Prev Next Index-> contents reference index search external Up-> CppAD ADFun Forward forward_order forward_order.cpp ADFun-> record_adfun drivers Forward Reverse sparsity_pattern sparse_derivative optimize abs_normal FunCheck check_for_nan Forward-> forward_zero forward_one forward_two forward_order forward_dir size_order compare_change capacity_order number_skip forward_order-> forward.cpp forward_order.cpp forward_order.cpp Headings

$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Forward Mode: Example and Test of Multiple Orders
# include <limits> # include <cppad/cppad.hpp> bool forward_order(void) { bool ok = true; using CppAD::AD; using CppAD::NearEqual; double eps = 10. * 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 starting 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 tape recording CppAD::ADFun<double> f(ax, ay); // initially, the variable values during taping are stored in f ok &= f.size_order() == 1; // Compute three forward orders at one size_t q = 2, q1 = q+1; CPPAD_TESTVECTOR(double) xq(n*q1), yq; xq[q1*0 + 0] = 3.; xq[q1*1 + 0] = 4.; // x^0 (order zero) xq[q1*0 + 1] = 1.; xq[q1*1 + 1] = 0.; // x^1 (order one) xq[q1*0 + 2] = 0.; xq[q1*1 + 2] = 0.; // x^2 (order two) // X(t) = x^0 + x^1 * t + x^2 * t^2 // = [ 3 + t, 4 ] yq = f.Forward(q, xq); ok &= size_t( yq.size() ) == m*q1; // Y(t) = F[X(t)] // = (3 + t) * (3 + t) * 4 // = y^0 + y^1 * t + y^2 * t^2 + o(t^3) // // check y^0 (order zero) CPPAD_TESTVECTOR(double) x0(n); x0[0] = xq[q1*0 + 0]; x0[1] = xq[q1*1 + 0]; ok &= NearEqual(yq[q1*0 + 0] , x0[0]*x0[0]*x0[1], eps, eps); // // check y^1 (order one) ok &= NearEqual(yq[q1*0 + 1] , 2.*x0[0]*x0[1], eps, eps); // // check y^2 (order two) double F_00 = 2. * yq[q1*0 + 2]; // second partial F w.r.t. x_0, x_0 ok &= NearEqual(F_00, 2.*x0[1], eps, eps); // check number of orders per variable ok &= f.size_order() == 3; return ok; } 
Input File: example/general/forward_order.cpp