void PolynomialFinderBase::solve (int n)
{
assert (n <= m_maxN);
double c0,c1;
int i,j,k;
k = (n-1)/2;
//
// form vector of 'a' constants
//
if (n & 1) { // odd
for (i=0;i<=k;i++) {
m_a[i] = (2.0*i+1.0)/(m_sqrt2()*(k+1.0));
}
} // even
else {
for (i=0;i<k+1;i++) {
m_a[i] = 0.0;
}
if (k & 1) {
for (i=1;i<=k;i+=2) {
m_a[i] = (2*i+1)/sqrt(double((k+1)*(k+2)));
}
}
else {
for (i=0;i<=k;i+=2) {
m_a[i] = (2*i+1)/sqrt(double((k+1)*(k+2)));
}
}
}
for (i=0;i<=n;i++){
m_s[i] = 0.0;
m_w[i] = 0.0;
}
//
// form s[] = sum of a[i]*P[i]
//
m_s[0] = m_a[0];
m_s[1] = m_a[1];
for (i=2;i<=k;i++) {
legendre(m_p,i);
for (j=0;j<=i;j++) {
m_s[j] += m_a[i]*m_p[j];
}
}
//
// form v[] = square of s[]
//
for (i=0;i<=2*k+2;i++) {
m_v[i] = 0.0;
}
for (i=0;i<=k;i++) {
for (j=0;j<=k;j++) {
m_v[i+j] += m_s[i]*m_s[j];
}
}
//
// modify integrand for even 'n'
//
m_v[2*k+1] = 0.0;
if ((n & 1) == 0) {
for (i=n;i>=0;i--) {
m_v[i+1] += m_v[i];
}
}
//
// form integral of v[]
//
for (i=n+1;i>=0;i--) {
m_v[i+1] = m_v[i]/(double)(i+1.0);
}
m_v[0] = 0.0;
//
// clear s[] for use in computing definite integral
//
for (i=0;i<(n+2);i++){
m_s[i] = 0.0;
}
m_s[0] = -1.0;
m_s[1] = 2.0;
//
// calculate definite integral
//
for (i=1;i<=n;i++) {
if (i > 1) {
c0 = -m_s[0];
for (j=1;j<i+1;j++) {
c1 = -m_s[j] + 2.0*m_s[j-1];
m_s[j-1] = c0;
c0 = c1;
}
c1 = 2.0*m_s[i];
m_s[i] = c0;
m_s[i+1] = c1;
}
for (j=i;j>0;j--) {
m_w[j] += (m_v[i]*m_s[j]);
}
}
if ((n & 1) == 0) m_w[1] = 0.0;
}
static void tst3() {
enable_trace("nlsat_interval");
unsynch_mpq_manager qm;
anum_manager am(qm);
small_object_allocator allocator;
nlsat::interval_set_manager ism(am, allocator);
scoped_anum sqrt2(am), m_sqrt2(am), two(am), m_two(am), three(am), one(am), zero(am);
am.set(two, 2);
am.set(m_two, -2);
am.set(one, 1);
am.root(two, 2, sqrt2);
am.set(m_sqrt2, sqrt2);
am.neg(m_sqrt2);
am.set(three, 3);
nlsat::literal p1(1, false);
nlsat::literal p2(2, false);
nlsat::literal p3(3, false);
nlsat::literal p4(4, false);
nlsat::literal np2(2, true);
nlsat::interval_set_ref s1(ism), s2(ism), s3(ism), s4(ism);
s1 = ism.mk_empty();
std::cout << "s1: " << s1 << "\n";
s2 = ism.mk(true, true, zero, false, false, sqrt2, np2);
std::cout << "s2: " << s2 << "\n";
s3 = ism.mk(false, false, zero, false, false, two, p1);
std::cout << "s3: " << s3 << "\n";
s4 = ism.mk_union(s2, s3);
std::cout << "s4: " << s4 << "\n";
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, zero, false, false, two, p1);
s2 = ism.mk(false, false, zero, false, false, two, p2);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, zero, false, false, two, p1);
s2 = ism.mk(false, false, m_sqrt2, false, false, one, p2);
s3 = ism.mk_union(s1, s2);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, one, p1);
s2 = ism.mk(false, false, zero, false, false, two, p2);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, one, p1);
s2 = ism.mk(false, false, two, false, false, three, p2);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_sqrt2, false, false, three, p1);
s2 = ism.mk(false, false, zero, false, false, two, p2);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ]
// s2: [ ... ] [ ... ]
s1 = ism.mk(false, false, m_two, false, false, two, p1);
s2 = ism.mk(false, false, m_sqrt2, false, false, zero, p2);
s3 = ism.mk(false, false, one, false, false, three, p2);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 2);
// Case
// s1: [ ... ]
// s2: [ ... ]
s1 = ism.mk(false, false, m_two, false, false, two, p1);
s2 = ism.mk(false, false, two, false, false, three, p2);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, two, false, false, three, p2);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, two, false, false, three, p1);
tst_interval(s1, s2, 1);
s1 = ism.mk(false, false, m_two, true, false, two, p1);
tst_interval(s1, s2, 2);
s1 = ism.mk(false, false, two, false, false, two, p1);
s2 = ism.mk(false, false, two, false, false, three, p2);
tst_interval(s1, s2, 1);
// Case
// s1: [ ... ] [ ... ]
// s2: [ .. ] [ ... ] [ ... ]
s1 = ism.mk(false, false, m_two, false, false, zero, p1);
s3 = ism.mk(false, false, one, false, false, three, p1);
s1 = ism.mk_union(s1, s3);
s2 = ism.mk(true, true, zero, false, false, m_sqrt2, p2);
tst_interval(s1, s2, 3);
s3 = ism.mk(false, false, one, false, false, sqrt2, p2);
s2 = ism.mk_union(s2, s3);
s3 = ism.mk(false, false, two, true, true, zero, p2);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 4);
// Case
s1 = ism.mk(true, true, zero, false, false, one, p1);
s2 = ism.mk(true, false, one, true, true, zero, p2);
tst_interval(s1, s2, 2);
s2 = ism.mk(true, false, one, false, false, two, p2);
s3 = ism.mk(false, false, two, true, true, zero, p1);
s2 = ism.mk_union(s2, s3);
tst_interval(s1, s2, 3);
}
