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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Forward Mode: Example and Test of Multiple Directions
# include <limits> # include <cppad/cppad.hpp> bool forward_dir(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * std::numeric_limits<double>::epsilon(); size_t j; // domain space vector size_t n = 3; CPPAD_TESTVECTOR(AD<double>) ax(n); ax[0] = 0.; ax[1] = 1.; ax[2] = 2.; // declare independent variables and starting recording CppAD::Independent(ax); // range space vector size_t m = 1; CPPAD_TESTVECTOR(AD<double>) ay(m); ay[0] = ax[0] * ax[1] * ax[2]; // create f: x -> y and stop tape recording CppAD::ADFun<double> f(ax, ay); // initially, the variable values during taping are stored in f ok &= f.size_order() == 1; // zero order Taylor coefficients CPPAD_TESTVECTOR(double) x0(n), y0; for(j = 0; j < n; j++) x0[j] = double(j+1); y0 = f.Forward(0, x0); ok &= size_t( y0.size() ) == m; double y_0 = 1.*2.*3.; ok &= NearEqual(y0[0], y_0, eps, eps); // first order Taylor coefficients size_t r = 2, ell; CPPAD_TESTVECTOR(double) x1(r*n), y1; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x1[ r * j + ell ] = double(j + 1 + ell); } y1 = f.Forward(1, r, x1); ok &= size_t( y1.size() ) == r*m; // secondorder Taylor coefficients CPPAD_TESTVECTOR(double) x2(r*n), y2; for(ell = 0; ell < r; ell++) { for(j = 0; j < n; j++) x2[ r * j + ell ] = 0.0; } y2 = f.Forward(2, r, x2); ok &= size_t( y2.size() ) == r*m; // // Y_0 (t) = F[X_0(t)] // = (1 + 1t)(2 + 2t)(3 + 3t) double y_1_0 = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.; double y_2_0 = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.; // // Y_1 (t) = F[X_1(t)] // = (1 + 2t)(2 + 3t)(3 + 4t) double y_1_1 = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.; double y_2_1 = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.; // ok &= NearEqual(y1[0] , y_1_0, eps, eps); ok &= NearEqual(y1[1] , y_1_1, eps, eps); ok &= NearEqual(y2[0] , y_2_0, eps, eps); ok &= NearEqual(y2[1] , y_2_1, eps, eps); // // check number of orders ok &= f.size_order() == 3; // // check number of directions ok &= f.size_direction() == 2; // return ok; } 
Input File: example/general/forward_dir.cpp