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
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
|
/*
[auto_generated]
libs/numeric/odeint/test/integrate.cpp
[begin_description]
This file tests the integrate function and its variants.
[end_description]
Copyright 2011-2012 Mario Mulansky
Copyright 2011-2012 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)
*/
#define BOOST_TEST_MODULE odeint_integrate_functions
#include <boost/type_traits.hpp>
#include <vector>
#include <cmath>
#include <iostream>
#include <boost/numeric/odeint/config.hpp>
#include <boost/array.hpp>
#include <boost/ref.hpp>
#include <boost/iterator/counting_iterator.hpp>
#include <boost/test/unit_test.hpp>
#include <boost/mpl/vector.hpp>
// nearly everything from odeint is used in these tests
#ifndef ODEINT_INTEGRATE_ITERATOR
#include <boost/numeric/odeint/integrate/integrate_const.hpp>
#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>
#include <boost/numeric/odeint/integrate/integrate_times.hpp>
#include <boost/numeric/odeint/integrate/integrate_n_steps.hpp>
#else
#include <boost/numeric/odeint/iterator/integrate/integrate_const.hpp>
#include <boost/numeric/odeint/iterator/integrate/integrate_adaptive.hpp>
#include <boost/numeric/odeint/iterator/integrate/integrate_times.hpp>
#include <boost/numeric/odeint/iterator/integrate/integrate_n_steps.hpp>
#endif
#include <boost/numeric/odeint/stepper/euler.hpp>
#include <boost/numeric/odeint/stepper/modified_midpoint.hpp>
#include <boost/numeric/odeint/stepper/runge_kutta4.hpp>
#include <boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp>
#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
#include <boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp>
#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
#include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp>
#include <boost/numeric/odeint/stepper/dense_output_runge_kutta.hpp>
#include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp>
#include <boost/numeric/odeint/stepper/adaptive_adams_bashforth_moulton.hpp>
#include <boost/numeric/odeint/stepper/controlled_adams_bashforth_moulton.hpp>
#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
using namespace boost::unit_test;
using namespace boost::numeric::odeint;
namespace mpl = boost::mpl;
typedef double value_type;
typedef std::vector< value_type > state_type;
void lorenz( const state_type &x , state_type &dxdt , const value_type t )
{
//const value_type sigma( 10.0 );
const value_type R( 28.0 );
const value_type b( value_type( 8.0 ) / value_type( 3.0 ) );
// first component trivial
dxdt[0] = 1.0; //sigma * ( x[1] - x[0] );
dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
dxdt[2] = -b * x[2] + x[0] * x[1];
}
struct push_back_time
{
std::vector< double >& m_times;
state_type& m_x;
push_back_time( std::vector< double > × , state_type &x )
: m_times( times ) , m_x( x ) { }
void operator()( const state_type &x , double t )
{
m_times.push_back( t );
boost::numeric::odeint::copy( x , m_x );
}
};
template< class Stepper >
struct perform_integrate_const_test
{
void operator()( const value_type t_end , const value_type dt )
{
// std::cout << "Testing integrate_const with " << typeid( Stepper ).name() << std::endl;
state_type x( 3 , 10.0 ) , x_end( 3 );
std::vector< value_type > times;
size_t steps = integrate_const( Stepper() , lorenz , x , 0.0 , t_end ,
dt , push_back_time( times , x_end ) );
std::cout.precision(16);
std::cout << t_end << " (" << dt << "), " << steps << " , " << times.size() << " , " << 10.0+dt*steps << "=" << x_end[0] << std::endl;
std::cout << static_cast<int>(floor(t_end/dt)) << " , " << t_end/dt << std::endl;
BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , static_cast<int>(floor(t_end/dt))+1 );
for( size_t i=0 ; i<times.size() ; ++i )
{
//std::cout << i << " , " << times[i] << " , " << static_cast< value_type >(i)*dt << std::endl;
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL( times[i] - static_cast< value_type >(i)*dt , (i+1) * 2E-16 );
}
// check first, trivial, component
BOOST_CHECK_SMALL( (10.0 + times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
//BOOST_CHECK_EQUAL( x[1] , x_end[1] );
//BOOST_CHECK_EQUAL( x[2] , x_end[2] );
}
};
template< class Stepper >
struct perform_integrate_adaptive_test
{
void operator()( const value_type t_end = 10.0 , const value_type dt = 0.03 )
{
// std::cout << "Testing integrate_adaptive with " << typeid( Stepper ).name() << std::endl;
state_type x( 3 , 10.0 ) , x_end( 3 );
std::vector< value_type > times;
size_t steps = integrate_adaptive( Stepper() , lorenz , x , 0.0 , t_end ,
dt , push_back_time( times , x_end ) );
// std::cout << t_end << " , " << steps << " , " << times.size() << " , " << dt << " , " << 10.0+t_end << "=" << x_end[0] << std::endl;
BOOST_CHECK_EQUAL( times.size() , steps+1 );
BOOST_CHECK_SMALL( times[0] - 0.0 , 2E-16 );
BOOST_CHECK_SMALL( times[times.size()-1] - t_end , times.size() * 2E-16 );
// check first, trivial, component
BOOST_CHECK_SMALL( (10.0 + t_end) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
}
};
template< class Stepper >
struct perform_integrate_times_test
{
void operator()( const int n = 10 , const int dn=1 , const value_type dt = 0.03 )
{
// std::cout << "Testing integrate_times with " << typeid( Stepper ).name() << std::endl;
state_type x( 3 ) , x_end( 3 );
x[0] = x[1] = x[2] = 10.0;
std::vector< double > times;
std::vector< double > obs_times( abs(n) );
for( int i=0 ; boost::numeric::odeint::detail::less_with_sign( static_cast<double>(i) ,
static_cast<double>(obs_times.size()) ,
dt ) ; i+=dn )
{
obs_times[i] = i;
}
// simple stepper
integrate_times( Stepper() , lorenz , x , obs_times.begin() , obs_times.end() ,
dt , push_back_time( times , x_end ) );
BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , abs(n) );
for( size_t i=0 ; i<times.size() ; ++i )
// check if observer was called at times 0,1,2,...
BOOST_CHECK_EQUAL( times[i] , static_cast<double>(i) );
// check first, trivial, component
BOOST_CHECK_SMALL( (10.0 + 1.0*times[times.size()-1]) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
}
};
template< class Stepper >
struct perform_integrate_n_steps_test
{
void operator()( const int n = 200 , const value_type dt = 0.01 )
{
// std::cout << "Testing integrate_n_steps with " << typeid( Stepper ).name() << ". ";
// std::cout << "dt=" << dt << std::endl;
state_type x( 3 ) , x_end( 3 );
x[0] = x[1] = x[2] = 10.0;
std::vector< double > times;
// simple stepper
value_type end_time = integrate_n_steps( Stepper() , lorenz , x , 0.0 , dt , n , push_back_time( times , x_end ) );
BOOST_CHECK_SMALL( end_time - n*dt , 2E-16 );
BOOST_CHECK_EQUAL( static_cast<int>(times.size()) , n+1 );
for( size_t i=0 ; i<times.size() ; ++i )
{
// check if observer was called at times 0,1,2,...
BOOST_CHECK_SMALL(times[i] - static_cast< value_type >(i) * dt, 2E-16);
}
// check first, trivial, component
BOOST_CHECK_SMALL( (10.0 + end_time) - x_end[0] , 1E-6 ); // precision of steppers: 1E-6
// BOOST_CHECK_EQUAL( x[1] , x_end[1] );
// BOOST_CHECK_EQUAL( x[2] , x_end[2] );
}
};
class stepper_methods : public mpl::vector<
euler< state_type > ,
modified_midpoint< state_type > ,
runge_kutta4< state_type > ,
runge_kutta_cash_karp54< state_type > ,
runge_kutta_dopri5< state_type > ,
runge_kutta_fehlberg78< state_type > ,
controlled_runge_kutta< runge_kutta_cash_karp54< state_type > > ,
controlled_runge_kutta< runge_kutta_dopri5< state_type > > ,
controlled_runge_kutta< runge_kutta_fehlberg78< state_type > > ,
bulirsch_stoer< state_type > ,
dense_output_runge_kutta< controlled_runge_kutta< runge_kutta_dopri5< state_type > > >,
adaptive_adams_bashforth_moulton<3, state_type>,
adaptive_adams_bashforth_moulton<5, state_type>,
adaptive_adams_bashforth_moulton<7, state_type>,
controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<3, state_type> >,
controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<5, state_type> >
//bulirsch_stoer_dense_out< state_type >
> { };
BOOST_AUTO_TEST_SUITE( integrate_test )
BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_const_test_case , Stepper, stepper_methods )
{
perform_integrate_const_test< Stepper > tester;
tester( 1.005 , 0.01 );
tester( 1.0 , 0.01 );
tester( 1.1 , 0.01 );
tester( -1.005 , -0.01 );
}
BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_adaptive_test_case , Stepper, stepper_methods )
{
perform_integrate_adaptive_test< Stepper > tester;
tester( 1.005 , 0.01 );
tester( 1.0 , 0.01 );
tester( 1.1 , 0.01 );
tester( -1.005 , -0.01 );
}
BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_times_test_case , Stepper, stepper_methods )
{
perform_integrate_times_test< Stepper > tester;
tester();
//tester( -10 , -0.01 );
}
BOOST_AUTO_TEST_CASE_TEMPLATE( integrate_n_steps_test_case , Stepper, stepper_methods )
{
if(!boost::is_same<Stepper, controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<3, state_type> > >::value &&
!boost::is_same<Stepper, controlled_adams_bashforth_moulton<adaptive_adams_bashforth_moulton<5, state_type> > >::value)
{
perform_integrate_n_steps_test< Stepper > tester;
tester();
tester( 200 , 0.01 );
tester( 200 , 0.01 );
tester( 200 , 0.01 );
tester( 200 , -0.01 );
}
}
BOOST_AUTO_TEST_SUITE_END()
|
