$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# include <cppad/cppad.hpp> namespace { // ----------------------------------------------------------- // define the template function object Fun<Type,Vector> in empty namespace template <class Type, class Vector> class Fun { private: size_t n; public: // function constructor Fun(size_t n_) : n(n_) { } // function evaluator Vector operator() (const Vector &x) { Vector y(n); size_t i; for(i = 0; i < n; i++) { // This operaiton sequence depends on x if( x[i] >= 0 ) y[i] = exp(x[i]); else y[i] = exp(-x[i]); } return y; } }; // template function FunCheckCases<Vector, ADVector> in empty namespace template <class Vector, class ADVector> bool FunCheckCases(void) { bool ok = true; using CppAD::AD; using CppAD::ADFun; using CppAD::Independent; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); // use the ADFun default constructor ADFun<double> f; // domain space vector size_t n = 2; ADVector X(n); X[0] = -1.; X[1] = 1.; // declare independent variables and starting recording Independent(X); // create function object to use with AD<double> Fun< AD<double>, ADVector > G(n); // range space vector size_t m = n; ADVector Y(m); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(X, Y); ok &= (f.size_order() == 0); // no implicit forward operation // create function object to use with double Fun<double, Vector> g(n); // function values should agree when the independent variable // values are the same as during recording Vector x(n); size_t j; for(j = 0; j < n; j++) x[j] = Value(X[j]); double r = eps99; double a = eps99; ok &= FunCheck(f, g, x, a, r); // function values should not agree when the independent variable // values are the negative of values during recording for(j = 0; j < n; j++) x[j] = - Value(X[j]); ok &= ! FunCheck(f, g, x, a, r); // re-tape to obtain the new AD of double operation sequence for(j = 0; j < n; j++) X[j] = x[j]; Independent(X); Y = G(X); // stop tape and store operation sequence in f : X -> Y f.Dependent(X, Y); ok &= (f.size_order() == 0); // no implicit forward with this x // function values should agree now ok &= FunCheck(f, g, x, a, r); return ok; } } // End empty namespace # include <vector> # include <valarray> bool FunCheck(void) { bool ok = true; typedef CppAD::vector<double> Vector1; typedef CppAD::vector< CppAD::AD<double> > ADVector1; typedef std::vector<double> Vector2; typedef std::vector< CppAD::AD<double> > ADVector2; typedef std::valarray<double> Vector3; typedef std::valarray< CppAD::AD<double> > ADVector3; // Run with Vector and ADVector equal to three different cases // all of which are Simple Vectors with elements of type // double and AD<double> respectively. ok &= FunCheckCases< Vector1, ADVector2 >(); ok &= FunCheckCases< Vector2, ADVector3 >(); ok &= FunCheckCases< Vector3, ADVector1 >(); return ok; }