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dfad_example.cpp
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00001 // $Id$ 
00002 // $Source$ 
00003 // @HEADER
00004 // ***********************************************************************
00005 // 
00006 //                           Sacado Package
00007 //                 Copyright (2006) Sandia Corporation
00008 // 
00009 // Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
00010 // the U.S. Government retains certain rights in this software.
00011 // 
00012 // This library is free software; you can redistribute it and/or modify
00013 // it under the terms of the GNU Lesser General Public License as
00014 // published by the Free Software Foundation; either version 2.1 of the
00015 // License, or (at your option) any later version.
00016 //  
00017 // This library is distributed in the hope that it will be useful, but
00018 // WITHOUT ANY WARRANTY; without even the implied warranty of
00019 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00020 // Lesser General Public License for more details.
00021 //  
00022 // You should have received a copy of the GNU Lesser General Public
00023 // License along with this library; if not, write to the Free Software
00024 // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
00025 // USA
00026 // Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
00027 // (etphipp@sandia.gov).
00028 // 
00029 // ***********************************************************************
00030 // @HEADER
00031 
00032 // dfad_example
00033 //
00034 //  usage: 
00035 //     dfad_example
00036 //
00037 //  output:  
00038 //     prints the results of differentiating a simple function with forward
00039 //     mode AD using the Sacado::Fad::DFad class (uses dynamic memory
00040 //     allocation for number of derivative components).
00041 
00042 #include <iostream>
00043 #include <iomanip>
00044 
00045 #include "Sacado.hpp"
00046 
00047 // The function to differentiate
00048 template <typename ScalarT>
00049 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
00050   ScalarT r = c*std::log(b+1.)/std::sin(a);
00051 
00052   return r;
00053 }
00054 
00055 // The analytic derivative of func(a,b,c) with respect to a and b
00056 void func_deriv(double a, double b, double c, double& drda, double& drdb)
00057 {
00058   drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2))*std::cos(a);
00059   drdb = c / ((b+1.)*std::sin(a));
00060 }
00061 
00062 int main(int argc, char **argv)
00063 {
00064   double pi = std::atan(1.0)*4.0;
00065 
00066   // Values of function arguments
00067   double a = pi/4;
00068   double b = 2.0;
00069   double c = 3.0;
00070 
00071   // Number of independent variables
00072   int num_deriv = 2;
00073 
00074   // Fad objects
00075   Sacado::Fad::DFad<double> afad(num_deriv, 0, a); // First (0) indep. var
00076   Sacado::Fad::DFad<double> bfad(num_deriv, 1, b); // Second (1) indep. var
00077   Sacado::Fad::DFad<double> cfad(c);               // Passive variable
00078   Sacado::Fad::DFad<double> rfad;                  // Result
00079 
00080   // Compute function
00081   double r = func(a, b, c);
00082 
00083   // Compute derivative analytically
00084   double drda, drdb;
00085   func_deriv(a, b, c, drda, drdb);
00086 
00087   // Compute function and derivative with AD
00088   rfad = func(afad, bfad, cfad);
00089 
00090   // Extract value and derivatives
00091   double r_ad = rfad.val();     // r
00092   double drda_ad = rfad.dx(0);  // dr/da
00093   double drdb_ad = rfad.dx(1);  // dr/db
00094 
00095   // Print the results
00096   int p = 4;
00097   int w = p+7;
00098   std::cout.setf(std::ios::scientific);
00099   std::cout.precision(p);
00100   std::cout << "    r =  " << r << " (original) == " << std::setw(w) << r_ad
00101       << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
00102       << "dr/da = " << std::setw(w) << drda << " (analytic) == " 
00103       << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w) 
00104       << drda - drda_ad << std::endl
00105       << "dr/db = " << std::setw(w) << drdb << " (analytic) == " 
00106       << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w) 
00107       << drdb - drdb_ad << std::endl;
00108 
00109   double tol = 1.0e-14;
00110   if (std::fabs(r - r_ad)       < tol &&
00111       std::fabs(drda - drda_ad) < tol &&
00112       std::fabs(drdb - drdb_ad) < tol) {
00113     std::cout << "\nExample passed!" << std::endl;
00114     return 0;
00115   }
00116   else {
00117     std::cout <<"\nSomething is wrong, example failed!" << std::endl;
00118     return 1;
00119   }
00120 }
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