exp_eps: Verify First Order Reverse Sweep

exp_eps_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_eps: Verify First Order Reverse Sweep

# include <cstddef>                     // define size_t
# include <cmath>                       // for fabs function
extern bool exp_eps_for0(double *v0);   // computes zero order forward sweep
bool exp_eps_rev1(void)
{     bool ok = true;

     // set the value of v0[j] for j = 1 , ... , 7
     double v0[8];
     ok &= exp_eps_for0(v0);

     // initial all partial derivatives as zero
     double f_v[8];
     size_t j;
     for(j = 0; j < 8; j++)
          f_v[j] = 0.;

     // set partial derivative for f7
     f_v[7] = 1.;
     ok    &= std::fabs( f_v[7] - 1. ) <= 1e-10;     // f7_v7

     // f6( v1 , v2 , v3 , v4 , v5 , v6 )
     f_v[4] += f_v[7] * 1.;
     f_v[6] += f_v[7] * 1.;
     ok     &= std::fabs( f_v[4] - 1.  ) <= 1e-10;   // f6_v4
     ok     &= std::fabs( f_v[6] - 1.  ) <= 1e-10;   // f6_v6

     // f5( v1 , v2 , v3 , v4 , v5 )
     f_v[5] += f_v[6] / 2.;
     ok     &= std::fabs( f_v[5] - 0.5 ) <= 1e-10;   // f5_v5

     // f4( v1 , v2 , v3 , v4 )
     f_v[1] += f_v[5] * v0[3];
     f_v[3] += f_v[5] * v0[1];
     ok     &= std::fabs( f_v[1] - 0.25) <= 1e-10;   // f4_v1
     ok     &= std::fabs( f_v[3] - 0.25) <= 1e-10;   // f4_v3

     // f3( v1 , v2 , v3 )
     f_v[3] += f_v[4] * 1.;
     ok     &= std::fabs( f_v[3] - 1.25) <= 1e-10;   // f3_v3

     // f2( v1 , v2 )
     f_v[2] += f_v[3] / 1.;
     ok     &= std::fabs( f_v[2] - 1.25) <= 1e-10;   // f2_v2

     // f1( v1 )
     f_v[1] += f_v[2] * 1.;
     ok     &= std::fabs( f_v[1] - 1.5 ) <= 1e-10;   // f1_v2

     return ok;
}

Input File: introduction/exp_eps_rev1.cpp