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1 | [/============================================================================ | |
2 | Boost.odeint | |
3 | ||
4 | Copyright 2012 Karsten Ahnert | |
5 | Copyright 2012 Mario Mulansky | |
6 | ||
7 | Use, modification and distribution is subject to the Boost Software License, | |
8 | Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at | |
9 | http://www.boost.org/LICENSE_1_0.txt) | |
10 | =============================================================================/] | |
11 | ||
12 | [section Using boost::range] | |
13 | ||
14 | Most steppers in odeint also accept the state give as a range. A range is | |
15 | sequence of values modeled by a range concept. See __boost_range for an | |
16 | overview over existing concepts and examples of ranges. This means that the | |
17 | `state_type` of the stepper need not necessarily be used to call the `do_step` method. | |
18 | ||
19 | One use-case for __boost_range in odeint has been shown in __tut_chaotic_system where the state consists of two parts: one for the original system and one for the perturbations. The ranges are used to initialize (solve) only the system part where the perturbation part is not touched, that is a range consisting only of the system part is used. After that the complete state including the perturbations is solved. | |
20 | ||
21 | Another use case is a system consisting of coupled units where you want to initialize each unit separately with the ODE of the uncoupled unit. An example is a chain of coupled van-der-Pol-oscillators which are initialized uniformly from the uncoupled van-der-Pol-oscillator. Then you can use __boost_range to solve only one individual oscillator in the chain. | |
22 | ||
23 | In short, you can __boost_range to use one state within two system functions which expect states with different sizes. | |
24 | ||
25 | An example was given in the __tut_chaotic_system tutorial. Using Boost.Range usually means that your system function needs to adapt to the iterators of Boost.Range. That is, your function is called with a range and you need to get the iterators from that range. This can easily be done. You have to implement your system as a class or a struct and you have to templatize the `operator()`. Then you can use the `range_iterator`-meta function and `boost::begin` and `boost::end` to obtain the iterators of your range: | |
26 | ||
27 | `` | |
28 | class sys | |
29 | { | |
30 | template< class State , class Deriv > | |
31 | void operator()( const State &x_ , Deriv &dxdt_ , double t ) const | |
32 | { | |
33 | typename boost::range_iterator< const State >::type x = boost::begin( x_ ); | |
34 | typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ ); | |
35 | ||
36 | // fill dxdt | |
37 | } | |
38 | }; | |
39 | `` | |
40 | ||
41 | If your range is a random access-range you can also apply the bracket operator to the iterator to access the elements in the range: | |
42 | `` | |
43 | class sys | |
44 | { | |
45 | template< class State , class Deriv > | |
46 | void operator()( const State &x_ , Deriv &dxdt_ , double t ) const | |
47 | { | |
48 | typename boost::range_iterator< const State >::type x = boost::begin( x_ ); | |
49 | typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ ); | |
50 | ||
51 | dxdt[0] = f1( x[0] , x[1] ); | |
52 | dxdt[1] = f2( x[0] , x[1] ); | |
53 | } | |
54 | }; | |
55 | `` | |
56 | ||
57 | The following two tables show which steppers and which algebras are compatible with __boost_range. | |
58 | [include range_table.qbk] | |
59 | ||
60 | [endsect] |