* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <numeric>
-#include <stdexcept>
-
#include "pseries.h"
#include "add.h"
#include "inifcns.h" // for Order function
#include "archive.h"
#include "utils.h"
+#include <limits>
+#include <numeric>
+#include <stdexcept>
+
namespace GiNaC {
GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic,
* Default constructor
*/
-pseries::pseries() : inherited(TINFO_pseries) { }
+pseries::pseries() { }
/*
* @param rel_ expansion variable and point (must hold a relational)
* @param ops_ vector of {coefficient, power} pairs (coefficient must not be zero)
* @return newly constructed pseries */
-pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
+pseries::pseries(const ex &rel_, const epvector &ops_) : seq(ops_)
{
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
* Archiving
*/
-pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+void pseries::read_archive(const archive_node &n, lst &sym_lst)
{
- for (unsigned int i=0; true; ++i) {
+ inherited::read_archive(n, sym_lst);
+ archive_node::archive_node_cit first = n.find_first("coeff");
+ archive_node::archive_node_cit last = n.find_last("power");
+ ++last;
+ seq.reserve((last-first)/2);
+
+ for (archive_node::archive_node_cit loc = first; loc < last;) {
ex rest;
ex coeff;
- if (n.find_ex("coeff", rest, sym_lst, i) && n.find_ex("power", coeff, sym_lst, i))
- seq.push_back(expair(rest, coeff));
- else
- break;
+ n.find_ex_by_loc(loc++, rest, sym_lst);
+ n.find_ex_by_loc(loc++, coeff, sym_lst);
+ seq.push_back(expair(rest, coeff));
}
+
n.find_ex("var", var, sym_lst);
n.find_ex("point", point, sym_lst);
}
n.add_ex("point", point);
}
-DEFAULT_UNARCHIVE(pseries)
//////////
// functions overriding virtual functions from base classes
epvector::const_iterator it = seq.begin(), itend = seq.end();
if (it == itend)
return 0;
- int max_pow = INT_MIN;
+ int max_pow = std::numeric_limits<int>::min();
while (it != itend) {
int pow = it->rest.degree(s);
if (pow > max_pow)
epvector::const_iterator it = seq.begin(), itend = seq.end();
if (it == itend)
return 0;
- int min_pow = INT_MAX;
+ int min_pow = std::numeric_limits<int>::max();
while (it != itend) {
int pow = it->rest.ldegree(s);
if (pow < min_pow)
ex pseries::conjugate() const
{
+ if(!var.info(info_flags::real))
+ return conjugate_function(*this).hold();
+
epvector * newseq = conjugateepvector(seq);
- ex newvar = var.conjugate();
ex newpoint = point.conjugate();
- if (!newseq && are_ex_trivially_equal(newvar, var) && are_ex_trivially_equal(point, newpoint)) {
+ if (!newseq && are_ex_trivially_equal(point, newpoint)) {
return *this;
}
- ex result = (new pseries(newvar==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated);
+ ex result = (new pseries(var==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated);
if (newseq) {
delete newseq;
}
return result;
}
+ex pseries::real_part() const
+{
+ if(!var.info(info_flags::real))
+ return real_part_function(*this).hold();
+ ex newpoint = point.real_part();
+ if(newpoint != point)
+ return real_part_function(*this).hold();
+
+ epvector v;
+ v.reserve(seq.size());
+ for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+ v.push_back(expair((i->rest).real_part(), i->coeff));
+ return (new pseries(var==point, v))->setflag(status_flags::dynallocated);
+}
+
+ex pseries::imag_part() const
+{
+ if(!var.info(info_flags::real))
+ return imag_part_function(*this).hold();
+ ex newpoint = point.real_part();
+ if(newpoint != point)
+ return imag_part_function(*this).hold();
+
+ epvector v;
+ v.reserve(seq.size());
+ for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+ v.push_back(expair((i->rest).imag_part(), i->coeff));
+ return (new pseries(var==point, v))->setflag(status_flags::dynallocated);
+}
+
ex pseries::eval_integ() const
{
epvector *newseq = NULL;
return *this;
}
+ex pseries::evalm() const
+{
+ // evalm each coefficient
+ epvector newseq;
+ bool something_changed = false;
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (something_changed) {
+ ex newcoeff = i->rest.evalm();
+ if (!newcoeff.is_zero())
+ newseq.push_back(expair(newcoeff, i->coeff));
+ }
+ else {
+ ex newcoeff = i->rest.evalm();
+ if (!are_ex_trivially_equal(newcoeff, i->rest)) {
+ something_changed = true;
+ newseq.reserve(seq.size());
+ std::copy(seq.begin(), i, std::back_inserter<epvector>(newseq));
+ if (!newcoeff.is_zero())
+ newseq.push_back(expair(newcoeff, i->coeff));
+ }
+ }
+ }
+ if (something_changed)
+ return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated);
+ else
+ return *this;
+}
+
ex pseries::subs(const exmap & m, unsigned options) const
{
// If expansion variable is being substituted, convert the series to a
epvector::const_iterator b = other.seq.begin();
epvector::const_iterator a_end = seq.end();
epvector::const_iterator b_end = other.seq.end();
- int pow_a = INT_MAX, pow_b = INT_MAX;
+ int pow_a = std::numeric_limits<int>::max(), pow_b = std::numeric_limits<int>::max();
for (;;) {
// If a is empty, fill up with elements from b and stop
if (a == a_end) {
int cdeg_min = a_min + b_min;
int cdeg_max = a_max + b_max;
- int higher_order_a = INT_MAX;
- int higher_order_b = INT_MAX;
+ int higher_order_a = std::numeric_limits<int>::max();
+ int higher_order_b = std::numeric_limits<int>::max();
if (is_order_function(coeff(var, a_max)))
higher_order_a = a_max + b_min;
if (is_order_function(other.coeff(var, b_max)))
if (!co.is_zero())
new_seq.push_back(expair(co, numeric(cdeg)));
}
- if (higher_order_c < INT_MAX)
+ if (higher_order_c < std::numeric_limits<int>::max())
new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c)));
return pseries(relational(var, point), new_seq);
}
// holds ldegrees of the series of individual factors
std::vector<int> ldegrees;
+ std::vector<bool> ldegree_redo;
// find minimal degrees
const epvector::const_iterator itbeg = seq.begin();
const epvector::const_iterator itend = seq.end();
+ // first round: obtain a bound up to which minimal degrees have to be
+ // considered
for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
ex expon = it->coeff;
}
int real_ldegree = 0;
+ bool flag_redo = false;
try {
real_ldegree = buf.expand().ldegree(sym-r.rhs());
} catch (std::runtime_error) {}
if (real_ldegree == 0) {
+ if ( factor < 0 ) {
+ // This case must terminate, otherwise we would have division by
+ // zero.
+ int orderloop = 0;
+ do {
+ orderloop++;
+ real_ldegree = buf.series(r, orderloop, options).ldegree(sym);
+ } while (real_ldegree == orderloop);
+ } else {
+ // Here it is possible that buf does not have a ldegree, therefore
+ // check only if ldegree is negative, otherwise reconsider the case
+ // in the second round.
+ real_ldegree = buf.series(r, 0, options).ldegree(sym);
+ if (real_ldegree == 0)
+ flag_redo = true;
+ }
+ }
+
+ ldegrees.push_back(factor * real_ldegree);
+ ldegree_redo.push_back(flag_redo);
+ }
+
+ int degbound = order-std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
+ // Second round: determine the remaining positive ldegrees by the series
+ // method.
+ // here we can ignore ldegrees larger than degbound
+ size_t j = 0;
+ for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
+ if ( ldegree_redo[j] ) {
+ ex expon = it->coeff;
+ int factor = 1;
+ ex buf;
+ if (expon.info(info_flags::integer)) {
+ buf = it->rest;
+ factor = ex_to<numeric>(expon).to_int();
+ } else {
+ buf = recombine_pair_to_ex(*it);
+ }
+ int real_ldegree = 0;
int orderloop = 0;
do {
orderloop++;
real_ldegree = buf.series(r, orderloop, options).ldegree(sym);
- } while (real_ldegree == orderloop);
+ } while ((real_ldegree == orderloop)
+ && ( factor*real_ldegree < degbound));
+ ldegrees[j] = factor * real_ldegree;
+ degbound -= factor * real_ldegree;
}
-
- ldegrees.push_back(factor * real_ldegree);
+ j++;
}
int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
must_expand_basis = true;
}
+ bool exponent_is_regular = true;
+ try {
+ exponent.subs(r, subs_options::no_pattern);
+ } catch (pole_error) {
+ exponent_is_regular = false;
+ }
+
+ if (!exponent_is_regular) {
+ ex l = exponent*log(basis);
+ // this == exp(l);
+ ex le = l.series(r, order, options);
+ // Note: expanding exp(l) won't help, since that will attempt
+ // Taylor expansion, and fail (because exponent is "singular")
+ // Still l itself might be expanded in Taylor series.
+ // Examples:
+ // sin(x)/x*log(cos(x))
+ // 1/x*log(1 + x)
+ return exp(le).series(r, order, options);
+ // Note: if l happens to have a Laurent expansion (with
+ // negative powers of (var - point)), expanding exp(le)
+ // will barf (which is The Right Thing).
+ }
+
// Is the expression of type something^(-int)?
if (!must_expand_basis && !exponent.info(info_flags::negint)
&& (!is_a<add>(basis) || !is_a<numeric>(exponent)))
}
const ex& sym = r.lhs();
// find existing minimal degree
- int real_ldegree = basis.expand().ldegree(sym-r.rhs());
+ ex eb = basis.expand();
+ int real_ldegree = 0;
+ if (eb.info(info_flags::rational_function))
+ real_ldegree = eb.ldegree(sym-r.rhs());
if (real_ldegree == 0) {
int orderloop = 0;
do {
fexpansion.reserve(fseries.nops());
for (size_t i=0; i<fseries.nops(); ++i) {
ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
- fexpansion.push_back(expair(
- currcoeff == Order(_ex1)
- ? currcoeff
- : integral(x, a.subs(r), b.subs(r), currcoeff),
- ex_to<pseries>(fseries).exponop(i)
- ));
+ currcoeff = (currcoeff == Order(_ex1))
+ ? currcoeff
+ : integral(x, a.subs(r), b.subs(r), currcoeff);
+ if (currcoeff != 0)
+ fexpansion.push_back(
+ expair(currcoeff, ex_to<pseries>(fseries).exponop(i)));
}
// Expanding lower boundary
break;
ex currexpon = ex_to<pseries>(fseries).exponop(i);
int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
- currcoeff=currcoeff.series(r, orderforf);
+ currcoeff = currcoeff.series(r, orderforf);
ex term = ex_to<pseries>(aseries).power_const(ex_to<numeric>(currexpon+1),order);
term = ex_to<pseries>(term).mul_const(ex_to<numeric>(-1/(currexpon+1)));
term = ex_to<pseries>(term).mul_series(ex_to<pseries>(currcoeff));
break;
ex currexpon = ex_to<pseries>(fseries).exponop(i);
int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
- currcoeff=currcoeff.series(r, orderforf);
+ currcoeff = currcoeff.series(r, orderforf);
ex term = ex_to<pseries>(bseries).power_const(ex_to<numeric>(currexpon+1),order);
term = ex_to<pseries>(term).mul_const(ex_to<numeric>(1/(currexpon+1)));
term = ex_to<pseries>(term).mul_series(ex_to<pseries>(currcoeff));
else
throw (std::logic_error("ex::series(): expansion point has unknown type"));
- try {
- e = bp->series(rel_, order, options);
- } catch (std::exception &x) {
- throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")"));
- }
+ e = bp->series(rel_, order, options);
return e;
}
+GINAC_BIND_UNARCHIVER(pseries);
+
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff