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| <a name="boost.numeric.odeint.runge_kutta_ca_idp41420064"></a><div class="titlepage"></div> |
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| <h2><span class="refentrytitle">Class template runge_kutta_cash_karp54_classic</span></h2> |
| <p>boost::numeric::odeint::runge_kutta_cash_karp54_classic — The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm. </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/runge_kutta_cash_karp54_classic_hpp.html" title="Header <boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp>">boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp</a>> |
| |
| </span><span class="keyword">template</span><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">double</span><span class="special">,</span> <span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span><span class="special">,</span> |
| <span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span><span class="special">,</span> |
| <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span> |
| <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span> |
| <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="runge_kutta_ca_idp41420064.html" title="Class template runge_kutta_cash_karp54_classic">runge_kutta_cash_karp54_classic</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">explicit_error_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_error_stepper_base</span><span class="special"><</span> <a class="link" href="runge_kutta_ca_idp41420064.html" title="Class template runge_kutta_cash_karp54_classic">runge_kutta_cash_karp54_classic</a><span class="special"><</span> <span class="special">...</span> <span class="special">></span><span class="special">,</span><span class="special">...</span> <span class="special">></span> <a name="boost.numeric.odeint.runge_kutta_ca_idp41420064.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.runge_kutta_ca_idp41420064.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">value_type</span> <a name="boost.numeric.odeint.runge_kutta_ca_idp41420064.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.runge_kutta_ca_idp41420064.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">time_type</span> <a name="boost.numeric.odeint.runge_kutta_ca_idp41420064.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.runge_kutta_ca_idp41420064.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.runge_kutta_ca_idp41420064.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.runge_kutta_ca_idp41420064.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="runge_kutta_ca_idp41420064.html#boost.numeric.odeint.runge_kutta_ca_idp41420064construct-copy-destruct">construct/copy/destruct</a></span> |
| <a class="link" href="runge_kutta_ca_idp41420064.html#idp41474448-bb"><span class="identifier">runge_kutta_cash_karp54_classic</span></a><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="runge_kutta_ca_idp41420064.html#idp41440032-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">typename</span> Err<span class="special">></span> |
| <span class="keyword">void</span> <a class="link" href="runge_kutta_ca_idp41420064.html#idp41440592-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="identifier">Err</span> <span class="special">&</span><span class="special">)</span><span class="special">;</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="runge_kutta_ca_idp41420064.html#idp41456864-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="runge_kutta_ca_idp41420064.html#idp41470672-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="runge_kutta_ca_idp41420064.html#idp41477744-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="runge_kutta_ca_idp41420064.html#idp41478320-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="idp117947904"></a><h2>Description</h2> |
| <p>The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_method" target="_top">en.wikipedia.org/wiki/Cash-Karp_method</a>. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.</p> |
| <p>This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.</p> |
| <p> |
| </p> |
| <div class="refsect2"> |
| <a name="idp117950352"></a><h3>Template Parameters</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> State</pre> |
| <p>The state type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre> |
| <p>The value type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre> |
| <p>The type representing the time derivative of the state. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre> |
| <p>The time representing the independent variable - the time. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">algebra_type</span></pre> |
| <p>The algebra type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special"><</span> <span class="identifier">State</span> <span class="special">></span><span class="special">::</span><span class="identifier">operations_type</span></pre> |
| <p>The operations type. </p> |
| </li> |
| <li class="listitem"> |
| <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre> |
| <p>The resizer policy type. </p> |
| </li> |
| </ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp117980640"></a><h3> |
| <a name="boost.numeric.odeint.runge_kutta_ca_idp41420064construct-copy-destruct"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</code> |
| public |
| construct/copy/destruct</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> |
| <pre class="literallayout"><a name="idp41474448-bb"></a><span class="identifier">runge_kutta_cash_karp54_classic</span><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="runge_kutta_ca_idp41420064.html" title="Class template runge_kutta_cash_karp54_classic">runge_kutta_cash_karp54_classic</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <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">algebra</code></span></p></td> |
| <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td> |
| </tr></tbody> |
| </table></div></td> |
| </tr></tbody> |
| </table></div> |
| </li></ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="idp117995840"></a><h3> |
| <a name="idp41440032-bb"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</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">typename</span> Err<span class="special">></span> |
| <span class="keyword">void</span> <a name="idp41440592-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="identifier">Err</span> <span class="special">&</span> xerr<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. <p>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>. Futhermore, an estimation of the error is stored in <code class="computeroutput">xerr</code>. Access to this step functionality is provided by explicit_error_stepper_base and <code class="computeroutput">do_step_impl</code> should not be called directly.</p> |
| <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> |
| <tr> |
| <td><p><span class="term"><code class="computeroutput">xerr</code></span></p></td> |
| <td><p>The result of the error estimation is written in xerr. </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> 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="idp41456864-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_error_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="idp41470672-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="idp118087984"></a><h3> |
| <a name="idp41477744-bb"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</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="idp41478320-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> |
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| <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>) |
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