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| <a name="boost.numeric.odeint.explicit_generic_rk"></a><div class="titlepage"></div> |
| <div class="refnamediv"> |
| <h2><span class="refentrytitle">Class template explicit_generic_rk</span></h2> |
| <p>boost::numeric::odeint::explicit_generic_rk — A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers. </p> |
| </div> |
| <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2> |
| <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../../header/boost/numeric/odeint/stepper/explicit_generic_rk_hpp.html" title="Header <boost/numeric/odeint/stepper/explicit_generic_rk.hpp>">boost/numeric/odeint/stepper/explicit_generic_rk.hpp</a>> |
| |
| </span><span class="keyword">template</span><span class="special"><</span><span class="identifier">size_t</span> StageCount<span class="special">,</span> <span class="identifier">size_t</span> Order<span class="special">,</span> <span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value<span class="special">,</span> |
| <span class="keyword">typename</span> Deriv<span class="special">,</span> <span class="keyword">typename</span> Time<span class="special">,</span> <span class="keyword">typename</span> Algebra<span class="special">,</span> <span class="keyword">typename</span> Operations<span class="special">,</span> |
| <span class="keyword">typename</span> Resizer<span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">explicit_stepper_base</span> <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="comment">// types</span> |
| <span class="keyword">typedef</span> <span class="identifier">explicit_stepper_base</span><span class="special"><</span> <span class="special">...</span> <span class="special">></span> <a name="boost.numeric.odeint.explicit_generic_rk.stepper_base_type"></a><span class="identifier">stepper_base_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">state_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.state_type"></a><span class="identifier">state_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">wrapped_state_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.wrapped_state_type"></a><span class="identifier">wrapped_state_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">value_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.value_type"></a><span class="identifier">value_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">deriv_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">wrapped_deriv_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.wrapped_deriv_type"></a><span class="identifier">wrapped_deriv_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">time_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.time_type"></a><span class="identifier">time_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">algebra_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">operations_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">resizer_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="emphasis"><em><span class="identifier">unspecified</span></em></span> <a name="boost.numeric.odeint.explicit_generic_rk.rk_algorithm_type"></a><span class="identifier">rk_algorithm_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_a_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.coef_a_type"></a><span class="identifier">coef_a_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_b_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.coef_b_type"></a><span class="identifier">coef_b_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_c_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.coef_c_type"></a><span class="identifier">coef_c_type</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="explicit_generic_rk.html#boost.numeric.odeint.explicit_generic_rkconstruct-copy-destruct">construct/copy/destruct</a></span> |
| <a class="link" href="explicit_generic_rk.html#idp40863552-bb"><span class="identifier">explicit_generic_rk</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">coef_a_type</span> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&</span><span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span> <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="explicit_generic_rk.html#idp40845408-bb">public member functions</a></span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span> |
| <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="explicit_generic_rk.html#idp40845968-bb"><span class="identifier">do_step_impl</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> |
| <span class="identifier">StateOut</span> <span class="special">&</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">void</span> <a class="link" href="explicit_generic_rk.html#idp40859776-bb"><span class="identifier">adjust_size</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="explicit_generic_rk.html#idp40870208-bb">private member functions</a></span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a class="link" href="explicit_generic_rk.html#idp40870784-bb"><span class="identifier">resize_impl</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| <span class="special">}</span><span class="special">;</span></pre></div> |
| <div class="refsect1"> |
| <a name="idp114450768"></a><h2>Description</h2> |
| <p>This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!</p> |
| <p>This class derives explicit_stepper_base which provides the stepper interface.</p> |
| <p> |
| </p> |
| <div class="refsect2"> |
| <a name="idp114452320"></a><h3>Template Parameters</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="identifier">size_t</span> StageCount</pre> |
| <p>The number of stages of the Runge-Kutta algorithm. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="identifier">size_t</span> Order</pre> |
| <p>The order of the stepper. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> State</pre> |
| <p>The type representing the state of the ODE. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Value</pre> |
| <p>The floating point type which is used in the computations. </p> |
| </li> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">typename</span> Deriv</pre></li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Time</pre> |
| <p>The type representing the independent variable - the time - of the ODE. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Algebra</pre> |
| <p>The algebra type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Operations</pre> |
| <p>The operations type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Resizer</pre> |
| <p>The resizer policy type. </p> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp114471696"></a><h3> |
| <a name="boost.numeric.odeint.explicit_generic_rkconstruct-copy-destruct"></a><code class="computeroutput">explicit_generic_rk</code> |
| public |
| construct/copy/destruct</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> |
| <pre class="literallayout"><a name="idp40863552-bb"></a><span class="identifier">explicit_generic_rk</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">coef_a_type</span> <span class="special">&</span> a<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&</span> b<span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&</span> c<span class="special">,</span> |
| <span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&</span> algebra <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a></code> class. See examples section for details on the coefficients. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">a</code></span></p></td> |
| <td><p>Triangular matrix of parameters b in the Butcher tableau. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td> |
| <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">b</code></span></p></td> |
| <td><p>Last row of the butcher tableau. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">c</code></span></p></td> |
| <td><p>Parameters to calculate the time points in the Butcher tableau. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li></ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp114498656"></a><h3> |
| <a name="idp40845408-bb"></a><code class="computeroutput">explicit_generic_rk</code> public member functions</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> System<span class="special">,</span> <span class="keyword">typename</span> StateIn<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span> |
| <span class="keyword">typename</span> StateOut<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp40845968-bb"></a><span class="identifier">do_step_impl</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> in<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&</span> dxdt<span class="special">,</span> |
| <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">StateOut</span> <span class="special">&</span> out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre>This method performs one step. The derivative <code class="computeroutput">dxdt</code> of <code class="computeroutput">in</code> at the time <code class="computeroutput">t</code> is passed to the method. The result is updated out of place, hence the input is in <code class="computeroutput">in</code> and the output in <code class="computeroutput">out</code>. Access to this step functionality is provided by explicit_stepper_base and <code class="computeroutput">do_step_impl</code> should not be called directly. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td> |
| <td><p>The step size. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td> |
| <td><p>The derivative of x at t. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">in</code></span></p></td> |
| <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">out</code></span></p></td> |
| <td><p>The result of the step is written in out. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">system</code></span></p></td> |
| <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td> |
| </tr> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">t</code></span></p></td> |
| <td><p>The value of the time, at which the step should be performed. </p></td> |
| </tr> |
| </tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">void</span> <a name="idp40859776-bb"></a><span class="identifier">adjust_size</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre>Adjust the size of all temporaries in the stepper manually. <p> |
| </p> |
| <div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term">Parameters:</span></p></td> |
| <td><div class="variablelist"><table border="0" class="variablelist compact"> |
| <colgroup> |
| <col align="left" valign="top"> |
| <col> |
| </colgroup> |
| <tbody><tr> |
| <td><p><span class="term"><code class="computeroutput">x</code></span></p></td> |
| <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td> |
| </tr></tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp114549152"></a><h3> |
| <a name="idp40870208-bb"></a><code class="computeroutput">explicit_generic_rk</code> private member functions</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> StateIn<span class="special">></span> <span class="keyword">bool</span> <a name="idp40870784-bb"></a><span class="identifier">resize_impl</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateIn</span> <span class="special">&</span> x<span class="special">)</span><span class="special">;</span></pre></li></ol></div> |
| </div> |
| </div> |
| </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> |
| <hr> |
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