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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
The AD Power Function: Example and Test
 # include <cppad/cppad.hpp> # include <cmath> bool pow(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits<double>::epsilon(); // domain space vector size_t n = 2; double x = 0.5; double y = 2.; CPPAD_TESTVECTOR(AD<double>) axy(n); axy[0] = x; axy[1] = y; // declare independent variables and start tape recording CppAD::Independent(axy); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD<double>) az(m); az[0] = CppAD::pow(axy[0], axy[1]); // pow(variable, variable) az[1] = CppAD::pow(axy[0], y); // pow(variable, parameter) az[2] = CppAD::pow(x, axy[1]); // pow(parameter, variable) // create f: axy -> az and stop tape recording CppAD::ADFun<double> f(axy, az); // check value double check = std::pow(x, y); size_t i; for(i = 0; i < m; i++) ok &= NearEqual(az[i] , check, eps, eps); // forward computation of first partial w.r.t. x CPPAD_TESTVECTOR(double) dxy(n); CPPAD_TESTVECTOR(double) dz(m); dxy[0] = 1.; dxy[1] = 0.; dz = f.Forward(1, dxy); check = y * std::pow(x, y-1.); ok &= NearEqual(dz[0], check, eps, eps); ok &= NearEqual(dz[1], check, eps, eps); ok &= NearEqual(dz[2], 0., eps, eps); // forward computation of first partial w.r.t. y dxy[0] = 0.; dxy[1] = 1.; dz = f.Forward(1, dxy); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dz[0], check, eps, eps); ok &= NearEqual(dz[1], 0., eps, eps); ok &= NearEqual(dz[2], check, eps, eps); // reverse computation of derivative of z[0] + z[1] + z[2] CPPAD_TESTVECTOR(double) w(m); CPPAD_TESTVECTOR(double) dw(n); w[0] = 1.; w[1] = 1.; w[2] = 1.; dw = f.Reverse(1, w); check = y * std::pow(x, y-1.); ok &= NearEqual(dw[0], 2. * check, eps, eps); check = std::log(x) * std::pow(x, y); ok &= NearEqual(dw[1], 2. * check, eps, eps); // use a VecAD<Base>::reference object with pow CppAD::VecAD<double> v(2); AD<double> zero(0); AD<double> one(1); v[zero] = axy[0]; v[one] = axy[1]; AD<double> result = CppAD::pow(v[zero], v[one]); ok &= NearEqual(result, az[0], eps, eps); return ok; } 
Input File: example/general/pow.cpp