\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
sign¶
The Sign: sign¶
Description¶
Evaluates the sign
function which is defined by
\[\begin{split}{\rm sign} (x) =
\left\{ \begin{array}{rl}
+1 & {\rm if} \; x > 0 \\
0 & {\rm if} \; x = 0 \\
-1 & {\rm if} \; x < 0
\end{array} \right.\end{split}\]
x, y¶
See the Possible Types for a unary standard math function.
Atomic¶
This is an atomic operation .
Derivative¶
CppAD computes the derivative of the sign
function as zero for all
argument values x .
The correct mathematical derivative is different and
is given by
\[{\rm sign}^{(1)} (x) = 2 \delta (x)\]
where \(\delta (x)\) is the Dirac Delta function.