mirror of
https://github.com/Z3Prover/z3
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1550 lines
59 KiB
C++
1550 lines
59 KiB
C++
/*
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Copyright (c) 2017 Microsoft Corporation
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Author: Lev Nachmanson
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*/
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#pragma once
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#include "util/vector.h"
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#include <utility>
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#include "util/debug.h"
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#include "util/buffer.h"
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#include <unordered_map>
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#include <unordered_set>
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#include <string>
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#include "util/lp/lar_constraints.h"
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#include <functional>
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#include "util/lp/lar_core_solver.h"
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#include <algorithm>
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#include "util/lp/numeric_pair.h"
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#include "util/lp/scaler.h"
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#include "util/lp/lp_primal_core_solver.h"
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#include "util/lp/random_updater.h"
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#include <stack>
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#include "util/lp/stacked_map.h"
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#include "util/lp/stacked_value.h"
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#include "util/lp/stacked_vector.h"
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#include "util/lp/stacked_unordered_set.h"
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#include "util/lp/iterator_on_pivot_row.h"
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#include "util/lp/implied_bound.h"
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#include "util/lp/bound_analyzer_on_row.h"
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#include "util/lp/iterator_on_term_with_basis_var.h"
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#include "util/lp/iterator_on_row.h"
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#include "util/lp/quick_xplain.h"
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#include "util/lp/conversion_helper.h"
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namespace lean {
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class lar_solver : public column_namer {
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//////////////////// fields //////////////////////////
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lp_settings m_settings;
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stacked_value<lp_status> m_status;
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stacked_value<simplex_strategy_enum> m_simplex_strategy;
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std::unordered_map<unsigned, var_index> m_ext_vars_to_columns;
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vector<unsigned> m_columns_to_ext_vars_or_term_indices;
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stacked_vector<ul_pair> m_vars_to_ul_pairs;
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vector<lar_base_constraint*> m_constraints;
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stacked_value<unsigned> m_constraint_count;
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// the set of column indices j such that bounds have changed for j
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int_set m_columns_with_changed_bound;
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int_set m_rows_with_changed_bounds;
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int_set m_basic_columns_with_changed_cost;
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stacked_value<int> m_infeasible_column_index; // such can be found at the initialization step
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stacked_value<unsigned> m_term_count;
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vector<lar_term*> m_terms;
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vector<lar_term*> m_orig_terms;
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const var_index m_terms_start_index;
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indexed_vector<mpq> m_column_buffer;
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public:
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lar_core_solver m_mpq_lar_core_solver;
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unsigned constraint_count() const {
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return m_constraints.size();
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}
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const lar_base_constraint& get_constraint(unsigned ci) const {
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return *(m_constraints[ci]);
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}
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////////////////// methods ////////////////////////////////
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static_matrix<mpq, numeric_pair<mpq>> & A_r() { return m_mpq_lar_core_solver.m_r_A;}
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static_matrix<mpq, numeric_pair<mpq>> const & A_r() const { return m_mpq_lar_core_solver.m_r_A;}
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static_matrix<double, double> & A_d() { return m_mpq_lar_core_solver.m_d_A;}
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static_matrix<double, double > const & A_d() const { return m_mpq_lar_core_solver.m_d_A;}
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static bool valid_index(unsigned j){ return static_cast<int>(j) >= 0;}
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public:
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lp_settings & settings() { return m_settings;}
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lp_settings const & settings() const { return m_settings;}
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void clear() {lean_assert(false); // not implemented
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}
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lar_solver() : m_status(OPTIMAL),
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m_infeasible_column_index(-1),
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m_terms_start_index(1000000),
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m_mpq_lar_core_solver(m_settings, *this)
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{}
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void set_propagate_bounds_on_pivoted_rows_mode(bool v) {
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m_mpq_lar_core_solver.m_r_solver.m_pivoted_rows = v? (& m_rows_with_changed_bounds) : nullptr;
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}
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virtual ~lar_solver(){
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for (auto c : m_constraints)
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delete c;
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for (auto t : m_terms)
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delete t;
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for (auto t : m_orig_terms)
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delete t;
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}
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#include "util/lp/init_lar_solver.h"
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numeric_pair<mpq> const& get_value(var_index vi) const { return m_mpq_lar_core_solver.m_r_x[vi]; }
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bool is_term(var_index j) const {
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return j >= m_terms_start_index && j - m_terms_start_index < m_terms.size();
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}
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unsigned adjust_term_index(unsigned j) const {
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lean_assert(is_term(j));
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return j - m_terms_start_index;
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}
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bool use_lu() const { return m_settings.simplex_strategy() == simplex_strategy_enum::lu; }
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bool sizes_are_correct() const {
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lean_assert(strategy_is_undecided() || !m_mpq_lar_core_solver.need_to_presolve_with_double_solver() || A_r().column_count() == A_d().column_count());
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lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_column_types.size());
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lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_solver.m_costs.size());
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lean_assert(A_r().column_count() == m_mpq_lar_core_solver.m_r_x.size());
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return true;
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}
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void print_implied_bound(const implied_bound& be, std::ostream & out) const {
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out << "implied bound\n";
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unsigned v = be.m_j;
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if (is_term(v)) {
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out << "it is a term number " << be.m_j << std::endl;
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print_term(*m_orig_terms[be.m_j - m_terms_start_index], out);
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}
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else {
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out << get_column_name(v);
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}
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out << " " << lconstraint_kind_string(be.kind()) << " " << be.m_bound << std::endl;
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// for (auto & p : be.m_explanation) {
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// out << p.first << " : ";
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// print_constraint(p.second, out);
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// }
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// 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);
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out << "end of implied bound" << std::endl;
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}
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bool implied_bound_is_correctly_explained(implied_bound const & be, const vector<std::pair<mpq, unsigned>> & explanation) const {
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std::unordered_map<unsigned, mpq> coeff_map;
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auto rs_of_evidence = zero_of_type<mpq>();
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unsigned n_of_G = 0, n_of_L = 0;
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bool strict = false;
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for (auto & it : explanation) {
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mpq coeff = it.first;
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constraint_index con_ind = it.second;
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const auto & constr = *m_constraints[con_ind];
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lconstraint_kind kind = coeff.is_pos() ? constr.m_kind : flip_kind(constr.m_kind);
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register_in_map(coeff_map, constr, coeff);
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if (kind == GT || kind == LT)
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strict = true;
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if (kind == GE || kind == GT) n_of_G++;
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else if (kind == LE || kind == LT) n_of_L++;
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rs_of_evidence += coeff*constr.m_right_side;
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}
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lean_assert(n_of_G == 0 || n_of_L == 0);
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lconstraint_kind kind = n_of_G ? GE : (n_of_L ? LE : EQ);
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if (strict)
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kind = static_cast<lconstraint_kind>((static_cast<int>(kind) / 2));
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if (!is_term(be.m_j)) {
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if (coeff_map.size() != 1)
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return false;
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auto it = coeff_map.find(be.m_j);
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if (it == coeff_map.end()) return false;
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mpq ratio = it->second;
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if (ratio < zero_of_type<mpq>()) {
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kind = static_cast<lconstraint_kind>(-kind);
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}
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rs_of_evidence /= ratio;
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} else {
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const lar_term * t = m_orig_terms[adjust_term_index(be.m_j)];
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const auto first_coeff = *t->m_coeffs.begin();
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unsigned j = first_coeff.first;
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auto it = coeff_map.find(j);
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if (it == coeff_map.end())
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return false;
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mpq ratio = it->second / first_coeff.second;
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for (auto & p : t->m_coeffs) {
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it = coeff_map.find(p.first);
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if (it == coeff_map.end())
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return false;
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if (p.second * ratio != it->second)
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return false;
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}
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if (ratio < zero_of_type<mpq>()) {
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kind = static_cast<lconstraint_kind>(-kind);
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}
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rs_of_evidence /= ratio;
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rs_of_evidence += t->m_v * ratio;
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}
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return kind == be.kind() && rs_of_evidence == be.m_bound;
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}
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void analyze_new_bounds_on_row(
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unsigned row_index,
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bound_propagator & bp) {
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lean_assert(!use_tableau());
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iterator_on_pivot_row<mpq> it(m_mpq_lar_core_solver.get_pivot_row(), m_mpq_lar_core_solver.m_r_basis[row_index]);
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bound_analyzer_on_row ra_pos(it,
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zero_of_type<numeric_pair<mpq>>(),
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row_index,
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bp
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);
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ra_pos.analyze();
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}
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void analyze_new_bounds_on_row_tableau(
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unsigned row_index,
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bound_propagator & bp
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) {
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if (A_r().m_rows[row_index].size() > settings().max_row_length_for_bound_propagation)
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return;
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iterator_on_row<mpq> it(A_r().m_rows[row_index]);
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lean_assert(use_tableau());
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bound_analyzer_on_row::analyze_row(it,
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zero_of_type<numeric_pair<mpq>>(),
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row_index,
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bp
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);
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}
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void substitute_basis_var_in_terms_for_row(unsigned i) {
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// todo : create a map from term basic vars to the rows where they are used
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unsigned basis_j = m_mpq_lar_core_solver.m_r_solver.m_basis[i];
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for (unsigned k = 0; k < m_terms.size(); k++) {
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if (term_is_used_as_row(k))
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continue;
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if (!m_terms[k]->contains(basis_j))
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continue;
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m_terms[k]->subst(basis_j, m_mpq_lar_core_solver.m_r_solver.m_pivot_row);
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}
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}
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void calculate_implied_bounds_for_row(unsigned i, bound_propagator & bp) {
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if(use_tableau()) {
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analyze_new_bounds_on_row_tableau(i, bp);
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} else {
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m_mpq_lar_core_solver.calculate_pivot_row(i);
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substitute_basis_var_in_terms_for_row(i);
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analyze_new_bounds_on_row(i, bp);
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}
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}
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/*
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void process_new_implied_evidence_for_low_bound(
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implied_bound_explanation& implied_evidence, // not pushed yet
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vector<bound_evidence> & bound_evidences,
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std::unordered_map<unsigned, unsigned> & improved_low_bounds) {
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unsigned existing_index;
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if (try_get_val(improved_low_bounds, implied_evidence.m_j, existing_index)) {
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// we are improving the existent bound
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bound_evidences[existing_index] = fill_bound_evidence(implied_evidence);
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} else {
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improved_low_bounds[implied_evidence.m_j] = bound_evidences.size();
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bound_evidences.push_back(fill_bound_evidence(implied_evidence));
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}
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}
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void fill_bound_evidence_on_term(implied_bound & ie, implied_bound& be) {
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lean_assert(false);
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}
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void fill_implied_bound_on_row(implied_bound & ie, implied_bound& be) {
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iterator_on_row<mpq> it(A_r().m_rows[ie.m_row_or_term_index]);
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mpq a; unsigned j;
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bool toggle = ie.m_coeff_before_j_is_pos;
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if (!ie.m_is_low_bound)
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toggle = !toggle;
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while (it.next(a, j)) {
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if (j == ie.m_j) continue;
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const ul_pair & ul = m_vars_to_ul_pairs[j];
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if (is_neg(a)) { // so the monoid has a positive coeff on the right side
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constraint_index witness = toggle ? ul.m_low_bound_witness : ul.m_upper_bound_witness;
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lean_assert(is_valid(witness));
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be.m_explanation.emplace_back(a, witness);
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}
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}
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}
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*/
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/*
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implied_bound fill_implied_bound_for_low_bound(implied_bound& ie) {
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implied_bound be(ie.m_j, ie.m_bound.y.is_zero() ? GE : GT, ie.m_bound.x);
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if (is_term(ie.m_row_or_term_index)) {
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fill_implied_bound_for_low_bound_on_term(ie, be);
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}
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else {
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fill_implied_bound_for_low_bound_on_row(ie, be);
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}
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return be;
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}
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implied_bound fill_implied_bound_for_upper_bound(implied_bound& implied_evidence) {
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lean_assert(false);
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be.m_j = implied_evidence.m_j;
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be.m_bound = implied_evidence.m_bound.x;
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be.m_kind = implied_evidence.m_bound.y.is_zero() ? LE : LT;
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for (auto t : implied_evidence.m_vector_of_bound_signatures) {
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const ul_pair & ul = m_vars_to_ul_pairs[t.m_column_index];
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constraint_index witness = t.m_low_bound ? ul.m_low_bound_witness : ul.m_upper_bound_witness;
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lean_assert(is_valid(witness));
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be.m_explanation.emplace_back(t.m_coeff, witness);
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}
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}
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*/
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/*
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void process_new_implied_evidence_for_upper_bound(
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implied_bound& implied_evidence,
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vector<implied_bound> & implied_bounds,
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std::unordered_map<unsigned, unsigned> & improved_upper_bounds) {
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unsigned existing_index;
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if (try_get_val(improved_upper_bounds, implied_evidence.m_j, existing_index)) {
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implied_bound & be = implied_bounds[existing_index];
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be.m_explanation.clear();
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// we are improving the existent bound improve the existing bound
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be = fill_implied_bound_for_upper_bound(implied_evidence);
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} else {
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improved_upper_bounds[implied_evidence.m_j] = implied_bounds.size();
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implied_bounds.push_back(fill_implied_bound_for_upper_bound(implied_evidence));
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}
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}
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*/
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// implied_bound * get_existing_
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linear_combination_iterator<mpq> * create_new_iter_from_term(unsigned term_index) const {
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lean_assert(false); // not implemented
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return nullptr;
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// new linear_combination_iterator_on_vector<mpq>(m_terms[adjust_term_index(term_index)]->coeffs_as_vector());
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}
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unsigned adjust_column_index_to_term_index(unsigned j) const {
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unsigned ext_var_or_term = m_columns_to_ext_vars_or_term_indices[j];
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return ext_var_or_term < m_terms_start_index ? j : ext_var_or_term;
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}
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void propagate_bounds_on_a_term(const lar_term& t, bound_propagator & bp, unsigned term_offset) {
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lean_assert(false); // not implemented
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}
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void explain_implied_bound(implied_bound & ib, bound_propagator & bp) {
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unsigned i = ib.m_row_or_term_index;
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int bound_sign = ib.m_is_low_bound? 1: -1;
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int j_sign = (ib.m_coeff_before_j_is_pos ? 1 :-1) * bound_sign;
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unsigned m_j = ib.m_j;
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if (is_term(m_j)) {
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m_j = m_ext_vars_to_columns[m_j];
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}
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for (auto const& r : A_r().m_rows[i]) {
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unsigned j = r.m_j;
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mpq const& a = r.get_val();
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if (j == m_j) continue;
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if (is_term(j)) {
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j = m_ext_vars_to_columns[j];
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}
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int a_sign = is_pos(a)? 1: -1;
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int sign = j_sign * a_sign;
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const ul_pair & ul = m_vars_to_ul_pairs[j];
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auto witness = sign > 0? ul.upper_bound_witness(): ul.low_bound_witness();
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lean_assert(is_valid(witness));
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bp.consume(a, witness);
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}
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// lean_assert(implied_bound_is_correctly_explained(ib, explanation));
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}
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bool term_is_used_as_row(unsigned term) const {
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lean_assert(is_term(term));
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return contains(m_ext_vars_to_columns, term);
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}
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void propagate_bounds_on_terms(bound_propagator & bp) {
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for (unsigned i = 0; i < m_terms.size(); i++) {
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if (term_is_used_as_row(i + m_terms_start_index))
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continue; // this term is used a left side of a constraint,
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// it was processed as a touched row if needed
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propagate_bounds_on_a_term(*m_terms[i], bp, i);
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}
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}
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// goes over touched rows and tries to induce bounds
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void propagate_bounds_for_touched_rows(bound_propagator & bp) {
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if (!use_tableau())
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return; // ! todo : enable bound propagaion here. The current bug is that after the pop
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// the changed terms become incorrect!
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for (unsigned i : m_rows_with_changed_bounds.m_index) {
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calculate_implied_bounds_for_row(i, bp);
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}
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m_rows_with_changed_bounds.clear();
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if (!use_tableau()) {
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propagate_bounds_on_terms(bp);
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}
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}
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lp_status get_status() const { return m_status;}
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void set_status(lp_status s) {m_status = s;}
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lp_status find_feasible_solution() {
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if (strategy_is_undecided())
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decide_on_strategy_and_adjust_initial_state();
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m_mpq_lar_core_solver.m_r_solver.m_look_for_feasible_solution_only = true;
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return solve();
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}
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lp_status solve() {
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if (m_status == INFEASIBLE) {
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return m_status;
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}
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solve_with_core_solver();
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if (m_status != INFEASIBLE) {
|
|
if (m_settings.bound_propagation())
|
|
detect_rows_with_changed_bounds();
|
|
}
|
|
|
|
m_columns_with_changed_bound.clear();
|
|
return m_status;
|
|
}
|
|
|
|
void fill_explanation_from_infeasible_column(vector<std::pair<mpq, constraint_index>> & 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<mpq>::one(), ul.upper_bound_witness()));
|
|
evidence.push_back(std::make_pair(-numeric_traits<mpq>::one(), ul.low_bound_witness()));
|
|
}
|
|
|
|
|
|
unsigned 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<unsigned> get_list_of_all_var_indices() const {
|
|
vector<unsigned> ret;
|
|
for (unsigned j = 0; j < m_mpq_lar_core_solver.m_r_heading.size(); j++)
|
|
ret.push_back(j);
|
|
return ret;
|
|
}
|
|
void 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();
|
|
}
|
|
|
|
static void clean_large_elements_after_pop(unsigned n, int_set& set) {
|
|
vector<int> to_remove;
|
|
for (unsigned j: set.m_index)
|
|
if (j >= n)
|
|
to_remove.push_back(j);
|
|
for (unsigned j : to_remove)
|
|
set.erase(j);
|
|
}
|
|
|
|
static void shrink_inf_set_after_pop(unsigned n, int_set & set) {
|
|
clean_large_elements_after_pop(n, set);
|
|
set.resize(n);
|
|
}
|
|
|
|
|
|
void pop(unsigned k) {
|
|
int n_was = static_cast<int>(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<constraint_index> get_all_constraint_indices() const {
|
|
vector<constraint_index> ret;
|
|
constraint_index i = 0;
|
|
while ( i < m_constraints.size())
|
|
ret.push_back(i++);
|
|
return ret;
|
|
}
|
|
|
|
bool maximize_term_on_tableau(const vector<std::pair<mpq, var_index>> & 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 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 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 set_costs_to_zero(const vector<std::pair<mpq, var_index>> & 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<mpq>();
|
|
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<mpq>();
|
|
|
|
jset.clear();
|
|
|
|
lean_assert(reduced_costs_are_zeroes_for_r_solver());
|
|
lean_assert(costs_are_zeros_for_r_solver());
|
|
}
|
|
|
|
void prepare_costs_for_r_solver(const vector<std::pair<mpq, var_index>> & 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<mpq>());
|
|
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 maximize_term_on_corrected_r_solver(const vector<std::pair<mpq, var_index>> & 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 maximize_term(const vector<std::pair<mpq, var_index>> & 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 & get_term(unsigned j) const {
|
|
lean_assert(j >= m_terms_start_index);
|
|
return *m_terms[j - m_terms_start_index];
|
|
}
|
|
|
|
void pop_core_solver_params() {
|
|
pop_core_solver_params(1);
|
|
}
|
|
|
|
void pop_core_solver_params(unsigned k) {
|
|
A_r().pop(k);
|
|
A_d().pop(k);
|
|
}
|
|
|
|
|
|
void 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 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 substitute_terms(const mpq & mult,
|
|
const vector<std::pair<mpq, var_index>>& left_side_with_terms,
|
|
vector<std::pair<mpq, var_index>> &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<mpq, var_index>(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 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 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 use_tableau() const { return m_settings.use_tableau(); }
|
|
|
|
bool use_tableau_costs() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs;
|
|
}
|
|
|
|
void 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 adjust_x_of_column(unsigned j) {
|
|
lean_assert(false);
|
|
}
|
|
|
|
bool row_is_correct(unsigned i) const {
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
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 ax_is_correct() const {
|
|
for (unsigned i = 0; i < A_r().row_count(); i++) {
|
|
if (!row_is_correct(i))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool tableau_with_costs() const {
|
|
return m_settings.simplex_strategy() == simplex_strategy_enum::tableau_costs;
|
|
}
|
|
|
|
bool costs_are_used() const {
|
|
return m_settings.simplex_strategy() != simplex_strategy_enum::tableau_rows;
|
|
}
|
|
|
|
void change_basic_x_by_delta_on_column(unsigned j, const numeric_pair<mpq> & 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 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<mpq> 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 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 detect_rows_with_changed_bounds() {
|
|
for (auto j : m_columns_with_changed_bound.m_index)
|
|
detect_rows_with_changed_bounds_for_column(j);
|
|
}
|
|
|
|
void 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 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 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<mpq> get_basic_var_value_from_row_directly(unsigned i) {
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
|
|
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<mpq> get_basic_var_value_from_row(unsigned i) {
|
|
if (settings().use_tableau()) {
|
|
return get_basic_var_value_from_row_directly(i);
|
|
}
|
|
|
|
numeric_pair<mpq> r = zero_of_type<numeric_pair<mpq>>();
|
|
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 <typename K, typename L>
|
|
void add_last_rows_to_lu(lp_primal_core_solver<K,L> & 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 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<mpq> 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 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 constraint_stack_size() const {
|
|
return m_constraint_count.stack_size();
|
|
}
|
|
|
|
void fill_last_row_of_A_r(static_matrix<mpq, numeric_pair<mpq>> & 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 <typename U, typename V>
|
|
void create_matrix_A(static_matrix<U, V> & 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 <typename U, typename V>
|
|
void copy_from_mpq_matrix(static_matrix<U, V> & 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<U, mpq>::convert(it.get_val()));
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
bool try_to_set_fixed(column_info<mpq> & 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 get_column_type(const column_info<mpq> & 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 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 all_constrained_variables_are_registered(const vector<std::pair<mpq, var_index>>& left_side) {
|
|
for (auto it : left_side) {
|
|
if (! var_is_registered(it.second))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
constraint_index add_constraint(const vector<std::pair<mpq, var_index>>& left_side_with_terms, lconstraint_kind kind_par, const mpq& right_side_parm) {
|
|
/*
|
|
mpq rs = right_side_parm;
|
|
vector<std::pair<mpq, var_index>> left_side;
|
|
substitute_terms(one_of_type<mpq>(), 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 all_constraints_hold() const {
|
|
if (m_settings.get_cancel_flag())
|
|
return true;
|
|
std::unordered_map<var_index, mpq> 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 constraint_holds(const lar_base_constraint & constr, std::unordered_map<var_index, mpq> & 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 the_relations_are_of_same_type(const vector<std::pair<mpq, unsigned>> & 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<lconstraint_kind>((static_cast<int>(the_kind_of_sum) / 2));
|
|
|
|
return n_of_G == 0 || n_of_L == 0;
|
|
}
|
|
|
|
static void register_in_map(std::unordered_map<var_index, mpq> & 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 the_left_sides_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence) const {
|
|
std::unordered_map<var_index, mpq> 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<std::pair<mpq, var_index>> 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 the_right_sides_do_not_sum_to_zero(const vector<std::pair<mpq, unsigned>> & evidence) {
|
|
mpq ret = numeric_traits<mpq>::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<mpq>::is_zero(ret);
|
|
}
|
|
|
|
bool explanation_is_correct(const vector<std::pair<mpq, unsigned>>& 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<mpq>());
|
|
break;
|
|
case LT: lean_assert(rs <= zero_of_type<mpq>());
|
|
break;
|
|
case GE: lean_assert(rs > zero_of_type<mpq>());
|
|
break;
|
|
case GT: lean_assert(rs >= zero_of_type<mpq>());
|
|
break;
|
|
case EQ: lean_assert(rs != zero_of_type<mpq>());
|
|
break;
|
|
default:
|
|
lean_assert(false);
|
|
return false;
|
|
}
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
bool inf_explanation_is_correct() const {
|
|
#ifdef LEAN_DEBUG
|
|
vector<std::pair<mpq, unsigned>> explanation;
|
|
get_infeasibility_explanation(explanation);
|
|
return explanation_is_correct(explanation);
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
mpq sum_of_right_sides_of_explanation(const vector<std::pair<mpq, unsigned>> & explanation) const {
|
|
mpq ret = numeric_traits<mpq>::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 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<constraint_index>(-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 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<constraint_index>(-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 get_infeasibility_explanation(vector<std::pair<mpq, constraint_index>> & 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 get_infeasibility_explanation_for_inf_sign(
|
|
vector<std::pair<mpq, constraint_index>> & explanation,
|
|
const vector<std::pair<mpq, unsigned>> & 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 get_model(std::unordered_map<var_index, mpq> & 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<impq> set_of_different_pairs;
|
|
std::unordered_set<mpq> 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<mpq> & 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());
|
|
}
|
|
|
|
|
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std::string get_variable_name(var_index vi) const {
|
|
return get_column_name(vi);
|
|
}
|
|
|
|
// ********** print region start
|
|
void 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 print_constraints(std::ostream& out) const {
|
|
for (auto c : m_constraints) {
|
|
print_constraint(c, out);
|
|
}
|
|
}
|
|
|
|
void print_terms(std::ostream& out) const {
|
|
for (auto it : m_terms) {
|
|
print_term(*it, out);
|
|
out << "\n";
|
|
}
|
|
}
|
|
|
|
void 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();
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|
if (!is_zero(free_coeff))
|
|
out << " + " << free_coeff;
|
|
|
|
}
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|
|
|
void print_term(lar_term const& term, std::ostream & out) const {
|
|
if (!numeric_traits<mpq>::is_zero(term.m_v)) {
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|
out << term.m_v << " + ";
|
|
}
|
|
print_linear_combination_of_column_indices(term.coeffs_as_vector(), out);
|
|
}
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|
|
|
mpq get_left_side_val(const lar_base_constraint & cns, const std::unordered_map<var_index, mpq> & 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;
|
|
}
|
|
|
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void 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 fill_var_set_for_random_update(unsigned sz, var_index const * vars, vector<unsigned>& 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 random_update(unsigned sz, var_index const * vars) {
|
|
vector<unsigned> 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 try_pivot_fixed_vars_from_basis() {
|
|
m_mpq_lar_core_solver.m_r_solver.pivot_fixed_vars_from_basis();
|
|
}
|
|
|
|
void pop() {
|
|
pop(1);
|
|
}
|
|
|
|
|
|
bool column_represents_row_in_tableau(unsigned j) {
|
|
return m_vars_to_ul_pairs()[j].m_i != static_cast<row_index>(-1);
|
|
}
|
|
|
|
void 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<unsigned>(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 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 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 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<int>(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<int>(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 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 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 clean_inf_set_of_r_solver_after_pop() {
|
|
vector<unsigned> 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<unsigned> 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<mpq> 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<mpq>();
|
|
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.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 shrink_explanation_to_minimum(vector<std::pair<mpq, constraint_index>> & explanation) const {
|
|
// implementing quickXplain
|
|
quick_xplain::run(explanation, *this);
|
|
lean_assert(this->explanation_is_correct(explanation));
|
|
}
|
|
|
|
|
|
};
|
|
}
|