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Fix bug. Improve nl_nz_sqf_isolate_roots

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-10 12:51:54 -08:00
parent 71ab7759d1
commit 191e503418
1 changed files with 92 additions and 12 deletions
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104
src/math/realclosure/realclosure.cpp
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@ -1446,7 +1446,7 @@ namespace realclosure {
bool neg_root_upper_bound(unsigned n, value * const * p, int & N) {
value_ref_buffer q(*this);
reverse(n, p, q);
if (pos_root_lower_bound(n, q.c_ptr(), N)) {
if (neg_root_lower_bound(n, q.c_ptr(), N)) {
N = -N;
return true;
}
@ -1678,6 +1678,16 @@ namespace realclosure {
return r;
}
/**
\brief Add a new root of p that is isolated by (interval, sd, sdt_idx) to roots.
*/
void add_root(unsigned p_sz, value * const * p, mpbqi const & interval, sign_det * sd, unsigned sdt_idx, numeral_vector & roots) {
algebraic * a = mk_algebraic(p_sz, p, interval, sd, sdt_idx);
numeral r;
set(r, mk_rational_function_value(a));
roots.push_back(r);
}
/**
\brief Isolate roots of p in the given interval using sign conditions to distinguish between them.
We need this method when the polynomial contains roots that are infinitesimally close to each other.
@ -1895,10 +1905,7 @@ namespace realclosure {
SASSERT(M_s.n() == M_s.m()); SASSERT(M_s.n() == static_cast<unsigned>(num_roots));
sign_det * sd = mk_sign_det(M_s, prs, qs, scs);
for (unsigned idx = 0; idx < static_cast<unsigned>(num_roots); idx++) {
algebraic * a = mk_algebraic(p_sz, p, interval, sd, idx);
numeral r;
set(r, mk_rational_function_value(a));
roots.push_back(r);
add_root(p_sz, p, interval, sd, idx, roots);
}
}
@ -1915,6 +1922,63 @@ namespace realclosure {
}
return true;
}
/**
\brief magnitude -> mpbq
*/
void magnitude_to_mpbq(int mag, bool sign, mpbq & r) {
if (mag < 0) {
bqm().set(r, mpbq(1, -mag));
}
else {
bqm().set(r, mpbq(2));
bqm().power(r, mag);
}
if (sign)
bqm().neg(r);
}
/**
\brief Convert magnitudes for negative roots lower and upper bounds into an interval.
*/
void mk_neg_interval(bool has_neg_lower, int neg_lower_N, bool has_neg_upper, int neg_upper_N, mpbqi & r) {
scoped_mpbq aux(bqm());
if (!has_neg_lower) {
set_lower_inf(r);
}
else {
magnitude_to_mpbq(neg_lower_N, true, aux);
set_lower(r, aux);
}
if (!has_neg_upper) {
set_upper_zero(r);
}
else {
magnitude_to_mpbq(neg_upper_N, true, aux);
set_upper(r, aux);
}
}
/**
\brief Convert magnitudes for negative roots lower and upper bounds into an interval.
*/
void mk_pos_interval(bool has_pos_lower, int pos_lower_N, bool has_pos_upper, int pos_upper_N, mpbqi & r) {
scoped_mpbq aux(bqm());
if (!has_pos_lower) {
set_lower_zero(r);
}
else {
magnitude_to_mpbq(pos_lower_N, false, aux);
set_lower(r, aux);
}
if (!has_pos_upper) {
set_upper_inf(r);
}
else {
magnitude_to_mpbq(pos_upper_N, false, aux);
set_upper(r, aux);
}
}
/**
\brief Root isolation for polynomials that are
@ -1956,13 +2020,29 @@ namespace realclosure {
TRACE("rcf_isolate",
tout << "num_neg_roots: " << num_neg_roots << "\n";
tout << "num_pos_roots: " << num_pos_roots << "\n";);
// TODO
// Test sign_det_isolate_roots
if (num_neg_roots > 1)
sign_det_isolate_roots(n, p, num_neg_roots, minf_zero, roots);
if (num_pos_roots > 1)
sign_det_isolate_roots(n, p, num_pos_roots, zero_inf, roots);
scoped_mpbqi pos_interval(bqim());
scoped_mpbqi neg_interval(bqim());
mk_neg_interval(has_neg_lower, neg_lower_N, has_neg_upper, neg_upper_N, neg_interval);
mk_pos_interval(has_pos_lower, pos_lower_N, has_pos_upper, pos_upper_N, pos_interval);
if (num_neg_roots > 0) {
if (num_neg_roots == 1) {
add_root(n, p, neg_interval, 0, UINT_MAX, roots);
}
else {
// TODO bisection
sign_det_isolate_roots(n, p, num_neg_roots, minf_zero, roots);
}
}
if (num_pos_roots > 0) {
if (num_pos_roots == 1) {
add_root(n, p, pos_interval, 0, UINT_MAX, roots);
}
else {
// TODO bisection
sign_det_isolate_roots(n, p, num_pos_roots, zero_inf, roots);
}
}
}
/**