* Implementation of GiNaC's initially known functions. */
/*
- * GiNaC Copyright (C) 1999-2009 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2011 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
if (is_ex_the_function(arg, abs))
return arg;
+ if (is_ex_the_function(arg, exp))
+ return exp(arg.op(0).real_part());
+
+ if (is_exactly_a<power>(arg)) {
+ const ex& base = arg.op(0);
+ const ex& exponent = arg.op(1);
+ if (base.info(info_flags::positive) || exponent.info(info_flags::real))
+ return pow(abs(base), exponent.real_part());
+ }
+
+ if (is_ex_the_function(arg, conjugate_function))
+ return abs(arg.op(0));
+
+ if (is_ex_the_function(arg, step))
+ return arg;
+
return abs(arg).hold();
}
static ex abs_conjugate(const ex & arg)
{
- return abs(arg);
+ return abs(arg).hold();
}
static ex abs_real_part(const ex & arg)
static ex abs_power(const ex & arg, const ex & exp)
{
- if (arg.is_equal(arg.conjugate()) && is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
+ if (arg.is_equal(arg.conjugate()) && ((is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
+ || exp.info(info_flags::even)))
return power(arg, exp);
else
return power(abs(arg), exp).hold();
evalf_func(step_evalf).
series_func(step_series).
conjugate_func(step_conjugate).
- real_part_func(step_real_part).
- imag_part_func(step_imag_part));
+ real_part_func(step_real_part).
+ imag_part_func(step_imag_part));
//////////
// Complex sign
{
if (is_a<numeric>(exp) && exp.info(info_flags::positive) && ex_to<numeric>(exp).is_integer()) {
if (ex_to<numeric>(exp).is_odd())
- return csgn(arg);
+ return csgn(arg).hold();
else
return power(csgn(arg), _ex2).hold();
} else
static ex eta_conjugate(const ex & x, const ex & y)
{
- return -eta(x, y);
+ return -eta(x, y).hold();
}
static ex eta_real_part(const ex & x, const ex & y)
throw do_taylor(); // caught by function::series()
}
+static ex Li2_conjugate(const ex & x)
+{
+ // conjugate(Li2(x))==Li2(conjugate(x)) unless on the branch cuts which
+ // run along the positive real axis beginning at 1.
+ if (x.info(info_flags::negative)) {
+ return Li2(x).hold();
+ }
+ if (is_exactly_a<numeric>(x) &&
+ (!x.imag_part().is_zero() || x < *_num1_p)) {
+ return Li2(x.conjugate());
+ }
+ return conjugate_function(Li2(x)).hold();
+}
+
REGISTER_FUNCTION(Li2, eval_func(Li2_eval).
evalf_func(Li2_evalf).
derivative_func(Li2_deriv).
series_func(Li2_series).
+ conjugate_func(Li2_conjugate).
latex_name("\\mathrm{Li}_2"));
//////////
if (n.info(info_flags::numeric)) {
// zetaderiv(0,x) -> zeta(x)
if (n.is_zero())
- return zeta(x);
+ return zeta(x).hold();
}
return zetaderiv(n, x).hold();
do {
xxprev = xx[side];
fxprev = fx[side];
- xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
- fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
- if ((side==0 && xx[0]<xxprev) || (side==1 && xx[1]>xxprev) || xx[0]>xx[1]) {
+ ex dx_ = ff.subs(x == xx[side]).evalf();
+ if (!is_a<numeric>(dx_))
+ throw std::runtime_error("fsolve(): function derivative does not evaluate numerically");
+ xx[side] += ex_to<numeric>(dx_);
+ // Now check if Newton-Raphson method shot out of the interval
+ bool bad_shot = (side == 0 && xx[0] < xxprev) ||
+ (side == 1 && xx[1] > xxprev) || xx[0] > xx[1];
+ if (!bad_shot) {
+ // Compute f(x) only if new x is inside the interval.
+ // The function might be difficult to compute numerically
+ // or even ill defined outside the interval. Also it's
+ // a small optimization.
+ ex f_x = f.subs(x == xx[side]).evalf();
+ if (!is_a<numeric>(f_x))
+ throw std::runtime_error("fsolve(): function does not evaluate numerically");
+ fx[side] = ex_to<numeric>(f_x);
+ }
+ if (bad_shot) {
// Oops, Newton-Raphson method shot out of the interval.
// Restore, and try again with the other side instead!
xx[side] = xxprev;
side = !side;
xxprev = xx[side];
fxprev = fx[side];
- xx[side] += ex_to<numeric>(ff.subs(x==xx[side]).evalf());
- fx[side] = ex_to<numeric>(f.subs(x==xx[side]).evalf());
+
+ ex dx_ = ff.subs(x == xx[side]).evalf();
+ if (!is_a<numeric>(dx_))
+ throw std::runtime_error("fsolve(): function derivative does not evaluate numerically [2]");
+ xx[side] += ex_to<numeric>(dx_);
+
+ ex f_x = f.subs(x==xx[side]).evalf();
+ if (!is_a<numeric>(f_x))
+ throw std::runtime_error("fsolve(): function does not evaluate numerically [2]");
+ fx[side] = ex_to<numeric>(f_x);
}
if ((fx[side]<0 && fx[!side]<0) || (fx[side]>0 && fx[!side]>0)) {
// Oops, the root isn't bracketed any more.
static const double secant_weight = 0.984375; // == 63/64 < 1
numeric xxmid = (1-secant_weight)*0.5*(xx[0]+xx[1])
+ secant_weight*(xx[0]+fx[0]*(xx[0]-xx[1])/(fx[1]-fx[0]));
- numeric fxmid = ex_to<numeric>(f.subs(x==xxmid).evalf());
+ ex fxmid_ = f.subs(x == xxmid).evalf();
+ if (!is_a<numeric>(fxmid_))
+ throw std::runtime_error("fsolve(): function does not evaluate numerically [3]");
+ numeric fxmid = ex_to<numeric>(fxmid_);
if (fxmid.is_zero()) {
// Luck strikes...
return xxmid;
git://www.ginac.de / ginac.git / blobdiff