# include <cppad/cppad.hpp>
bool sparse_jac_for(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(size_t)     s_vector;
     //
     // domain space vector
     size_t n = 3;
     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 = 4;
     a_vector  a_y(m);
     a_y[0] = a_x[0] + a_x[2];
     a_y[1] = a_x[0] + a_x[2];
     a_y[2] = a_x[1] + a_x[2];
     a_y[3] = a_x[1] + a_x[2] * a_x[2] / 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 0 1   ]
     J(x) = [ 1 0 1   ]
            [ 0 1 1   ]
            [ 0 1 x_2 ]
     */
     d_vector check(m * n);
     //
     // column-major order values of J(x)
     size_t nnz = 8;
     s_vector check_row(nnz), check_col(nnz);
     d_vector check_val(nnz);
     for(size_t k = 0; k < nnz; k++)
     {     // check_val
          if( k < 7 )
               check_val[k] = 1.0;
          else
               check_val[k] = x[2];
          //
          // check_row and check_col
          check_row[k] = k;
          if( k < 2 )
               check_col[k] = 0;
          else if( k < 4 )
               check_col[k] = 1;
          else
          {     check_col[k] = 2;
               check_row[k] = k - 4;
          }
     }
     //
     // n by n identity matrix sparsity
     sparse_rc<s_vector> pattern_in;
     pattern_in.resize(n, n, n);
     for(size_t k = 0; k < n; k++)
          pattern_in.set(k, k, k);
     //
     // sparsity for J(x)
     bool transpose     = false;
     bool dependency    = false;
     bool internal_bool = true;
     sparse_rc<s_vector> pattern_jac;
     f.for_jac_sparsity(
          pattern_in, transpose, dependency, internal_bool, pattern_jac
     );
     //
     // compute entire forward mode Jacobian
     sparse_rcv<s_vector, d_vector> subset( pattern_jac );
     CppAD::sparse_jac_work work;
     std::string coloring = "cppad";
     size_t group_max = 10;
     size_t n_sweep = f.sparse_jac_for(
          group_max, x, subset, pattern_jac, coloring, work
     );
     ok &= n_sweep == 2;
     //
     const s_vector row( subset.row() );
     const s_vector col( subset.col() );
     const d_vector val( subset.val() );
     s_vector col_major = subset.col_major();
     ok  &= subset.nnz() == nnz;
     for(size_t k = 0; k < nnz; k++)
     {     ok &= row[ col_major[k] ] == check_row[k];
          ok &= col[ col_major[k] ] == check_col[k];
          ok &= val[ col_major[k] ] == check_val[k];
     }
     // compute non-zero in row 3 only
     sparse_rc<s_vector> pattern_row3;
     pattern_row3.resize(m, n, 2); // nr = m, nc = n, nnz = 2
     pattern_row3.set(0, 3, 1);    // row[0] = 3, col[0] = 1
     pattern_row3.set(1, 3, 2);    // row[1] = 3, col[1] = 2
     sparse_rcv<s_vector, d_vector> subset_row3( pattern_row3 );
     work.clear();
     n_sweep = f.sparse_jac_for(
          group_max, x, subset_row3, pattern_jac, coloring, work
     );
     ok &= n_sweep == 2;
     //
     const s_vector row_row3( subset_row3.row() );
     const s_vector col_row3( subset_row3.col() );
     const d_vector val_row3( subset_row3.val() );
     ok &= subset_row3.nnz() == 2;
     //
     ok &= row_row3[0] == 3;
     ok &= col_row3[0] == 1;
     ok &= val_row3[0] == 1.0;
     //
     ok &= row_row3[1] == 3;
     ok &= col_row3[1] == 2;
     ok &= val_row3[1] == x[2];
     //
     return ok;
}