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AD Absolute Value Functions: abs, fabs

Syntax
y = abs(x)  y = fabs(x)

x, y
See the possible types for a unary standard math function.

Atomic
In the case where x is an AD type, this is an atomic operation .

Complex Types
The functions abs and fabs are not defined for the base types std::complex<float> or std::complex<double> because the complex abs function is not complex differentiable (see complex types faq ).

Derivative
CppAD defines the derivative of the abs function is the sign function; i.e., $${\rm abs}^{(1)} ( x ) = {\rm sign} (x ) = \left\{ \begin{array}{rl} +1 & {\rm if} \; x > 0 \\ 0 & {\rm if} \; x = 0 \\ -1 & {\rm if} \; x < 0 \end{array} \right.$$ The result for x == 0 used to be a directional derivative.

Example
The file fabs.cpp contains an example and test of this function. It returns true if it succeeds and false otherwise.