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

eigen_array.cpp

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Using Eigen Arrays: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/example/cppad_eigen.hpp>

bool eigen_array(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   //
   typedef CppAD::eigen_vector< AD<double> > a_vector;
   //
   // domain and range space vectors
   size_t n  = 10, m = n;
   a_vector a_x(n), a_y(m);

   // set and declare independent variables and start tape recording
   for(size_t j = 0; j < n; j++)
      a_x[j] = double(1 + j);
   CppAD::Independent(a_x);

   // evaluate a component wise function
   for(size_t j = 0; j < n; j++)
      a_y[j] = a_x[j] + sin( a_x[j] );

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

   // compute the derivative of y w.r.t x using CppAD
   CPPAD_TESTVECTOR(double) x(n);
   for(size_t j = 0; j < n; j++)
      x[j] = double(j) + 1.0 / double(j+1);
   CPPAD_TESTVECTOR(double) jac = f.Jacobian(x);

   // check Jacobian
   double eps = 100. * CppAD::numeric_limits<double>::epsilon();
   for(size_t i = 0; i < m; i++)
   {  for(size_t j = 0; j < n; j++)
      {  double check = 1.0 + cos(x[i]);
         if( i != j )
            check = 0.0;
         ok &= NearEqual(jac[i * n + j], check, eps, eps);
      }
   }

   return ok;
}