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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Sign Function: Example and Test
 # include <cppad/cppad.hpp> bool sign(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // create f: x -> y where f(x) = sign(x) size_t n = 1; size_t m = 1; CPPAD_TESTVECTOR(AD<double>) ax(n), ay(m); ax[0] = 0.; CppAD::Independent(ax); ay[0] = sign(ax[0]); CppAD::ADFun<double> f(ax, ay); // check value during recording ok &= (ay[0] == 0.); // use f(x) to evaluate the sign function and its derivatives CPPAD_TESTVECTOR(double) x(n), y(m), dx(n), dy(m), w(m), dw(n); dx[0] = 1.; w[0] = 1.; // x[0] = 2.; y = f.Forward(0, x); ok &= (y[0] == 1.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // x[0] = 0.; y = f.Forward(0, x); ok &= (y[0] == 0.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // x[0] = -2.; y = f.Forward(0, x); ok &= (y[0] == -1.); dy = f.Forward(1, dx); ok &= (dy[0] == 0.); dw = f.Reverse(1, w); ok &= (dw[0] == 0.); // use a VecAD<Base>::reference object with sign CppAD::VecAD<double> v(1); AD<double> zero(0); v[zero] = 2.; AD<double> result = sign(v[zero]); ok &= (result == 1.); return ok; } 
Input File: example/general/sign.cpp