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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 Partial Driver: Example and Test
# include <cppad/cppad.hpp> namespace { // ------------------------------------------------------- // define the template function ForOneCases<Vector> in empty namespace template <typename Vector> bool ForOneCases() { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps99 = 99.0 * std::numeric_limits<double>::epsilon(); using CppAD::exp; using CppAD::sin; using CppAD::cos; // domain space vector size_t n = 2; CPPAD_TESTVECTOR(AD<double>) X(n); X[0] = 1.; X[1] = 2.; // declare independent variables and starting recording CppAD::Independent(X); // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD<double>) Y(m); Y[0] = X[0] * exp( X[1] ); Y[1] = X[0] * sin( X[1] ); Y[2] = X[0] * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun<double> f(X, Y); // new value for the independent variable vector Vector x(n); x[0] = 2.; x[1] = 1.; // compute partial of y w.r.t x[0] Vector dy(m); dy = f.ForOne(x, 0); ok &= NearEqual( dy[0], exp(x[1]), eps99, eps99); // for y[0] ok &= NearEqual( dy[1], sin(x[1]), eps99, eps99); // for y[1] ok &= NearEqual( dy[2], cos(x[1]), eps99, eps99); // for y[2] // compute partial of F w.r.t x[1] dy = f.ForOne(x, 1); ok &= NearEqual( dy[0], x[0]*exp(x[1]), eps99, eps99); ok &= NearEqual( dy[1], x[0]*cos(x[1]), eps99, eps99); ok &= NearEqual( dy[2], -x[0]*sin(x[1]), eps99, eps99); return ok; } } // End empty namespace # include <vector> # include <valarray> bool ForOne(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForOneCases< CppAD::vector <double> >(); ok &= ForOneCases< std::vector <double> >(); ok &= ForOneCases< std::valarray <double> >(); return ok; } 
Input File: example/general/for_one.cpp