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review of monotonicity lemma

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2020-05-15 15:13:42 -07:00
parent 30ce6f20f2
commit 31a96b3afa
5 changed files with 46 additions and 72 deletions
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40
src/math/lp/nla_monotone_lemmas.cpp
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@ -30,35 +30,49 @@ void monotone::monotonicity_lemma(monic const& m) {
const rational prod_val = abs(c().product_value(m));
const rational m_val = abs(var_val(m));
if (m_val < prod_val)
monotonicity_lemma_lt(m, prod_val);
monotonicity_lemma_lt(m);
else if (m_val > prod_val)
monotonicity_lemma_gt(m, prod_val);
monotonicity_lemma_gt(m);
}
void monotone::monotonicity_lemma_gt(const monic& m, const rational& prod_val) {
TRACE("nla_solver", tout << "prod_val = " << prod_val << "\n";
tout << "m = "; c().print_monic_with_vars(m, tout););
/** \brief enforce the inequality |m| <= product |m[i]| .
/\_i |m[i]| <= |val(m[i])| => |m| <= |product_i val(m[i])|
<=>
\/_i |m[i]| > |val(m[i])| or |m| <= |product_i val(m[i])|
implied by
m[i] > val(m[i]) for val(m[i]) > 0
m[i] < val(m[i]) for val(m[i]) < 0
m >= product m[i] for product m[i] < 0
m <= product m[i] for product m[i] > 0
*/
void monotone::monotonicity_lemma_gt(const monic& m) {
new_lemma lemma(c(), __FUNCTION__);
rational product(1);
for (lpvar j : m.vars()) {
c().add_abs_bound(lemma, j, llc::GT);
auto v = c().val(j);
lemma |= ineq(j, v.is_neg() ? llc::LT : llc::GT, v);
product *= v;
}
lpvar m_j = m.var();
c().add_abs_bound(lemma, m_j, llc::LE, prod_val);
lemma |= ineq(m.var(), product.is_neg() ? llc::GE : llc::LE, product);
}
/** \brief enforce the inequality |m| >= product |m[i]| .
/\_i |m[i]| >= |val(m[i])| => |m| >= |product_i val(m[i])|
<=>
\/_i |m[i]| < |val(m[i])} or |m| >= |product_i val(m[i])|
\/_i |m[i]| < |val(m[i])| or |m| >= |product_i val(m[i])|
*/
void monotone::monotonicity_lemma_lt(const monic& m, const rational& prod_val) {
void monotone::monotonicity_lemma_lt(const monic& m) {
new_lemma lemma(c(), __FUNCTION__);
rational product(1);
for (lpvar j : m.vars()) {
c().add_abs_bound(lemma, j, llc::LT);
auto v = c().val(j);
lemma |= ineq(j, v.is_neg() ? llc::GT : llc::LT, v);
product *= v;
}
lpvar m_j = m.var();
c().add_abs_bound(lemma, m_j, llc::GE, prod_val);
lemma |= ineq(m.var(), product.is_neg() ? llc::LE : llc::GE, product);
}