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dfad_dfad_example.cpp
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29 
30 // dfad_dfad_example
31 //
32 // usage:
33 // dfad_dfad_example
34 //
35 // output:
36 // prints the results of computing the second derivative a simple function // with forward nested forward mode AD using the Sacado::Fad::DFad class
37 // (uses dynamic memory allocation for number of derivative components).
38 
39 #include <iostream>
40 #include <iomanip>
41 
42 #include "Sacado.hpp"
43 
44 // The function to differentiate
45 template <typename ScalarT>
46 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
47  ScalarT r = c*std::log(b+1.)/std::sin(a);
48  return r;
49 }
50 
51 // The analytic derivative of func(a,b,c) with respect to a and b
52 void func_deriv(double a, double b, double c, double& drda, double& drdb)
53 {
54  drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2.))*std::cos(a);
55  drdb = c / ((b+1.)*std::sin(a));
56 }
57 
58 // The analytic second derivative of func(a,b,c) with respect to a and b
59 void func_deriv2(double a, double b, double c, double& d2rda2, double& d2rdb2,
60  double& d2rdadb)
61 {
62  d2rda2 = c*std::log(b+1.)/std::sin(a) + 2.*(c*std::log(b+1.)/std::pow(std::sin(a),3.))*std::pow(std::cos(a),2.);
63  d2rdb2 = -c / (std::pow(b+1.,2.)*std::sin(a));
64  d2rdadb = -c / ((b+1.)*std::pow(std::sin(a),2.))*std::cos(a);
65 }
66 
67 int main(int argc, char **argv)
68 {
69  double pi = std::atan(1.0)*4.0;
70 
71  // Values of function arguments
72  double a = pi/4;
73  double b = 2.0;
74  double c = 3.0;
75 
76  // Number of independent variables
77  int num_deriv = 2;
78 
79  // Fad objects
81  Sacado::Fad::DFad<DFadType> afad(num_deriv, 0, a);
82  Sacado::Fad::DFad<DFadType> bfad(num_deriv, 1, b);
85 
86  afad.val() = Sacado::Fad::DFad<double>(num_deriv, 0, a);
87  bfad.val() = Sacado::Fad::DFad<double>(num_deriv, 1, b);
88 
89  // Compute function
90  double r = func(a, b, c);
91 
92  // Compute derivative analytically
93  double drda, drdb;
94  func_deriv(a, b, c, drda, drdb);
95 
96  // Compute second derivative analytically
97  double d2rda2, d2rdb2, d2rdadb;
98  func_deriv2(a, b, c, d2rda2, d2rdb2, d2rdadb);
99 
100  // Compute function and derivative with AD
101  rfad = func(afad, bfad, cfad);
102 
103  // Extract value and derivatives
104  double r_ad = rfad.val().val(); // r
105  double drda_ad = rfad.dx(0).val(); // dr/da
106  double drdb_ad = rfad.dx(1).val(); // dr/db
107  double d2rda2_ad = rfad.dx(0).dx(0); // d^2r/da^2
108  double d2rdadb_ad = rfad.dx(0).dx(1); // d^2r/dadb
109  double d2rdbda_ad = rfad.dx(1).dx(0); // d^2r/dbda
110  double d2rdb2_ad = rfad.dx(1).dx(1); // d^2/db^2
111 
112  // Print the results
113  int p = 4;
114  int w = p+7;
115  std::cout.setf(std::ios::scientific);
116  std::cout.precision(p);
117  std::cout << " r = " << std::setw(w) << r << " (original) == "
118  << std::setw(w) << r_ad << " (AD) Error = " << std::setw(w)
119  << r - r_ad << std::endl
120  << " dr/da = " << std::setw(w) << drda << " (analytic) == "
121  << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w)
122  << drda - drda_ad << std::endl
123  << " dr/db = " << std::setw(w) << drdb << " (analytic) == "
124  << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w)
125  << drdb - drdb_ad << std::endl
126  << "d^2r/da^2 = " << std::setw(w) << d2rda2 << " (analytic) == "
127  << std::setw(w) << d2rda2_ad << " (AD) Error = " << std::setw(w)
128  << d2rda2 - d2rda2_ad << std::endl
129  << "d^2r/db^2 = " << std::setw(w) << d2rdb2 << " (analytic) == "
130  << std::setw(w) << d2rdb2_ad << " (AD) Error = " << std::setw(w)
131  << d2rdb2 - d2rdb2_ad << std::endl
132  << "d^2r/dadb = " << std::setw(w) << d2rdadb << " (analytic) == "
133  << std::setw(w) << d2rdadb_ad << " (AD) Error = " << std::setw(w)
134  << d2rdadb - d2rdadb_ad << std::endl
135  << "d^2r/dbda = " << std::setw(w) << d2rdadb << " (analytic) == "
136  << std::setw(w) << d2rdbda_ad << " (AD) Error = " << std::setw(w)
137  << d2rdadb - d2rdbda_ad << std::endl;
138 
139  double tol = 1.0e-14;
140  if (std::fabs(r - r_ad) < tol &&
141  std::fabs(drda - drda_ad) < tol &&
142  std::fabs(drdb - drdb_ad) < tol &&
143  std::fabs(d2rda2 - d2rda2_ad) < tol &&
144  std::fabs(d2rdb2 - d2rdb2_ad) < tol &&
145  std::fabs(d2rdadb - d2rdadb_ad) < tol) {
146  std::cout << "\nExample passed!" << std::endl;
147  return 0;
148  }
149  else {
150  std::cout <<"\nSomething is wrong, example failed!" << std::endl;
151  return 1;
152  }
153 }
Sacado::Fad::DFad< double > DFadType
void func_deriv2(double a, double b, double c, double &d2rda2, double &d2rdb2, double &d2rdadb)
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())