z3-z3-4.13.0.src.math.lp.nla_intervals.cpp Maven / Gradle / Ivy
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#include "math/lp/nla_core.h"
#include "math/interval/interval_def.h"
#include "math/lp/nla_intervals.h"
#include "util/mpq.h"
namespace nla {
intervals::intervals(core* c, reslimit& lim):
m_dep_intervals(c->lra.dep_manager(), lim),
m_core(c) {}
typedef enum dep_intervals::with_deps_t e_with_deps;
const nex* intervals::get_inf_interval_child(const nex_sum& e) const {
for (auto * c : e) {
if (has_inf_interval(*c))
return c;
}
return nullptr;
}
bool intervals::mul_has_inf_interval(const nex_mul& e) const {
bool has_inf = false;
for (const auto & p : e) {
const nex &c = *p.e();
if (!c.is_elementary())
return false;
if (has_zero_interval(c))
return false;
has_inf |= has_inf_interval(c);
}
return has_inf;
}
bool intervals::has_inf_interval(const nex& e) const {
if (e.is_var())
return m_core->no_bounds(e.to_var().var());
if (e.is_mul())
return mul_has_inf_interval(e.to_mul());
if (e.is_scalar())
return false;
for (auto * c : e.to_sum())
if (has_inf_interval(*c))
return true;
return false;
}
bool intervals::has_zero_interval(const nex& e) const {
SASSERT(!e.is_scalar() || !e.to_scalar().value().is_zero());
return e.is_var() && m_core->var_is_fixed_to_zero(e.to_var().var());
}
const nex* intervals::get_zero_interval_child(const nex_mul& e) const {
for (const auto & p : e) {
const nex * c = p.e();
if (has_zero_interval(*c))
return c;
}
return nullptr;
}
std::ostream & intervals::print_dependencies(u_dependency* deps , std::ostream& out) const {
svector expl;
m_dep_intervals.linearize(deps, expl);
{
lp::explanation e(expl);
if (!expl.empty()) {
m_core->print_explanation(e, out);
expl.clear();
} else {
out << "\nno constraints\n";
}
}
return out;
}
std::ostream& intervals::display_separating_interval(std::ostream& out, const nex*n, const scoped_dep_interval& interv_wd, u_dependency* initial_deps) {
out << "conflict: interv_wd = "; display(out, interv_wd ) <<"expr = " << *n << "\n, initial deps\n"; print_dependencies(initial_deps, out);
out << ", expressions vars = \n";
for(lpvar j: m_core->get_vars_of_expr_with_opening_terms(n)) {
m_core->print_var(j, out);
}
out << "\n";
return out;
}
// return true iff the interval of n is does not contain 0
bool intervals::check_nex(const nex* n, u_dependency* initial_deps) {
m_core->lp_settings().stats().m_cross_nested_forms++;
scoped_dep_interval i(get_dep_intervals());
std::function f = [this](const lp::explanation& e) {
new_lemma lemma(*m_core, "check_nex");
lemma &= e;
};
if (!interval_of_expr(n, 1, i, f)) {
// found a conflict during the interval calculation
return true;
}
if (!m_dep_intervals.separated_from_zero(i)) {
return false;
}
scoped_dep_interval interv_wd(get_dep_intervals());
interval_of_expr(n, 1, interv_wd, f);
TRACE("nla_intervals", display_separating_interval(tout, n, interv_wd, initial_deps););
m_dep_intervals.check_interval_for_conflict_on_zero(interv_wd, initial_deps, f);
return true;
}
void intervals::add_mul_of_degree_one_to_vector(const nex_mul* e, vector> &v) {
TRACE("nla_intervals_details", tout << *e << "\n";);
SASSERT(e->size() == 1);
SASSERT((*e)[0].pow() == 1);
const nex *ev = (*e)[0].e();
lpvar j = to_var(ev)->var();
v.push_back(std::make_pair(e->coeff(), j));
}
void intervals::add_linear_to_vector(const nex* e, vector> &v) {
TRACE("nla_intervals_details", tout << *e << "\n";);
switch (e->type()) {
case expr_type::MUL:
add_mul_of_degree_one_to_vector(to_mul(e), v);
break;
case expr_type::VAR:
v.push_back(std::make_pair(rational(1), to_var(e)->var()));
break;
default:
SASSERT(!e->is_sum());
// noop
}
}
// e = a * can_t + b
lp::lar_term intervals::expression_to_normalized_term(const nex_sum* e, rational& a, rational& b) {
TRACE("nla_intervals_details", tout << *e << "\n";);
lpvar smallest_j = 0;
vector> v;
b = rational(0);
unsigned a_index = UINT_MAX;
for (const nex* c : *e) {
if (c->is_scalar()) {
b += c->to_scalar().value();
} else {
add_linear_to_vector(c, v);
if (v.empty())
continue;
if (v.size() == 1 || smallest_j > v.back().second) {
smallest_j = v.back().second;
a_index = v.size() - 1;
}
}
}
TRACE("nla_intervals_details", tout << "a_index = " << a_index << ", v="; print_vector(v, tout) << "\n";);
a = v[a_index].first;
lp::lar_term t;
if (a.is_one()) {
for (auto& p : v) {
t.add_monomial(p.first, p.second);
}
} else {
for (unsigned k = 0; k < v.size(); k++) {
auto& p = v[k];
if (k != a_index)
t.add_monomial(p.first/a, p.second);
else
t.add_var(p.second);
}
}
TRACE("nla_intervals_details", tout << a << "* (";
lp::lar_solver::print_term_as_indices(t, tout) << ") + " << b << std::endl;);
SASSERT(t.is_normalized());
return t;
}
// we should have in the case of found a * m_terms[k] + b = e,
// where m_terms[k] corresponds to the returned lpvar
lpvar intervals::find_term_column(const lp::lar_term & norm_t, rational& a) const {
std::pair a_j;
if (m_core->lra.fetch_normalized_term_column(norm_t, a_j)) {
a /= a_j.first;
return a_j.second;
}
return -1;
}
void intervals::set_zero_interval_with_explanation(interval& i, const lp::explanation& exp) {
auto val = rational(0);
m_dep_intervals.set_lower(i, val);
m_dep_intervals.set_lower_is_open(i, false);
m_dep_intervals.set_lower_is_inf(i, false);
m_dep_intervals.set_upper(i, val);
m_dep_intervals.set_upper_is_open(i, false);
m_dep_intervals.set_upper_is_inf(i, false);
i.m_lower_dep = i.m_upper_dep = mk_dep(exp);
}
void intervals::set_zero_interval(interval& i) {
auto val = rational(0);
m_dep_intervals.set_lower(i, val);
m_dep_intervals.set_lower_is_open(i, false);
m_dep_intervals.set_lower_is_inf(i, false);
m_dep_intervals.set_upper(i, val);
m_dep_intervals.set_upper_is_open(i, false);
m_dep_intervals.set_upper_is_inf(i, false);
}
void intervals::set_zero_interval_deps_for_mult(interval& a) {
a.m_lower_dep = mk_join(a.m_lower_dep, a.m_upper_dep);
a.m_upper_dep = a.m_lower_dep;
}
u_dependency* intervals::mk_dep(const lp::explanation& expl) {
u_dependency * r = nullptr;
for (auto p : expl)
r = m_dep_intervals.mk_join(r, m_dep_intervals.mk_leaf(p.ci()));
return r;
}
std::ostream& intervals::display(std::ostream& out, const interval& i) const {
if (m_dep_intervals.lower_is_inf(i)) {
out << "(-oo";
} else {
out << (m_dep_intervals.lower_is_open(i)? "(":"[") << rational(m_dep_intervals.lower(i));
}
out << ",";
if (m_dep_intervals.upper_is_inf(i)) {
out << "oo)";
} else {
out << rational(m_dep_intervals.upper(i)) << (m_dep_intervals.upper_is_open(i)? ")":"]");
}
svector expl;
if (i.m_lower_dep) {
out << "\nlower deps\n";
print_dependencies(i.m_lower_dep, out);
}
if (i.m_upper_dep) {
out << "\nupper deps\n";
print_dependencies(i.m_upper_dep, out);
}
return out;
}
template
void intervals::set_var_interval(lpvar v, interval& b) {
TRACE("nla_intervals_details", m_core->print_var(v, tout) << "\n";);
u_dependency* dep = nullptr;
rational val;
bool is_strict;
if (ls().has_lower_bound(v, dep, val, is_strict)) {
m_dep_intervals.set_lower(b, val);
m_dep_intervals.set_lower_is_open(b, is_strict);
m_dep_intervals.set_lower_is_inf(b, false);
if (wd == e_with_deps::with_deps) b.m_lower_dep = dep;
}
else {
m_dep_intervals.set_lower_is_open(b, true);
m_dep_intervals.set_lower_is_inf(b, true);
if (wd == e_with_deps::with_deps) b.m_lower_dep = nullptr;
}
if (ls().has_upper_bound(v, dep, val, is_strict)) {
m_dep_intervals.set_upper(b, val);
m_dep_intervals.set_upper_is_open(b, is_strict);
m_dep_intervals.set_upper_is_inf(b, false);
if (wd == e_with_deps::with_deps) b.m_upper_dep = dep;
}
else {
m_dep_intervals.set_upper_is_open(b, true);
m_dep_intervals.set_upper_is_inf(b, true);
if (wd == e_with_deps::with_deps) b.m_upper_dep = nullptr;
}
}
template
bool intervals::interval_from_term(const nex& e, scoped_dep_interval& i) {
rational a, b;
lp::lar_term norm_t = expression_to_normalized_term(&e.to_sum(), a, b);
lp::explanation exp;
if (m_core->explain_by_equiv(norm_t, exp)) {
m_dep_intervals.set_interval_for_scalar(i, b);
if (wd == e_with_deps::with_deps) {
for (auto p : exp) {
i.get().m_lower_dep = mk_join(i.get().m_lower_dep, mk_leaf(p.ci()));
}
i.get().m_upper_dep = i.get().m_lower_dep;
}
TRACE("nla_intervals", tout << "explain_by_equiv\n";);
return true;
}
lpvar j = find_term_column(norm_t, a);
if (j + 1 == 0)
return false;
set_var_interval(j, i);
interval bi;
m_dep_intervals.mul(a, i, bi);
m_dep_intervals.add(b, bi);
m_dep_intervals.set(i, bi);
TRACE("nla_intervals",
m_core->lra.print_column_info(j, tout) << "\n";
tout << "a=" << a << ", b=" << b << "\n";
tout << e << ", interval = "; display(tout, i););
return true;
}
template
bool intervals::interval_of_sum_no_term(const nex_sum& e, scoped_dep_interval & sdi, const std::function& f) {
if (has_inf_interval(e)) {
SASSERT(m_dep_intervals.lower_is_inf(sdi) && m_dep_intervals.upper_is_inf(sdi));
return true; // no conflict
}
if (!interval_of_expr(e[0], 1, sdi, f))
return false;
for (unsigned k = 1; k < e.size(); k++) {
TRACE("nla_intervals_details", tout << "e[" << k << "]= " << *e[k] << "\n";);
scoped_dep_interval b(get_dep_intervals());
if (!interval_of_expr(e[k], 1, b, f)) {
return false;
}
scoped_dep_interval c(get_dep_intervals());
TRACE("nla_intervals_details", tout << "sdi = "; display(tout, sdi) << "\nb = "; display(tout, b) << "\n";);
m_dep_intervals.add(sdi, b, c);
m_dep_intervals.set(sdi, c);
TRACE("nla_intervals_details", tout << *e[k] << ", ";
display(tout, sdi); tout << "\n";);
}
TRACE("nla_intervals_details", tout << "e=" << e << "\n";
tout << " interv = "; display(tout, sdi););
return true; // no conflict
}
// return true iff a.upper < b.lower, or a.upper == b.lower and one of these bounds is open
bool intervals::conflict_u_l(const interval& a, const interval& b) const {
if (a.m_upper_inf) {
return false;
}
if (b.m_lower_inf) {
return false;
}
if (m_dep_intervals.num_manager().lt(a.m_upper, b.m_lower)) {
return true;
}
if (m_dep_intervals.num_manager().gt(a.m_upper, b.m_lower)) {
return false;
}
return a.m_upper_open || b.m_upper_open;
}
template
bool intervals::interval_of_sum(const nex_sum& e, scoped_dep_interval& a, const std::function& f) {
TRACE("nla_intervals_details", tout << "e=" << e << "\n";);
if(! interval_of_sum_no_term(e, a, f)) {
return false;
}
TRACE("nla_intervals_details", tout << "a = "; display(tout, a););
if (e.is_a_linear_term()) {
SASSERT(e.is_sum() && e.size() > 1);
scoped_dep_interval i_from_term(get_dep_intervals());
if (interval_from_term(e, i_from_term)) {
scoped_dep_interval r(get_dep_intervals());
m_dep_intervals.intersect(a, i_from_term, r);
TRACE("nla_intervals_details", tout << "intersection="; display(tout, r) << "\n";);
if (m_dep_intervals.is_empty(r)) {
TRACE("nla_intervals_details", tout << "empty\n";);
if (wd == e_with_deps::with_deps) {
T expl;
if (conflict_u_l(a, i_from_term)) {
get_dep_intervals().linearize(a.get().m_upper_dep, expl);
get_dep_intervals().linearize(r.get().m_lower_dep, expl);
} else {
get_dep_intervals().linearize(r.get().m_upper_dep, expl);
get_dep_intervals().linearize(a.get().m_lower_dep, expl);
}
f(expl);
} else {
// need to recalculate the interval with dependencies
scoped_dep_interval sa(get_dep_intervals());
interval_of_sum(e, sa, f);
}
return false;
}
m_dep_intervals.set(a, r);
}
}
return true;
}
template
bool intervals::interval_of_mul(const nex_mul& e, scoped_dep_interval& a, const std::function& f) {
TRACE("nla_intervals_details", tout << "e = " << e << "\n";);
const nex* zero_interval_child = get_zero_interval_child(e);
if (zero_interval_child) {
bool r = interval_of_expr(zero_interval_child, 1, a, f);
SASSERT(r);
(void)r;
if(wd == e_with_deps::with_deps)
set_zero_interval_deps_for_mult(a);
TRACE("nla_intervals_details", tout << "zero_interval_child = " << *zero_interval_child << std::endl << "a = "; display(tout, a); );
return true; // regural calculation: no conflict
}
m_dep_intervals.set_interval_for_scalar(a, e.coeff());
TRACE("nla_intervals_details", tout << "a = "; display(tout, a); );
for (const auto& ep : e) {
scoped_dep_interval b(get_dep_intervals());
if (!interval_of_expr(ep.e(), ep.pow(), b, f))
return false;
TRACE("nla_intervals_details", tout << "ep = " << ep << ", "; display(tout, b); );
scoped_dep_interval c(get_dep_intervals());
m_dep_intervals.mul(a, b, c);
TRACE("nla_intervals_details", tout << "a "; display(tout, a););
TRACE("nla_intervals_details", tout << "c "; display(tout, c););
m_dep_intervals.set(a, c);
TRACE("nla_intervals_details", tout << "part mult "; display(tout, a););
}
TRACE("nla_intervals_details", tout << "e=" << e << "\n";
tout << " return "; display(tout, a););
return true;
}
template
void intervals::to_power(scoped_dep_interval& a, unsigned p) {
if (p == 1) return;
scoped_dep_interval b(m_dep_intervals);
m_dep_intervals.power(a, p, b);
m_dep_intervals.set(a, b);
}
template
bool intervals::interval_of_expr(const nex* e, unsigned p, scoped_dep_interval& a, const std::function& f) {
switch (e->type()) {
case expr_type::SCALAR:
{
m_dep_intervals.set_interval_for_scalar(a, power(to_scalar(e)->value(), p));
}
break;
case expr_type::SUM: {
if (!interval_of_sum(e->to_sum(), a, f))
return false;
if (p != 1) {
to_power(a, p);
}
break;
}
case expr_type::MUL: {
if (!interval_of_mul(e->to_mul(), a, f))
return false;
if (p != 1) {
to_power(a, p);
}
break;
}
case expr_type::VAR:
set_var_interval(e->to_var().var(), a);
if (p != 1) {
to_power(a, p);
}
break;
default:
TRACE("nla_intervals_details", tout << e->type() << "\n";);
UNREACHABLE();
}
return true; // no conflict
}
lp::lar_solver& intervals::ls() { return m_core->lra; }
const lp::lar_solver& intervals::ls() const { return m_core->lra; }
} // end of nla namespace