$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# include <cppad/cppad.hpp> namespace { struct tape_size { size_t n_var; size_t n_op; }; template <class Vector> void fun( const Vector& x, Vector& y, tape_size& before, tape_size& after ) { typedef typename Vector::value_type scalar; // phantom variable with index 0 and independent variables // begin operator, independent variable operators and end operator before.n_var = 1 + x.size(); before.n_op = 2 + x.size(); after.n_var = 1 + x.size(); after.n_op = 2 + x.size(); // initilized product of even and odd variables scalar prod_even = x[0]; scalar prod_odd = x[1]; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; // // compute product of even and odd variables for(size_t i = 2; i < size_t( x.size() ); i++) { if( i % 2 == 0 ) { // prod_even will affect dependent variable prod_even = prod_even * x[i]; before.n_var += 1; before.n_op += 1; after.n_var += 1; after.n_op += 1; } else { // prod_odd will not affect dependent variable prod_odd = prod_odd * x[i]; before.n_var += 1; before.n_op += 1; after.n_var += 0; after.n_op += 0; } } // dependent variable for this operation sequence y[0] = prod_even; before.n_var += 0; before.n_op += 0; after.n_var += 0; after.n_op += 0; } } bool reverse_active(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps10 = 10.0 * std::numeric_limits<double>::epsilon(); // domain space vector size_t n = 6; CPPAD_TESTVECTOR(AD<double>) ax(n); for(size_t i = 0; i < n; i++) ax[i] = AD<double>(i + 1); // declare independent variables and start tape recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) ay(m); tape_size before, after; fun(ax, ay, before, after); // create f: x -> y and stop tape recording CppAD::ADFun<double> f(ax, ay); ok &= f.size_var() == before.n_var; ok &= f.size_op() == before.n_op; // Optimize the operation sequence f.optimize(); ok &= f.size_var() == after.n_var; ok &= f.size_op() == after.n_op; // check zero order forward with different argument value CPPAD_TESTVECTOR(double) x(n), y(m), check(m); for(size_t i = 0; i < n; i++) x[i] = double(i + 2); y = f.Forward(0, x); fun(x, check, before, after); ok &= NearEqual(y[0], check[0], eps10, eps10); return ok; }