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simplify tang lemma

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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2020-01-16 20:54:58 -08:00
parent 052814d165
commit a38f58e49f
1 changed files with 22 additions and 56 deletions
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78
src/math/lp/nla_tangent_lemmas.cpp
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@ -26,8 +26,6 @@ struct imp {
point m_a; point m_a;
point m_b; point m_b;
point m_xy; point m_xy;
bool m_a_is_ok;
bool m_b_is_ok;
rational m_correct_v; rational m_correct_v;
// "below" means that the incorrect value is less than the correct one, that is m_v < m_correct_v // "below" means that the incorrect value is less than the correct one, that is m_v < m_correct_v
bool m_below; bool m_below;
@ -71,10 +69,8 @@ struct imp {
get_tang_points(); get_tang_points();
TRACE("nla_solver", tout << "tang domain = "; print_tangent_domain(tout) << std::endl;); TRACE("nla_solver", tout << "tang domain = "; print_tangent_domain(tout) << std::endl;);
generate_two_tang_lines(); generate_two_tang_lines();
if (m_a_is_ok) generate_tang_plane(m_a);
generate_tang_plane(m_a); generate_tang_plane(m_b);
if (m_b_is_ok)
generate_tang_plane(m_b);
} }
@ -110,9 +106,14 @@ struct imp {
void get_initial_tang_points() { void get_initial_tang_points() {
const rational& x = m_xy.x; const rational& x = m_xy.x;
const rational& y = m_xy.y; const rational& y = m_xy.y;
bool all_ints = m_v.is_int() && x.is_int() && y.is_int();
rational delta = rational(1);
if (!all_ints )
delta = std::min(delta, abs(m_correct_v - m_v));
TRACE("nla_solver", tout << "delta = " << delta << "\n";);
if (!m_below){ if (!m_below){
m_a = point(x - rational(1), y + rational(1)); m_a = point(x - delta, y + delta);
m_b = point(x + rational(1), y - rational(1)); m_b = point(x + delta, y - delta);
} }
else { else {
// denote x = xy.x and y = xy.y, and vx, vy - the value of x and y. // denote x = xy.x and y = xy.y, and vx, vy - the value of x and y.
@ -121,13 +122,16 @@ struct imp {
// vx*y + vy*x - vx*vy + y + x - xv*vy - vx - vy - 1 = pl(x, y) - 1 // vx*y + vy*x - vx*vy + y + x - xv*vy - vx - vy - 1 = pl(x, y) - 1
// For integers the last expression is greater than or equal to val(xy) when x = vx and y = vy. // For integers the last expression is greater than or equal to val(xy) when x = vx and y = vy.
// If x <= vx+1 and y <= vy+1 then (vx+1-x)*(vy+1-y) > 0, that creates a cut // If x <= vx+1 and y <= vy+1 then (vx+1-x)*(vy+1-y) > 0, that creates a cut
// - (vx + 1)y - (vy + 1)x + xy > - (vx+1)*(vx+1) // - (vx + 1)y - (vy + 1)x + xy > - (vx+1)*(vx+1).
m_a = point(x - rational(1), y - rational(1)); // If all_ints is false then we use the fact that
m_b = point(x + rational(1), y + rational(1)); // tang_plane() will not change more than on delta*delta
m_a = point(x - delta, y - delta);
m_b = point(x + delta, y + delta);
} }
} }
void push_tang_point(point & a) { void push_tang_point(point & a) {
SASSERT(plane_is_correct_cut(a));
int steps = 10; int steps = 10;
point del = a - m_xy; point del = a - m_xy;
while (steps--) { while (steps--) {
@ -142,24 +146,6 @@ struct imp {
} }
} }
bool pull_tang_point(point & a ) {
if (plane_is_correct_cut(a))
return true;
point del = a - m_xy;
unsigned steps = 10;
while (steps--) {
del /= rational(2);
point na = m_xy + del;
TRACE("nla_solver_tp", tout << "del = " << del << std::endl;);
if (plane_is_correct_cut(na)) {
a = na;
TRACE("nla_solver_tp", tout << "exit";tout << std::endl;);
return true;
}
}
return false;
}
rational tang_plane(const point& a) const { rational tang_plane(const point& a) const {
return a.x * m_xy.y + a.y * m_xy.x - a.x * a.y; return a.x * m_xy.y + a.y * m_xy.x - a.x * a.y;
} }
@ -168,37 +154,17 @@ struct imp {
get_initial_tang_points(); get_initial_tang_points();
TRACE("nla_solver", tout << "xy = " << m_xy << ", correct val = " << m_correct_v; TRACE("nla_solver", tout << "xy = " << m_xy << ", correct val = " << m_correct_v;
tout << "\ntang points:"; print_tangent_domain(tout);tout << std::endl;); tout << "\ntang points:"; print_tangent_domain(tout);tout << std::endl;);
bool all_ints = m_v.is_int() && m_xy.x.is_int() && m_xy.y.is_int(); push_tang_point(m_a);
if (!all_ints) { TRACE("nla_solver", tout << "pushed a = " << m_a << std::endl;);
m_a_is_ok = pull_tang_point(m_a);
m_b_is_ok = pull_tang_point(m_b); push_tang_point(m_b);
} else { TRACE("nla_solver", tout << "pushed b = " << m_b << std::endl;);
m_a_is_ok = m_b_is_ok = true;
}
if (m_a_is_ok) {
push_tang_point(m_a);
TRACE("nla_solver", tout << "pushed a = " << m_a << std::endl;);
}
if (m_b_is_ok) {
push_tang_point(m_b);
TRACE("nla_solver", tout << "pushed b = " << m_b << std::endl;);
}
TRACE("nla_solver", TRACE("nla_solver",
if (m_a_is_ok) { tout << "tang_plane(a) = " << tang_plane(m_a) << " , val = " << m_v; } tout << "tang_plane(a) = " << tang_plane(m_a) << " , val = " << m_v << ", tang_plane(b) = " << tang_plane(m_b) << " , val = " << std::endl;);
if (m_b_is_ok) { tout << "\ntang_plane(b) = " << tang_plane(m_b) << " , val = " << m_v << std::endl;});
} }
std::ostream& print_tangent_domain(std::ostream& out) { std::ostream& print_tangent_domain(std::ostream& out) {
if (m_a_is_ok && m_b_is_ok) { out << "(" << m_a << ", " << m_b << ")";
out << "(" << m_a << ", " << m_b << ")";
} else if (m_a_is_ok) {
out << m_a;
}
else if (m_b_is_ok) {
out << m_b;
} else {
out << "no a, no b";
}
return out; return out;
} }