$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
# include <cppad/cppad.hpp> namespace { // -------------------------------------------------------- // define the template function Test<VectorAD>(void) in empty namespace template <class VectorAD> bool Test(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 = 2; VectorAD X(n); // VectorAD is the template parameter in call to Test X[0] = 0.; X[1] = 1.; // declare independent variables and start recording // use the template parameter VectorAD for the vector type CppAD::Independent(X); AD<double> a = X[0] + X[1]; // first AD operation AD<double> b = X[0] * X[1]; // second AD operation // range space vector size_t m = 2; VectorAD Y(m); // VectorAD is the template paraemter in call to Test Y[0] = a; Y[1] = b; // create f: X -> Y and stop tape recording // use the template parameter VectorAD for the vector type CppAD::ADFun<double> f(X, Y); // check value ok &= NearEqual(Y[0] , 1., eps99 , eps99); ok &= NearEqual(Y[1] , 0., eps99 , eps99); // compute f(1, 2) CPPAD_TESTVECTOR(double) x(n); CPPAD_TESTVECTOR(double) y(m); x[0] = 1.; x[1] = 2.; y = f.Forward(0, x); ok &= NearEqual(y[0] , 3., eps99 , eps99); ok &= NearEqual(y[1] , 2., eps99 , eps99); // compute partial of f w.r.t x[0] at (1, 2) 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] , 1., eps99 , eps99); ok &= NearEqual(dy[1] , x[1], eps99 , eps99); // compute partial of f w.r.t x[1] at (1, 2) dx[0] = 0.; dx[1] = 1.; dy = f.Forward(1, dx); ok &= NearEqual(dy[0] , 1., eps99 , eps99); ok &= NearEqual(dy[1] , x[0], eps99 , eps99); return ok; } } // End of empty namespace ------------------------------------------- # include <vector> # include <valarray> bool Independent(void) { bool ok = true; typedef CppAD::AD<double> ADdouble; // Run with VectorAD equal to three different cases // all of which are Simple Vectors with elements of type AD<double>. ok &= Test< CppAD::vector <ADdouble> >(); ok &= Test< std::vector <ADdouble> >(); ok &= Test< std::valarray <ADdouble> >(); return ok; }