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dfad_example.cpp
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31 
32 // dfad_example
33 //
34 // usage:
35 // dfad_example
36 //
37 // output:
38 // prints the results of differentiating a simple function with forward
39 // mode AD using the Sacado::Fad::DFad class (uses dynamic memory
40 // allocation for number of derivative components).
41 
42 #include <iostream>
43 #include <iomanip>
44 
45 #include "Sacado.hpp"
46 
47 // The function to differentiate
48 template <typename ScalarT>
49 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
50  ScalarT r = c*std::log(b+1.)/std::sin(a);
51 
52  return r;
53 }
54 
55 // The analytic derivative of func(a,b,c) with respect to a and b
56 void func_deriv(double a, double b, double c, double& drda, double& drdb)
57 {
58  drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2.))*std::cos(a);
59  drdb = c / ((b+1.)*std::sin(a));
60 }
61 
62 int main(int argc, char **argv)
63 {
64  double pi = std::atan(1.0)*4.0;
65 
66  // Values of function arguments
67  double a = pi/4;
68  double b = 2.0;
69  double c = 3.0;
70 
71  // Number of independent variables
72  int num_deriv = 2;
73 
74  // Fad objects
75  Sacado::Fad::DFad<double> afad(num_deriv, 0, a); // First (0) indep. var
76  Sacado::Fad::DFad<double> bfad(num_deriv, 1, b); // Second (1) indep. var
77  Sacado::Fad::DFad<double> cfad(c); // Passive variable
78  Sacado::Fad::DFad<double> rfad; // Result
79 
80  // Compute function
81  double r = func(a, b, c);
82 
83  // Compute derivative analytically
84  double drda, drdb;
85  func_deriv(a, b, c, drda, drdb);
86 
87  // Compute function and derivative with AD
88  rfad = func(afad, bfad, cfad);
89 
90  // Extract value and derivatives
91  double r_ad = rfad.val(); // r
92  double drda_ad = rfad.dx(0); // dr/da
93  double drdb_ad = rfad.dx(1); // dr/db
94 
95  // Print the results
96  int p = 4;
97  int w = p+7;
98  std::cout.setf(std::ios::scientific);
99  std::cout.precision(p);
100  std::cout << " r = " << r << " (original) == " << std::setw(w) << r_ad
101  << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
102  << "dr/da = " << std::setw(w) << drda << " (analytic) == "
103  << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w)
104  << drda - drda_ad << std::endl
105  << "dr/db = " << std::setw(w) << drdb << " (analytic) == "
106  << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w)
107  << drdb - drdb_ad << std::endl;
108 
109  double tol = 1.0e-14;
110  if (std::fabs(r - r_ad) < tol &&
111  std::fabs(drda - drda_ad) < tol &&
112  std::fabs(drdb - drdb_ad) < tol) {
113  std::cout << "\nExample passed!" << std::endl;
114  return 0;
115  }
116  else {
117  std::cout <<"\nSomething is wrong, example failed!" << std::endl;
118  return 1;
119  }
120 }
atan(expr.val())
KOKKOS_INLINE_FUNCTION mpl::enable_if_c< ExprLevel< Expr< T1 > >::value==ExprLevel< Expr< T2 > >::value, Expr< PowerOp< Expr< T1 >, Expr< T2 > > > >::type pow(const Expr< T1 > &expr1, const Expr< T2 > &expr2)
expr expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c *expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr2 expr1 expr2 expr1 expr1 expr1 c
int main()
Definition: ad_example.cpp:191
void func_deriv(double a, double b, double c, double &drda, double &drdb)
sin(expr.val())
log(expr.val())
const double tol
const T func(int n, T *x)
Definition: ad_example.cpp:49
fabs(expr.val())
cos(expr.val())