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move hnf cut functionality
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
9451dd9a74
commit
c8b98d8b48
5 changed files with 318 additions and 266 deletions
275
src/math/lp/hnf_cutter.cpp
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275
src/math/lp/hnf_cutter.cpp
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/*++
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Copyright (c) 2017 Microsoft Corporation
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Module Name:
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hnf_cutter.cpp
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Author:
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Lev Nachmanson (levnach)
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--*/
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#include "math/lp/int_solver.h"
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#include "math/lp/lar_solver.h"
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#include "math/lp/hnf_cutter.h"
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namespace lp {
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hnf_cutter::hnf_cutter(int_solver& lia):
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lia(lia),
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lra(lia.lra),
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m_settings(lia.settings()),
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m_abs_max(zero_of_type<mpq>()),
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m_var_register(0) {}
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bool hnf_cutter::is_full() const {
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return
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terms_count() >= lia.settings().limit_on_rows_for_hnf_cutter ||
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vars().size() >= lia.settings().limit_on_columns_for_hnf_cutter;
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}
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void hnf_cutter::clear() {
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// m_A will be filled from scratch in init_matrix_A
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m_var_register.clear();
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m_terms.clear();
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m_terms_upper.clear();
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m_constraints_for_explanation.clear();
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m_right_sides.clear();
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m_abs_max = zero_of_type<mpq>();
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m_overflow = false;
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}
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void hnf_cutter::add_term(const lar_term* t, const mpq &rs, constraint_index ci, bool upper_bound) {
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m_terms.push_back(t);
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m_terms_upper.push_back(upper_bound);
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if (upper_bound)
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m_right_sides.push_back(rs);
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else
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m_right_sides.push_back(-rs);
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m_constraints_for_explanation.push_back(ci);
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for (const auto &p : *t) {
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m_var_register.add_var(p.var());
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mpq t = abs(ceil(p.coeff()));
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if (t > m_abs_max)
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m_abs_max = t;
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}
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}
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void hnf_cutter::print(std::ostream & out) {
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out << "terms = " << m_terms.size() << ", var = " << m_var_register.size() << std::endl;
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}
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void hnf_cutter::initialize_row(unsigned i) {
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mpq sign = m_terms_upper[i]? one_of_type<mpq>(): - one_of_type<mpq>();
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m_A.init_row_from_container(i, * m_terms[i], [this](unsigned j) { return m_var_register.add_var(j);}, sign);
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}
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void hnf_cutter::init_matrix_A() {
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m_A = general_matrix(terms_count(), vars().size());
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for (unsigned i = 0; i < terms_count(); i++)
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initialize_row(i);
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}
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// todo: as we need only one row i with non integral b[i] need to optimize later
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void hnf_cutter::find_h_minus_1_b(const general_matrix& H, vector<mpq> & b) {
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// the solution will be put into b
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for (unsigned i = 0; i < H.row_count() ;i++) {
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for (unsigned j = 0; j < i; j++) {
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b[i] -= H[i][j]*b[j];
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}
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b[i] /= H[i][i];
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// consider return from here if b[i] is not an integer and return i
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}
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}
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vector<mpq> hnf_cutter::create_b(const svector<unsigned> & basis_rows) {
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if (basis_rows.size() == m_right_sides.size())
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return m_right_sides;
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vector<mpq> b;
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for (unsigned i : basis_rows) {
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b.push_back(m_right_sides[i]);
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}
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return b;
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}
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int hnf_cutter::find_cut_row_index(const vector<mpq> & b) {
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int ret = -1;
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int n = 0;
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for (int i = 0; i < static_cast<int>(b.size()); i++) {
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if (is_integer(b[i])) continue;
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if (n == 0 ) {
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lp_assert(ret == -1);
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n = 1;
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ret = i;
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} else {
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if (m_settings.random_next() % (++n) == 0) {
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ret = i;
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}
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}
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}
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return ret;
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}
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// fills e_i*H_minus_1
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void hnf_cutter::get_ei_H_minus_1(unsigned i, const general_matrix& H, vector<mpq> & row) {
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// we solve x = ei * H_min_1
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// or x * H = ei
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unsigned m = H.row_count();
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for (unsigned k = i + 1; k < m; k++) {
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row[k] = zero_of_type<mpq>();
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}
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row[i] = one_of_type<mpq>() / H[i][i];
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for(int k = i - 1; k >= 0; k--) {
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mpq t = zero_of_type<mpq>();
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for (unsigned l = k + 1; l <= i; l++) {
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t += H[l][k]*row[l];
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}
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row[k] = -t / H[k][k];
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}
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// // test region
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// vector<mpq> ei(H.row_count(), zero_of_type<mpq>());
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// ei[i] = one_of_type<mpq>();
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// vector<mpq> pr = row * H;
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// pr.shrink(ei.size());
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// lp_assert(ei == pr);
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// // end test region
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}
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void hnf_cutter::fill_term(const vector<mpq> & row, lar_term& t) {
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for (unsigned j = 0; j < row.size(); j++) {
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if (!is_zero(row[j]))
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t.add_monomial(row[j], m_var_register.local_to_external(j));
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}
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}
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#ifdef Z3DEBUG
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vector<mpq> hnf_cutter::transform_to_local_columns(const vector<impq> & x) const {
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vector<mpq> ret;
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for (unsigned j = 0; j < vars().size(); j++) {
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ret.push_back(x[m_var_register.local_to_external(j)].x);
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}
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return ret;
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}
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#endif
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void hnf_cutter::shrink_explanation(const svector<unsigned>& basis_rows) {
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svector<unsigned> new_expl;
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for (unsigned i : basis_rows) {
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new_expl.push_back(m_constraints_for_explanation[i]);
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}
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m_constraints_for_explanation = new_expl;
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}
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bool hnf_cutter::overflow() const { return m_overflow; }
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lia_move hnf_cutter::create_cut(lar_term& t, mpq& k, explanation* ex, bool & upper, const vector<mpq> & x0) {
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// we suppose that x0 has at least one non integer element
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(void)x0;
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init_matrix_A();
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svector<unsigned> basis_rows;
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mpq big_number = m_abs_max.expt(3);
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mpq d = hnf_calc::determinant_of_rectangular_matrix(m_A, basis_rows, big_number);
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if (d >= big_number) {
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return lia_move::undef;
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}
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if (m_settings.get_cancel_flag()) {
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return lia_move::undef;
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}
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if (basis_rows.size() < m_A.row_count()) {
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m_A.shrink_to_rank(basis_rows);
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shrink_explanation(basis_rows);
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}
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hnf<general_matrix> h(m_A, d);
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vector<mpq> b = create_b(basis_rows);
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lp_assert(m_A * x0 == b);
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find_h_minus_1_b(h.W(), b);
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int cut_row = find_cut_row_index(b);
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if (cut_row == -1) {
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return lia_move::undef;
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}
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// the matrix is not square - we can get
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// all integers in b's projection
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vector<mpq> row(m_A.column_count());
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get_ei_H_minus_1(cut_row, h.W(), row);
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vector<mpq> f = row * m_A;
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fill_term(f, t);
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k = floor(b[cut_row]);
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upper = true;
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return lia_move::cut;
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}
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svector<unsigned> hnf_cutter::vars() const { return m_var_register.vars(); }
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void hnf_cutter::try_add_term_to_A_for_hnf(unsigned i) {
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mpq rs;
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const lar_term* t = lra.terms()[i];
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constraint_index ci;
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bool upper_bound;
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if (!is_full() && lra.get_equality_and_right_side_for_term_on_current_x(i, rs, ci, upper_bound)) {
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add_term(t, rs, ci, upper_bound);
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}
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}
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bool hnf_cutter::hnf_has_var_with_non_integral_value() const {
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for (unsigned j : vars())
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if (!lia.get_value(j).is_int())
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return true;
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return false;
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}
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bool hnf_cutter::init_terms_for_hnf_cut() {
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clear();
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for (unsigned i = 0; i < lra.terms().size() && !is_full(); i++) {
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try_add_term_to_A_for_hnf(i);
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}
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return hnf_has_var_with_non_integral_value();
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}
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lia_move hnf_cutter::make_hnf_cut() {
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if (!init_terms_for_hnf_cut()) {
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return lia_move::undef;
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}
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lia.settings().stats().m_hnf_cutter_calls++;
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TRACE("hnf_cut", tout << "settings().stats().m_hnf_cutter_calls = " << lia.settings().stats().m_hnf_cutter_calls << "\n";
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for (unsigned i : constraints_for_explanation()) {
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lra.constraints().display(tout, i);
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}
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tout << lra.constraints();
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);
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#ifdef Z3DEBUG
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vector<mpq> x0 = transform_to_local_columns(lra.m_mpq_lar_core_solver.m_r_x);
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#else
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vector<mpq> x0;
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#endif
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lia_move r = create_cut(lia.m_t, lia.m_k, lia.m_ex, lia.m_upper, x0);
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if (r == lia_move::cut) {
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TRACE("hnf_cut",
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lra.print_term(lia.m_t, tout << "cut:");
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tout << " <= " << lia.m_k << std::endl;
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for (unsigned i : constraints_for_explanation()) {
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lra.constraints().display(tout, i);
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}
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);
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lp_assert(lia.current_solution_is_inf_on_cut());
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lia.settings().stats().m_hnf_cuts++;
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lia.m_ex->clear();
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for (unsigned i : constraints_for_explanation()) {
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lia.m_ex->push_justification(i);
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}
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}
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return r;
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}
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}
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