| [/============================================================================ |
| Boost.odeint |
| |
| Copyright 2012 Karsten Ahnert |
| Copyright 2012 Mario Mulansky |
| |
| Use, modification and distribution is subject to 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) |
| =============================================================================/] |
| |
| [section Using boost::range] |
| |
| Most steppers in odeint also accept the state give as a range. A range is |
| sequence of values modeled by a range concept. See __boost_range for an |
| overview over existing concepts and examples of ranges. This means that the |
| `state_type` of the stepper need not necessarily be used to call the `do_step` method. |
| |
| 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. |
| |
| 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. |
| |
| In short, you can __boost_range to use one state within two system functions which expect states with different sizes. |
| |
| 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: |
| |
| `` |
| class sys |
| { |
| template< class State , class Deriv > |
| void operator()( const State &x_ , Deriv &dxdt_ , double t ) const |
| { |
| typename boost::range_iterator< const State >::type x = boost::begin( x_ ); |
| typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ ); |
| |
| // fill dxdt |
| } |
| }; |
| `` |
| |
| 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: |
| `` |
| class sys |
| { |
| template< class State , class Deriv > |
| void operator()( const State &x_ , Deriv &dxdt_ , double t ) const |
| { |
| typename boost::range_iterator< const State >::type x = boost::begin( x_ ); |
| typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ ); |
| |
| dxdt[0] = f1( x[0] , x[1] ); |
| dxdt[1] = f2( x[0] , x[1] ); |
| } |
| }; |
| `` |
| |
| The following two tables show which steppers and which algebras are compatible with __boost_range. |
| [include range_table.qbk] |
| |
| [endsect] |