Prev Next Index-> contents reference index search external Up-> CppAD ADFun Forward forward_order forward.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.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
# include <limits> # include <cppad/cppad.hpp> namespace { // -------------------------------------------------------- // define the template function ForwardCases<Vector> in empty namespace template <class Vector> bool ForwardCases(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; // zero order forward mode using notation in forward_zero // use the template parameter Vector for the vector type Vector x0(n), y0(m); x0[0] = 3.; x0[1] = 4.; y0 = f.Forward(0, x0); ok &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps, eps); ok &= f.size_order() == 1; // first order forward mode using notation in forward_one // X(t) = x0 + x1 * t // Y(t) = F[X(t)] = y0 + y1 * t + o(t) Vector x1(n), y1(m); x1[0] = 1.; x1[1] = 0.; y1 = f.Forward(1, x1); // partial F w.r.t. x_0 ok &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps, eps); ok &= f.size_order() == 2; // second order forward mode using notation in forward_order // X(t) = x0 + x1 * t + x2 * t^2 // Y(t) = F[X(t)] = y0 + y1 * t + y2 * t^2 + o(t^3) Vector x2(n), y2(m); x2[0] = 0.; x2[1] = 0.; y2 = f.Forward(2, x2); double F_00 = 2. * y2[0]; // second partial F w.r.t. x_0, x_0 ok &= NearEqual(F_00, 2.*x0[1], eps, eps); ok &= f.size_order() == 3; return ok; } } // End empty namespace # include <vector> # include <valarray> bool Forward(void) { bool ok = true; // Run with Vector equal to three different cases // all of which are Simple Vectors with elements of type double. ok &= ForwardCases< CppAD::vector <double> >(); ok &= ForwardCases< std::vector <double> >(); ok &= ForwardCases< std::valarray <double> >(); return ok; } 
Input File: example/general/forward.cpp