* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2018 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();
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)
* 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
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, it->coeff));
- ++it;
- }
+ for (auto & it : seq)
+ new_seq.push_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;
- }
+ for (auto & it : seq)
+ new_seq.push_back(expair(it.rest, it.coeff));
+
return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}
// 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)));
git://www.ginac.de / ginac.git / blobdiff