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First Order Reverse Mode: Example and Test
# include <cppad/cppad.hpp>
namespace { // ----------------------------------------------------------
// define the template function reverse_one_cases<Vector> in empty namespace
template <typename Vector>
bool reverse_one_cases(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>) ax(n);
     ax[0] = 0.;
     ax[1] = 1.;

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

     // range space vector
     size_t m = 1;
     CPPAD_TESTVECTOR(AD<double>) ay(m);
     ay[0] = ax[0] * ax[0] * ax[1];

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

     // use first order reverse mode to evaluate derivative of y[0]
     // and use the values in x for the independent variables.
     CPPAD_TESTVECTOR(double) w(m), dw(n);
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok  &= NearEqual(dw[0] , 2.*ax[0]*ax[1], eps99, eps99);
     ok  &= NearEqual(dw[1] ,    ax[0]*ax[0], eps99, eps99);

     // use zero order forward mode to evaluate y at x = (3, 4)
     // and use the template parameter Vector for the vector type
     Vector x(n), y(m);
     x[0]    = 3.;
     x[1]    = 4.;
     y       = f.Forward(0, x);
     ok     &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99);

     // use first order reverse mode to evaluate derivative of y[0]
     // and using the values in x for the independent variables.
     w[0] = 1.;
     dw   = f.Reverse(1, w);
     ok  &= NearEqual(dw[0] , 2.*x[0]*x[1], eps99, eps99);
     ok  &= NearEqual(dw[1] ,    x[0]*x[0], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool reverse_one(void)
{     bool ok = true;
     // Run with Vector equal to three different cases
     // all of which are Simple Vectors with elements of type double.
     ok &= reverse_one_cases< CppAD::vector  <double> >();
     ok &= reverse_one_cases< std::vector    <double> >();
     ok &= reverse_one_cases< std::valarray  <double> >();
     return ok;
}

Input File: example/general/reverse_one.cpp