# include <cppad/cppad.hpp>
namespace { // -----------------------------------------------------
// define the template function in empty namespace
// bool ForTwoCases<VectorBase, VectorSize_t>(void)
template <class VectorBase, class VectorSize_t>
bool ForTwoCases()
{     bool ok = true;
     using CppAD::AD;
     using CppAD::NearEqual;
     double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
     using CppAD::exp;
     using CppAD::sin;
     using CppAD::cos;

     // domain space vector
     size_t n = 2;
     CPPAD_TESTVECTOR(AD<double>)  X(n);
     X[0] = 1.;
     X[1] = 2.;

     // declare independent variables and starting recording
     CppAD::Independent(X);

     // a calculation between the domain and range values
     AD<double> Square = X[0] * X[0];

     // range space vector
     size_t m = 3;
     CPPAD_TESTVECTOR(AD<double>)  Y(m);
     Y[0] = Square * exp( X[1] );
     Y[1] = Square * sin( X[1] );
     Y[2] = Square * cos( X[1] );

     // create f: X -> Y and stop tape recording
     CppAD::ADFun<double> f(X, Y);

     // new value for the independent variable vector
     VectorBase x(n);
     x[0] = 2.;
     x[1] = 1.;

     // set j and k to compute specific second partials of y
     size_t p = 2;
     VectorSize_t j(p);
     VectorSize_t k(p);
     j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0]
     j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1]

     // compute the second partials
     VectorBase ddy(m * p);
     ddy = f.ForTwo(x, j, k);
     /*
     partial of y w.r.t x[0] is
     [ 2 * x[0] * exp(x[1]) ]
     [ 2 * x[0] * sin(x[1]) ]
     [ 2 * x[0] * cos(x[1]) ]
     */
     // second partial of y w.r.t x[0] and x[1]
     ok &=  NearEqual( 2.*exp(x[1]), ddy[0*p+0], eps99, eps99);
     ok &=  NearEqual( 2.*sin(x[1]), ddy[1*p+0], eps99, eps99);
     ok &=  NearEqual( 2.*cos(x[1]), ddy[2*p+0], eps99, eps99);

     // second partial of F w.r.t x[0] and x[1]
     ok &=  NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], eps99, eps99);
     ok &=  NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], eps99, eps99);
     ok &=  NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], eps99, eps99);

     return ok;
}
} // End empty namespace
# include <vector>
# include <valarray>
bool ForTwo(void)
{     bool ok = true;
        // Run with VectorBase equal to three different cases
        // all of which are Simple Vectors with elements of type double.
     ok &= ForTwoCases< CppAD::vector <double>, std::vector<size_t> >();
     ok &= ForTwoCases< std::vector   <double>, std::vector<size_t> >();
     ok &= ForTwoCases< std::valarray <double>, std::vector<size_t> >();

        // Run with VectorSize_t equal to two other cases
        // which are Simple Vectors with elements of type size_t.
     ok &= ForTwoCases< std::vector <double>, CppAD::vector<size_t> >();
     ok &= ForTwoCases< std::vector <double>, std::valarray<size_t> >();

     return ok;
}