// forward declaration
ex shuffle_G(const Gparameter & a0, const Gparameter & a1, const Gparameter & a2,
const Gparameter& pendint, const Gparameter& a_old, int scale,
- const exvector& gsyms);
+ const exvector& gsyms, bool flag_trailing_zeros_only);
// G transformation [VSW]
ex G_transform(const Gparameter& pendint, const Gparameter& a, int scale,
- const exvector& gsyms)
+ const exvector& gsyms, bool flag_trailing_zeros_only)
{
// main recursion routine
//
if (trailing_zeros > 0) {
ex result;
Gparameter new_a(a.begin(), a.end()-1);
- result += G_eval1(0, scale, gsyms) * G_transform(pendint, new_a, scale, gsyms);
+ result += G_eval1(0, scale, gsyms) * G_transform(pendint, new_a, scale, gsyms, flag_trailing_zeros_only);
for (Gparameter::const_iterator it = a.begin(); it != firstzero; ++it) {
Gparameter new_a(a.begin(), it);
new_a.push_back(0);
new_a.insert(new_a.end(), it, a.end()-1);
- result -= G_transform(pendint, new_a, scale, gsyms);
+ result -= G_transform(pendint, new_a, scale, gsyms, flag_trailing_zeros_only);
}
return result / trailing_zeros;
}
- // convergence case
- if (convergent) {
+ // convergence case or flag_trailing_zeros_only
+ if (convergent || flag_trailing_zeros_only) {
if (pendint.size() > 0) {
return G_eval(convert_pending_integrals_G(pendint),
pendint.front(), gsyms)*
Gparameter a1(a.begin(),min_it+1);
Gparameter a2(min_it+1,a.end());
- ex result = G_transform(pendint, a2, scale, gsyms)*
- G_transform(empty, a1, scale, gsyms);
+ ex result = G_transform(pendint, a2, scale, gsyms, flag_trailing_zeros_only)*
+ G_transform(empty, a1, scale, gsyms, flag_trailing_zeros_only);
- result -= shuffle_G(empty, a1, a2, pendint, a, scale, gsyms);
+ result -= shuffle_G(empty, a1, a2, pendint, a, scale, gsyms, flag_trailing_zeros_only);
return result;
}
Gparameter new_pendint = prepare_pending_integrals(pendint, a[min_it_pos]);
Gparameter new_a = a;
new_a[min_it_pos] = 0;
- ex result = G_transform(empty, new_a, scale, gsyms);
+ ex result = G_transform(empty, new_a, scale, gsyms, flag_trailing_zeros_only);
if (pendint.size() > 0) {
result *= trailing_zeros_G(convert_pending_integrals_G(pendint),
pendint.front(), gsyms);
new_pendint.push_back(*changeit);
result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint),
new_pendint.front(), gsyms)*
- G_transform(empty, new_a, scale, gsyms);
+ G_transform(empty, new_a, scale, gsyms, flag_trailing_zeros_only);
int buffer = *changeit;
*changeit = *min_it;
- result += G_transform(new_pendint, new_a, scale, gsyms);
+ result += G_transform(new_pendint, new_a, scale, gsyms, flag_trailing_zeros_only);
*changeit = buffer;
new_pendint.pop_back();
--changeit;
new_pendint.push_back(*changeit);
result += trailing_zeros_G(convert_pending_integrals_G(new_pendint),
new_pendint.front(), gsyms)*
- G_transform(empty, new_a, scale, gsyms);
+ G_transform(empty, new_a, scale, gsyms, flag_trailing_zeros_only);
*changeit = *min_it;
- result -= G_transform(new_pendint, new_a, scale, gsyms);
+ result -= G_transform(new_pendint, new_a, scale, gsyms, flag_trailing_zeros_only);
} else {
// smallest at the front
new_pendint.push_back(scale);
result += trailing_zeros_G(convert_pending_integrals_G(new_pendint),
new_pendint.front(), gsyms)*
- G_transform(empty, new_a, scale, gsyms);
+ G_transform(empty, new_a, scale, gsyms, flag_trailing_zeros_only);
new_pendint.back() = *changeit;
result -= trailing_zeros_G(convert_pending_integrals_G(new_pendint),
new_pendint.front(), gsyms)*
- G_transform(empty, new_a, scale, gsyms);
+ G_transform(empty, new_a, scale, gsyms, flag_trailing_zeros_only);
*changeit = *min_it;
- result += G_transform(new_pendint, new_a, scale, gsyms);
+ result += G_transform(new_pendint, new_a, scale, gsyms, flag_trailing_zeros_only);
}
return result;
}
// for the one that is equal to a_old
ex shuffle_G(const Gparameter & a0, const Gparameter & a1, const Gparameter & a2,
const Gparameter& pendint, const Gparameter& a_old, int scale,
- const exvector& gsyms)
+ const exvector& gsyms, bool flag_trailing_zeros_only)
{
if (a1.size()==0 && a2.size()==0) {
// veto the one configuration we don't want
if ( a0 == a_old ) return 0;
- return G_transform(pendint, a0, scale, gsyms);
+ return G_transform(pendint, a0, scale, gsyms, flag_trailing_zeros_only);
}
if (a2.size()==0) {
Gparameter empty;
Gparameter aa0 = a0;
aa0.insert(aa0.end(),a1.begin(),a1.end());
- return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms);
+ return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms, flag_trailing_zeros_only);
}
if (a1.size()==0) {
Gparameter empty;
Gparameter aa0 = a0;
aa0.insert(aa0.end(),a2.begin(),a2.end());
- return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms);
+ return shuffle_G(aa0, empty, empty, pendint, a_old, scale, gsyms, flag_trailing_zeros_only);
}
Gparameter a1_removed(a1.begin()+1,a1.end());
a01.push_back( a1[0] );
a02.push_back( a2[0] );
- return shuffle_G(a01, a1_removed, a2, pendint, a_old, scale, gsyms)
- + shuffle_G(a02, a1, a2_removed, pendint, a_old, scale, gsyms);
+ return shuffle_G(a01, a1_removed, a2, pendint, a_old, scale, gsyms, flag_trailing_zeros_only)
+ + shuffle_G(a02, a1, a2_removed, pendint, a_old, scale, gsyms, flag_trailing_zeros_only);
}
// handles the transformations and the numerical evaluation of G
std::vector<int> qlsts;
for (std::size_t j = r; j >= 1; --j) {
qlstx.push_back(cln::cl_N(1) - x[j-1]);
- if (instanceof(x[j-1], cln::cl_R_ring) &&
- realpart(x[j-1]) > 1 && realpart(x[j-1]) <= 2) {
- qlsts.push_back(s[j-1]);
+ if (instanceof(x[j-1], cln::cl_R_ring) && realpart(x[j-1]) > 1) {
+ qlsts.push_back(1);
} else {
qlsts.push_back(-s[j-1]);
}
return result;
}
+class less_object_for_cl_N
+{
+public:
+ bool operator() (const cln::cl_N & a, const cln::cl_N & b) const
+ {
+ // absolute value?
+ if (abs(a) != abs(b))
+ return (abs(a) < abs(b)) ? true : false;
+
+ // complex phase?
+ if (phase(a) != phase(b))
+ return (phase(a) < phase(b)) ? true : false;
+
+ // equal, therefore "less" is not true
+ return false;
+ }
+};
+
+
// convergence transformation, used for numerical evaluation of G function.
// the parameter x, s and y must only contain numerics
static cln::cl_N
G_do_trafo(const std::vector<cln::cl_N>& x, const std::vector<int>& s,
- const cln::cl_N& y)
+ const cln::cl_N& y, bool flag_trailing_zeros_only)
{
// sort (|x|<->position) to determine indices
- typedef std::multimap<cln::cl_R, std::size_t> sortmap_t;
+ typedef std::multimap<cln::cl_N, std::size_t, less_object_for_cl_N> sortmap_t;
sortmap_t sortmap;
std::size_t size = 0;
for (std::size_t i = 0; i < x.size(); ++i) {
if (!zerop(x[i])) {
- sortmap.insert(std::make_pair(abs(x[i]), i));
+ sortmap.insert(std::make_pair(x[i], i));
++size;
}
}
// include upper limit (scale)
- sortmap.insert(std::make_pair(abs(y), x.size()));
+ sortmap.insert(std::make_pair(y, x.size()));
// generate missing dummy-symbols
int i = 1;
// do transformation
Gparameter pendint;
- ex result = G_transform(pendint, a, scale, gsyms);
+ ex result = G_transform(pendint, a, scale, gsyms, flag_trailing_zeros_only);
// replace dummy symbols with their values
result = result.eval().expand();
result = result.subs(subslst).evalf();
need_hoelder = true;
}
}
- if (zerop(x[x.size() - 1])) {
+ if (zerop(x.back())) {
have_trailing_zero = true;
need_trafo = true;
}
// convergence transformation
if (need_trafo)
- return G_do_trafo(x, s, y);
+ return G_do_trafo(x, s, y, have_trailing_zero);
// do summation
std::vector<cln::cl_N> newx;
git://www.ginac.de / ginac.git / blobdiff