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| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_numeric_odeint.odeint_in_detail.using_boost__range"></a><a class="link" href="using_boost__range.html" title="Using boost::range">Using |
| boost::range</a> |
| </h3></div></div></div> |
| <p> |
| Most steppers in odeint also accept the state give as a range. A range is |
| sequence of values modeled by a range concept. See <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a> |
| for an overview over existing concepts and examples of ranges. This means |
| that the <code class="computeroutput"><span class="identifier">state_type</span></code> of the |
| stepper need not necessarily be used to call the <code class="computeroutput"><span class="identifier">do_step</span></code> |
| method. |
| </p> |
| <p> |
| One use-case for <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a> |
| in odeint has been shown in <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic |
| System</a> 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. |
| </p> |
| <p> |
| 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 <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a> |
| to solve only one individual oscillator in the chain. |
| </p> |
| <p> |
| In short, you can <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a> |
| to use one state within two system functions which expect states with different |
| sizes. |
| </p> |
| <p> |
| An example was given in the <a class="link" href="../tutorial/chaotic_systems_and_lyapunov_exponents.html" title="Chaotic systems and Lyapunov exponents">Chaotic |
| System</a> 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 <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>. Then you can use the <code class="computeroutput"><span class="identifier">range_iterator</span></code>-meta |
| function and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">end</span></code> to |
| obtain the iterators of your range: |
| </p> |
| <p> |
| </p> |
| <pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span> |
| <span class="special">{</span> |
| <span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">></span> |
| <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span> |
| <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="identifier">Deriv</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span> |
| |
| <span class="comment">// fill dxdt</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| 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: |
| </p> |
| <pre class="programlisting"><span class="keyword">class</span> <span class="identifier">sys</span> |
| <span class="special">{</span> |
| <span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">State</span> <span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Deriv</span> <span class="special">></span> |
| <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">&</span><span class="identifier">x_</span> <span class="special">,</span> <span class="identifier">Deriv</span> <span class="special">&</span><span class="identifier">dxdt_</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="keyword">const</span> <span class="identifier">State</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">x_</span> <span class="special">);</span> |
| <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_iterator</span><span class="special"><</span> <span class="identifier">Deriv</span> <span class="special">>::</span><span class="identifier">type</span> <span class="identifier">dxdt</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">begin</span><span class="special">(</span> <span class="identifier">dxdt_</span> <span class="special">);</span> |
| |
| <span class="identifier">dxdt</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f1</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span> |
| <span class="identifier">dxdt</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">f2</span><span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">);</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| </p> |
| <p> |
| The following two tables show which steppers and which algebras are compatible |
| with <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>. |
| </p> |
| <div class="table"> |
| <a name="boost_numeric_odeint.odeint_in_detail.using_boost__range.steppers_supporting_boost_range"></a><p class="title"><b>Table 1.9. Steppers supporting Boost.Range</b></p> |
| <div class="table-contents"><table class="table" summary="Steppers supporting Boost.Range"> |
| <colgroup><col></colgroup> |
| <thead><tr><th> |
| <p> |
| Stepper |
| </p> |
| </th></tr></thead> |
| <tbody> |
| <tr><td> |
| <p> |
| adams_bashforth_moulton |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| bulirsch_stoer_dense_out |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| bulirsch_stoer |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| controlled_runge_kutta |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| dense_output_runge_kutta |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| euler |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| explicit_error_generic_rk |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| explicit_generic_rk |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| rosenbrock4_controller |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| rosenbrock4_dense_output |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| rosenbrock4 |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta4_classic |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta4 |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta_cash_karp54_classic |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta_cash_karp54 |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta_dopri5 |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| runge_kutta_fehlberg78 |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| symplectic_euler |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| symplectic_rkn_sb3a_mclachlan |
| </p> |
| </td></tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"><div class="table"> |
| <a name="boost_numeric_odeint.odeint_in_detail.using_boost__range.algebras_supporting_boost_range"></a><p class="title"><b>Table 1.10. Algebras supporting Boost.Range</b></p> |
| <div class="table-contents"><table class="table" summary="Algebras supporting Boost.Range"> |
| <colgroup><col></colgroup> |
| <thead><tr><th> |
| <p> |
| algebra |
| </p> |
| </th></tr></thead> |
| <tbody> |
| <tr><td> |
| <p> |
| range_algebra |
| </p> |
| </td></tr> |
| <tr><td> |
| <p> |
| thrust_algebra |
| </p> |
| </td></tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"> |
| </div> |
| <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> |
| <td align="left"></td> |
| <td align="right"><div class="copyright-footer">Copyright © 2009-2012 Karsten |
| Ahnert and Mario Mulansky<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
| </p> |
| </div></td> |
| </tr></table> |
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