$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# include <cppad/cppad.hpp> bool Mul(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); // domain space vector size_t n = 1; double x0 = .5; CPPAD_TESTVECTOR(AD<double>) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // some binary multiplication operations AD<double> a = x[0] * 1.; // AD<double> * double AD<double> b = a * 2; // AD<double> * int AD<double> c = 3. * b; // double * AD<double> AD<double> d = 4 * c; // int * AD<double> // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) y(m); y[0] = x[0] * d; // AD<double> * AD<double> // create f: x -> y and stop tape recording CppAD::ADFun<double> f(x, y); // check value ok &= NearEqual(y[0] , x0*(4.*3.*2.*1.)*x0, eps99 , eps99); // forward computation of partials w.r.t. x[0] CPPAD_TESTVECTOR(double) dx(n); CPPAD_TESTVECTOR(double) dy(m); dx[0] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], (4.*3.*2.*1.)*2.*x0, eps99 , eps99); // reverse computation of derivative of y[0] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0], (4.*3.*2.*1.)*2.*x0, eps99 , eps99); // use a VecAD<Base>::reference object with multiplication CppAD::VecAD<double> v(1); AD<double> zero(0); v[zero] = c; AD<double> result = 4 * v[zero]; ok &= (result == d); return ok; }