dmfad_example.cpp

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00001 // $Id$ 
00002 // $Source$ 
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00006 //                           Sacado Package
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00013 // it under the terms of the GNU Lesser General Public License as
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00031 
00032 // dmfad_example
00033 //
00034 //  usage: 
00035 //     dmfad_example
00036 //
00037 //  output:  
00038 //     prints the results of differentiating a simple function with forward
00039 //     mode AD using the Sacado::Fad::DMFad class (uses dynamic memory
00040 //     allocation for number of derivative components using a custom memory
00041 //     manager).
00042 
00043 #include <iostream>
00044 #include <iomanip>
00045 
00046 #include "Sacado.hpp"
00047 
00048 template <>
00049 Sacado::Fad::MemPool* Sacado::Fad::MemPoolStorage<double>::defaultPool_ = NULL;
00050 
00051 // The function to differentiate
00052 template <typename ScalarT>
00053 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
00054   ScalarT r = c*std::log(b+1.)/std::sin(a);
00055 
00056   return r;
00057 }
00058 
00059 // The analytic derivative of func(a,b,c) with respect to a and b
00060 void func_deriv(double a, double b, double c, double& drda, double& drdb)
00061 {
00062   drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2))*std::cos(a);
00063   drdb = c / ((b+1.)*std::sin(a));
00064 }
00065 
00066 int main(int argc, char **argv)
00067 {
00068   double pi = std::atan(1.0)*4.0;
00069 
00070   // Values of function arguments
00071   double a = pi/4;
00072   double b = 2.0;
00073   double c = 3.0;
00074 
00075   // Number of independent variables
00076   int num_deriv = 2;
00077 
00078   // Memory pool & manager
00079   Sacado::Fad::MemPoolManager<double> poolManager(10);
00080   Sacado::Fad::MemPool* pool = poolManager.getMemoryPool(num_deriv);
00081   Sacado::Fad::DMFad<double>::setDefaultPool(pool);
00082 
00083   // Fad objects
00084   Sacado::Fad::DMFad<double> afad(num_deriv, 0, a); // First (0) indep. var
00085   Sacado::Fad::DMFad<double> bfad(num_deriv, 1, b); // Second (1) indep. var
00086   Sacado::Fad::DMFad<double> cfad(c);               // Passive variable
00087   Sacado::Fad::DMFad<double> rfad;                  // Result
00088 
00089   // Compute function
00090   double r = func(a, b, c);
00091 
00092   // Compute derivative analytically
00093   double drda, drdb;
00094   func_deriv(a, b, c, drda, drdb);
00095 
00096   // Compute function and derivative with AD
00097   rfad = func(afad, bfad, cfad);
00098 
00099   // Extract value and derivatives
00100   double r_ad = rfad.val();     // r
00101   double drda_ad = rfad.dx(0);  // dr/da
00102   double drdb_ad = rfad.dx(1);  // dr/db
00103 
00104   // Print the results
00105   int p = 4;
00106   int w = p+7;
00107   std::cout.setf(std::ios::scientific);
00108   std::cout.precision(p);
00109   std::cout << "    r =  " << r << " (original) == " << std::setw(w) << r_ad
00110       << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
00111       << "dr/da = " << std::setw(w) << drda << " (analytic) == " 
00112       << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w) 
00113       << drda - drda_ad << std::endl
00114       << "dr/db = " << std::setw(w) << drdb << " (analytic) == " 
00115       << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w) 
00116       << drdb - drdb_ad << std::endl;
00117 
00118   double tol = 1.0e-14;
00119   if (std::fabs(r - r_ad)       < tol &&
00120       std::fabs(drda - drda_ad) < tol &&
00121       std::fabs(drdb - drdb_ad) < tol) {
00122     std::cout << "\nExample passed!" << std::endl;
00123     return 0;
00124   }
00125   else {
00126     std::cout <<"\nSomething is wrong, example failed!" << std::endl;
00127     return 1;
00128   }
00129 }
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