# include <cppad/cppad.hpp>

bool sparsity_sub(void)
{     // C++ source code
     bool ok = true;
     //
     using std::cout;
     using CppAD::vector;
     using CppAD::AD;
     using CppAD::vectorBool;

     size_t n = 4;
     size_t m = n-1;
     vector< AD<double> > ax(n), ay(m);
     for(size_t j = 0; j < n; j++)
          ax[j] = double(j+1);
     CppAD::Independent(ax);
     for(size_t i = 0; i < m; i++)
          ay[i] = (ax[i+1] - ax[i]) * (ax[i+1] - ax[i]);
     CppAD::ADFun<double> f(ax, ay);

     // Evaluate the full Jacobian sparsity pattern for f
     vectorBool r(n * n), s(m * n);
     for(size_t j = 0 ; j < n; j++)
     {     for(size_t i = 0; i < n; i++)
               r[i * n + j] = (i == j);
     }
     s = f.ForSparseJac(n, r);

     // evaluate the sparsity for the Hessian of f_0 + ... + f_{m-1}
     vectorBool t(m), h(n * n);
     for(size_t i = 0; i < m; i++)
          t[i] = true;
     h = f.RevSparseHes(n, t);

     // evaluate the Jacobian sparsity pattern for first n/2 components of x
     size_t n2 = n / 2;
     vectorBool r2(n * n2), s2(m * n2);
     for(size_t j = 0 ; j < n2; j++)
     {     for(size_t i = 0; i < n; i++)
               r2[i * n2 + j] = (i == j);
     }
     s2 = f.ForSparseJac(n2, r2);

     // evaluate the sparsity for the subset of Hessian of
     // f_0 + ... + f_{m-1} where first partial has only first n/2 components
     vectorBool h2(n2 * n);
     h2 = f.RevSparseHes(n2, t);

     // check sparsity pattern for Jacobian
     for(size_t i = 0; i < m; i++)
     {     for(size_t j = 0; j < n2; j++)
               ok &= s2[i * n2 + j] == s[i * n + j];
     }

     // check sparsity pattern for Hessian
     for(size_t i = 0; i < n2; i++)
     {     for(size_t j = 0; j < n; j++)
               ok &= h2[i * n + j] == h[i * n + j];
     }
     return ok;
}