sfad_example.cpp

Go to the documentation of this file.
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 // sfad_example
00033 //
00034 //  usage: 
00035 //     sfad_example
00036 //
00037 //  output:  
00038 //     prints the results of differentiating a simple function with forward
00039 //     mode AD using the Sacado::Fad::SFad class (uses static memory allocation
00040 //     for the number of derivative components, meaning this must be known
00041 //     at compile time.
00042 
00043 #include <iostream>
00044 #include <iomanip>
00045 
00046 #include "Sacado.hpp"
00047 
00048 // The function to differentiate
00049 template <typename ScalarT>
00050 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
00051   ScalarT r = c*std::log(b+1.)/std::sin(a);
00052 
00053   return r;
00054 }
00055 
00056 // The analytic derivative of func(a,b,c) with respect to a and b
00057 void func_deriv(double a, double b, double c, double& drda, double& drdb)
00058 {
00059   drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2))*std::cos(a);
00060   drdb = c / ((b+1.)*std::sin(a));
00061 }
00062 
00063 int main(int argc, char **argv)
00064 {
00065   double pi = std::atan(1.0)*4.0;
00066 
00067   // Values of function arguments
00068   double a = pi/4;
00069   double b = 2.0;
00070   double c = 3.0;
00071 
00072   // Number of independent variables
00073   int num_deriv = 2;    // Must be == 2 (see below)
00074 
00075   // Fad objects
00076   Sacado::Fad::SFad<double,2> afad(num_deriv, 0, a); // First (0) indep. var
00077   Sacado::Fad::SFad<double,2> bfad(num_deriv, 1, b); // Second (1) indep. var
00078   Sacado::Fad::SFad<double,2> cfad(c);               // Passive variable
00079   Sacado::Fad::SFad<double,2> rfad;                  // Result
00080 
00081   // Compute function
00082   double r = func(a, b, c);
00083 
00084   // Compute derivative analytically
00085   double drda, drdb;
00086   func_deriv(a, b, c, drda, drdb);
00087 
00088   // Compute function and derivative with AD
00089   rfad = func(afad, bfad, cfad);
00090 
00091   // Extract value and derivatives
00092   double r_ad = rfad.val();     // r
00093   double drda_ad = rfad.dx(0);  // dr/da
00094   double drdb_ad = rfad.dx(1);  // dr/db
00095 
00096   // Print the results
00097   int p = 4;
00098   int w = p+7;
00099   std::cout.setf(std::ios::scientific);
00100   std::cout.precision(p);
00101   std::cout << "    r =  " << r << " (original) == " << std::setw(w) << r_ad
00102       << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
00103       << "dr/da = " << std::setw(w) << drda << " (analytic) == " 
00104       << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w) 
00105       << drda - drda_ad << std::endl
00106       << "dr/db = " << std::setw(w) << drdb << " (analytic) == " 
00107       << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w) 
00108       << drdb - drdb_ad << std::endl;
00109 
00110   double tol = 1.0e-14;
00111   if (std::fabs(r - r_ad)       < tol &&
00112       std::fabs(drda - drda_ad) < tol &&
00113       std::fabs(drdb - drdb_ad) < tol) {
00114     std::cout << "\nExample passed!" << std::endl;
00115     return 0;
00116   }
00117   else {
00118     std::cout <<"\nSomething is wrong, example failed!" << std::endl;
00119     return 1;
00120   }
00121 }

Generated on Wed May 12 21:39:39 2010 for Sacado Package Browser (Single Doxygen Collection) by  doxygen 1.4.7