1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
/* Boost numeric test of the runge kutta steppers test file
Copyright 2012 Mario Mulansky
Copyright 2012 Karsten Ahnert
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or
copy at http://www.boost.org/LICENSE_1_0.txt)
*/
// disable checked iterator warning for msvc
#include <boost/config.hpp>
#ifdef BOOST_MSVC
#pragma warning(disable:4996)
#endif
#define BOOST_TEST_MODULE numeric_runge_kutta
#include <iostream>
#include <cmath>
#include <boost/array.hpp>
#include <boost/test/unit_test.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/numeric/odeint.hpp>
using namespace boost::unit_test;
using namespace boost::numeric::odeint;
namespace mpl = boost::mpl;
typedef double value_type;
typedef boost::array< double , 2 > state_type;
// harmonic oscillator, analytic solution x[0] = sin( t )
struct osc
{
void operator()( const state_type &x , state_type &dxdt , const double t ) const
{
dxdt[0] = x[1];
dxdt[1] = -x[0];
}
};
/* reset dispatcher */
template< class StepperCategory >
struct resetter
{
template< class Stepper >
static void reset( Stepper &stepper ) { }
};
template< >
struct resetter< explicit_error_stepper_fsal_tag >
{
template< class Stepper >
static void reset( Stepper &stepper )
{ stepper.reset(); }
};
BOOST_AUTO_TEST_SUITE( numeric_runge_kutta_test )
/* generic test for all runge kutta steppers */
template< class Stepper >
struct perform_runge_kutta_test
{
void operator()( void )
{
Stepper stepper;
const int o = stepper.order()+1; //order of the error is order of approximation + 1
const state_type x0 = {{ 0.0 , 1.0 }};
state_type x1;
const double t = 0.0;
/* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
double dt = 0.5;
stepper.do_step( osc() , x0 , t , x1 , dt );
const double f = 2.0 * std::abs( sin(dt) - x1[0] ) / std::pow( dt , o ); // upper bound
std::cout << o << " , " << f << std::endl;
/* as long as we have errors above machine precision */
while( f*std::pow( dt , o ) > 1E-16 )
{
// reset stepper which require resetting (fsal steppers)
resetter< typename Stepper::stepper_category >::reset( stepper );
stepper.do_step( osc() , x0 , t , x1 , dt );
std::cout << "Testing dt=" << dt << std::endl;
BOOST_CHECK_LT( std::abs( sin(dt) - x1[0] ) , f*std::pow( dt , o ) );
dt *= 0.5;
}
}
};
/* generic error test for all runge kutta steppers */
template< class Stepper >
struct perform_runge_kutta_error_test
{
void operator()( void )
{
Stepper stepper;
const int o = stepper.error_order()+1; //order of the error is order of approximation + 1
const state_type x0 = {{ 0.0 , 1.0 }};
state_type x1 , x_err;
const double t = 0.0;
/* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
double dt = 0.5;
stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
const double f = 2.0 * std::abs( x_err[0] ) / std::pow( dt , o );
std::cout << o << " , " << f << " , " << x0[0] << std::endl;
/* as long as we have errors above machine precision */
while( f*std::pow( dt , o ) > 1E-16 )
{
// reset stepper which require resetting (fsal steppers)
resetter< typename Stepper::stepper_category >::reset( stepper );
stepper.do_step( osc() , x0 , t , x1 , dt , x_err );
std::cout << "Testing dt=" << dt << ": " << x_err[1] << std::endl;
BOOST_CHECK_SMALL( std::abs( x_err[0] ) , f*std::pow( dt , o ) );
dt *= 0.5;
}
}
};
typedef mpl::vector<
euler< state_type > ,
modified_midpoint< state_type > ,
runge_kutta4< state_type > ,
runge_kutta4_classic< state_type > ,
runge_kutta_cash_karp54_classic< state_type > ,
runge_kutta_cash_karp54< state_type > ,
runge_kutta_dopri5< state_type > ,
runge_kutta_fehlberg78< state_type >
> runge_kutta_steppers;
BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_test , Stepper, runge_kutta_steppers )
{
perform_runge_kutta_test< Stepper > tester;
tester();
}
typedef mpl::vector<
runge_kutta_cash_karp54_classic< state_type > ,
runge_kutta_cash_karp54< state_type > ,
runge_kutta_dopri5< state_type > ,
runge_kutta_fehlberg78< state_type >
> runge_kutta_error_steppers;
BOOST_AUTO_TEST_CASE_TEMPLATE( runge_kutta_error_test , Stepper, runge_kutta_error_steppers )
{
perform_runge_kutta_error_test< Stepper > tester;
tester();
}
BOOST_AUTO_TEST_SUITE_END()
|
