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z3/src/math/lp/lp_bound_propagator.h
2021-04-10 08:54:52 -07:00

713 lines
26 KiB
C++

/*
Copyright (c) 2017 Microsoft Corporation
Author:
Nikolaj Bjorner (nbjorner)
Lev Nachmanson (levnach)
*/
#pragma once
#include "math/lp/lp_settings.h"
#include <utility>
namespace lp {
template <typename T>
class lp_bound_propagator {
class edge; // forward definition
// vertex represents a column
// The set of vertices is organised in a tree.
// The edges of the tree are rows,
// Vertices with m_neg set to false grow with the same rate as the root.
// Vertices with m_neq set to true diminish with the same rate as the roow grows.
// When two vertices with the same m_neg have the same value of columns
// then we have an equality betweet the columns.
class vertex {
unsigned m_column;
vector<edge> m_edges;
edge m_edge_from_parent;
unsigned m_level; // the distance in hops to the root;
// it is handy to find the common ancestor
public:
vertex() {}
vertex(unsigned column) :
m_column(column),
m_level(0)
{}
unsigned column() const { return m_column; }
const vertex* parent() const { return m_edge_from_parent.source(); }
vertex* parent() { return m_edge_from_parent.source(); }
unsigned level() const { return m_level; }
void set_edge_from_parent(edge &e) { m_edge_from_parent = e; }
const edge& edge_from_parent() const { return m_edge_from_parent; }
void add_child(int row, vertex* child) {
SASSERT(*this != *child);
SASSERT(child->parent() == nullptr);
edge e = edge(this, child, row);
m_edges.push_back(e);
child->set_edge_from_parent(e);
child->m_level = m_level + 1;
}
const vector<edge> & edges() const { return m_edges; }
bool operator==(const vertex& o) const {
return m_column == o.m_column;
}
bool operator!=(const vertex& o) const {
return m_column != o.m_column;
}
};
class edge {
vertex* m_source;
vertex* m_target;
int m_row;
public:
edge(vertex* source, vertex* target, int row) : m_source(source), m_target(target), m_row(row) {}
edge() : m_source(nullptr), m_target(nullptr), m_row(-1) {}
const vertex* source() const { return m_source; }
vertex* source() { return m_source; }
const vertex* target() const { return m_target; }
vertex* target() { return m_target; }
int row() const { return m_row; }
edge reverse() const { return edge(m_target, m_source, m_row); }
};
static int other(int x, int y, int z) { SASSERT(x == z || y == z); return x == z ? y : x; }
std::ostream& print_vert(std::ostream & out, const vertex* v) const {
out << "(c = " << v->column() << ", parent = {";
if (v->parent()) { out << "(" << v->parent()->column() << ")";}
else { out << "null"; }
out << "} , lvl = " << v->level();
if (m_pol.contains(v->column())) {
out << (pol(v) == -1? " -":" +");
} else {
out << " not in m_pol";
}
out << ')';
return out;
}
hashtable<unsigned, u_hash, u_eq> m_visited_rows;
hashtable<unsigned, u_hash, u_eq> m_visited_columns;
u_map<vertex*> m_vertices;
vertex* m_root;
// At some point we can find a row with a single vertex non fixed vertex
// then we can fix the whole tree,
// by adjusting the vertices offsets, so they become absolute.
// If the tree is fixed then in addition to checking with the m_vals_to_verts
// we are going to check with the m_fixed_var_tables.
const vertex* m_fixed_vertex;
explanation m_fixed_vertex_explanation;
// a pair (o, j) belongs to m_vals_to_verts iff x[j] = x[m_root->column()] + o
map<mpq, const vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts;
// a pair (o, j) belongs to m_vals_to_verts_neg iff -x[j] = x[m_root->column()] + o
map<mpq, const vertex*, obj_hash<mpq>, default_eq<mpq>> m_vals_to_verts_neg;
// x[m_root->column()] - m_pol[j].pol()*x[j] == const;
// to bind polarity and the vertex in the table
u_map<int> m_pol;
// if m_pos.contains(j) then x[j] = x[m_root->column()] + o
uint_set m_pos;
// these maps map a column index to the corresponding index in ibounds
std::unordered_map<unsigned, unsigned> m_improved_lower_bounds;
std::unordered_map<unsigned, unsigned> m_improved_upper_bounds;
T& m_imp;
vector<implied_bound> m_ibounds;
public:
const vector<implied_bound>& ibounds() const { return m_ibounds; }
void init() {
m_improved_upper_bounds.clear();
m_improved_lower_bounds.clear();
m_ibounds.reset();
}
lp_bound_propagator(T& imp): m_root(nullptr),
m_fixed_vertex(nullptr),
m_imp(imp) {}
const lar_solver& lp() const { return m_imp.lp(); }
lar_solver& lp() { return m_imp.lp(); }
column_type get_column_type(unsigned j) const {
return m_imp.lp().get_column_type(j);
}
const impq & get_lower_bound(unsigned j) const {
return m_imp.lp().get_lower_bound(j);
}
const mpq & get_lower_bound_rational(unsigned j) const {
return m_imp.lp().get_lower_bound(j).x;
}
const impq & get_upper_bound(unsigned j) const {
return m_imp.lp().get_upper_bound(j);
}
const mpq & get_upper_bound_rational(unsigned j) const {
return m_imp.lp().get_upper_bound(j).x;
}
// require also the zero infinitesemal part
bool column_is_fixed(lpvar j) const {
return lp().column_is_fixed(j) && get_lower_bound(j).y.is_zero();
}
void try_add_bound(mpq const& v, unsigned j, bool is_low, bool coeff_before_j_is_pos, unsigned row_or_term_index, bool strict) {
j = m_imp.lp().column_to_reported_index(j);
lconstraint_kind kind = is_low? GE : LE;
if (strict)
kind = static_cast<lconstraint_kind>(kind / 2);
if (!m_imp.bound_is_interesting(j, kind, v))
return;
unsigned k; // index to ibounds
if (is_low) {
if (try_get_value(m_improved_lower_bounds, j, k)) {
auto & found_bound = m_ibounds[k];
if (v > found_bound.m_bound || (v == found_bound.m_bound && !found_bound.m_strict && strict)) {
found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
TRACE("try_add_bound", m_imp.lp().print_implied_bound(found_bound, tout););
}
} else {
m_improved_lower_bounds[j] = m_ibounds.size();
m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
TRACE("try_add_bound", m_imp.lp().print_implied_bound(m_ibounds.back(), tout););
}
} else { // the upper bound case
if (try_get_value(m_improved_upper_bounds, j, k)) {
auto & found_bound = m_ibounds[k];
if (v < found_bound.m_bound || (v == found_bound.m_bound && !found_bound.m_strict && strict)) {
found_bound = implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict);
TRACE("try_add_bound", m_imp.lp().print_implied_bound(found_bound, tout););
}
} else {
m_improved_upper_bounds[j] = m_ibounds.size();
m_ibounds.push_back(implied_bound(v, j, is_low, coeff_before_j_is_pos, row_or_term_index, strict));
TRACE("try_add_bound", m_imp.lp().print_implied_bound(m_ibounds.back(), tout););
}
}
}
void consume(const mpq& a, constraint_index ci) {
m_imp.consume(a, ci);
}
const mpq& val(unsigned j) const {
return lp().get_column_value(j).x;
}
const mpq& val(const vertex* v) const {
return val(v->column());
}
void try_add_equation_with_lp_fixed_tables(const vertex *v) {
SASSERT(m_fixed_vertex);
unsigned v_j = v->column();
unsigned j = null_lpvar;
if (!lp().find_in_fixed_tables(val(v_j), is_int(v_j), j))
return;
TRACE("cheap_eq", tout << "v_j = "; lp().print_column_info(v_j, tout) << std::endl;);
TRACE("cheap_eq", tout << "v = "; print_vert(tout, v) << std::endl;);
TRACE("cheap_eq", tout << "found j " << j << std::endl;
lp().print_column_info(j, tout)<< std::endl;);
TRACE("cheap_eq", tout << "found j = " << j << std::endl;);
vector<edge> path = connect_in_tree(v, m_fixed_vertex);
explanation ex = get_explanation_from_path(path);
ex.add_expl(m_fixed_vertex_explanation);
explain_fixed_column(j, ex);
add_eq_on_columns(ex, j, v->column());
}
void try_add_equation_with_val_table(const vertex *v) {
SASSERT(m_fixed_vertex);
unsigned v_j = v->column();
const vertex *u = nullptr;
if (!m_vals_to_verts.find(val(v_j), u)) {
m_vals_to_verts.insert(val(v_j), v);
return;
}
unsigned j = u->column();
if (j == v_j || is_int(j) != is_int(v_j))
return;
TRACE("cheap_eq", tout << "found j=" << j << " for v=";
print_vert(tout, v) << "\n in m_vals_to_verts\n";);
vector<edge> path = connect_in_tree(u, v);
explanation ex = get_explanation_from_path(path);
ex.add_expl(m_fixed_vertex_explanation);
add_eq_on_columns(ex, j, v_j);
}
bool tree_contains_r(vertex* root, vertex *v) const {
if (*root == *v)
return true;
for (auto e : root->edges()) {
if (tree_contains_r(e.target(), v))
return true;
}
return false;
}
// pol for polarity
int pol(const vertex* v) const { return pol(v->column()); }
int pol(unsigned j) const { return m_pol[j]; }
void set_polarity(const vertex* v, int p) {
SASSERT(p == 1 || p == -1);
unsigned j = v->column();
SASSERT(!m_pol.contains(j));
m_pol.insert(j, p);
}
void check_and_set_polarity(vertex* v, int polarity, unsigned row_index, vertex*v_parent) {
int prev_pol;
if (!m_pol.find(v->column(), prev_pol)) {
set_polarity(v, polarity);
return;
}
if (prev_pol == polarity)
return;
// we have a path L between v and parent with p(L) = -1, that means we can
// create an equality of the form x + x = a, where x = v->column() = u->column()
vector<edge> path = connect_in_tree(v, v_parent);
m_fixed_vertex_explanation = get_explanation_from_path(path);
explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
set_fixed_vertex(v);
TRACE("cheap_eq",
tout << "polarity switch: " << polarity << "\nv = "; print_vert(tout , v) << "\nu = "; tout << "fixed vertex explanation\n";
for (auto p : m_fixed_vertex_explanation)
lp().constraints().display(tout, [this](lpvar j) { return lp().get_variable_name(j);}, p.ci()););
}
bool tree_contains(vertex *v) const {
if (!m_root)
return false;
return tree_contains_r(m_root, v);
}
vertex * alloc_v(unsigned column) {
vertex * v = alloc(vertex, column);
m_vertices.insert(column, v);
SASSERT(!tree_contains(v));
return v;
}
static bool not_set(unsigned j) { return j == UINT_MAX; }
static bool is_set(unsigned j) { return j != UINT_MAX; }
void create_root(unsigned row_index) {
SASSERT(!m_root && !m_fixed_vertex);
unsigned x, y;
int polarity;
TRACE("cheap_eq_det", print_row(tout, row_index););
if (!is_tree_offset_row(row_index, x, y, polarity)) {
TRACE("cheap_eq_det", tout << "not an offset row\n";);
return;
}
TRACE("cheap_eq", print_row(tout, row_index););
m_root = alloc_v(x);
set_polarity(m_root, 1); // keep m_root in the positive table
if (not_set(y)) {
set_fixed_vertex(m_root);
explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
} else {
vertex *v = add_child_with_check(row_index, y, m_root, polarity);
if (v)
explore_under(v);
}
explore_under(m_root);
}
unsigned column(unsigned row, unsigned index) {
return lp().get_row(row)[index].var();
}
bool fixed_phase() const { return m_fixed_vertex; }
// Returns the vertex to start exploration from, or nullptr.
// It is assumed that parent->column() is present in the row
vertex* get_child_from_row(unsigned row_index, vertex* parent) {
TRACE("cheap_eq_det", print_row(tout, row_index););
unsigned x, y; int row_polarity;
if (!is_tree_offset_row(row_index, x, y, row_polarity)) {
TRACE("cheap_eq_det", tout << "not an offset row\n"; );
return nullptr;
}
if (not_set(y)) { // there is only one fixed variable in the row
if (!fixed_phase()) {
set_fixed_vertex(parent);
explain_fixed_in_row(row_index, m_fixed_vertex_explanation);
}
return nullptr;
}
SASSERT(is_set(x) && is_set(y));
unsigned col = other(x, y, parent->column());
return add_child_with_check(row_index, col, parent, row_polarity);
}
vertex * add_child_with_check(unsigned row_index, unsigned col, vertex* parent, int row_polarity) {
vertex* vy;
if (m_vertices.find(col, vy)) {
SASSERT(vy != nullptr);
if (!fixed_phase()) {
check_and_set_polarity(vy, pol(parent) * row_polarity, row_index, parent);
}
return nullptr; // it is not a new vertex
}
vy = alloc_v(col);
parent->add_child(row_index, vy);
if (!fixed_phase())
check_and_set_polarity(vy, row_polarity * pol(parent), row_index, parent);
return vy;
}
bool is_equal(lpvar j, lpvar k) const {
return m_imp.is_equal(col_to_imp(j), col_to_imp(k));
}
void check_for_eq_and_add_to_val_table(vertex* v, map<mpq, const vertex*, obj_hash<mpq>, default_eq<mpq>>& table) {
TRACE("cheap_eq", tout << "v = "; print_vert(tout, v) << "\n";);
const vertex *k; // the other vertex
if (table.find(val(v), k)) {
TRACE("cheap_eq", tout << "found k " ; print_vert(tout, k) << "\n";);
if (k->column() != v->column() &&
is_int(k->column()) == is_int(v->column()) &&
!is_equal(k->column(), v->column())) {
report_eq(k, v);
} else {
TRACE("cheap_eq", tout << "no report\n";);
}
} else {
TRACE("cheap_eq", tout << "registered: " << val(v) << " -> { "; print_vert(tout, v) << "} \n";);
table.insert(val(v), v);
}
}
void check_for_eq_and_add_to_val_tables(vertex* v) {
TRACE("cheap_eq_det", print_vert(tout, v) << "\n";);
if (!fixed_phase()) {
if (pol(v->column()) == -1)
check_for_eq_and_add_to_val_table(v, m_vals_to_verts_neg);
else
check_for_eq_and_add_to_val_table(v, m_vals_to_verts);
}
}
void clear_for_eq() {
m_visited_rows.reset();
m_visited_columns.reset();
m_root = nullptr;
}
std::ostream& print_edge(const edge& e, std::ostream& out) const {
out << e.source()->column() << "->" << e.target()->column() << "\n";
return print_row(out, e.row());
}
std::ostream& print_path(const vector<edge>& path, std::ostream& out) const {
out << "path = \n";
for (const edge& k : path) {
print_edge(k, out) << "\n";
}
return out;
}
// we have v_i and v_j, indices of vertices at the same offsets
void report_eq(const vertex* v_i, const vertex* v_j) {
SASSERT(v_i != v_j);
SASSERT(lp().get_column_value(v_i->column()) == lp().get_column_value(v_j->column()));
TRACE("cheap_eq", tout << v_i->column() << " = " << v_j->column() << "\nu = ";
print_vert(tout, v_i) << "\nv = "; print_vert(tout, v_j) <<"\n";
);
vector<edge> path = connect_in_tree(v_i, v_j);
lp::explanation exp = get_explanation_from_path(path);
add_eq_on_columns(exp, v_i->column(), v_j->column());
}
std::ostream& print_expl(std::ostream & out, const explanation& exp) const {
for (auto p : exp) {
lp().constraints().display(out, [this](lpvar j) { return lp().get_variable_name(j);}, p.ci());
}
return out;
}
void add_eq_on_columns(const explanation& exp, lpvar j, lpvar k) {
SASSERT(j != k);
unsigned je = lp().column_to_reported_index(j);
unsigned ke = lp().column_to_reported_index(k);
TRACE("cheap_eq",
tout << "reporting eq " << j << ", " << k << "\n";
tout << "reported idx " << je << ", " << ke << "\n";
print_expl(tout, exp);
tout << "theory_vars v" << lp().local_to_external(je) << " == v" << lp().local_to_external(ke) << "\n";
);
m_imp.add_eq(je, ke, exp);
lp().settings().stats().m_cheap_eqs++;
}
// column to theory_var
unsigned col_to_imp(unsigned j) const {
return lp().local_to_external(lp().column_to_reported_index(j));
}
// theory_var to column
unsigned imp_to_col(unsigned j) const {
return lp().external_to_column_index(j);
}
bool is_int(lpvar j) const {
return lp().column_is_int(j);
}
explanation get_explanation_from_path(vector<edge>& path) const {
explanation ex;
for (edge &e : path)
explain_fixed_in_row(e.row(), ex);
return ex;
}
void explain_fixed_in_row(unsigned row, explanation& ex) const {
TRACE("cheap_eq",
tout << lp().get_row(row) << std::endl;
);
for (const auto & c : lp().get_row(row)) {
if (lp().is_fixed(c.var())) {
explain_fixed_column(c.var(), ex);
}
}
}
void explain_fixed_column(unsigned j, explanation & ex) const {
SASSERT(column_is_fixed(j));
constraint_index lc, uc;
lp().get_bound_constraint_witnesses_for_column(j, lc, uc);
ex.push_back(lc);
ex.push_back(uc);
}
vector<edge> connect_in_tree(const vertex* u, const vertex* v) const {
vector<edge> path;
TRACE("cheap_eq_details", tout << "u = " ; print_vert(tout, u); tout << "\nv = ";print_vert(tout, v) << "\n";);
vector<edge> v_branch;
// equalize the levels
while (u->level() > v->level()) {
path.push_back(u->edge_from_parent().reverse());
u = u->parent();
}
while (u->level() < v->level()) {
v_branch.push_back(v->edge_from_parent());
v = v->parent();
}
SASSERT(u->level() == v->level());
TRACE("cheap_eq_details", tout << "u = " ; print_vert(tout, u); tout << "\nv = "; print_vert(tout, v) << "\n";);
while (u != v) {
path.push_back(u->edge_from_parent().reverse());
v_branch.push_back(v->edge_from_parent());
u = u->parent();
v = v->parent();
}
for (unsigned i = v_branch.size(); i--; ) {
path.push_back(v_branch[i]);
}
TRACE("cheap_eq", print_path(path, tout););
return path;
}
bool tree_is_correct() const {
std::unordered_set<int> vs;
return tree_is_correct(m_root, vs);
}
bool tree_is_correct(vertex* v, std::unordered_set<int>& visited_verts) const {
if (fixed_phase())
return true;
if (visited_verts.find(v->column()) != visited_verts.end())
return false;
visited_verts.insert(v->column());
for (auto e : v->edges()) {
if (!tree_is_correct(e.target(), visited_verts))
return false;
}
return true;
}
std::ostream& print_tree(std::ostream & out, vertex* v) const {
print_vert(out, v);
out << "\nchildren :\n";
for (auto c : v->edges()) {
out << "row = ";
print_row(out, c.row());
print_tree(out, c.target());
}
return out;
}
void try_add_equation_with_fixed_tables(const vertex* v) {
try_add_equation_with_lp_fixed_tables(v);
try_add_equation_with_val_table(v);
}
void create_fixed_eqs(const vertex* v) {
try_add_equation_with_fixed_tables(v);
for (auto e: v->edges())
try_add_equation_with_fixed_tables(e.target());
}
void handle_fixed_phase() {
create_fixed_eqs(m_root);
}
void cheap_eq_tree(unsigned row_index) {
TRACE("cheap_eq_det", tout << "row_index = " << row_index << "\n";);
if (!check_insert(m_visited_rows, row_index))
return; // already explored
create_root(row_index);
if (m_root == nullptr) {
return;
}
TRACE("cheap_eq", tout << "tree = "; print_tree(tout, m_root) << "\n";);
SASSERT(tree_is_correct());
if (fixed_phase())
handle_fixed_phase();
TRACE("cheap_eq", tout << "done for row_index " << row_index << "\n";);
TRACE("cheap_eq", tout << "tree size = " << verts_size(););
delete_tree(m_root);
m_root = nullptr;
set_fixed_vertex(nullptr);
m_fixed_vertex_explanation.clear();
m_vals_to_verts.reset();
m_vals_to_verts_neg.reset();
m_pol.reset();
m_vertices.reset();
}
std::ostream& print_row(std::ostream & out, unsigned row_index) const {
unsigned x, y; int polarity;
if (true || !is_tree_offset_row(row_index, x, y, polarity))
return lp().get_int_solver()->display_row_info(out, row_index);
bool first = true;
for (const auto &c: lp().A_r().m_rows[row_index]) {
if (lp().column_is_fixed(c.var()))
continue;
if (c.coeff().is_one()) {
if (!first)
out << "+";
}
else if (c.coeff().is_minus_one())
out << "-";
out << lp().get_variable_name(c.var()) << " ";
first = false;
}
out << "\n";
return out;
}
void set_fixed_vertex(vertex *v) {
TRACE("cheap_eq", if (v) print_vert(tout, v); else tout << "set m_fixed_vertex to nullptr"; tout << "\n";);
SASSERT(!m_fixed_vertex || v == nullptr);
m_fixed_vertex = v;
}
unsigned verts_size() const {
return subtree_size(m_root);
}
unsigned subtree_size(vertex* v) const {
unsigned r = 1; // 1 for v
for (auto e : v->edges())
r += subtree_size(e.target());
return r;
}
void delete_tree(vertex * v) {
for (auto p : v->edges())
delete_tree(p.target());
dealloc(v);
}
template <typename C>
bool check_insert(C& table, unsigned j) {
if (table.contains(j))
return false;
table.insert(j);
return true;
}
void go_over_vertex_column(vertex * v) {
lpvar j = v->column();
if (!check_insert(m_visited_columns, j))
return;
for (const auto & c : lp().get_column(j)) {
unsigned row_index = c.var();
if (!check_insert(m_visited_rows, row_index))
continue;
vertex *u = get_child_from_row(row_index, v);
if (u) {
// debug
// if (verts_size() > 3) {
// std::cout << "big tree\n";
// TRACE("cheap_eq", print_tree(tout, m_root););
// exit(1);
// } // end debug
explore_under(u);
}
}
}
void explore_under(vertex * v) {
check_for_eq_and_add_to_val_tables(v);
go_over_vertex_column(v);
}
// In case of only one non fixed column, and the function returns true,
// this column would be represened by x.
bool is_tree_offset_row( unsigned row_index,
unsigned & x, unsigned & y, int & polarity ) const {
x = y = UINT_MAX;
const row_cell<mpq>* x_cell = nullptr;
const row_cell<mpq>* y_cell = nullptr;
const auto & row = lp().get_row(row_index);
for (unsigned k = 0; k < row.size(); k++) {
const auto& c = row[k];
if (column_is_fixed(c.var()))
continue;
if (not_set(x)) {
if (c.coeff().is_one() || c.coeff().is_minus_one()) {
x = c.var();
x_cell = & c;
} else {
return false;
}
} else if (not_set(y)) {
if (c.coeff().is_one() || c.coeff().is_minus_one()) {
y = c.var();
y_cell = & c;
} else
return false;
} else
return false;
}
if (is_set(x)) {
if (is_set(y))
polarity = x_cell->coeff().is_pos() == y_cell->coeff().is_pos()? -1 : 1;
else
polarity = 1;
return true;
}
return false;
}
};
}