EQ2EMu/EQ2/source/depends/boost_1_72_0/libs/numeric/odeint/doc/details_boost_range.qbk

[/============================================================================
  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]