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ADFun Assignment: Example and Test
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    # include <cppad/cppad.hpp>
    # include <limits>

    bool fun_assign(void)
    {     bool ok = true;
         using CppAD::AD;
         using CppAD::NearEqual;
         size_t i, j;

         // ten times machine percision
         double eps = 10. * CppAD::numeric_limits<double>::epsilon();

         // two ADFun<double> objects
         CppAD::ADFun<double> g;

         // domain space vector
         size_t n  = 3;
         CPPAD_TESTVECTOR(AD<double>) x(n);
         for(j = 0; j < n; j++)
              x[j] = AD<double>(j + 2);

         // declare independent variables and start tape recording
         CppAD::Independent(x);

         // range space vector
         size_t m = 2;
         CPPAD_TESTVECTOR(AD<double>) y(m);
         y[0] = x[0] + x[0] * x[1];
         y[1] = x[1] * x[2] + x[2];

         // Store operation sequence, and order zero forward results, in f.
         CppAD::ADFun<double> f(x, y);

         // sparsity pattern for the identity matrix
         CPPAD_TESTVECTOR(std::set<size_t>) r(n);
         for(j = 0; j < n; j++)
              r[j].insert(j);

         // Store forward mode sparsity pattern in f
         f.ForSparseJac(n, r);

         // make a copy in g
         g = f;

         // check values that should be equal
         ok &= ( g.size_order() == f.size_order() );
         ok &= ( (g.size_forward_bool() > 0) == (f.size_forward_bool() > 0) );
         ok &= ( (g.size_forward_set() > 0)  == (f.size_forward_set() > 0) );

         // Use zero order Taylor coefficient from f for first order
         // calculation using g.
         CPPAD_TESTVECTOR(double) dx(n), dy(m);
         for(i = 0; i < n; i++)
              dx[i] = 0.;
         dx[1] = 1;
         dy    = g.Forward(1, dx);
         ok &= NearEqual(dy[0], x[0], eps, eps); // partial y[0] w.r.t x[1]
         ok &= NearEqual(dy[1], x[2], eps, eps); // partial y[1] w.r.t x[1]

         // Use forward Jacobian sparsity pattern from f to calculate
         // Hessian sparsity pattern using g.
         CPPAD_TESTVECTOR(std::set<size_t>) s(1), h(n);
         s[0].insert(0); // Compute sparsity pattern for Hessian of y[0]
         h =  f.RevSparseHes(n, s);

         // check sparsity pattern for Hessian of y[0] = x[0] + x[0] * x[1]
         ok  &= ( h[0].find(0) == h[0].end() ); // zero     w.r.t x[0], x[0]
         ok  &= ( h[0].find(1) != h[0].end() ); // non-zero w.r.t x[0], x[1]
         ok  &= ( h[0].find(2) == h[0].end() ); // zero     w.r.t x[0], x[2]

         ok  &= ( h[1].find(0) != h[1].end() ); // non-zero w.r.t x[1], x[0]
         ok  &= ( h[1].find(1) == h[1].end() ); // zero     w.r.t x[1], x[1]
         ok  &= ( h[1].find(2) == h[1].end() ); // zero     w.r.t x[1], x[2]

         ok  &= ( h[2].find(0) == h[2].end() ); // zero     w.r.t x[2], x[0]
         ok  &= ( h[2].find(1) == h[2].end() ); // zero     w.r.t x[2], x[1]
         ok  &= ( h[2].find(2) == h[2].end() ); // zero     w.r.t x[2], x[2]

         return ok;
    }

`

Input File: example/general/fun_assign.cpp