<?xml version='1.0'?> <?xml-stylesheet type='text/xsl' href='pmathml.xsl'?> <html xmlns='http://www.w3.org/1999/xhtml'> <head> <title>exp_eps: Verify Second Order Reverse Sweep</title> <meta name="description" id="description" content="exp_eps: Verify Second Order Reverse Sweep"/> <meta name="keywords" id="keywords" content=" reverse exp_eps "/> <style type='text/css'> body { color : black } body { background-color : white } A:link { color : blue } A:visited { color : purple } A:active { color : purple } </style> <script type='text/javascript' language='JavaScript' src='_exp_eps_rev2.cpp_xml.js'> </script> </head> <body> <table><tr> <td> <a href="http://www.coin-or.org/CppAD/" target="_top"><img border="0" src="_image.gif"/></a> </td> <td><a href="exp_eps_rev2.xml" target="_top">Prev</a> </td><td><a href="exp_eps_cppad.xml" target="_top">Next</a> </td><td> <select onchange='choose_across0(this)'> <option>Index-></option> <option>contents</option> <option>reference</option> <option>index</option> <option>search</option> <option>external</option> </select> </td> <td> <select onchange='choose_up0(this)'> <option>Up-></option> <option>CppAD</option> <option>Introduction</option> <option>exp_eps</option> <option>exp_eps_rev2</option> <option>exp_eps_rev2.cpp</option> </select> </td> <td> <select onchange='choose_down3(this)'> <option>Introduction-></option> <option>get_started.cpp</option> <option>exp_2</option> <option>exp_eps</option> <option>exp_apx_main.cpp</option> </select> </td> <td> <select onchange='choose_down2(this)'> <option>exp_eps-></option> <option>exp_eps.hpp</option> <option>exp_eps.cpp</option> <option>exp_eps_for0</option> <option>exp_eps_for1</option> <option>exp_eps_rev1</option> <option>exp_eps_for2</option> <option>exp_eps_rev2</option> <option>exp_eps_cppad</option> </select> </td> <td> <select onchange='choose_down1(this)'> <option>exp_eps_rev2-></option> <option>exp_eps_rev2.cpp</option> </select> </td> <td>exp_eps_rev2.cpp</td> <td>Headings</td> </tr></table><br/> <center><b><big><big>exp_eps: Verify Second Order Reverse Sweep</big></big></b></center> <code><font color='blue'><pre style='display:inline'> # 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; } </pre></font></code> <hr/>Input File: introduction/exp_apx/exp_eps_rev2.cpp </body> </html>