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taylor_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// taylor_example
33//
34// usage:
35// taylor_example
36//
37// output:
38// prints the results of computing a single Taylor series expansion of
39// the solution to:
40//
41// dx/dt = 1 + x^2, x(0) = 1.0;
42//
43// The exact solution is x(t) = tan(t + pi/4)
44
45#include <iostream>
46
47#include "Sacado_No_Kokkos.hpp"
48
49// Function implementing RHS of ODE
50template <typename ScalarT>
51void func(ScalarT& f, const ScalarT& x) {
52 f = 1.0 + x*x;
53}
54
55int main(int argc, char **argv)
56{
57 double x0 = 1.0; // Initial condition
58 int deg = 40; // Degree of Taylor series solution
59
60 Sacado::Tay::Taylor<double> x = x0; // Taylor polynomial for independent
61 Sacado::Tay::Taylor<double> f; // Taylor polynomial for dependent
62
63 // Reserve space for degree deg coefficients
64 x.reserve(deg);
65
66 // Compute Taylor series solution to dx/dt = f(x)
67 for (int k=0; k<deg; k++) {
68 func(f, x);
69
70 // Set next coefficient
71 x.resize(k+1, true);
72
73 // x_{k+1} = f_k / (k+1)
74 x.fastAccessCoeff(k+1) = f.coeff(k) / (k+1);
75 }
76
77 // Print Taylor series solution
78 std::cout << "Taylor series solution = " << std::endl
79 << x << std::endl;
80
81 // Compute Taylor series expansion of solution x(t) = tan(t+pi/4)
82 double pi = std::atan(1.0)*4.0;
84 t.fastAccessCoeff(0) = pi/4.0;
85 t.fastAccessCoeff(1) = 1.0;
86 Sacado::Tay::Taylor<double> u = std::tan(t);
87
88 // Print expansion of solution
89 std::cout << "Exact expansion = " << std::endl
90 << u << std::endl;
91
92 // Compute maximum relative error
93 double max_err = 0.0;
94 double err = 0.0;
95 for (int k=0; k<=deg; k++) {
96 err = std::fabs(x.coeff(k) - u.coeff(k)) / (1.0 + fabs(u.coeff(k)));
97 if (err > max_err) max_err = err;
98 }
99 std::cout << "Maximum relative error = " << max_err << std::endl;
100
101 double tol = 1.0e-12;
102 if (max_err < tol){
103 std::cout << "\nExample passed!" << std::endl;
104 return 0;
105 }
106 else {
107 std::cout <<"\nSomething is wrong, example failed!" << std::endl;
108 return 1;
109 }
110}
111
112
113
fabs(expr.val())
int main()
Definition: ad_example.cpp:191
Taylor polynomial class.
T & fastAccessCoeff(int i)
Returns degree i term without bounds checking.
const T * coeff() const
Returns Taylor coefficient array.
void func(ScalarT &f, const ScalarT &x)
const double tol