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dfad_example.cpp
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1// $Id$
2// $Source$
3// @HEADER
4// ***********************************************************************
5//
6// Sacado Package
7// Copyright (2006) Sandia Corporation
8//
9// Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
10// the U.S. Government retains certain rights in this software.
11//
12// This library is free software; you can redistribute it and/or modify
13// it under the terms of the GNU Lesser General Public License as
14// published by the Free Software Foundation; either version 2.1 of the
15// License, or (at your option) any later version.
16//
17// This library is distributed in the hope that it will be useful, but
18// WITHOUT ANY WARRANTY; without even the implied warranty of
19// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
20// Lesser General Public License for more details.
21//
22// You should have received a copy of the GNU Lesser General Public
23// License along with this library; if not, write to the Free Software
24// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
25// USA
26// Questions? Contact David M. Gay (dmgay@sandia.gov) or Eric T. Phipps
27// (etphipp@sandia.gov).
28//
29// ***********************************************************************
30// @HEADER
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
48template <typename ScalarT>
49ScalarT 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
56void 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
62int 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}
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)
ScalarT func(const ScalarT &a, const ScalarT &b, const ScalarT &c)
const char * p
const double tol