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

pow_int.cpp

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The Pow Integer Exponent: Example and Test

# include <cppad/cppad.hpp>
# include <cmath>

bool pow_int(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // declare independent variables and start tape recording
   size_t n  = 1;
   double x0 = -0.5;
   CPPAD_TESTVECTOR(AD<double>) x(n);
   x[0]      = x0;
   CppAD::Independent(x);

   // dependent variable vector
   size_t m = 7;
   CPPAD_TESTVECTOR(AD<double>) y(m);
   for(size_t i = 0; i < m; i++)
      y[i] = CppAD::pow(x[0], int(i) - 3);

   // create f: x -> y and stop tape recording
   CppAD::ADFun<double> f(x, y);

   // check value
   double check;
   for(size_t i = 0; i < m; i++)
   {  check = std::pow(x0, double(i) - 3.0);
      ok &= NearEqual(y[i] , check,  eps99 , eps99);
   }

   // forward computation of first partial w.r.t. x[0]
   CPPAD_TESTVECTOR(double) dx(n);
   CPPAD_TESTVECTOR(double) dy(m);
   dx[0] = 1.;
   dy    = f.Forward(1, dx);
   for(size_t i = 0; i < m; i++)
   {  check = (double(i) - 3.0) * std::pow(x0, double(i) - 4.0);
      ok &= NearEqual(dy[i] , check,  eps99 , eps99);
   }

   // reverse computation of derivative of y[i]
   CPPAD_TESTVECTOR(double)  w(m);
   CPPAD_TESTVECTOR(double) dw(n);
   for(size_t i = 0; i < m; i++)
      w[i] = 0.;
   for(size_t i = 0; i < m; i++)
   {  w[i] = 1.;
      dw    = f.Reverse(1, w);
      check = (double(i) - 3.0) * std::pow(x0, double(i) - 4.0);
      ok &= NearEqual(dw[0] , check,  eps99 , eps99);
      w[i] = 0.;
   }

   return ok;
}