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trad_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// trad_dfad_example
33//
34// usage:
35// trad_dfad_example
36//
37// output:
38// prints the results of computing the second derivative a simple function // with forward nested forward and reverse mode AD using the
39// Sacado::Fad::DFad and Sacado::Rad::ADvar classes.
40
41#include <iostream>
42#include <iomanip>
43
44#include "Sacado_No_Kokkos.hpp"
45
46// The function to differentiate
47template <typename ScalarT>
48ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
49 ScalarT r = c*std::log(b+1.)/std::sin(a);
50 return r;
51}
52
53// The analytic derivative of func(a,b,c) with respect to a and b
54void func_deriv(double a, double b, double c, double& drda, double& drdb)
55{
56 drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2.))*std::cos(a);
57 drdb = c / ((b+1.)*std::sin(a));
58}
59
60// The analytic second derivative of func(a,b,c) with respect to a and b
61void func_deriv2(double a, double b, double c, double& d2rda2, double& d2rdb2,
62 double& d2rdadb)
63{
64 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.);
65 d2rdb2 = -c / (std::pow(b+1.,2.)*std::sin(a));
66 d2rdadb = -c / ((b+1.)*std::pow(std::sin(a),2.))*std::cos(a);
67}
68
69int main(int argc, char **argv)
70{
71 double pi = std::atan(1.0)*4.0;
72
73 // Values of function arguments
74 double a = pi/4;
75 double b = 2.0;
76 double c = 3.0;
77
78 // Number of independent variables
79 int num_deriv = 2;
80
81 // Fad objects
83 Sacado::Fad::DFad<double>(num_deriv, 0, a);
85 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 rrad = func(arad, brad, crad);
102
104
105 // Extract value and derivatives
106 double r_ad = rrad.val().val(); // r
107 double drda_ad = arad.adj().val(); // dr/da
108 double drdb_ad = brad.adj().val(); // dr/db
109 double d2rda2_ad = arad.adj().dx(0); // d^2r/da^2
110 double d2rdadb_ad = arad.adj().dx(1); // d^2r/dadb
111 double d2rdbda_ad = brad.adj().dx(0); // d^2r/dbda
112 double d2rdb2_ad = brad.adj().dx(1); // d^2/db^2
113
114 // Print the results
115 int p = 4;
116 int w = p+7;
117 std::cout.setf(std::ios::scientific);
118 std::cout.precision(p);
119 std::cout << " r = " << std::setw(w) << r << " (original) == "
120 << std::setw(w) << r_ad << " (AD) Error = " << std::setw(w)
121 << r - r_ad << std::endl
122 << " dr/da = " << std::setw(w) << drda << " (analytic) == "
123 << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w)
124 << drda - drda_ad << std::endl
125 << " dr/db = " << std::setw(w) << drdb << " (analytic) == "
126 << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w)
127 << drdb - drdb_ad << std::endl
128 << "d^2r/da^2 = " << std::setw(w) << d2rda2 << " (analytic) == "
129 << std::setw(w) << d2rda2_ad << " (AD) Error = " << std::setw(w)
130 << d2rda2 - d2rda2_ad << std::endl
131 << "d^2r/db^2 = " << std::setw(w) << d2rdb2 << " (analytic) == "
132 << std::setw(w) << d2rdb2_ad << " (AD) Error = " << std::setw(w)
133 << d2rdb2 - d2rdb2_ad << std::endl
134 << "d^2r/dadb = " << std::setw(w) << d2rdadb << " (analytic) == "
135 << std::setw(w) << d2rdadb_ad << " (AD) Error = " << std::setw(w)
136 << d2rdadb - d2rdadb_ad << std::endl
137 << "d^2r/dbda = " << std::setw(w) << d2rdadb << " (analytic) == "
138 << std::setw(w) << d2rdbda_ad << " (AD) Error = " << std::setw(w)
139 << d2rdadb - d2rdbda_ad << std::endl;
140
141 // Free Rad's memory to avoid memory leaks. The zero_out() call is
142 // necessary to destroy dynamically allocated DFad arrays (which are
143 // stored outside of Rad's memory management).
146
147 double tol = 1.0e-14;
148 if (std::fabs(r - r_ad) < tol &&
149 std::fabs(drda - drda_ad) < tol &&
150 std::fabs(drdb - drdb_ad) < tol &&
151 std::fabs(d2rda2 - d2rda2_ad) < tol &&
152 std::fabs(d2rdb2 - d2rdb2_ad) < tol &&
153 std::fabs(d2rdadb - d2rdadb_ad) < tol) {
154 std::cout << "\nExample passed!" << std::endl;
155 return 0;
156 }
157 else {
158 std::cout <<"\nSomething is wrong, example failed!" << std::endl;
159 return 1;
160 }
161}
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
const char * p
void func_deriv(double a, double b, double c, double &drda, double &drdb)
void func_deriv2(double a, double b, double c, double &d2rda2, double &d2rdb2, double &d2rdadb)
ScalarT func(const ScalarT &a, const ScalarT &b, const ScalarT &c)
const double tol