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ColPack: Sparse Jacobian Example and Test
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    # 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;
    }

`

Input File: example/sparse/colpack_jacobian.cpp