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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.