exp_eps: Verify First Order Reverse Sweep
Keywords: exp_eps: verify first order reverse sweep exp_eps

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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;
    }

`

Input File: introduction/exp_apx/exp_eps_rev1.cpp