\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
exp_eps.hpp¶
View page sourceexp_eps: Implementation¶
template <class Type>
Type exp_eps(const Type &x, const Type &epsilon)
{ // abs_x = |x|
Type abs_x = x;
if( Type(0) > x )
abs_x = - x;
// initialize
int k = 0; // initial order
Type term = 1.; // term = |x|^k / k !
Type sum = term; // initial sum
while(term > epsilon)
{ k = k + 1; // order for next term
Type temp = term * abs_x; // term = |x|^k / (k-1)!
term = temp / Type(k); // term = |x|^k / k !
sum = sum + term; // sum = 1 + ... + |x|^k / k !
}
// In the case where x is negative, use exp(x) = 1 / exp(-|x|)
if( Type(0) > x )
sum = Type(1) / sum;
return sum;
}