\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

sign

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The Sign: sign

Syntax

y = sign ( x )

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.

Example

The file sign.cpp contains an example and test of this function.