* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2015 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
* @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_) : 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()));
+ point = rel_.rhs();
+ var = rel_.lhs();
+}
+pseries::pseries(const ex &rel_, epvector &&ops_)
+ : seq(std::move(ops_))
{
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
void pseries::read_archive(const archive_node &n, lst &sym_lst)
{
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");
+ auto first = n.find_first("coeff");
+ auto last = n.find_last("power");
++last;
seq.reserve((last-first)/2);
- for (archive_node::archive_node_cit loc = first; loc < last;) {
+ for (auto loc = first; loc < last;) {
ex rest;
ex coeff;
n.find_ex_by_loc(loc++, rest, sym_lst);
void pseries::archive(archive_node &n) const
{
inherited::archive(n);
- epvector::const_iterator i = seq.begin(), iend = seq.end();
- while (i != iend) {
- n.add_ex("coeff", i->rest);
- n.add_ex("power", i->coeff);
- ++i;
+ for (auto & it : seq) {
+ n.add_ex("coeff", it.rest);
+ n.add_ex("power", it.coeff);
}
n.add_ex("var", var);
n.add_ex("point", point);
if (seq.empty())
c.s << '0';
- epvector::const_iterator i = seq.begin(), end = seq.end();
+ auto i = seq.begin(), end = seq.end();
while (i != end) {
// print a sign, if needed
new_seq.push_back(expair(it->rest.eval(level-1), it->coeff));
++it;
}
- return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
/** Evaluate coefficients numerically. */
new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
++it;
}
- return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
ex pseries::conjugate() const
if(!var.info(info_flags::real))
return conjugate_function(*this).hold();
- epvector * newseq = conjugateepvector(seq);
+ std::unique_ptr<epvector> newseq(conjugateepvector(seq));
ex newpoint = point.conjugate();
- if (!newseq && are_ex_trivially_equal(point, newpoint)) {
+ if (!newseq && are_ex_trivially_equal(point, newpoint)) {
return *this;
}
- ex result = (new pseries(var==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated);
- if (newseq) {
- delete newseq;
- }
- return result;
+ return (new pseries(var==newpoint, newseq ? std::move(*newseq) : seq))->setflag(status_flags::dynallocated);
}
ex pseries::real_part() const
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);
+ for (auto & it : seq)
+ v.push_back(expair((it.rest).real_part(), it.coeff));
+ return (new pseries(var==point, std::move(v)))->setflag(status_flags::dynallocated);
}
ex pseries::imag_part() const
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);
+ for (auto & it : seq)
+ v.push_back(expair((it.rest).imag_part(), it.coeff));
+ return (new pseries(var==point, std::move(v)))->setflag(status_flags::dynallocated);
}
ex pseries::eval_integ() const
{
- epvector *newseq = NULL;
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ std::unique_ptr<epvector> newseq(nullptr);
+ for (auto i=seq.begin(); i!=seq.end(); ++i) {
if (newseq) {
newseq->push_back(expair(i->rest.eval_integ(), i->coeff));
continue;
}
ex newterm = i->rest.eval_integ();
if (!are_ex_trivially_equal(newterm, i->rest)) {
- newseq = new epvector;
+ newseq.reset(new epvector);
newseq->reserve(seq.size());
- for (epvector::const_iterator j=seq.begin(); j!=i; ++j)
+ for (auto j=seq.begin(); j!=i; ++j)
newseq->push_back(*j);
newseq->push_back(expair(newterm, i->coeff));
}
ex newpoint = point.eval_integ();
if (newseq || !are_ex_trivially_equal(newpoint, point))
- return (new pseries(var==newpoint, *newseq))
+ return (new pseries(var==newpoint, std::move(*newseq)))
->setflag(status_flags::dynallocated);
return *this;
}
// evalm each coefficient
epvector newseq;
bool something_changed = false;
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ for (auto i=seq.begin(); i!=seq.end(); ++i) {
if (something_changed) {
ex newcoeff = i->rest.evalm();
if (!newcoeff.is_zero())
}
}
if (something_changed)
- return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated);
+ return (new pseries(var==point, std::move(newseq)))->setflag(status_flags::dynallocated);
else
return *this;
}
// expansion point
epvector newseq;
newseq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- newseq.push_back(expair(it->rest.subs(m, options), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated);
+ for (auto & it : seq)
+ newseq.push_back(expair(it.rest.subs(m, options), it.coeff));
+ return (new pseries(relational(var,point.subs(m, options)), std::move(newseq)))->setflag(status_flags::dynallocated);
}
/** Implementation of ex::expand() for a power series. It expands all the
ex pseries::expand(unsigned options) const
{
epvector newseq;
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- ex restexp = i->rest.expand();
+ for (auto & it : seq) {
+ ex restexp = it.rest.expand();
if (!restexp.is_zero())
- newseq.push_back(expair(restexp, i->coeff));
- ++i;
+ newseq.push_back(expair(restexp, it.coeff));
}
- return (new pseries(relational(var,point), newseq))
+ return (new pseries(relational(var,point), std::move(newseq)))
->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
ex pseries::derivative(const symbol & s) const
{
epvector new_seq;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
if (s == var) {
// FIXME: coeff might depend on var
- while (it != itend) {
- if (is_order_function(it->rest)) {
- new_seq.push_back(expair(it->rest, it->coeff - 1));
+ for (auto & it : seq) {
+ if (is_order_function(it.rest)) {
+ new_seq.push_back(expair(it.rest, it.coeff - 1));
} else {
- ex c = it->rest * it->coeff;
+ ex c = it.rest * it.coeff;
if (!c.is_zero())
- new_seq.push_back(expair(c, it->coeff - 1));
+ new_seq.push_back(expair(c, it.coeff - 1));
}
- ++it;
}
} else {
- while (it != itend) {
- if (is_order_function(it->rest)) {
- new_seq.push_back(*it);
+ for (auto & it : seq) {
+ if (is_order_function(it.rest)) {
+ new_seq.push_back(it);
} else {
- ex c = it->rest.diff(s);
+ ex c = it.rest.diff(s);
if (!c.is_zero())
- new_seq.push_back(expair(c, it->coeff));
+ new_seq.push_back(expair(c, it.coeff));
}
- ++it;
}
}
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
ex pseries::convert_to_poly(bool no_order) const
{
ex e;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
-
- while (it != itend) {
- if (is_order_function(it->rest)) {
+ for (auto & it : seq) {
+ if (is_order_function(it.rest)) {
if (!no_order)
- e += Order(power(var - point, it->coeff));
+ e += Order(power(var - point, it.coeff));
} else
- e += it->rest * power(var - point, it->coeff);
- ++it;
+ e += it.rest * power(var - point, it.coeff);
}
return e;
}
ex pseries::coeffop(size_t i) const
{
- if (i >=nops())
+ if (i >= nops())
throw (std::out_of_range("coeffop() out of range"));
return seq[i].rest;
}
// default for order-values that make no sense for Taylor expansion
if ((order <= 0) && this->has(s)) {
seq.push_back(expair(Order(_ex1), order));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
// do Taylor expansion
// zero. Expanding the term occasionally helps a little...
deriv = deriv.diff(s).expand();
if (deriv.is_zero()) // Series terminates
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
coeff = deriv.subs(r, subs_options::no_pattern);
if (!coeff.is_zero())
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
seq.push_back(expair(Order(_ex1), n));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
seq.push_back(expair(Order(_ex1), numeric(order)));
} else
seq.push_back(expair(*this, _ex0));
- return pseries(r, seq);
+ return pseries(r, std::move(seq));
}
// Adding two series with different variables or expansion points
// results in an empty (constant) series
if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1), _ex0));
- return pseries(relational(var,point), nul);
+ epvector nul { expair(Order(_ex1), _ex0) };
+ return pseries(relational(var,point), std::move(nul));
}
// Series addition
epvector new_seq;
- epvector::const_iterator a = seq.begin();
- epvector::const_iterator b = other.seq.begin();
- epvector::const_iterator a_end = seq.end();
- epvector::const_iterator b_end = other.seq.end();
+ auto a = seq.begin(), a_end = seq.end();
+ auto b = other.seq.begin(), b_end = other.seq.end();
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
}
}
}
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
acc = overall_coeff.series(r, order, options);
// Add remaining terms
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- for (; it!=itend; ++it) {
+ for (auto & it : seq) {
ex op;
- if (is_exactly_a<pseries>(it->rest))
- op = it->rest;
+ if (is_exactly_a<pseries>(it.rest))
+ op = it.rest;
else
- op = it->rest.series(r, order, options);
- if (!it->coeff.is_equal(_ex1))
- op = ex_to<pseries>(op).mul_const(ex_to<numeric>(it->coeff));
+ op = it.rest.series(r, order, options);
+ if (!it.coeff.is_equal(_ex1))
+ op = ex_to<pseries>(op).mul_const(ex_to<numeric>(it.coeff));
// Series addition
acc = ex_to<pseries>(acc).add_series(ex_to<pseries>(op));
epvector new_seq;
new_seq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- if (!is_order_function(it->rest))
- new_seq.push_back(expair(it->rest * other, it->coeff));
+ for (auto & it : seq) {
+ if (!is_order_function(it.rest))
+ new_seq.push_back(expair(it.rest * other, it.coeff));
else
- new_seq.push_back(*it);
- ++it;
+ new_seq.push_back(it);
}
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
// Multiplying two series with different variables or expansion points
// results in an empty (constant) series
if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1), _ex0));
- return pseries(relational(var,point), nul);
+ epvector nul { expair(Order(_ex1), _ex0) };
+ return pseries(relational(var,point), std::move(nul));
}
if (seq.empty() || other.seq.empty()) {
}
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);
+ return pseries(relational(var, point), std::move(new_seq));
}
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) {
+ for (auto & it : seq) {
- ex expon = it->coeff;
+ ex expon = it.coeff;
int factor = 1;
ex buf;
if (expon.info(info_flags::integer)) {
- buf = it->rest;
+ buf = it.rest;
factor = ex_to<numeric>(expon).to_int();
} else {
- buf = recombine_pair_to_ex(*it);
+ buf = recombine_pair_to_ex(it);
}
int real_ldegree = 0;
// method.
// here we can ignore ldegrees larger than degbound
size_t j = 0;
- for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
+ for (auto & it : seq) {
if ( ldegree_redo[j] ) {
- ex expon = it->coeff;
+ ex expon = it.coeff;
int factor = 1;
ex buf;
if (expon.info(info_flags::integer)) {
- buf = it->rest;
+ buf = it.rest;
factor = ex_to<numeric>(expon).to_int();
} else {
- buf = recombine_pair_to_ex(*it);
+ buf = recombine_pair_to_ex(it);
}
int real_ldegree = 0;
int orderloop = 0;
orderloop++;
real_ldegree = buf.series(r, orderloop, options).ldegree(sym);
} while ((real_ldegree == orderloop)
- && ( factor*real_ldegree < degbound));
+ && (factor*real_ldegree < degbound));
ldegrees[j] = factor * real_ldegree;
degbound -= factor * real_ldegree;
}
int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
if (degsum >= order) {
- epvector epv;
- epv.push_back(expair(Order(_ex1), order));
- return (new pseries(r, epv))->setflag(status_flags::dynallocated);
+ epvector epv { expair(Order(_ex1), order) };
+ return (new pseries(r, std::move(epv)))->setflag(status_flags::dynallocated);
}
// Multiply with remaining terms
- std::vector<int>::const_iterator itd = ldegrees.begin();
- for (epvector::const_iterator it=itbeg; it!=itend; ++it, ++itd) {
+ auto itd = ldegrees.begin();
+ for (auto it=seq.begin(), itend=seq.end(); it!=itend; ++it, ++itd) {
// do series expansion with adjusted order
ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options);
// Series multiplication
- if (it == itbeg)
+ if (it == seq.begin())
acc = ex_to<pseries>(op);
else
acc = ex_to<pseries>(acc.mul_series(ex_to<pseries>(op)));
// adjust number of coefficients
int numcoeff = deg - (p*ldeg).to_int();
if (numcoeff <= 0) {
- epvector epv;
- epv.reserve(1);
- epv.push_back(expair(Order(_ex1), deg));
- return (new pseries(relational(var,point), epv))
+ epvector epv { expair(Order(_ex1), deg) };
+ return (new pseries(relational(var,point), std::move(epv)))
->setflag(status_flags::dynallocated);
}
if (!higher_order)
new_seq.push_back(expair(Order(_ex1), p * ldeg + numcoeff));
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var,point), std::move(new_seq));
}
pseries pseries::shift_exponents(int deg) const
{
epvector newseq = seq;
- epvector::iterator i = newseq.begin(), end = newseq.end();
- while (i != end) {
- i->coeff += deg;
- ++i;
- }
- return pseries(relational(var, point), newseq);
+ for (auto & it : newseq)
+ it.coeff += deg;
+ return pseries(relational(var, point), std::move(newseq));
}
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)))
new_seq.push_back(expair(_ex1, exponent));
else
new_seq.push_back(expair(Order(_ex1), exponent));
- return pseries(r, new_seq);
+ return pseries(r, std::move(new_seq));
}
// No, expand basis into series
try {
result = ex_to<pseries>(e).power_const(numexp, order);
} catch (pole_error) {
- epvector ser;
- ser.push_back(expair(Order(_ex1), order));
- result = pseries(r, ser);
+ epvector ser { expair(Order(_ex1), order) };
+ result = pseries(r, std::move(ser));
}
return result;
return *this;
else {
epvector new_seq;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- int o = ex_to<numeric>(it->coeff).to_int();
+ for (auto & it : seq) {
+ int o = ex_to<numeric>(it.coeff).to_int();
if (o >= order) {
new_seq.push_back(expair(Order(_ex1), o));
break;
}
- new_seq.push_back(*it);
- ++it;
+ new_seq.push_back(it);
}
- return pseries(r, new_seq);
+ return pseries(r, std::move(new_seq));
}
} else
return convert_to_poly().series(r, order, options);
if (x.subs(r) != x)
throw std::logic_error("Cannot series expand wrt dummy variable");
- // Expanding integrant with r substituted taken in boundaries.
+ // Expanding integrand with r substituted taken in boundaries.
ex fseries = f.series(r, order, options);
epvector fexpansion;
fexpansion.reserve(fseries.nops());
}
// Expanding lower boundary
- ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated);
+ ex result = (new pseries(r, std::move(fexpansion)))->setflag(status_flags::dynallocated);
ex aseries = (a-a.subs(r)).series(r, order, options);
fseries = f.series(x == (a.subs(r)), order, options);
for (size_t i=0; i<fseries.nops(); ++i) {
git://www.ginac.de / ginac.git / blobdiff