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$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
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