From 4e51633e6f0d5198c37754f89e1cef4b9f51750b Mon Sep 17 00:00:00 2001
From: Nikolaj Bjorner <nbjorner@microsoft.com>
Date: Wed, 13 May 2020 18:44:04 -0700
Subject: [PATCH] adding monomial bounds
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
---
src/math/interval/dep_intervals.cpp | 28 +++---
src/math/interval/dep_intervals.h | 2 -
src/math/lp/monomial_bounds.cpp | 130 ++++++++++++++++++----------
src/math/lp/monomial_bounds.h | 7 +-
src/math/lp/nla_core.cpp | 82 +++++++-----------
src/math/lp/nla_core.h | 4 +-
6 files changed, 136 insertions(+), 117 deletions(-)
diff --git a/src/math/interval/dep_intervals.cpp b/src/math/interval/dep_intervals.cpp
index 860647883..56f3e1a0c 100644
--- a/src/math/interval/dep_intervals.cpp
+++ b/src/math/interval/dep_intervals.cpp
@@ -89,21 +89,23 @@ bool dep_intervals::separated_from_zero_on_upper(const interval& i) const {
std::ostream& dep_intervals::display(std::ostream& out, const interval& i) const {
if (m_imanager.lower_is_inf(i)) {
out << "(-oo";
- } else {
+ }
+ else {
out << (m_imanager.lower_is_open(i)? "(":"[") << rational(m_imanager.lower(i));
}
out << ",";
if (m_imanager.upper_is_inf(i)) {
out << "oo)";
- } else {
+ }
+ else {
out << rational(m_imanager.upper(i)) << (m_imanager.upper_is_open(i)? ")":"]");
}
if (i.m_lower_dep) {
- out << "\nlower deps\n";
+ // out << "\nlower deps\n";
// TBD: print_dependencies(i.m_lower_dep, out);
}
if (i.m_upper_dep) {
- out << "\nupper deps\n";
+ // out << "\nupper deps\n";
// TBD: print_dependencies(i.m_upper_dep, out);
}
return out;
@@ -125,21 +127,21 @@ bool dep_intervals::is_empty(interval const& a) const {
bool dep_intervals::is_above(const interval& i, const rational& r) const {
if (lower_is_inf(i))
return false;
- if (m_num_manager.lt(lower(i), r.to_mpq()))
- return false;
- if (m_num_manager.eq(lower(i), r.to_mpq()) && !m_config.lower_is_open(i))
- return false;
- return true;
+ if (m_num_manager.lt(r.to_mpq(), lower(i)))
+ return true;
+ if (m_num_manager.eq(lower(i), r.to_mpq()) && m_config.lower_is_open(i))
+ return true;
+ return false;
}
bool dep_intervals::is_below(const interval& i, const rational& r) const {
if (upper_is_inf(i))
return false;
if (m_num_manager.lt(upper(i), r.to_mpq()))
- return false;
- if (m_num_manager.eq(upper(i), r.to_mpq()) && !m_config.upper_is_open(i))
- return false;
- return true;
+ return true;
+ if (m_num_manager.eq(upper(i), r.to_mpq()) && m_config.upper_is_open(i))
+ return true;
+ return false;
}
diff --git a/src/math/interval/dep_intervals.h b/src/math/interval/dep_intervals.h
index b0b752e36..e316c8095 100644
--- a/src/math/interval/dep_intervals.h
+++ b/src/math/interval/dep_intervals.h
@@ -411,12 +411,10 @@ private:
void add(const interval& a, const interval& b, interval& c, interval_deps_combine_rule& deps) { m_imanager.add(a, b, c, deps); }
void combine_deps(interval const& a, interval const& b, interval_deps_combine_rule const& deps, interval& i) const {
- SASSERT(&a != &i && &b != &i);
m_config.add_deps(a, b, deps, i);
}
void combine_deps(interval const& a, interval_deps_combine_rule const& deps, interval& i) const {
- SASSERT(&a != &i);
m_config.add_deps(a, deps, i);
}
diff --git a/src/math/lp/monomial_bounds.cpp b/src/math/lp/monomial_bounds.cpp
index 09bed9554..69cdb3364 100644
--- a/src/math/lp/monomial_bounds.cpp
+++ b/src/math/lp/monomial_bounds.cpp
@@ -13,7 +13,9 @@
namespace nla {
- monomial_bounds::monomial_bounds(core* c):common(c) {}
+ monomial_bounds::monomial_bounds(core* c):
+ common(c),
+ dep(c->m_intervals.get_dep_intervals()) {}
bool monomial_bounds::operator()() {
bool propagated = false;
@@ -29,9 +31,7 @@ namespace nla {
* Accumulate product of variables in monomial starting at position 'start'
*/
void monomial_bounds::compute_product(unsigned start, monic const& m, scoped_dep_interval& product) {
- auto & intervals = c().m_intervals;
- auto & dep_intervals = intervals.get_dep_intervals();
- scoped_dep_interval vi(dep_intervals);
+ scoped_dep_interval vi(dep);
for (unsigned i = start; i < m.size(); ) {
lpvar v = m.vars()[i];
unsigned power = 1;
@@ -40,8 +40,8 @@ namespace nla {
for (; i < m.size() && m.vars()[i] == v; ++i) {
++power;
}
- dep_intervals.power<dep_intervals::with_deps>(vi, power, vi);
- dep_intervals.mul<dep_intervals::with_deps>(product, vi, product);
+ dep.power<dep_intervals::with_deps>(vi, power, vi);
+ dep.mul<dep_intervals::with_deps>(product, vi, product);
}
}
@@ -51,26 +51,27 @@ namespace nla {
* a bounds axiom.
*/
bool monomial_bounds::propagate_value(dep_interval& range, lpvar v) {
- auto & intervals = c().m_intervals;
- auto & dep_intervals = intervals.get_dep_intervals();
- if (dep_intervals.is_below(range, c().val(v))) {
+ auto val = c().val(v);
+ if (dep.is_below(range, val)) {
lp::explanation ex;
- dep_intervals.get_upper_dep(range, ex);
- auto const& upper = dep_intervals.upper(range);
- auto cmp = dep_intervals.upper_is_open(range) ? llc::LT : llc::LE;
+ dep.get_upper_dep(range, ex);
+ auto const& upper = dep.upper(range);
+ auto cmp = dep.upper_is_open(range) ? llc::LT : llc::LE;
new_lemma lemma(c(), "propagate value - upper bound of range is below value");
lemma &= ex;
lemma |= ineq(v, cmp, upper);
+ TRACE("nla_solver", dep.display(tout << val << " > ", range) << "\n" << lemma << "\n";);
return true;
}
- else if (dep_intervals.is_above(range, c().val(v))) {
+ else if (dep.is_above(range, val)) {
lp::explanation ex;
- dep_intervals.get_lower_dep(range, ex);
- auto const& lower = dep_intervals.lower(range);
- auto cmp = dep_intervals.lower_is_open(range) ? llc::GT : llc::GE;
+ dep.get_lower_dep(range, ex);
+ auto const& lower = dep.lower(range);
+ auto cmp = dep.lower_is_open(range) ? llc::GT : llc::GE;
new_lemma lemma(c(), "propagate value - lower bound of range is above value");
lemma &= ex;
lemma |= ineq(v, cmp, lower);
+ TRACE("nla_solver", dep.display(tout << val << " < ", range) << "\n" << lemma << "\n";);
return true;
}
else {
@@ -79,26 +80,26 @@ namespace nla {
}
void monomial_bounds::var2interval(lpvar v, scoped_dep_interval& i) {
- auto & intervals = c().m_intervals;
- auto & dep_intervals = intervals.get_dep_intervals();
lp::constraint_index ci;
rational bound;
bool is_strict;
if (c().has_lower_bound(v, ci, bound, is_strict)) {
- dep_intervals.set_lower_is_open(i, is_strict);
- dep_intervals.set_lower(i, bound);
- dep_intervals.set_lower_dep(i, dep_intervals.mk_leaf(ci));
+ dep.set_lower_is_open(i, is_strict);
+ dep.set_lower(i, bound);
+ dep.set_lower_dep(i, dep.mk_leaf(ci));
+ dep.set_lower_is_inf(i, false);
}
else {
- dep_intervals.set_lower_is_inf(i, true);
+ dep.set_lower_is_inf(i, true);
}
if (c().has_upper_bound(v, ci, bound, is_strict)) {
- dep_intervals.set_upper_is_open(i, is_strict);
- dep_intervals.set_upper(i, bound);
- dep_intervals.set_upper_dep(i, dep_intervals.mk_leaf(ci));
+ dep.set_upper_is_open(i, is_strict);
+ dep.set_upper(i, bound);
+ dep.set_upper_dep(i, dep.mk_leaf(ci));
+ dep.set_upper_is_inf(i, false);
}
else {
- dep_intervals.set_upper_is_inf(i, true);
+ dep.set_upper_is_inf(i, true);
}
}
@@ -110,15 +111,22 @@ namespace nla {
* If the value of m.var() is outside of product_of_all_vars, add a bounds lemma.
*/
bool monomial_bounds::propagate(monic const& m) {
- auto & intervals = c().m_intervals;
- auto & dep_intervals = intervals.get_dep_intervals();
- scoped_dep_interval product(dep_intervals);
- scoped_dep_interval vi(dep_intervals), mi(dep_intervals);
- scoped_dep_interval other_product(dep_intervals);
- var2interval(m.var(), mi);
- if (dep_intervals.lower_is_inf(mi) && dep_intervals.upper_is_inf(mi))
+ unsigned num_free, power;
+ lpvar free_var;
+ analyze_monomial(m, num_free, free_var, power);
+ bool m_is_free = is_free(m.var());
+ if (num_free >= 2)
return false;
- dep_intervals.set_value(product, rational::one());
+ if (num_free >= 1 && m_is_free)
+ return false;
+ SASSERT(num_free == 0 || !m_is_free);
+ bool do_propagate_up = num_free == 0;
+ bool do_propagate_down = !m_is_free;
+ scoped_dep_interval product(dep);
+ scoped_dep_interval vi(dep), mi(dep);
+ scoped_dep_interval other_product(dep);
+ var2interval(m.var(), mi);
+ dep.set_value(product, rational::one());
for (unsigned i = 0; i < m.size(); ) {
lpvar v = m.vars()[i];
++i;
@@ -126,28 +134,60 @@ namespace nla {
for (; i < m.size() && v == m.vars()[i]; ++i)
++power;
var2interval(v, vi);
- dep_intervals.power<dep_intervals::with_deps>(vi, power, vi);
- if (power == 1) {
- dep_intervals.set<dep_intervals::with_deps>(other_product, product);
+ dep.power<dep_intervals::with_deps>(vi, power, vi);
+
+ if (power == 1 && do_propagate_down && (num_free == 0 || free_var == v)) {
+ dep.set<dep_intervals::with_deps>(other_product, product);
compute_product(i, m, other_product);
if (propagate_down(m, mi, v, other_product))
return true;
}
- dep_intervals.mul<dep_intervals::with_deps>(product, vi, product);
+ dep.mul<dep_intervals::with_deps>(product, vi, product);
}
- return propagate_value(product, m.var());
+ return do_propagate_up && propagate_value(product, m.var());
}
bool monomial_bounds::propagate_down(monic const& m, dep_interval& mi, lpvar v, dep_interval& product) {
- auto & intervals = c().m_intervals;
- auto & dep_intervals = intervals.get_dep_intervals();
- if (!dep_intervals.separated_from_zero(product))
+ if (!dep.separated_from_zero(product))
return false;
- scoped_dep_interval range(dep_intervals);
- dep_intervals.set<dep_intervals::with_deps>(range, mi);
- dep_intervals.div<dep_intervals::with_deps>(range, product, range);
+ scoped_dep_interval range(dep);
+ dep.div<dep_intervals::with_deps>(mi, product, range);
return propagate_value(range, v);
}
+ bool monomial_bounds::is_free(lpvar v) const {
+ return !c().has_lower_bound(v) && !c().has_upper_bound(v);
+ }
+
+ bool monomial_bounds::is_zero(lpvar v) const {
+ return
+ c().has_lower_bound(v) &&
+ c().has_upper_bound(v) &&
+ c().get_lower_bound(v).is_zero() &&
+ c().get_lower_bound(v) == c().get_upper_bound(v);
+ }
+
+ void monomial_bounds::analyze_monomial(monic const& m, unsigned& num_free, lpvar& fv, unsigned& fv_power) const {
+ unsigned power = 0;
+ num_free = 0;
+ fv = null_lpvar;
+ fv_power = 0;
+ for (unsigned i = 0; i < m.vars().size(); ) {
+ lpvar v = m.vars()[i];
+ unsigned power = 1;
+ ++i;
+ for (; i < m.vars().size() && m.vars()[i] == v; ++i, ++power);
+ if (is_zero(v)) {
+ num_free = 0;
+ return;
+ }
+ if (power % 2 == 1 && is_free(v)) {
+ ++num_free;
+ fv_power = power;
+ fv = v;
+ }
+ }
+ }
+
}
diff --git a/src/math/lp/monomial_bounds.h b/src/math/lp/monomial_bounds.h
index 714bcbd51..aaf39d175 100644
--- a/src/math/lp/monomial_bounds.h
+++ b/src/math/lp/monomial_bounds.h
@@ -10,20 +10,21 @@
#include "math/lp/nla_common.h"
#include "math/lp/nla_intervals.h"
-#include "math/lp/nex.h"
-#include "math/lp/cross_nested.h"
#include "math/lp/u_set.h"
namespace nla {
class core;
-
class monomial_bounds : common {
+ dep_intervals& dep;
void var2interval(lpvar v, scoped_dep_interval& i);
bool propagate_down(monic const& m, lpvar u);
bool propagate_value(dep_interval& range, lpvar v);
void compute_product(unsigned start, monic const& m, scoped_dep_interval& i);
bool propagate(monic const& m);
bool propagate_down(monic const& m, dep_interval& mi, lpvar v, dep_interval& product);
+ void analyze_monomial(monic const& m, unsigned& num_free, lpvar& free_v, unsigned& power) const;
+ bool is_free(lpvar v) const;
+ bool is_zero(lpvar v) const;
public:
monomial_bounds(core* core);
bool operator()();
diff --git a/src/math/lp/nla_core.cpp b/src/math/lp/nla_core.cpp
index 08f3841d9..d83bc89c5 100644
--- a/src/math/lp/nla_core.cpp
+++ b/src/math/lp/nla_core.cpp
@@ -29,6 +29,7 @@ core::core(lp::lar_solver& s, reslimit & lim) :
m_monotone(this),
m_intervals(this, lim),
m_horner(this),
+ m_monomial_bounds(this),
m_pdd_manager(s.number_of_vars()),
m_pdd_grobner(lim, m_pdd_manager),
m_emons(m_evars),
@@ -137,13 +138,13 @@ void core::add_monic(lpvar v, unsigned sz, lpvar const* vs) {
}
void core::push() {
- TRACE("nla_solver",);
+ TRACE("nla_solver_verbose", tout << "\n";);
m_emons.push();
}
void core::pop(unsigned n) {
- TRACE("nla_solver", tout << "n = " << n << "\n";);
+ TRACE("nla_solver_verbose", tout << "n = " << n << "\n";);
m_emons.pop(n);
SASSERT(elists_are_consistent(false));
}
@@ -403,10 +404,8 @@ bool core::explain_by_equiv(const lp::lar_term& t, lp::explanation& e) const {
m_evars.explain(signed_var(i, false), signed_var(j, sign), e);
TRACE("nla_solver", tout << "explained :"; m_lar_solver.print_term_as_indices(t, tout););
- return true;
-
+ return true;
}
-
void core::mk_ineq_no_expl_check(new_lemma& lemma, lp::lar_term& t, llc cmp, const rational& rs) {
TRACE("nla_solver_details", m_lar_solver.print_term_as_indices(t, tout << "t = "););
@@ -424,8 +423,7 @@ llc apply_minus(llc cmp) {
default: break;
}
return cmp;
-}
-
+}
// the monics should be equal by modulo sign but this is not so in the model
void core::fill_explanation_and_lemma_sign(new_lemma& lemma, const monic& a, const monic & b, rational const& sign) {
@@ -475,9 +473,7 @@ int core::vars_sign(const svector<lpvar>& v) {
}
return sign;
}
-
-
-
+
bool core::has_upper_bound(lpvar j) const {
return m_lar_solver.column_has_upper_bound(j);
}
@@ -1214,10 +1210,8 @@ std::ostream& new_lemma::display(std::ostream & out) const {
for (lpvar j : c.collect_vars(lemma)) {
c.print_var(j, out);
}
-
return out;
}
-
void core::negate_relation(new_lemma& lemma, unsigned j, const rational& a) {
SASSERT(val(j) != a);
@@ -1238,21 +1232,6 @@ bool core::done() const {
lp_settings().get_cancel_flag();
}
-void core::incremental_linearization(bool constraint_derived) {
- TRACE("nla_solver_details", print_terms(tout); tout << m_lar_solver.constraints(););
- m_basics.basic_lemma(constraint_derived);
- if (!m_lemma_vec->empty() || constraint_derived || done())
- return;
- TRACE("nla_solver", tout << "passed constraint_derived and basic lemmas\n";);
- SASSERT(elists_are_consistent(true));
- if (!done())
- m_order.order_lemma();
- if (!done())
- m_monotone.monotonicity_lemma();
- if (!done())
- m_tangents.tangent_lemma();
-}
-
bool core::elist_is_consistent(const std::unordered_set<lpvar> & list) const {
bool first = true;
bool p;
@@ -1359,12 +1338,9 @@ bool core::patch_blocker(lpvar u, const monic& m) const {
}
bool core::try_to_patch(lpvar k, const rational& v, const monic & m) {
- return m_lar_solver.try_to_patch(k, v,
- [this, k, m](lpvar u) {
- if (u == k)
- return false; // ok to patch
- return patch_blocker(u, m); },
- [this](lpvar u) { update_to_refine_of_var(u); });
+ auto blocker = [this, k, m](lpvar u) { return u != k && patch_blocker(u, m); };
+ auto change_report = [this](lpvar u) { update_to_refine_of_var(u); };
+ return m_lar_solver.try_to_patch(k, v, blocker, change_report);
}
bool in_power(const svector<lpvar>& vs, unsigned l) {
@@ -1465,22 +1441,25 @@ lbool core::check(vector<lemma>& l_vec) {
patch_monomials_with_real_vars();
if (m_to_refine.is_empty()) { return l_true; }
init_search();
-
+
+ lbool ret = l_undef;
+
set_use_nra_model(false);
- if (need_to_call_algebraic_methods()) {
- if (!m_horner.horner_lemmas() && m_nla_settings.run_grobner() && !done()) {
- clear_and_resize_active_var_set();
- find_nl_cluster();
- run_grobner();
- }
- }
- TRACE("nla_solver_details", print_terms(tout); tout << m_lar_solver.constraints(););
- if (!done())
- m_basics.basic_lemma(true);
+ if (false && l_vec.empty() && !done())
+ m_monomial_bounds();
+
+ if (l_vec.empty() && !done () && need_to_call_algebraic_methods())
+ m_horner.horner_lemmas();
- TRACE("nla_solver", tout << "passed constraint_derived and basic lemmas\n";);
- SASSERT(!l_vec.empty() || elists_are_consistent(true));
+ if (l_vec.empty() && !done() && m_nla_settings.run_grobner()) {
+ clear_and_resize_active_var_set();
+ find_nl_cluster();
+ run_grobner();
+ }
+
+ if (l_vec.empty() && !done())
+ m_basics.basic_lemma(true);
if (l_vec.empty() && !done())
m_basics.basic_lemma(false);
@@ -1495,16 +1474,13 @@ lbool core::check(vector<lemma>& l_vec) {
m_tangents.tangent_lemma();
}
- if (!m_reslim.inc())
- return l_undef;
-
- lbool ret = l_vec.empty() ? l_undef : l_false;
-
#if 0
- if (l_vec.empty())
+ if (l_vec.empty() && !done())
ret = m_nra.check();
- }
#endif
+
+ if (ret == l_undef && !l_vec.empty() && m_reslim.inc())
+ ret = l_false;
TRACE("nla_solver", tout << "ret = " << ret << ", lemmas count = " << l_vec.size() << "\n";);
IF_VERBOSE(2, if(ret == l_undef) {verbose_stream() << "Monomials\n"; print_monics(verbose_stream());});
diff --git a/src/math/lp/nla_core.h b/src/math/lp/nla_core.h
index 669f26114..fc303d8b1 100644
--- a/src/math/lp/nla_core.h
+++ b/src/math/lp/nla_core.h
@@ -22,6 +22,7 @@
#include "math/lp/nla_settings.h"
#include "math/lp/nex.h"
#include "math/lp/horner.h"
+#include "math/lp/monomial_bounds.h"
#include "math/lp/nla_intervals.h"
#include "math/grobner/pdd_solver.h"
#include "nlsat/nlsat_solver.h"
@@ -148,7 +149,8 @@ public:
basics m_basics;
order m_order;
monotone m_monotone;
- intervals m_intervals;
+ intervals m_intervals;
+ monomial_bounds m_monomial_bounds;
horner m_horner;
nla_settings m_nla_settings;
dd::pdd_manager m_pdd_manager;