| Brian Silverman | 7c33ab2 | 2018-08-04 17:14:51 -0700 | [diff] [blame^] | 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] |