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Sparsity Patterns For a Subset of Variables: Example and Test
See Also
sparse_sub_hes.cpp , sub_sparse_hes.cpp .
ForSparseJac
The routine ForSparseJac is used to compute the sparsity for both the full Jacobian (see `s` ) and a subset of the Jacobian (see `s2` ).
RevSparseHes
The routine RevSparseHes is used to compute both sparsity for both the full Hessian (see `h` ) and a subset of the Hessian (see `h2` ). `

    # 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;
    }

`

Input File: example/sparse/sparsity_sub.cpp