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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 acosh Function: Example and Test
 # include <cppad/cppad.hpp> bool acosh(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; // 10 times machine epsilon double eps = 10. * std::numeric_limits<double>::epsilon(); // domain space vector size_t n = 1; double x0 = 0.5; CPPAD_TESTVECTOR(AD<double>) x(n); x[0] = x0; // declare independent variables and start tape recording CppAD::Independent(x); // a temporary value AD<double> cosh_of_x0 = CppAD::cosh(x[0]); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) y(m); y[0] = CppAD::acosh(cosh_of_x0); // create f: x -> y and stop tape recording CppAD::ADFun<double> f(x, y); // check value ok &= NearEqual(y[0] , x0, eps, eps); // forward computation of first partial 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], 1., eps, eps); // 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], 1., eps, eps); // use a VecAD<Base>::reference object with acosh CppAD::VecAD<double> v(1); AD<double> zero(0); v[zero] = cosh_of_x0; AD<double> result = CppAD::acosh(v[zero]); ok &= NearEqual(result, x0, eps, eps); return ok; } 
Input File: example/general/acosh.cpp