$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# include <cppad/cppad.hpp> bool Compare(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); // declare independent variables and start tape recording size_t n = 2; double x0 = 0.5; double x1 = 1.5; CPPAD_TESTVECTOR(AD<double>) x(n); x[0] = x0; x[1] = x1; CppAD::Independent(x); // some binary comparision operations AD<double> p; if( x[0] < x[1] ) p = x[0]; // values in x choose this case else p = x[1]; if( x[0] <= x[1] ) p *= x[0]; // values in x choose this case else p *= x[1]; if( x[0] > x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] >= x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] == x[1] ) p *= x[0]; else p *= x[1]; // values in x choose this case if( x[0] != x[1] ) p *= x[0]; // values in x choose this case else p *= x[1]; // dependent variable vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) y(m); y[0] = p; // create f: x -> y and stop tape recording CppAD::ADFun<double> f(x, y); // check value ok &= NearEqual(y[0] , x0*x0*x1*x1*x1*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.; dx[1] = 0.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3.*x0*x0*x1*x1*x1, eps99, eps99); // forward computation of partials w.r.t. x[1] dx[0] = 0.; dx[1] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0], 3.*x0*x0*x1*x1*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], 3.*x0*x0*x1*x1*x1, eps99, eps99); ok &= NearEqual(dw[1], 3.*x0*x0*x1*x1*x0, eps99, eps99); return ok; }