# include <cppad/cppad.hpp>
bool colpack_jacobian(void)
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
     typedef CPPAD_TESTVECTOR(double)     d_vector;
     typedef CppAD::vector<size_t>        i_vector;
     size_t i, j, k, ell;
     double eps = 10. * CppAD::numeric_limits<double>::epsilon();

     // domain space vector
     size_t n = 4;
     a_vector  a_x(n);
     for(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(j = 0; j < n; j++)
          x[j] = double(j);

     /*
           [ 1 1 0 0  ]
     jac = [ 0 0 1 1  ]
           [ 1 1 1 x_3]
     */
     d_vector check(m * n);
     check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
     check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
     check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];

     // Normally one would use f.ForSparseJac or f.RevSparseJac to compute
     // sparsity pattern, but for this example we extract it from check.
     std::vector< std::set<size_t> >  p(m);

     // using row and column indices to compute non-zero in rows 1 and 2
     i_vector row, col;
     for(i = 0; i < m; i++)
     {     for(j = 0; j < n; j++)
          {     ell = i * n + j;
               if( check[ell] != 0. )
               {     row.push_back(i);
                    col.push_back(j);
                    p[i].insert(j);
               }
          }
     }
     size_t K = row.size();
     d_vector jac(K);

     // empty work structure
     CppAD::sparse_jacobian_work work;
     ok &= work.color_method == "cppad";

     // choose to use ColPack
     work.color_method = "colpack";

     // forward mode
     size_t n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 4;

     // reverse mode
     work.clear();
     work.color_method = "colpack";
     n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work);
     for(k = 0; k < K; k++)
     {     ell = row[k] * n + col[k];
          ok &= NearEqual(check[ell], jac[k], eps, eps);
     }
     ok &= n_sweep == 2;

     return ok;
}