exp_2: Verify First Order Reverse Sweep

exp_2_rev1.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}} }@)@exp_2: Verify First Order Reverse Sweep

# include <cstddef>                 // define size_t
# include <cmath>                   // prototype for fabs
extern bool exp_2_for0(double *v0); // computes zero order forward sweep
bool exp_2_rev1(void)
{     bool ok = true;

     // set the value of v0[j] for j = 1 , ... , 5
     double v0[6];
     ok &= exp_2_for0(v0);

     // initial all partial derivatives as zero
     double f_v[6];
     size_t j;
     for(j = 0; j < 6; j++)
          f_v[j] = 0.;

     // set partial derivative for f5
     f_v[5] = 1.;
     ok &= std::fabs( f_v[5] - 1. ) <= 1e-10; // f5_v5

     // f4 = f5( v1 , v2 , v3 , v4 , v2 + v4 )
     f_v[2] += f_v[5] * 1.;
     f_v[4] += f_v[5] * 1.;
     ok &= std::fabs( f_v[2] - 1. ) <= 1e-10; // f4_v2
     ok &= std::fabs( f_v[4] - 1. ) <= 1e-10; // f4_v4

     // f3 = f4( v1 , v2 , v3 , v3 / 2 )
     f_v[3] += f_v[4] / 2.;
     ok &= std::fabs( f_v[3] - 0.5) <= 1e-10; // f3_v3

     // f2 = f3( v1 , v2 , v1 * v1 )
     f_v[1] += f_v[3] * 2. * v0[1];
     ok &= std::fabs( f_v[1] - 0.5) <= 1e-10; // f2_v1

     // f1 = f2( v1 , 1 + v1 )
     f_v[1] += f_v[2] * 1.;
     ok &= std::fabs( f_v[1] - 1.5) <= 1e-10; // f1_v1

     return ok;
}

Input File: introduction/exp_2_rev1.cpp