# include <cppad/cppad.hpp>
bool subgraph_reverse(void)
{     bool ok = true;
     //
     using CppAD::AD;
     using CppAD::NearEqual;
     using CppAD::sparse_rc;
     using CppAD::sparse_rcv;
     //
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)     d_vector;
     typedef CPPAD_TESTVECTOR(bool)       b_vector;
     typedef CPPAD_TESTVECTOR(size_t)     s_vector;
     //
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     //
     // domain space vector
     size_t n = 4;
     a_vector  a_x(n);
     for(size_t j = 0; j < n; j++)
          a_x[j] = AD<double> (0);
     //
     // declare independent variables and starting recording
     CppAD::Independent(a_x);
     //
     size_t m = 3;
     a_vector  a_y(m);
     a_y[0] = a_x[0] + a_x[1];
     a_y[1] = a_x[2] + a_x[3];
     a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 2.;
     //
     // create f: x -> y and stop tape recording
     CppAD::ADFun<double> f(a_x, a_y);
     //
     // new value for the independent variable vector
     d_vector x(n);
     for(size_t j = 0; j < n; j++)
          x[j] = double(j);
     f.Forward(0, x);
     /*
            [ 1 1 0 0  ]
     J(x) = [ 0 0 1 1  ]
            [ 1 1 1 x_3]
     */
     double J[] = {
          1.0, 1.0, 0.0, 0.0,
          0.0, 0.0, 1.0, 1.0,
          1.0, 1.0, 1.0, 0.0
     };
     J[11] = x[3];
     //
     // exclude x[0] from the calculations
     b_vector select_domain(n);
     select_domain[0] = false;
     for(size_t j = 1; j < n; j++)
          select_domain[j] = true;
     //
     // initilaize for reverse mode derivatives computation on subgraphs
     f.subgraph_reverse(select_domain);
     //
     // compute the derivative for each range component
     for(size_t i = 0; i < m; i++)
     {     d_vector dw;
          s_vector col;
          size_t   q = 1; // derivative of one Taylor coefficient (zero order)
          f.subgraph_reverse(q, i, col, dw);
          //
          // check order in col
          for(size_t c = 1; c < size_t( col.size() ); c++)
               ok &= col[c] > col[c-1];
          //
          // check that x[0] has been excluded by select_domain
          if( size_t( col.size() ) > 0 )
               ok &= col[0] != 0;
          //
          // check derivatives for i-th row of J(x)
          // note that dw is only specified for j in col
          size_t c = 0;
          for(size_t j = 1; j < n; j++)
          {     while( c < size_t( col.size() ) && col[c] < j )
                    ++c;
               if( c < size_t( col.size() ) && col[c] == j )
                    ok &= NearEqual(dw[j], J[i * n + j], eps99, eps99);
               else
                    ok &= NearEqual(0.0, J[i * n + j], eps99, eps99);
          }
     }
     return ok;
}