* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2019 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
pseries::pseries(const ex &rel_, const epvector &ops_)
: seq(ops_)
{
+#ifdef DO_GINAC_ASSERT
+ auto i = seq.begin();
+ while (i != seq.end()) {
+ auto ip1 = i+1;
+ if (ip1 != seq.end())
+ GINAC_ASSERT(!is_order_function(i->rest));
+ else
+ break;
+ GINAC_ASSERT(is_a<numeric>(i->coeff));
+ GINAC_ASSERT(ex_to<numeric>(i->coeff) < ex_to<numeric>(ip1->coeff));
+ ++i;
+ }
+#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
point = rel_.rhs();
pseries::pseries(const ex &rel_, epvector &&ops_)
: seq(std::move(ops_))
{
+#ifdef DO_GINAC_ASSERT
+ auto i = seq.begin();
+ while (i != seq.end()) {
+ auto ip1 = i+1;
+ if (ip1 != seq.end())
+ GINAC_ASSERT(!is_order_function(i->rest));
+ else
+ break;
+ GINAC_ASSERT(is_a<numeric>(i->coeff));
+ GINAC_ASSERT(ex_to<numeric>(i->coeff) < ex_to<numeric>(ip1->coeff));
+ ++i;
+ }
+#endif // def DO_GINAC_ASSERT
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
point = rel_.rhs();
void pseries::read_archive(const archive_node &n, lst &sym_lst)
{
inherited::read_archive(n, sym_lst);
- auto first = n.find_first("coeff");
- auto last = n.find_last("power");
- ++last;
- seq.reserve((last-first)/2);
+ auto range = n.find_property_range("coeff", "power");
+ seq.reserve((range.end-range.begin)/2);
- for (auto loc = first; loc < last;) {
+ for (auto loc = range.begin; loc < range.end;) {
ex rest;
ex coeff;
n.find_ex_by_loc(loc++, rest, sym_lst);
n.find_ex_by_loc(loc++, coeff, sym_lst);
- seq.push_back(expair(rest, coeff));
+ seq.emplace_back(expair(rest, coeff));
}
n.find_ex("var", var, sym_lst);
}
}
} else
- Order(power(var-point,i->coeff)).print(c);
+ Order(pow(var - point, i->coeff)).print(c);
++i;
}
return cmpval;
// ...and if that failed the individual elements
- epvector::const_iterator it = seq.begin(), o_it = o.seq.begin();
+ auto it = seq.begin(), o_it = o.seq.begin();
while (it!=seq.end() && o_it!=o.seq.end()) {
cmpval = it->compare(*o_it);
if (cmpval)
throw (std::out_of_range("op() out of range"));
if (is_order_function(seq[i].rest))
- return Order(power(var-point, seq[i].coeff));
- return seq[i].rest * power(var - point, seq[i].coeff);
+ return Order(pow(var-point, seq[i].coeff));
+ return seq[i].rest * pow(var - point, seq[i].coeff);
}
/** Return degree of highest power of the series. This is usually the exponent
* series is examined termwise. */
int pseries::degree(const ex &s) const
{
- if (var.is_equal(s)) {
- // Return last exponent
- if (seq.size())
- return ex_to<numeric>((seq.end()-1)->coeff).to_int();
- else
- return 0;
- } else {
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- if (it == itend)
- return 0;
- int max_pow = std::numeric_limits<int>::min();
- while (it != itend) {
- int pow = it->rest.degree(s);
- if (pow > max_pow)
- max_pow = pow;
- ++it;
- }
- return max_pow;
- }
+ if (seq.empty())
+ return 0;
+
+ if (var.is_equal(s))
+ // Return last/greatest exponent
+ return ex_to<numeric>((seq.end()-1)->coeff).to_int();
+
+ int max_pow = std::numeric_limits<int>::min();
+ for (auto & it : seq)
+ max_pow = std::max(max_pow, it.rest.degree(s));
+ return max_pow;
}
/** Return degree of lowest power of the series. This is usually the exponent
* I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */
int pseries::ldegree(const ex &s) const
{
- if (var.is_equal(s)) {
- // Return first exponent
- if (seq.size())
- return ex_to<numeric>((seq.begin())->coeff).to_int();
- else
- return 0;
- } else {
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- if (it == itend)
- return 0;
- int min_pow = std::numeric_limits<int>::max();
- while (it != itend) {
- int pow = it->rest.ldegree(s);
- if (pow < min_pow)
- min_pow = pow;
- ++it;
- }
- return min_pow;
- }
+ if (seq.empty())
+ return 0;
+
+ if (var.is_equal(s))
+ // Return first/smallest exponent
+ return ex_to<numeric>((seq.begin())->coeff).to_int();
+
+ int min_pow = std::numeric_limits<int>::max();
+ for (auto & it : seq)
+ min_pow = std::min(min_pow, it.rest.degree(s));
+ return min_pow;
}
/** Return coefficient of degree n in power series if s is the expansion
}
/** Perform coefficient-wise automatic term rewriting rules in this class. */
-ex pseries::eval(int level) const
+ex pseries::eval() const
{
- if (level == 1)
- return this->hold();
-
- if (level == -max_recursion_level)
- throw (std::runtime_error("pseries::eval(): recursion limit exceeded"));
-
+ if (flags & status_flags::evaluated) {
+ return *this;
+ }
+
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- new_seq.push_back(expair(it->rest.eval(level-1), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ for (auto & it : seq)
+ new_seq.emplace_back(expair(it.rest, it.coeff));
+
+ return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}
/** Evaluate coefficients numerically. */
-ex pseries::evalf(int level) const
+ex pseries::evalf() const
{
- if (level == 1)
- return *this;
-
- if (level == -max_recursion_level)
- throw (std::runtime_error("pseries::evalf(): recursion limit exceeded"));
-
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point), std::move(new_seq)))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ for (auto & it : seq)
+ new_seq.emplace_back(expair(it.rest.evalf(), it.coeff));
+
+ return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}
ex pseries::conjugate() const
return *this;
}
- return (new pseries(var==newpoint, newseq ? std::move(*newseq) : seq))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==newpoint, newseq ? std::move(*newseq) : seq);
}
ex pseries::real_part() const
epvector v;
v.reserve(seq.size());
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);
+ v.emplace_back(expair(it.rest.real_part(), it.coeff));
+ return dynallocate<pseries>(var==point, std::move(v));
}
ex pseries::imag_part() const
epvector v;
v.reserve(seq.size());
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);
+ v.emplace_back(expair(it.rest.imag_part(), it.coeff));
+ return dynallocate<pseries>(var==point, std::move(v));
}
ex pseries::eval_integ() const
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));
+ newseq->emplace_back(expair(i->rest.eval_integ(), i->coeff));
continue;
}
ex newterm = i->rest.eval_integ();
newseq->reserve(seq.size());
for (auto j=seq.begin(); j!=i; ++j)
newseq->push_back(*j);
- newseq->push_back(expair(newterm, i->coeff));
+ newseq->emplace_back(expair(newterm, i->coeff));
}
}
ex newpoint = point.eval_integ();
if (newseq || !are_ex_trivially_equal(newpoint, point))
- return (new pseries(var==newpoint, std::move(*newseq)))
- ->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==newpoint, std::move(*newseq));
return *this;
}
if (something_changed) {
ex newcoeff = i->rest.evalm();
if (!newcoeff.is_zero())
- newseq.push_back(expair(newcoeff, i->coeff));
- }
- else {
+ newseq.emplace_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));
+ newseq.emplace_back(expair(newcoeff, i->coeff));
}
}
}
if (something_changed)
- return (new pseries(var==point, std::move(newseq)))->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, std::move(newseq));
else
return *this;
}
epvector newseq;
newseq.reserve(seq.size());
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);
+ newseq.emplace_back(expair(it.rest.subs(m, options), it.coeff));
+ return dynallocate<pseries>(relational(var,point.subs(m, options)), std::move(newseq));
}
/** Implementation of ex::expand() for a power series. It expands all the
for (auto & it : seq) {
ex restexp = it.rest.expand();
if (!restexp.is_zero())
- newseq.push_back(expair(restexp, it.coeff));
+ newseq.emplace_back(expair(restexp, it.coeff));
}
- return (new pseries(relational(var,point), std::move(newseq)))
- ->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+ return dynallocate<pseries>(relational(var,point), std::move(newseq)).setflag(options == 0 ? status_flags::expanded : 0);
}
/** Implementation of ex::diff() for a power series.
// FIXME: coeff might depend on var
for (auto & it : seq) {
if (is_order_function(it.rest)) {
- new_seq.push_back(expair(it.rest, it.coeff - 1));
+ new_seq.emplace_back(expair(it.rest, it.coeff - 1));
} else {
ex c = it.rest * it.coeff;
if (!c.is_zero())
- new_seq.push_back(expair(c, it.coeff - 1));
+ new_seq.emplace_back(expair(c, it.coeff - 1));
}
}
} else {
ex c = it.rest.diff(s);
if (!c.is_zero())
- new_seq.push_back(expair(c, it.coeff));
+ new_seq.emplace_back(expair(c, it.coeff));
}
}
}
for (auto & it : seq) {
if (is_order_function(it.rest)) {
if (!no_order)
- e += Order(power(var - point, it.coeff));
+ e += Order(pow(var - point, it.coeff));
} else
- e += it.rest * power(var - point, it.coeff);
+ e += it.rest * pow(var - point, it.coeff);
}
return e;
}
// default for order-values that make no sense for Taylor expansion
if ((order <= 0) && this->has(s)) {
- seq.push_back(expair(Order(_ex1), order));
+ seq.emplace_back(expair(Order(_ex1), order));
return pseries(r, std::move(seq));
}
ex coeff = deriv.subs(r, subs_options::no_pattern);
if (!coeff.is_zero()) {
- seq.push_back(expair(coeff, _ex0));
+ seq.emplace_back(expair(coeff, _ex0));
}
int n;
for (n=1; n<order; ++n) {
- fac = fac.mul(n);
+ fac = fac.div(n);
// We need to test for zero in order to see if the series terminates.
// The problem is that there is no such thing as a perfect test for
// zero. Expanding the term occasionally helps a little...
coeff = deriv.subs(r, subs_options::no_pattern);
if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, n));
+ seq.emplace_back(expair(fac * coeff, n));
}
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1), n));
+ seq.emplace_back(expair(Order(_ex1), n));
return pseries(r, std::move(seq));
}
if (this->is_equal_same_type(ex_to<symbol>(r.lhs()))) {
if (order > 0 && !point.is_zero())
- seq.push_back(expair(point, _ex0));
+ seq.emplace_back(expair(point, _ex0));
if (order > 1)
- seq.push_back(expair(_ex1, _ex1));
+ seq.emplace_back(expair(_ex1, _ex1));
else
- seq.push_back(expair(Order(_ex1), numeric(order)));
+ seq.emplace_back(expair(Order(_ex1), numeric(order)));
} else
- seq.push_back(expair(*this, _ex0));
+ seq.emplace_back(expair(*this, _ex0));
return pseries(r, std::move(seq));
}
} else {
// Add coefficient of a and b
if (is_order_function((*a).rest) || is_order_function((*b).rest)) {
- new_seq.push_back(expair(Order(_ex1), (*a).coeff));
+ new_seq.emplace_back(expair(Order(_ex1), (*a).coeff));
break; // Order term ends the sequence
} else {
ex sum = (*a).rest + (*b).rest;
if (!(sum.is_zero()))
- new_seq.push_back(expair(sum, numeric(pow_a)));
+ new_seq.emplace_back(expair(sum, numeric(pow_a)));
++a;
++b;
}
for (auto & it : seq) {
if (!is_order_function(it.rest))
- new_seq.push_back(expair(it.rest * other, it.coeff));
+ new_seq.emplace_back(expair(it.rest * other, it.coeff));
else
new_seq.push_back(it);
}
}
if (seq.empty() || other.seq.empty()) {
- return (new pseries(var==point, epvector()))
- ->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(var==point, epvector());
}
// Series multiplication
epvector new_seq;
- int a_max = degree(var);
- int b_max = other.degree(var);
- int a_min = ldegree(var);
- int b_min = other.ldegree(var);
- int cdeg_min = a_min + b_min;
+ const int a_max = degree(var);
+ const int b_max = other.degree(var);
+ const int a_min = ldegree(var);
+ const int b_min = other.ldegree(var);
+ const int cdeg_min = a_min + b_min;
int cdeg_max = a_max + b_max;
int higher_order_a = std::numeric_limits<int>::max();
higher_order_a = a_max + b_min;
if (is_order_function(other.coeff(var, b_max)))
higher_order_b = b_max + a_min;
- int higher_order_c = std::min(higher_order_a, higher_order_b);
+ const int higher_order_c = std::min(higher_order_a, higher_order_b);
if (cdeg_max >= higher_order_c)
cdeg_max = higher_order_c - 1;
-
+
+ std::map<int, ex> rest_map_a, rest_map_b;
+ for (const auto& it : seq)
+ rest_map_a[ex_to<numeric>(it.coeff).to_int()] = it.rest;
+
+ if (other.var.is_equal(var))
+ for (const auto& it : other.seq)
+ rest_map_b[ex_to<numeric>(it.coeff).to_int()] = it.rest;
+
for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) {
ex co = _ex0;
// c(i)=a(0)b(i)+...+a(i)b(0)
for (int i=a_min; cdeg-i>=b_min; ++i) {
- ex a_coeff = coeff(var, i);
- ex b_coeff = other.coeff(var, cdeg-i);
- if (!is_order_function(a_coeff) && !is_order_function(b_coeff))
- co += a_coeff * b_coeff;
+ const auto& ita = rest_map_a.find(i);
+ if (ita == rest_map_a.end())
+ continue;
+ const auto& itb = rest_map_b.find(cdeg-i);
+ if (itb == rest_map_b.end())
+ continue;
+ if (!is_order_function(ita->second) && !is_order_function(itb->second))
+ co += ita->second * itb->second;
}
if (!co.is_zero())
- new_seq.push_back(expair(co, numeric(cdeg)));
+ new_seq.emplace_back(expair(co, numeric(cdeg)));
}
if (higher_order_c < std::numeric_limits<int>::max())
- new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c)));
+ new_seq.emplace_back(expair(Order(_ex1), numeric(higher_order_c)));
return pseries(relational(var, point), std::move(new_seq));
}
int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
- if (degsum >= order) {
- epvector epv { expair(Order(_ex1), order) };
- return (new pseries(r, std::move(epv)))->setflag(status_flags::dynallocated);
+ if (degsum > order) {
+ return dynallocate<pseries>(r, epvector{{Order(_ex1), order}});
}
// Multiply with remaining terms
int numcoeff = deg - (p*ldeg).to_int();
if (numcoeff <= 0) {
epvector epv { expair(Order(_ex1), deg) };
- return (new pseries(relational(var,point), std::move(epv)))
- ->setflag(status_flags::dynallocated);
+ return dynallocate<pseries>(relational(var,point), std::move(epv));
}
// O(x^n)^(-m) is undefined
// Compute coefficients of the powered series
exvector co;
co.reserve(numcoeff);
- co.push_back(power(coeff(var, ldeg), p));
+ co.push_back(pow(coeff(var, ldeg), p));
for (int i=1; i<numcoeff; ++i) {
ex sum = _ex0;
for (int j=1; j<=i; ++j) {
bool higher_order = false;
for (int i=0; i<numcoeff; ++i) {
if (!co[i].is_zero())
- new_seq.push_back(expair(co[i], p * ldeg + i));
+ new_seq.emplace_back(expair(co[i], p * ldeg + i));
if (is_order_function(co[i])) {
higher_order = true;
break;
}
}
if (!higher_order)
- new_seq.push_back(expair(Order(_ex1), p * ldeg + numcoeff));
+ new_seq.emplace_back(expair(Order(_ex1), p * ldeg + numcoeff));
return pseries(relational(var,point), std::move(new_seq));
}
if (basis.is_equal(r.lhs() - r.rhs())) {
epvector new_seq;
if (ex_to<numeric>(exponent).to_int() < order)
- new_seq.push_back(expair(_ex1, exponent));
+ new_seq.emplace_back(expair(_ex1, exponent));
else
- new_seq.push_back(expair(Order(_ex1), exponent));
+ new_seq.emplace_back(expair(Order(_ex1), exponent));
return pseries(r, std::move(new_seq));
}
for (auto & it : seq) {
int o = ex_to<numeric>(it.coeff).to_int();
if (o >= order) {
- new_seq.push_back(expair(Order(_ex1), o));
+ new_seq.emplace_back(expair(Order(_ex1), o));
break;
}
new_seq.push_back(it);
? currcoeff
: integral(x, a.subs(r), b.subs(r), currcoeff);
if (currcoeff != 0)
- fexpansion.push_back(
+ fexpansion.emplace_back(
expair(currcoeff, ex_to<pseries>(fseries).exponop(i)));
}
// Expanding lower boundary
- ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated);
+ ex result = dynallocate<pseries>(r, std::move(fexpansion));
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