# include <cppad/cppad.hpp>
bool subgraph_hes2jac(void)
{     bool ok = true;
     using CppAD::NearEqual;
     typedef CppAD::AD<double>                      a1double;
     typedef CppAD::AD<a1double>                    a2double;
     typedef CPPAD_TESTVECTOR(double)               d_vector;
     typedef CPPAD_TESTVECTOR(a1double)             a1vector;
     typedef CPPAD_TESTVECTOR(a2double)             a2vector;
     typedef CPPAD_TESTVECTOR(size_t)               s_vector;
     typedef CPPAD_TESTVECTOR(bool)                 b_vector;
     typedef CppAD::sparse_rcv<s_vector, d_vector>  sparse_matrix;
     //
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();
     //
     // double version of x
     size_t n = 12;
     d_vector x(n);
     for(size_t j = 0; j < n; j++)
          x[j] = double(j + 2);
     //
     // a1double version of x
     a1vector a1x(n);
     for(size_t j = 0; j < n; j++)
          a1x[j] = x[j];
     //
     // a2double version of x
     a2vector a2x(n);
     for(size_t j = 0; j < n; j++)
          a2x[j] = a1x[j];
     //
     // declare independent variables and starting recording
     CppAD::Independent(a2x);
     //
     // a2double version of y = f(x) = 5 * x0 * x1 + sum_j xj^3
     size_t m = 1;
     a2vector a2y(m);
     a2y[0] = 5.0 * a2x[0] * a2x[1];
     for(size_t j = 0; j < n; j++)
          a2y[0] += a2x[j] * a2x[j] * a2x[j];
     //
     // create a1double version of f: x -> y and stop tape recording
     // (without executing zero order forward calculation)
     CppAD::ADFun<a1double> a1f;
     a1f.Dependent(a2x, a2y);
     //
     // Optimize this function to reduce future computations.
     // Perhaps only one optimization at the end would be faster.
     a1f.optimize();
     //
     // declare independent variables and start recording g(x) = f'(x)
     Independent(a1x);
     //
     // Use one reverse mode pass to compute z = f'(x)
     a1vector a1w(m), a1z(n);
     a1w[0] = 1.0;
     a1f.Forward(0, a1x);
     a1z = a1f.Reverse(1, a1w);
     //
     // create double version of g : x -> f'(x)
     CppAD::ADFun<double> g;
     g.Dependent(a1x, a1z);
     //
     // Optimize this function to reduce future computations.
     // Perhaps no optimization would be faster.
     g.optimize();
     //
     // compute f''(x) = g'(x)
     b_vector select_domain(n), select_range(n);
     for(size_t j = 0; j < n; ++j)
     {     select_domain[j] = true;
          select_range[j]  = true;
     }
     sparse_matrix hessian;
     g.subgraph_jac_rev(select_domain, select_range, x, hessian);
     // -------------------------------------------------------------------
     // check number of non-zeros in the Hessian
     // (only x0 * x1 generates off diagonal terms)
     ok &= hessian.nnz() == n + 2;
     //
     for(size_t k = 0; k < hessian.nnz(); ++k)
     {     size_t r = hessian.row()[k];
          size_t c = hessian.col()[k];
          double v = hessian.val()[k];
          //
          if( r == c )
          {     // a diagonal element
               double check = 6.0 * x[r];
               ok          &= NearEqual(v, check, eps, eps);
          }
          else
          {     // off diagonal element
               ok   &= (r == 0 && c == 1) || (r == 1 && c == 0);
               double check = 5.0;
               ok          &= NearEqual(v, check, eps, eps);
          }
     }
     return ok;
}