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

fabs.cpp

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AD Absolute Value Function: Example and Test

# include <cppad/cppad.hpp>

bool fabs(void)
{  bool ok = true;

   using CppAD::AD;
   using CppAD::NearEqual;

   // domain space vector
   size_t n = 1;
   CPPAD_TESTVECTOR(AD<double>) ax(n);
   ax[0] = 0.;

   // declare independent variables and start tape recording
   CppAD::Independent(ax);

   // range space vector
   size_t m = 3;
   CPPAD_TESTVECTOR(AD<double>) ay(m);
   ay[0]     = fabs(ax[0] - 1.);
   ay[1]     = fabs(ax[0]);
   ay[2]     = fabs(ax[0] + 1.);
   //
   // create f: x -> y and stop tape recording
   CppAD::ADFun<double> f(ax, ay);

   // check values
   ok &= (ay[0] == 1.);
   ok &= (ay[1] == 0.);
   ok &= (ay[2] == 1.);
   //
   // forward computation of partials w.r.t. a positive x[0] direction
   size_t p = 1;
   CPPAD_TESTVECTOR(double) dx(n), dy(m);
   dx[0] = 1.;
   dy    = f.Forward(p, dx);
   ok  &= (dy[0] == - dx[0]);
   ok  &= (dy[1] ==   0.   );
   ok  &= (dy[2] == + dx[0]);
   //
   // forward computation of partials w.r.t. a negative x[0] direction
   dx[0] = -1.;
   dy    = f.Forward(p, dx);
   ok  &= (dy[0] == - dx[0]);
   ok  &= (dy[1] ==   0.   );
   ok  &= (dy[2] == + dx[0]);
   //
   // reverse computation of derivative of y[0]
   p    = 1;
   CPPAD_TESTVECTOR(double)  w(m), dw(n);
   w[0] = 1.; w[1] = 0.; w[2] = 0;
   dw   = f.Reverse(p, w);
   ok  &= (dw[0] == -1.);

   // reverse computation of derivative of y[1]
   w[0] = 0.; w[1] = 1.; w[2] = 0;
   dw   = f.Reverse(p, w);
   ok  &= (dw[0] == 0.);

   // reverse computation of derivative of y[3]
   w[0] = 0.; w[1] = 0.; w[2] = 1;
   dw   = f.Reverse(p, w);
   ok  &= (dw[0] == 1.);

   // use a VecAD<Base>::reference object with fabs
   CppAD::VecAD<double> av(1);
   AD<double> az(0);
   av[az]   = -1;
   AD<double> a_result = fabs(av[az]);
   ok  &= a_result == 1.0;

   return ok;
}