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ColPack: Sparse Jacobian Example and Test
`

    # include <cppad/cppad.hpp>
    bool colpack_jac(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;
         typedef CppAD::sparse_rc<i_vector>              sparsity;
         typedef CppAD::sparse_rcv<i_vector, d_vector>   sparse_matrix;

         // 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);

         /*
               [ 1 1 0 0  ]
         jac = [ 0 0 1 1  ]
               [ 1 1 1 x_3]
         */
         // Normally one would use CppAD to compute sparsity pattern, but for this
         // example we set it directly
         size_t nr  = m;
         size_t nc  = n;
         size_t nnz = 8;
         sparsity pattern(nr, nc, nnz);
         d_vector check(nnz);
         for(size_t k = 0; k < nnz; k++)
         {     size_t r, c;
              if( k < 2 )
              {     r = 0;
                   c = k;
              }
              else if( k < 4 )
              {     r = 1;
                   c = k;
              }
              else
              {     r = 2;
                   c = k - 4;
              }
              pattern.set(k, r, c);
              if( k == nnz - 1 )
                   check[k] = x[3];
              else
                   check[k] = 1.0;
         }

         // using row and column indices to compute non-zero in rows 1 and 2
         sparse_matrix subset( pattern );

         // check results for both CppAD and Colpack
         for(size_t i_method = 0; i_method < 4; i_method++)
         {     // coloring method
              std::string coloring;
              if( i_method % 2 == 0 )
                   coloring = "cppad";
              else
                   coloring = "colpack";
              //
              CppAD::sparse_jac_work work;
              size_t group_max = 1;
              if( i_method / 2 == 0 )
              {     size_t n_sweep = f.sparse_jac_for(
                        group_max, x, subset, pattern, coloring, work
                   );
                   ok &= n_sweep == 4;
              }
              else
              {     size_t n_sweep = f.sparse_jac_rev(
                        x, subset, pattern, coloring, work
                   );
                   ok &= n_sweep == 2;
              }
              const d_vector& hes( subset.val() );
              for(size_t k = 0; k < nnz; k++)
                   ok &= check[k] == hes[k];
         }
         return ok;
    }

`

Input File: example/sparse/colpack_jac.cpp