author Richard Kreckel Wed, 6 Jan 2016 21:34:23 +0000 (22:34 +0100) committer Richard Kreckel Wed, 6 Jan 2016 21:37:26 +0000 (22:37 +0100)
At the branch cut, the series expansions of log(), atan(), and atanh()
assembled pseries objects which contained both x^0 and Order(x^0) terms.
This patch removes the extra x^0 term if the order is 0. It also adds
a GINAC_ASSERT for these kinds of invariants to the pseries ctor and
simplifies the loops in pseries' degree(), ldegree(), eval() and evalf()
member functions.

 ginac/inifcns_trans.cpp patch | blob | history ginac/pseries.cpp patch | blob | history

index 9982853..98e0caf 100644 (file)
@@ -265,8 +265,12 @@ static ex log_series(const ex &arg,
const ex &point = rel.rhs();
const symbol foo;
const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
const ex &point = rel.rhs();
const symbol foo;
const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
-               epvector seq { expair(-I*csgn(arg*I)*Pi, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
return series(replarg - I*Pi + pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();  // caught by function::series()
return series(replarg - I*Pi + pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();  // caught by function::series()
@@ -928,8 +932,12 @@ static ex atan_series(const ex &arg,
Order0correction += log((I*arg_pt+_ex_1)/(I*arg_pt+_ex1))*I*_ex_1_2;
else
Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2;
Order0correction += log((I*arg_pt+_ex_1)/(I*arg_pt+_ex1))*I*_ex_1_2;
else
Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2;
-               epvector seq { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(Order0correction, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
@@ -1534,8 +1542,12 @@ static ex atanh_series(const ex &arg,
Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2;
else
Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2;
Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2;
else
Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2;
-               epvector seq { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               if (order > 0) {
+                       seq.reserve(2);
+                       seq.push_back(expair(Order0correction, _ex0));
+               }
+               seq.push_back(expair(Order(_ex1), order));
return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
index 12f4fed..2d0b7ad 100644 (file)
@@ -71,6 +71,19 @@ pseries::pseries() { }
pseries::pseries(const ex &rel_, const epvector &ops_)
: seq(ops_)
{
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();
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
point = rel_.rhs();
@@ -79,6 +92,19 @@ pseries::pseries(const ex &rel_, const epvector &ops_)
pseries::pseries(const ex &rel_, epvector &&ops_)
: seq(std::move(ops_))
{
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();
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
point = rel_.rhs();
@@ -290,25 +316,17 @@ ex pseries::op(size_t i) const
*  series is examined termwise. */
int pseries::degree(const ex &s) const
{
*  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
}

/** Return degree of lowest power of the series.  This is usually the exponent
@@ -318,25 +336,17 @@ int pseries::degree(const ex &s) const
*  I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */
int pseries::ldegree(const ex &s) const
{
*  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
}

/** Return coefficient of degree n in power series if s is the expansion
@@ -389,15 +399,13 @@ ex pseries::eval() const
if (flags & status_flags::evaluated) {
return *this;
}
if (flags & status_flags::evaluated) {
return *this;
}
-
+
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
// 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);
}

return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}

@@ -413,11 +421,9 @@ ex pseries::evalf(int level) const
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
// 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);
}

return dynallocate<pseries>(relational(var,point), std::move(new_seq)).setflag(status_flags::evaluated);
}