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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-05-10 13:42:19 -07:00
parent e74faf42ad
commit caee936af5
3 changed files with 64 additions and 59 deletions
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3
src/math/lp/lar_term.h
View file

@ -70,6 +70,9 @@ public:
lar_term(lpvar v1) {
add_monomial(rational::one(), v1);
}
lar_term(rational const& a, lpvar v1) {
add_monomial(a, v1);
}
lar_term(lpvar v1, rational const& b, lpvar v2) {
add_monomial(rational::one(), v1);
add_monomial(b, v2);

62
src/math/lp/nla_basics_lemmas.cpp
View file

@ -290,7 +290,7 @@ bool basics::basic_lemma_for_mon_derived(const monic& rm) {
// x = 0 or y = 0 -> xy = 0
bool basics::basic_lemma_for_mon_non_zero_derived(const monic& rm, const factorization& f) {
TRACE("nla_solver", c().trace_print_monic_and_factorization(rm, f, tout););
if (! c().var_is_separated_from_zero(var(rm)))
if (!c().var_is_separated_from_zero(var(rm)))
return false;
lpvar zero_j = null_lpvar;
for (auto j : f) {
@ -309,6 +309,7 @@ bool basics::basic_lemma_for_mon_non_zero_derived(const monic& rm, const factori
explain(rm);
return true;
}
// use the fact that
// |xabc| = |x| and x != 0 -> |a| = |b| = |c| = 1
// it holds for integers, and for reals for a pair of factors
@ -423,8 +424,8 @@ NSB review:
sign_m*m < 0 or f_j = 0 or \/_{i != j} sign_m*m >= sign_i*f_i
- or even without reference to factor index:
sign_m*m < 0 or \/_{i} sign_m*m >= sign_i*f_i
- or even, without reference to factor index:
sign_m*m < 0 or \/_i sign_m*m >= sign_i*f_i
*/
void basics::generate_pl_on_mon(const monic& m, unsigned factor_index) {
@ -448,9 +449,15 @@ void basics::generate_pl_on_mon(const monic& m, unsigned factor_index) {
}
}
}
// none of the factors is zero and the product is not zero
// -> |fc[factor_index]| <= |rm|
/**
none of the factors is zero and the product is not zero
-> |fc[factor_index]| <= |rm|
m := f1 * .. * f_n
sign_m*m < 0 or f_i = 0 or \/_{j != i} sign_m*m >= sign_j*f_j
*/
void basics::generate_pl(const monic& m, const factorization& fc, int factor_index) {
if (factorization_has_real(fc))
return;
@ -467,23 +474,21 @@ void basics::generate_pl(const monic& m, const factorization& fc, int factor_ind
rational mv = var_val(m);
rational sm = rational(nla::rat_sign(mv));
unsigned mon_var = var(m);
c().mk_ineq(sm, mon_var, llc::LT);
lemma |= ineq(term(sm, mon_var), llc::LT, 0);
for (factor f : fc) {
if (fi++ != factor_index) {
c().mk_ineq(var(f), llc::EQ);
lemma |= ineq(var(f), llc::EQ, 0);
} else {
lpvar j = var(f);
rational jv = val(j);
rational sj = rational(nla::rat_sign(jv));
SASSERT(sm*mv < sj*jv);
c().mk_ineq(sj, j, llc::LT);
c().mk_ineq(sm, mon_var, -sj, j, llc::GE);
// NSB review: removed SASSERT(sm*mv < sj*jv);
// NSB review: removed lemma |= ineq(term(sj, j), llc::LT, 0);
lemma |= ineq(term(sm, mon_var, -sj, j), llc::GE, 0);
}
}
if (!fc.is_mon()) {
explain(fc);
explain(m);
}
explain(fc);
explain(m);
}
bool basics::is_separated_from_zero(const factorization& f) const {
@ -520,12 +525,12 @@ void basics::basic_lemma_for_mon_zero_model_based(const monic& rm, const factori
SASSERT(var_val(rm).is_zero() && !c().rm_check(rm));
new_lemma lemma(c(), "xy = 0 -> x = 0 or y = 0");
if (!is_separated_from_zero(f)) {
c().mk_ineq(var(rm), llc::NE);
lemma |= ineq(var(rm), llc::NE, 0);
for (auto j : f) {
c().mk_ineq(var(j), llc::EQ);
lemma |= ineq(var(j), llc::EQ, 0);
}
} else {
c().mk_ineq(var(rm), llc::NE);
lemma |= ineq(var(rm), llc::NE, 0);
for (auto j : f) {
c().explain_separation_from_zero(var(j));
}
@ -583,19 +588,19 @@ bool basics::basic_lemma_for_mon_neutral_monic_to_factor_model_based_fm(const mo
new_lemma lemma(c(), __FUNCTION__);
// mon_var = 0
c().mk_ineq(mon_var, llc::EQ);
lemma |= ineq(mon_var, llc::EQ, 0);
// negate abs(jl) == abs()
if (val(jl) == - val(mon_var))
c().mk_ineq(jl, mon_var, llc::NE, rational::zero());
lemma |= ineq(term(jl, mon_var), llc::NE, 0);
else // jl == mon_var
c().mk_ineq(jl, -rational(1), mon_var, llc::NE);
lemma |= ineq(term(jl, -rational(1), mon_var), llc::NE, 0);
// not_one_j = 1
c().mk_ineq(not_one_j, llc::EQ, rational(1));
lemma |= ineq(not_one_j, llc::EQ, 1);
// not_one_j = -1
c().mk_ineq(not_one_j, llc::EQ, -rational(1));
lemma |= ineq(not_one_j, llc::EQ, -1);
return true;
}
@ -641,14 +646,13 @@ bool basics::basic_lemma_for_mon_neutral_from_factors_to_monic_model_based_fm(co
new_lemma lemma(c(), __FUNCTION__);
for (auto j : m.vars()) {
if (not_one == j) continue;
c().mk_ineq(j, llc::NE, val(j));
lemma |= ineq(j, llc::NE, val(j));
}
if (not_one == null_lpvar) {
c().mk_ineq(m.var(), llc::EQ, sign);
} else {
c().mk_ineq(m.var(), -sign, not_one, llc::EQ);
}
if (not_one == null_lpvar)
lemma |= ineq(m.var(), llc::EQ, sign);
else
lemma |= ineq(term(m.var(), -sign, not_one), llc::EQ, 0);
return true;
}

58
src/test/lp/nla_solver_test.cpp
View file

@ -197,14 +197,14 @@ void test_basic_lemma_for_mon_neutral_from_factors_to_monomial_0() {
nla.get_core().print_lemma(std::cout);
ineq i0(llc::NE, lp::lar_term(), rational(1));
i0.m_term.add_var(lp_ac);
ineq i1(llc::EQ, lp::lar_term(), rational(0));
i1.m_term.add_var(lp_bde);
i1.m_term.add_monomial(-rational(1), lp_abcde);
ineq i2(llc::EQ, lp::lar_term(), rational(0));
i2.m_term.add_var(lp_abcde);
i2.m_term.add_monomial(-rational(1), lp_bde);
ineq i0(lp_ac, llc::NE, 1);
lp::lar_term t1, t2;
t1.add_var(lp_bde);
t1.add_monomial(-rational(1), lp_abcde);
ineq i1(llc::EQ, t1, rational(0));
t2.add_var(lp_abcde);
t2.add_monomial(-rational(1), lp_bde);
ineq i2(llc::EQ, t2, rational(0));
bool found0 = false;
bool found1 = false;
bool found2 = false;
@ -263,14 +263,15 @@ void test_basic_lemma_for_mon_neutral_from_factors_to_monomial_1() {
SASSERT(lemma[0].size() == 4);
nla.get_core().print_lemma(std::cout);
ineq i0(llc::NE, lp::lar_term(), rational(1));
i0.m_term.add_var(lp_b);
ineq i1(llc::NE, lp::lar_term(), rational(1));
i1.m_term.add_var(lp_d);
ineq i2(llc::NE, lp::lar_term(), rational(1));
i2.m_term.add_var(lp_e);
ineq i3(llc::EQ, lp::lar_term(), rational(1));
i3.m_term.add_var(lp_bde);
lp::lar_term t0, t1, t2, t3;
t0.add_var(lp_b);
t1.add_var(lp_d);
t2.add_var(lp_e);
t3.add_var(lp_bde);
ineq i0(llc::NE, t0, rational(1));
ineq i1(llc::NE, t1, rational(1));
ineq i2(llc::NE, t2, rational(1));
ineq i3(llc::EQ, t3, rational(1));
bool found0 = false;
bool found1 = false;
bool found2 = false;
@ -346,10 +347,12 @@ void test_basic_lemma_for_mon_zero_from_factors_to_monomial() {
SASSERT(nla.get_core().test_check(lemma) == l_false);
nla.get_core().print_lemma(std::cout);
SASSERT(lemma.size() == 1 && lemma[0].size() == 2);
ineq i0(llc::NE, lp::lar_term(), rational(0));
i0.m_term.add_var(lp_b);
ineq i1(llc::EQ, lp::lar_term(), rational(0));
i1.m_term.add_var(lp_be);
lp::lar_term t0, t1;
t0.add_var(lp_b);
t1.add_var(lp_be);
ineq i0(llc::NE, t0, rational(0));
ineq i1(llc::EQ, t1, rational(0));
bool found0 = false;
bool found1 = false;
@ -396,12 +399,9 @@ void test_basic_lemma_for_mon_zero_from_monomial_to_factors() {
nla.get_core().print_lemma(std::cout);
ineq i0(llc::EQ, lp::lar_term(), rational(0));
i0.m_term.add_var(lp_a);
ineq i1(llc::EQ, lp::lar_term(), rational(0));
i1.m_term.add_var(lp_c);
ineq i2(llc::EQ, lp::lar_term(), rational(0));
i2.m_term.add_var(lp_d);
ineq i0(lp_a, llc::EQ, 0);
ineq i1(lp_c, llc::EQ, 0);
ineq i2(lp_d, llc::EQ, 0);
bool found0 = false;
bool found1 = false;
bool found2 = false;
@ -475,10 +475,8 @@ void test_basic_lemma_for_mon_neutral_from_monomial_to_factors() {
nla.get_core().print_lemma(std::cout);
ineq i0(llc::EQ, lp::lar_term(), rational(1));
i0.m_term.add_var(lp_d);
ineq i1(llc::EQ, lp::lar_term(), -rational(1));
i1.m_term.add_var(lp_d);
ineq i0(lp_d, llc::EQ, 1);
ineq i1(lp_d, llc::EQ, -1);
bool found0 = false;
bool found1 = false;