Prev Next Index-> contents reference index search external Up-> CppAD Introduction exp_eps exp_eps_rev2 exp_eps_rev2.cpp Introduction-> exp_2 exp_eps exp_apx.cpp exp_eps-> exp_eps.hpp exp_eps.cpp exp_eps_for0 exp_eps_for1 exp_eps_rev1 exp_eps_for2 exp_eps_rev2 exp_eps_cppad exp_eps_rev2-> exp_eps_rev2.cpp exp_eps_rev2.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 Second 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
extern bool exp_eps_for1(double *v1);   // computes first order forward sweep
bool exp_eps_rev2(void)
{     bool ok = true;

// set the value of v0[j], v1[j] for j = 1 , ... , 7
double v0[8], v1[8];
ok &= exp_eps_for0(v0);
ok &= exp_eps_for1(v1);

// initial all partial derivatives as zero
double f_v0[8], f_v1[8];
size_t j;
for(j = 0; j < 8; j++)
{     f_v0[j] = 0.;
f_v1[j] = 0.;
}

// set partial derivative for f_7
f_v1[7] = 1.;
ok &= std::fabs( f_v1[7] - 1.  ) <= 1e-10; // partial f_7 w.r.t. v_7^1

// f_6 = f_7( v_1^0 , ... , v_6^1 , v_4^0 + v_6^0, v_4^1 , v_6^1 )
f_v0[4] += f_v0[7];
f_v0[6] += f_v0[7];
f_v1[4] += f_v1[7];
f_v1[6] += f_v1[7];
ok &= std::fabs( f_v0[4] - 0.  ) <= 1e-10; // partial f_6 w.r.t. v_4^0
ok &= std::fabs( f_v0[6] - 0.  ) <= 1e-10; // partial f_6 w.r.t. v_6^0
ok &= std::fabs( f_v1[4] - 1.  ) <= 1e-10; // partial f_6 w.r.t. v_4^1
ok &= std::fabs( f_v1[6] - 1.  ) <= 1e-10; // partial f_6 w.r.t. v_6^1

// f_5 = f_6( v_1^0 , ... , v_5^1 , v_5^0 / 2 , v_5^1 / 2 )
f_v0[5] += f_v0[6] / 2.;
f_v1[5] += f_v1[6] / 2.;
ok &= std::fabs( f_v0[5] - 0.  ) <= 1e-10; // partial f_5 w.r.t. v_5^0
ok &= std::fabs( f_v1[5] - 0.5 ) <= 1e-10; // partial f_5 w.r.t. v_5^1

// f_4 = f_5( v_1^0 , ... , v_4^1 , v_3^0 * v_1^0 ,
//            v_3^1 * v_1^0 + v_3^0 * v_1^1 )
f_v0[1] += f_v0[5] * v0[3] + f_v1[5] * v1[3];
f_v0[3] += f_v0[5] * v0[1] + f_v1[5] * v1[1];
f_v1[1] += f_v1[5] * v0[3];
f_v1[3] += f_v1[5] * v0[1];
ok &= std::fabs( f_v0[1] - 0.5  ) <= 1e-10; // partial f_4 w.r.t. v_1^0
ok &= std::fabs( f_v0[3] - 0.5  ) <= 1e-10; // partial f_4 w.r.t. v_3^0
ok &= std::fabs( f_v1[1] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_1^1
ok &= std::fabs( f_v1[3] - 0.25 ) <= 1e-10; // partial f_4 w.r.t. v_3^1

// f_3 = f_4(  v_1^0 , ... , v_3^1 , 1 + v_3^0 , v_3^1 )
f_v0[3] += f_v0[4];
f_v1[3] += f_v1[4];
ok &= std::fabs( f_v0[3] - 0.5 ) <= 1e-10;  // partial f_3 w.r.t. v_3^0
ok &= std::fabs( f_v1[3] - 1.25) <= 1e-10;  // partial f_3 w.r.t. v_3^1

// f_2 = f_3( v_1^0 , ... , v_2^1 , v_2^0 , v_2^1 )
f_v0[2] += f_v0[3];
f_v1[2] += f_v1[3];
ok &= std::fabs( f_v0[2] - 0.5 ) <= 1e-10;  // partial f_2 w.r.t. v_2^0
ok &= std::fabs( f_v1[2] - 1.25) <= 1e-10;  // partial f_2 w.r.t. v_2^1

// f_1 = f_2 ( v_1^0 , v_2^0 , v_1^0 , v_2^0 )
f_v0[1] += f_v0[2];
f_v1[1] += f_v1[2];
ok &= std::fabs( f_v0[1] - 1.  ) <= 1e-10;  // partial f_1 w.r.t. v_1^0
ok &= std::fabs( f_v1[1] - 1.5 ) <= 1e-10;  // partial f_1 w.r.t. v_1^1

return ok;
}

Input File: introduction/exp_eps_rev2.cpp