pair<constraint_index, constraint_index> add_equality(lpvar j, lpvar k);
void get_bound_constraint_witnesses_for_column(unsigned j, constraint_index & lc, constraint_index & uc) const {
const ul_pair & ul = m_columns_to_ul_pairs[j];
lc = ul.lower_bound_witness();
uc = ul.upper_bound_witness();
}
indexed_vector<mpq> & get_column_in_lu_mode(unsigned j) {
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);
return m_column_buffer;
}
bool bound_is_integer_for_integer_column(unsigned j, const mpq & right_side) const;
const row_strip<mpq> & get_row(unsigned i) {
return A_r().m_rows[i];
}
unsigned get_base_column_in_row(unsigned row_index) const {
return m_mpq_lar_core_solver.m_r_solver.get_base_column_in_row(row_index);
}
constraint_index get_column_upper_bound_witness(unsigned j) const {
if (tv::is_term(j)) {
j = m_var_register.external_to_local(j);
}
return m_columns_to_ul_pairs()[j].upper_bound_witness();
}
constraint_index get_column_lower_bound_witness(unsigned j) const {
if (tv::is_term(j)) {
j = m_var_register.external_to_local(j);
}
return m_columns_to_ul_pairs()[j].lower_bound_witness();
}
void subs_term_columns(lar_term& t) {
vector<std::pair<unsigned,unsigned>> columns_to_subs;
for (const auto & m : t) {
unsigned tj = adjust_column_index_to_term_index(m.var());
if (tj == m.var()) continue;
columns_to_subs.push_back(std::make_pair(m.var(), tj));
}
for (const auto & p : columns_to_subs) {
t.subst_index(p.first, p.second);
}
}
std::ostream& print_column_info(unsigned j, std::ostream& out) const {
m_mpq_lar_core_solver.m_r_solver.print_column_info(j, out);
if (tv::is_term(j)) {
const lar_term& t = * m_terms[tv::unmask_term(j)];
print_term_as_indices(t, out) << "\n";
} else if(column_corresponds_to_term(j)) {
const lar_term& t = * m_terms[tv::unmask_term(m_var_register.local_to_external(j))];
print_term_as_indices(t, out) << "\n";
}
return out;
}
bool has_int_var() const;
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;
}
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;
}
lar_core_solver & get_core_solver() { return m_mpq_lar_core_solver; }
bool column_corresponds_to_term(unsigned) const;
void catch_up_in_updating_int_solver();
var_index to_column(unsigned ext_j) const;
bool tighten_term_bounds_by_delta(unsigned, const impq&);
void round_to_integer_solution();
void fix_terms_with_rounded_columns();
void update_delta_for_terms(const impq & delta, unsigned j, const vector<unsigned>&);
void fill_vars_to_terms(vector<vector<unsigned>> & vars_to_terms);
unsigned column_count() const { return A_r().column_count(); }
unsigned row_count() const { return A_r().row_count(); }
const vector<unsigned> & r_basis() const { return m_mpq_lar_core_solver.r_basis(); }
const vector<unsigned> & r_nbasis() const { return m_mpq_lar_core_solver.r_nbasis(); }
bool get_equality_and_right_side_for_term_on_current_x(unsigned i, mpq &rs, constraint_index& ci, bool &upper_bound) const;
bool remove_from_basis(unsigned);
lar_term get_term_to_maximize(unsigned ext_j) const;
void set_cut_strategy(unsigned cut_frequency);
bool sum_first_coords(const lar_term& t, mpq & val) const;
void collect_rounded_rows_to_fix();
void register_existing_terms();
void register_normalized_term(const lar_term&, lpvar);
void deregister_normalized_term(const lar_term&);
bool fetch_normalized_term_column(const lar_term& t, std::pair<mpq, lpvar>& ) const;
};
}