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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Subset of Second Order Partials: Example and Test
# include <cppad/cppad.hpp> namespace { // ----------------------------------------------------- // define the template function in empty namespace // bool ForTwoCases<VectorBase, VectorSize_t>(void) template <class VectorBase, class VectorSize_t> bool ForTwoCases() { 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); // a calculation between the domain and range values AD<double> Square = X[0] * X[0]; // range space vector size_t m = 3; CPPAD_TESTVECTOR(AD<double>) Y(m); Y[0] = Square * exp( X[1] ); Y[1] = Square * sin( X[1] ); Y[2] = Square * cos( X[1] ); // create f: X -> Y and stop tape recording CppAD::ADFun<double> f(X, Y); // new value for the independent variable vector VectorBase x(n); x[0] = 2.; x[1] = 1.; // set j and k to compute specific second partials of y size_t p = 2; VectorSize_t j(p); VectorSize_t k(p); j[0] = 0; k[0] = 0; // for second partial w.r.t. x[0] and x[0] j[1] = 0; k[1] = 1; // for second partial w.r.t x[0] and x[1] // compute the second partials VectorBase ddy(m * p); ddy = f.ForTwo(x, j, k); /* partial of y w.r.t x[0] is [ 2 * x[0] * exp(x[1]) ] [ 2 * x[0] * sin(x[1]) ] [ 2 * x[0] * cos(x[1]) ] */ // second partial of y w.r.t x[0] and x[1] ok &= NearEqual( 2.*exp(x[1]), ddy[0*p+0], eps99, eps99); ok &= NearEqual( 2.*sin(x[1]), ddy[1*p+0], eps99, eps99); ok &= NearEqual( 2.*cos(x[1]), ddy[2*p+0], eps99, eps99); // second partial of F w.r.t x[0] and x[1] ok &= NearEqual( 2.*x[0]*exp(x[1]), ddy[0*p+1], eps99, eps99); ok &= NearEqual( 2.*x[0]*cos(x[1]), ddy[1*p+1], eps99, eps99); ok &= NearEqual(-2.*x[0]*sin(x[1]), ddy[2*p+1], eps99, eps99); return ok; } } // End empty namespace # include <vector> # include <valarray> bool ForTwo(void) { bool ok = true; // Run with VectorBase equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForTwoCases< CppAD::vector <double>, std::vector<size_t> >(); ok &= ForTwoCases< std::vector <double>, std::vector<size_t> >(); ok &= ForTwoCases< std::valarray <double>, std::vector<size_t> >(); // Run with VectorSize_t equal to two other cases // which are Simple Vectors with elements of type size_t. ok &= ForTwoCases< std::vector <double>, CppAD::vector<size_t> >(); ok &= ForTwoCases< std::vector <double>, std::valarray<size_t> >(); return ok; } 
Input File: example/general/for_two.cpp