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move hnf cut functionality

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-02-09 09:22:02 -08:00
parent 9451dd9a74
commit c8b98d8b48
5 changed files with 318 additions and 266 deletions
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1
src/math/lp/CMakeLists.txt
View file

@ -10,6 +10,7 @@ z3_add_component(lp
factorization.cpp
factorization_factory_imp.cpp
gomory.cpp
hnf_cutter.cpp
horner.cpp
indexed_vector.cpp
int_branch.cpp

275
src/math/lp/hnf_cutter.cpp Normal file
View file

@ -0,0 +1,275 @@
/*++
Copyright (c) 2017 Microsoft Corporation
Module Name:
hnf_cutter.cpp
Author:
Lev Nachmanson (levnach)
--*/
#include "math/lp/int_solver.h"
#include "math/lp/lar_solver.h"
#include "math/lp/hnf_cutter.h"
namespace lp {
hnf_cutter::hnf_cutter(int_solver& lia):
lia(lia),
lra(lia.lra),
m_settings(lia.settings()),
m_abs_max(zero_of_type<mpq>()),
m_var_register(0) {}
bool hnf_cutter::is_full() const {
return
terms_count() >= lia.settings().limit_on_rows_for_hnf_cutter ||
vars().size() >= lia.settings().limit_on_columns_for_hnf_cutter;
}
void hnf_cutter::clear() {
// m_A will be filled from scratch in init_matrix_A
m_var_register.clear();
m_terms.clear();
m_terms_upper.clear();
m_constraints_for_explanation.clear();
m_right_sides.clear();
m_abs_max = zero_of_type<mpq>();
m_overflow = false;
}
void hnf_cutter::add_term(const lar_term* t, const mpq &rs, constraint_index ci, bool upper_bound) {
m_terms.push_back(t);
m_terms_upper.push_back(upper_bound);
if (upper_bound)
m_right_sides.push_back(rs);
else
m_right_sides.push_back(-rs);
m_constraints_for_explanation.push_back(ci);
for (const auto &p : *t) {
m_var_register.add_var(p.var());
mpq t = abs(ceil(p.coeff()));
if (t > m_abs_max)
m_abs_max = t;
}
}
void hnf_cutter::print(std::ostream & out) {
out << "terms = " << m_terms.size() << ", var = " << m_var_register.size() << std::endl;
}
void hnf_cutter::initialize_row(unsigned i) {
mpq sign = m_terms_upper[i]? one_of_type<mpq>(): - one_of_type<mpq>();
m_A.init_row_from_container(i, * m_terms[i], [this](unsigned j) { return m_var_register.add_var(j);}, sign);
}
void hnf_cutter::init_matrix_A() {
m_A = general_matrix(terms_count(), vars().size());
for (unsigned i = 0; i < terms_count(); i++)
initialize_row(i);
}
// todo: as we need only one row i with non integral b[i] need to optimize later
void hnf_cutter::find_h_minus_1_b(const general_matrix& H, vector<mpq> & b) {
// the solution will be put into b
for (unsigned i = 0; i < H.row_count() ;i++) {
for (unsigned j = 0; j < i; j++) {
b[i] -= H[i][j]*b[j];
}
b[i] /= H[i][i];
// consider return from here if b[i] is not an integer and return i
}
}
vector<mpq> hnf_cutter::create_b(const svector<unsigned> & basis_rows) {
if (basis_rows.size() == m_right_sides.size())
return m_right_sides;
vector<mpq> b;
for (unsigned i : basis_rows) {
b.push_back(m_right_sides[i]);
}
return b;
}
int hnf_cutter::find_cut_row_index(const vector<mpq> & b) {
int ret = -1;
int n = 0;
for (int i = 0; i < static_cast<int>(b.size()); i++) {
if (is_integer(b[i])) continue;
if (n == 0 ) {
lp_assert(ret == -1);
n = 1;
ret = i;
} else {
if (m_settings.random_next() % (++n) == 0) {
ret = i;
}
}
}
return ret;
}
// fills e_i*H_minus_1
void hnf_cutter::get_ei_H_minus_1(unsigned i, const general_matrix& H, vector<mpq> & row) {
// we solve x = ei * H_min_1
// or x * H = ei
unsigned m = H.row_count();
for (unsigned k = i + 1; k < m; k++) {
row[k] = zero_of_type<mpq>();
}
row[i] = one_of_type<mpq>() / H[i][i];
for(int k = i - 1; k >= 0; k--) {
mpq t = zero_of_type<mpq>();
for (unsigned l = k + 1; l <= i; l++) {
t += H[l][k]*row[l];
}
row[k] = -t / H[k][k];
}
// // test region
// vector<mpq> ei(H.row_count(), zero_of_type<mpq>());
// ei[i] = one_of_type<mpq>();
// vector<mpq> pr = row * H;
// pr.shrink(ei.size());
// lp_assert(ei == pr);
// // end test region
}
void hnf_cutter::fill_term(const vector<mpq> & row, lar_term& t) {
for (unsigned j = 0; j < row.size(); j++) {
if (!is_zero(row[j]))
t.add_monomial(row[j], m_var_register.local_to_external(j));
}
}
#ifdef Z3DEBUG
vector<mpq> hnf_cutter::transform_to_local_columns(const vector<impq> & x) const {
vector<mpq> ret;
for (unsigned j = 0; j < vars().size(); j++) {
ret.push_back(x[m_var_register.local_to_external(j)].x);
}
return ret;
}
#endif
void hnf_cutter::shrink_explanation(const svector<unsigned>& basis_rows) {
svector<unsigned> new_expl;
for (unsigned i : basis_rows) {
new_expl.push_back(m_constraints_for_explanation[i]);
}
m_constraints_for_explanation = new_expl;
}
bool hnf_cutter::overflow() const { return m_overflow; }
lia_move hnf_cutter::create_cut(lar_term& t, mpq& k, explanation* ex, bool & upper, const vector<mpq> & x0) {
// we suppose that x0 has at least one non integer element
(void)x0;
init_matrix_A();
svector<unsigned> basis_rows;
mpq big_number = m_abs_max.expt(3);
mpq d = hnf_calc::determinant_of_rectangular_matrix(m_A, basis_rows, big_number);
if (d >= big_number) {
return lia_move::undef;
}
if (m_settings.get_cancel_flag()) {
return lia_move::undef;
}
if (basis_rows.size() < m_A.row_count()) {
m_A.shrink_to_rank(basis_rows);
shrink_explanation(basis_rows);
}
hnf<general_matrix> h(m_A, d);
vector<mpq> b = create_b(basis_rows);
lp_assert(m_A * x0 == b);
find_h_minus_1_b(h.W(), b);
int cut_row = find_cut_row_index(b);
if (cut_row == -1) {
return lia_move::undef;
}
// the matrix is not square - we can get
// all integers in b's projection
vector<mpq> row(m_A.column_count());
get_ei_H_minus_1(cut_row, h.W(), row);
vector<mpq> f = row * m_A;
fill_term(f, t);
k = floor(b[cut_row]);
upper = true;
return lia_move::cut;
}
svector<unsigned> hnf_cutter::vars() const { return m_var_register.vars(); }
void hnf_cutter::try_add_term_to_A_for_hnf(unsigned i) {
mpq rs;
const lar_term* t = lra.terms()[i];
constraint_index ci;
bool upper_bound;
if (!is_full() && lra.get_equality_and_right_side_for_term_on_current_x(i, rs, ci, upper_bound)) {
add_term(t, rs, ci, upper_bound);
}
}
bool hnf_cutter::hnf_has_var_with_non_integral_value() const {
for (unsigned j : vars())
if (!lia.get_value(j).is_int())
return true;
return false;
}
bool hnf_cutter::init_terms_for_hnf_cut() {
clear();
for (unsigned i = 0; i < lra.terms().size() && !is_full(); i++) {
try_add_term_to_A_for_hnf(i);
}
return hnf_has_var_with_non_integral_value();
}
lia_move hnf_cutter::make_hnf_cut() {
if (!init_terms_for_hnf_cut()) {
return lia_move::undef;
}
lia.settings().stats().m_hnf_cutter_calls++;
TRACE("hnf_cut", tout << "settings().stats().m_hnf_cutter_calls = " << lia.settings().stats().m_hnf_cutter_calls << "\n";
for (unsigned i : constraints_for_explanation()) {
lra.constraints().display(tout, i);
}
tout << lra.constraints();
);
#ifdef Z3DEBUG
vector<mpq> x0 = transform_to_local_columns(lra.m_mpq_lar_core_solver.m_r_x);
#else
vector<mpq> x0;
#endif
lia_move r = create_cut(lia.m_t, lia.m_k, lia.m_ex, lia.m_upper, x0);
if (r == lia_move::cut) {
TRACE("hnf_cut",
lra.print_term(lia.m_t, tout << "cut:");
tout << " <= " << lia.m_k << std::endl;
for (unsigned i : constraints_for_explanation()) {
lra.constraints().display(tout, i);
}
);
lp_assert(lia.current_solution_is_inf_on_cut());
lia.settings().stats().m_hnf_cuts++;
lia.m_ex->clear();
for (unsigned i : constraints_for_explanation()) {
lia.m_ex->push_justification(i);
}
}
return r;
}
}

228
src/math/lp/hnf_cutter.h
View file

@ -3,19 +3,17 @@ Copyright (c) 2017 Microsoft Corporation
Module Name:
<name>
hnf_cutter.h
Abstract:
<abstract>
Cuts (branches) from Hermite matrices
Author:
Lev Nachmanson (levnach)
Revision History:
--*/
#pragma once
#include "math/lp/lar_term.h"
#include "math/lp/hnf.h"
@ -25,212 +23,64 @@ Revision History:
#include "math/lp/explanation.h"
namespace lp {
class int_solver;
class lar_solver;
class hnf_cutter {
int_solver& lia;
lar_solver& lra;
lp_settings & m_settings;
general_matrix m_A;
vector<const lar_term*> m_terms;
vector<bool> m_terms_upper;
svector<constraint_index> m_constraints_for_explanation;
vector<mpq> m_right_sides;
lp_settings & m_settings;
mpq m_abs_max;
bool m_overflow;
var_register m_var_register;
public:
hnf_cutter(int_solver& lia);
lia_move hnf_cutter::make_hnf_cut();
bool hnf_cutter::init_terms_for_hnf_cut();
bool hnf_cutter::hnf_has_var_with_non_integral_value() const;
void hnf_cutter::try_add_term_to_A_for_hnf(unsigned i);
unsigned terms_count() const { return m_terms.size(); }
const mpq & abs_max() const { return m_abs_max; }
hnf_cutter(lp_settings & settings) : m_settings(settings),
m_abs_max(zero_of_type<mpq>()),
m_var_register(0) {}
unsigned terms_count() const {
return m_terms.size();
}
const vector<const lar_term*>& terms() const { return m_terms; }
const svector<unsigned>& constraints_for_explanation() const {
return m_constraints_for_explanation;
}
const svector<unsigned>& constraints_for_explanation() const { return m_constraints_for_explanation; }
const vector<mpq> & right_sides() const { return m_right_sides; }
void clear() {
// m_A will be filled from scratch in init_matrix_A
m_var_register.clear();
m_terms.clear();
m_terms_upper.clear();
m_constraints_for_explanation.clear();
m_right_sides.clear();
m_abs_max = zero_of_type<mpq>();
m_overflow = false;
}
void add_term(const lar_term* t, const mpq &rs, constraint_index ci, bool upper_bound) {
m_terms.push_back(t);
m_terms_upper.push_back(upper_bound);
if (upper_bound)
m_right_sides.push_back(rs);
else
m_right_sides.push_back(-rs);
m_constraints_for_explanation.push_back(ci);
for (const auto &p : *t) {
m_var_register.add_var(p.var());
mpq t = abs(ceil(p.coeff()));
if (t > m_abs_max)
m_abs_max = t;
}
}
bool is_full() const;
void clear();
void add_term(const lar_term* t, const mpq &rs, constraint_index ci, bool upper_bound);
void print(std::ostream & out) {
out << "terms = " << m_terms.size() << ", var = " << m_var_register.size() << std::endl;
}
void print(std::ostream & out);
void initialize_row(unsigned i) {
mpq sign = m_terms_upper[i]? one_of_type<mpq>(): - one_of_type<mpq>();
m_A.init_row_from_container(i, * m_terms[i], [this](unsigned j) { return m_var_register.add_var(j);}, sign);
}
void initialize_row(unsigned i);
void init_matrix_A();
void find_h_minus_1_b(const general_matrix& H, vector<mpq> & b);
void init_matrix_A() {
m_A = general_matrix(terms_count(), vars().size());
for (unsigned i = 0; i < terms_count(); i++)
initialize_row(i);
}
vector<mpq> create_b(const svector<unsigned> & basis_rows);
// todo: as we need only one row i with non integral b[i] need to optimize later
void find_h_minus_1_b(const general_matrix& H, vector<mpq> & b) {
// the solution will be put into b
for (unsigned i = 0; i < H.row_count() ;i++) {
for (unsigned j = 0; j < i; j++) {
b[i] -= H[i][j]*b[j];
}
b[i] /= H[i][i];
// consider return from here if b[i] is not an integer and return i
}
}
vector<mpq> create_b(const svector<unsigned> & basis_rows) {
if (basis_rows.size() == m_right_sides.size())
return m_right_sides;
vector<mpq> b;
for (unsigned i : basis_rows) {
b.push_back(m_right_sides[i]);
}
return b;
}
int find_cut_row_index(const vector<mpq> & b) {
int ret = -1;
int n = 0;
for (int i = 0; i < static_cast<int>(b.size()); i++) {
if (is_integer(b[i])) continue;
if (n == 0 ) {
lp_assert(ret == -1);
n = 1;
ret = i;
} else {
if (m_settings.random_next() % (++n) == 0) {
ret = i;
}
}
}
return ret;
}
int find_cut_row_index(const vector<mpq> & b);
// fills e_i*H_minus_1
void get_ei_H_minus_1(unsigned i, const general_matrix& H, vector<mpq> & row) {
// we solve x = ei * H_min_1
// or x * H = ei
unsigned m = H.row_count();
for (unsigned k = i + 1; k < m; k++) {
row[k] = zero_of_type<mpq>();
}
row[i] = one_of_type<mpq>() / H[i][i];
for(int k = i - 1; k >= 0; k--) {
mpq t = zero_of_type<mpq>();
for (unsigned l = k + 1; l <= i; l++) {
t += H[l][k]*row[l];
}
row[k] = -t / H[k][k];
}
void get_ei_H_minus_1(unsigned i, const general_matrix& H, vector<mpq> & row);
// // test region
// vector<mpq> ei(H.row_count(), zero_of_type<mpq>());
// ei[i] = one_of_type<mpq>();
// vector<mpq> pr = row * H;
// pr.shrink(ei.size());
// lp_assert(ei == pr);
// // end test region
}
void fill_term(const vector<mpq> & row, lar_term& t) {
for (unsigned j = 0; j < row.size(); j++) {
if (!is_zero(row[j]))
t.add_monomial(row[j], m_var_register.local_to_external(j));
}
}
void fill_term(const vector<mpq> & row, lar_term& t);
#ifdef Z3DEBUG
vector<mpq> transform_to_local_columns(const vector<impq> & x) const {
vector<mpq> ret;
for (unsigned j = 0; j < vars().size(); j++) {
ret.push_back(x[m_var_register.local_to_external(j)].x);
}
return ret;
}
vector<mpq> transform_to_local_columns(const vector<impq> & x) const;
#endif
void shrink_explanation(const svector<unsigned>& basis_rows) {
svector<unsigned> new_expl;
for (unsigned i : basis_rows) {
new_expl.push_back(m_constraints_for_explanation[i]);
}
m_constraints_for_explanation = new_expl;
}
bool overflow() const { return m_overflow; }
lia_move create_cut(lar_term& t, mpq& k, explanation* ex, bool & upper, const vector<mpq> & x0) {
// we suppose that x0 has at least one non integer element
(void)x0;
init_matrix_A();
svector<unsigned> basis_rows;
mpq big_number = m_abs_max.expt(3);
mpq d = hnf_calc::determinant_of_rectangular_matrix(m_A, basis_rows, big_number);
if (d >= big_number) {
return lia_move::undef;
}
if (m_settings.get_cancel_flag()) {
return lia_move::undef;
}
if (basis_rows.size() < m_A.row_count()) {
m_A.shrink_to_rank(basis_rows);
shrink_explanation(basis_rows);
}
hnf<general_matrix> h(m_A, d);
vector<mpq> b = create_b(basis_rows);
lp_assert(m_A * x0 == b);
find_h_minus_1_b(h.W(), b);
int cut_row = find_cut_row_index(b);
if (cut_row == -1) {
return lia_move::undef;
}
// the matrix is not square - we can get
// all integers in b's projection
vector<mpq> row(m_A.column_count());
get_ei_H_minus_1(cut_row, h.W(), row);
vector<mpq> f = row * m_A;
fill_term(f, t);
k = floor(b[cut_row]);
upper = true;
return lia_move::cut;
}
svector<unsigned> vars() const { return m_var_register.vars(); }
void shrink_explanation(const svector<unsigned>& basis_rows);
bool overflow() const;
lia_move create_cut(lar_term& t, mpq& k, explanation* ex, bool & upper, const vector<mpq> & x0);
svector<unsigned> vars() const;
};
}

72
src/math/lp/int_solver.cpp
View file

@ -18,7 +18,7 @@ namespace lp {
int_solver::int_solver(lar_solver& lar_slv) :
lra(lar_slv),
m_number_of_calls(0),
m_hnf_cutter(settings()),
m_hnf_cutter(*this),
m_hnf_cut_period(settings().hnf_cut_period()) {
lra.set_int_solver(this);
}
@ -172,80 +172,12 @@ bool int_solver::should_gomory_cut() {
return m_number_of_calls % settings().m_int_gomory_cut_period == 0;
}
void int_solver::try_add_term_to_A_for_hnf(unsigned i) {
mpq rs;
const lar_term* t = lra.terms()[i];
constraint_index ci;
bool upper_bound;
if (!hnf_cutter_is_full() && lra.get_equality_and_right_side_for_term_on_current_x(i, rs, ci, upper_bound)) {
m_hnf_cutter.add_term(t, rs, ci, upper_bound);
}
}
bool int_solver::hnf_cutter_is_full() const {
return
m_hnf_cutter.terms_count() >= settings().limit_on_rows_for_hnf_cutter
||
m_hnf_cutter.vars().size() >= settings().limit_on_columns_for_hnf_cutter;
}
bool int_solver::hnf_has_var_with_non_integral_value() const {
for (unsigned j : m_hnf_cutter.vars())
if (!get_value(j).is_int())
return true;
return false;
}
bool int_solver::init_terms_for_hnf_cut() {
m_hnf_cutter.clear();
for (unsigned i = 0; i < lra.terms().size() && !hnf_cutter_is_full(); i++) {
try_add_term_to_A_for_hnf(i);
}
return hnf_has_var_with_non_integral_value();
}
lia_move int_solver::make_hnf_cut() {
if (!init_terms_for_hnf_cut()) {
return lia_move::undef;
}
settings().stats().m_hnf_cutter_calls++;
TRACE("hnf_cut", tout << "settings().stats().m_hnf_cutter_calls = " << settings().stats().m_hnf_cutter_calls << "\n";
for (unsigned i : m_hnf_cutter.constraints_for_explanation()) {
lra.constraints().display(tout, i);
}
tout << lra.constraints();
);
#ifdef Z3DEBUG
vector<mpq> x0 = m_hnf_cutter.transform_to_local_columns(lra.m_mpq_lar_core_solver.m_r_x);
#else
vector<mpq> x0;
#endif
lia_move r = m_hnf_cutter.create_cut(m_t, m_k, m_ex, m_upper, x0);
if (r == lia_move::cut) {
TRACE("hnf_cut",
lra.print_term(m_t, tout << "cut:");
tout << " <= " << m_k << std::endl;
for (unsigned i : m_hnf_cutter.constraints_for_explanation()) {
lra.constraints().display(tout, i);
}
);
lp_assert(current_solution_is_inf_on_cut());
settings().stats().m_hnf_cuts++;
m_ex->clear();
for (unsigned i : m_hnf_cutter.constraints_for_explanation()) {
m_ex->push_justification(i);
}
}
return r;
}
bool int_solver::should_hnf_cut() {
return settings().m_enable_hnf && m_number_of_calls % m_hnf_cut_period == 0;
}
lia_move int_solver::hnf_cut() {
lia_move r = make_hnf_cut();
lia_move r = m_hnf_cutter.make_hnf_cut();
if (r == lia_move::undef) {
m_hnf_cut_period *= 2;
}

8
src/math/lp/int_solver.h
View file

@ -36,6 +36,7 @@ class int_solver {
friend class int_cube;
friend class int_branch;
friend class int_gcd_test;
friend class hnf_cutter;
lar_solver& lra;
unsigned m_number_of_calls;
@ -55,7 +56,6 @@ public:
lar_term const& get_term() const { return m_t; }
mpq const& get_offset() const { return m_k; }
bool is_upper() const { return m_upper; }
//lia_move check_wrapper(lar_term& t, mpq& k, explanation& ex);
bool is_base(unsigned j) const;
bool is_real(unsigned j) const;
const impq & lower_bound(unsigned j) const;
@ -106,12 +106,6 @@ public:
bool all_columns_are_bounded() const;
void find_feasible_solution();
lia_move hnf_cut();
lia_move make_hnf_cut();
bool init_terms_for_hnf_cut();
bool hnf_matrix_is_empty() const;
void try_add_term_to_A_for_hnf(unsigned term_index);
bool hnf_has_var_with_non_integral_value() const;
bool hnf_cutter_is_full() const;
void patch_nbasic_column(unsigned j);
};
}