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Tune Grobner equations

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\brief convert p == 0 into a solved form v == r, such that
   v has bounds [lo, oo) iff r has bounds [lo', oo)
   v has bounds (oo,hi]  iff r has bounds (oo,hi']

   The solved form allows the Grobner solver identify more bounds conflicts.
   A bad leading term can miss bounds conflicts.
   For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
   we prefer to solve z == -x - y instead of x == -z - y
   because the solution -z - y has neither an upper, nor a lower bound.

The Grobner solver is augmented with a notion of a substitution that is applied before the solver is run.
This commit is contained in:
Nikolaj Bjorner 2022-07-11 16:14:26 -07:00
parent f33c933241
commit 316ed778e0
5 changed files with 127 additions and 13 deletions
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75
src/math/lp/nla_core.cpp
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@ -1716,7 +1716,7 @@ void core::configure_grobner() {
for (lpvar k : emons()[j].vars())
r *= pdd_expr(rational::one(), k, dep);
r -= val_of_fixed_var_with_deps(j, dep);
m_pdd_grobner.add(r, dep);
add_eq_to_grobner(r, dep);
}
}
}
@ -1880,6 +1880,76 @@ dd::pdd core::pdd_expr(const rational& c, lpvar j, u_dependency*& dep) {
return r;
}
/**
\brief convert p == 0 into a solved form v == r, such that
v has bounds [lo, oo) iff r has bounds [lo', oo)
v has bounds (oo,hi] iff r has bounds (oo,hi']
The solved form allows the Grobner solver identify more bounds conflicts.
A bad leading term can miss bounds conflicts.
For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
we prefer to solve z == -x - y instead of x == -z - y
because the solution -z - y has neither an upper, nor a lower bound.
*/
bool core::is_solved(dd::pdd const& p, unsigned& v, dd::pdd& r) {
if (!p.is_linear())
return false;
r = p;
unsigned num_lo = 0, num_hi = 0;
unsigned lo = 0, hi = 0;
rational lc, hc, c;
while (!r.is_val()) {
SASSERT(r.hi().is_val());
v = r.var();
rational val = r.hi().val();
switch (m_lar_solver.get_column_type(v)) {
case lp::column_type::lower_bound:
if (val > 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
break;
case lp::column_type::upper_bound:
if (val < 0) num_lo++, lo = v, lc = val; else num_hi++, hi = v, hc = val;
break;
case lp::column_type::fixed:
case lp::column_type::boxed:
break;
default:
return false;
}
if (num_lo > 1 && num_hi > 1)
return false;
r = r.lo();
}
if (num_lo == 1 && num_hi > 1) {
v = lo;
c = lc;
}
else if (num_hi == 1 && num_lo > 1) {
v = hi;
c = hc;
}
else
return false;
r = c*m_pdd_manager.mk_var(v) - p;
if (c != 1)
r = r * (1/c);
return true;
}
/**
\brief add an equality to grobner solver, convert it to solved form if available.
*/
void core::add_eq_to_grobner(dd::pdd& p, u_dependency* dep) {
unsigned v;
dd::pdd q(m_pdd_manager);
m_pdd_grobner.simplify(p, dep);
if (is_solved(p, v, q))
m_pdd_grobner.add_subst(v, q, dep);
else
m_pdd_grobner.add(p, dep);
}
void core::add_row_to_grobner(const vector<lp::row_cell<rational>> & row) {
u_dependency *dep = nullptr;
rational val;
@ -1887,7 +1957,7 @@ void core::add_row_to_grobner(const vector<lp::row_cell<rational>> & row) {
for (const auto &p : row)
sum += pdd_expr(p.coeff(), p.var(), dep);
TRACE("grobner", print_row(row, tout) << " " << sum << "\n");
m_pdd_grobner.add(sum, dep);
add_eq_to_grobner(sum, dep);
}
@ -1907,7 +1977,6 @@ void core::find_nl_cluster() {
TRACE("grobner", tout << "vars in cluster: ";
for (lpvar j : active_var_set()) tout << "j" << j << " "; tout << "\n";
display_matrix_of_m_rows(tout);
/*emons().display(tout << "emons\n");*/
);
}