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Up-> CppAD AD ADValued unary_standard_math sign

AD-> ad_ctor ad_assign Convert ADValued BoolValued VecAD base_require

ADValued-> Arithmetic unary_standard_math binary_math CondExp Discrete numeric_limits atomic

unary_standard_math-> acos asin atan cos cosh exp log log10 sin sinh sqrt tan tanh abs acosh asinh atanh erf expm1 log1p sign

sign-> sign.cpp

Headings-> Syntax Description x, y Atomic Derivative Example

@(@\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}} }@)@The Sign: sign
Syntax
y = sign(x)

Description
Evaluates the sign function which is defined by @[@ {\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. @]@

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. It returns true if it succeeds and false otherwise.

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Input File: cppad/core/sign.hpp