libs/numeric/odeint/doc/html/boost/numeric/odeint/explicit_generic_rk.html


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<title>Class template explicit_generic_rk</title>
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<div class="refentry">
<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 &#8212; 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: &lt;<a class="link" href="../../../header/boost/numeric/odeint/stepper/explicit_generic_rk_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/explicit_generic_rk.hpp&gt;">boost/numeric/odeint/stepper/explicit_generic_rk.hpp</a>&gt;

</span><span class="keyword">template</span><span class="special">&lt;</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">&gt;</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">&lt;</span> <span class="special">...</span> <span class="special">&gt;</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">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&amp;</span><span class="special">,</span> 
                      <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&amp;</span><span class="special">,</span> 
                      <span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</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">&lt;</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">&gt;</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">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">,</span> 
                      <span class="identifier">StateOut</span> <span class="special">&amp;</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">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</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">&amp;</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">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</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">&amp;</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">&amp;</span> a<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&amp;</span> b<span class="special">,</span> 
                    <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&amp;</span> c<span class="special">,</span> 
                    <span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</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">&lt;</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">&gt;</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">&amp;</span> in<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</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">&amp;</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">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</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">&amp;</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">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</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">&amp;</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 &#169; 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>
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