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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
First Order Reverse Mode: Example and Test
# include <cppad/cppad.hpp> namespace { // ---------------------------------------------------------- // define the template function reverse_one_cases<Vector> in empty namespace template <typename Vector> bool reverse_one_cases(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; CPPAD_TESTVECTOR(AD<double>) ax(n); ax[0] = 0.; ax[1] = 1.; // declare independent variables and start recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) ay(m); ay[0] = ax[0] * ax[0] * ax[1]; // create f : x -> y and stop recording CppAD::ADFun<double> f(ax, ay); // use first order reverse mode to evaluate derivative of y[0] // and use the values in x for the independent variables. CPPAD_TESTVECTOR(double) w(m), dw(n); w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0] , 2.*ax[0]*ax[1], eps99, eps99); ok &= NearEqual(dw[1] , ax[0]*ax[0], eps99, eps99); // use zero order forward mode to evaluate y at x = (3, 4) // and use the template parameter Vector for the vector type Vector x(n), y(m); x[0] = 3.; x[1] = 4.; y = f.Forward(0, x); ok &= NearEqual(y[0] , x[0]*x[0]*x[1], eps99, eps99); // use first order reverse mode to evaluate derivative of y[0] // and using the values in x for the independent variables. w[0] = 1.; dw = f.Reverse(1, w); ok &= NearEqual(dw[0] , 2.*x[0]*x[1], eps99, eps99); ok &= NearEqual(dw[1] , x[0]*x[0], eps99, eps99); return ok; } } // End empty namespace # include <vector> # include <valarray> bool reverse_one(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= reverse_one_cases< CppAD::vector <double> >(); ok &= reverse_one_cases< std::vector <double> >(); ok &= reverse_one_cases< std::valarray <double> >(); return ok; } 
Input File: example/general/reverse_one.cpp