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90 lines
2.4 KiB
C++
90 lines
2.4 KiB
C++
/*++
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Copyright (c) 2017 Microsoft Corporation
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Author:
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Lev Nachmanson (levnach)
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Nikolaj Bjorner (nbjorner)
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--*/
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#include "math/lp/nla_basics_lemmas.h"
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#include "math/lp/nla_core.h"
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namespace nla {
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monotone::monotone(core * c) : common(c) {}
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void monotone::monotonicity_lemma() {
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unsigned shift = random();
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unsigned size = c().m_to_refine.size();
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for (unsigned i = 0; i < size && !done(); i++) {
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lpvar v = c().m_to_refine[(i + shift) % size];
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monotonicity_lemma(c().emons()[v]);
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}
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}
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void monotone::monotonicity_lemma(monic const& m) {
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SASSERT(!check_monic(m));
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if (c().mon_has_zero(m.vars()))
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return;
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if (c().has_big_num(m))
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return;
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const rational prod_val = abs(c().product_value(m));
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const rational m_val = abs(var_val(m));
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if (m_val < prod_val)
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monotonicity_lemma_lt(m);
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else if (m_val > prod_val)
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monotonicity_lemma_gt(m);
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}
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/** \brief enforce the inequality |m| <= product |m[i]| .
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/\_i |m[i]| <= |val(m[i])| => |m| <= |product_i val(m[i])|
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<=>
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\/_i |m[i]| > |val(m[i])| or |m| <= |product_i val(m[i])|
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implied by
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m[i] > val(m[i]) for val(m[i]) > 0
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m[i] < val(m[i]) for val(m[i]) < 0
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m >= product m[i] for product m[i] < 0
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m <= product m[i] for product m[i] > 0
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Example:
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0 >= x >= -2 & 0 <= y <= 3 => x*y >= -6
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0 >= x >= -2 & 0 <= y <= 3 => x*x*y <= 12
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*/
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void monotone::monotonicity_lemma_gt(const monic& m) {
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new_lemma lemma(c(), "monotonicity > ");
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rational product(1);
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for (lpvar j : m.vars()) {
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auto v = c().val(j);
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lemma |= ineq(j, v.is_neg() ? llc::LT : llc::GT, v);
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lemma |= ineq(j, v.is_neg() ? llc::GT : llc::LT, 0);
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product *= v;
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}
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lemma |= ineq(m.var(), product.is_neg() ? llc::GE : llc::LE, product);
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}
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/** \brief enforce the inequality |m| >= product |m[i]| .
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/\_i |m[i]| >= |val(m[i])| => |m| >= |product_i val(m[i])|
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<=>
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\/_i |m[i]| < |val(m[i])| or |m| >= |product_i val(m[i])|
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Example:
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x <= -2 & y >= 3 => x*y <= -6
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*/
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void monotone::monotonicity_lemma_lt(const monic& m) {
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new_lemma lemma(c(), "monotonicity <");
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rational product(1);
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for (lpvar j : m.vars()) {
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auto v = c().val(j);
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lemma |= ineq(j, v.is_neg() ? llc::GT : llc::LT, v);
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product *= v;
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}
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lemma |= ineq(m.var(), product.is_neg() ? llc::LE : llc::GE, product);
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}
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}
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