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

exp_eps_rev1.cpp

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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;
}