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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.runge_kutta_ca_idp61774384"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template runge_kutta_cash_karp54_classic</span></h2>
  29 <p>boost::numeric::odeint::runge_kutta_cash_karp54_classic &#8212; The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm. </p>
  30 </div>
  31 <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
  32 <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/runge_kutta_cash_karp54_classic_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp&gt;">boost/numeric/odeint/stepper/runge_kutta_cash_karp54_classic.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</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>
  35          <span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span><span class="special">,</span>
  36          <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span>
  37          <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span>
  38          <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">&gt;</span>
  39 <span class="keyword">class</span> <a class="link" href="runge_kutta_ca_idp61774384.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>
  40 <span class="keyword">public</span><span class="special">:</span>
  41   <span class="comment">// types</span>
  42   <span class="keyword">typedef</span> <span class="identifier">explicit_error_stepper_base</span><span class="special">&lt;</span> <a class="link" href="runge_kutta_ca_idp61774384.html" title="Class template runge_kutta_cash_karp54_classic">runge_kutta_cash_karp54_classic</a><span class="special">&lt;</span> <span class="special">...</span> <span class="special">&gt;</span><span class="special">,</span><span class="special">...</span> <span class="special">&gt;</span> <a name="boost.numeric.odeint.runge_kutta_ca_idp61774384.stepper_base_type"></a><span class="identifier">stepper_base_type</span><span class="special">;</span>
  43   <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_idp61774384.state_type"></a><span class="identifier">state_type</span><span class="special">;</span>
  44   <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_idp61774384.value_type"></a><span class="identifier">value_type</span><span class="special">;</span>
  45   <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_idp61774384.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span>
  46   <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_idp61774384.time_type"></a><span class="identifier">time_type</span><span class="special">;</span>
  47   <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_idp61774384.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span>
  48   <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_idp61774384.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span>
  49   <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_idp61774384.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_kutta_ca_idp61774384.html#boost.numeric.odeint.runge_kutta_ca_idp61774384construct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_kutta_ca_idp61774384.html#idp61814944-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">&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>
  53
  54   <span class="comment">// <a class="link" href="runge_kutta_ca_idp61774384.html#idp61794352-bb">public member functions</a></span>
  55   <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>
  56            <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
  57     <span class="keyword">void</span> <a class="link" href="runge_kutta_ca_idp61774384.html#idp61794912-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>
  58                       <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="identifier">Err</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  59   <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>
  60            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  61     <span class="keyword">void</span> <a class="link" href="runge_kutta_ca_idp61774384.html#idp61803664-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>
  62                       <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>
  63   <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="runge_kutta_ca_idp61774384.html#idp61811168-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>
  64
  65   <span class="comment">// <a class="link" href="runge_kutta_ca_idp61774384.html#idp61818240-bb">private member functions</a></span>
  66   <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="runge_kutta_ca_idp61774384.html#idp61818816-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>
  67 <span class="special">}</span><span class="special">;</span></pre></div>
  68 <div class="refsect1">
  69 <a name="idp99380160"></a><h2>Description</h2>
  70 <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>
  71 <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>
  72 <p>
  73 </p>
  74 <div class="refsect2">
  75 <a name="idp99382608"></a><h3>Template Parameters</h3>
  76 <div class="orderedlist"><ol class="orderedlist" type="1">
  77 <li class="listitem">
  78 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  79 <p>The state type. </p>
  80 </li>
  81 <li class="listitem">
  82 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
  83 <p>The value type. </p>
  84 </li>
  85 <li class="listitem">
  86 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
  87 <p>The type representing the time derivative of the state. </p>
  88 </li>
  89 <li class="listitem">
  90 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
  91 <p>The time representing the independent variable - the time. </p>
  92 </li>
  93 <li class="listitem">
  94 <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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span></pre>
  95 <p>The algebra type. </p>
  96 </li>
  97 <li class="listitem">
  98 <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">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span></pre>
  99 <p>The operations type. </p>
 100 </li>
 101 <li class="listitem">
 102 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
 103 <p>The resizer policy type. </p>
 104 </li>
 105 </ol></div>
 106 </div>
 107 <div class="refsect2">
 108 <a name="idp99412976"></a><h3>
 109 <a name="boost.numeric.odeint.runge_kutta_ca_idp61774384construct-copy-destruct"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</code>
 110         public
 111        construct/copy/destruct</h3>
 112 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 113 <pre class="literallayout"><a name="idp61814944-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">&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="runge_kutta_ca_idp61774384.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>
 114 </p>
 115 <div class="variablelist"><table border="0" class="variablelist compact">
 116 <colgroup>
 117 <col align="left" valign="top">
 118 <col>
 119 </colgroup>
 120 <tbody><tr>
 121 <td><p><span class="term">Parameters:</span></p></td>
 122 <td><div class="variablelist"><table border="0" class="variablelist compact">
 123 <colgroup>
 124 <col align="left" valign="top">
 125 <col>
 126 </colgroup>
 127 <tbody><tr>
 128 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 129 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 130 </tr></tbody>
 131 </table></div></td>
 132 </tr></tbody>
 133 </table></div>
 134 </li></ol></div>
 135 </div>
 136 <div class="refsect2">
 137 <a name="idp99428160"></a><h3>
 138 <a name="idp61794352-bb"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</code> public member functions</h3>
 139 <div class="orderedlist"><ol class="orderedlist" type="1">
 140 <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>
 141          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 142   <span class="keyword">void</span> <a name="idp61794912-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>
 143                     <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="identifier">Err</span> <span class="special">&amp;</span> xerr<span class="special">)</span><span class="special">;</span></pre></li>
 144 <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>
 145          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 146   <span class="keyword">void</span> <a name="idp61803664-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>
 147                     <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></li>
 148 <li class="listitem">
 149 <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="idp61811168-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>
 150 </p>
 151 <div class="variablelist"><table border="0" class="variablelist compact">
 152 <colgroup>
 153 <col align="left" valign="top">
 154 <col>
 155 </colgroup>
 156 <tbody><tr>
 157 <td><p><span class="term">Parameters:</span></p></td>
 158 <td><div class="variablelist"><table border="0" class="variablelist compact">
 159 <colgroup>
 160 <col align="left" valign="top">
 161 <col>
 162 </colgroup>
 163 <tbody><tr>
 164 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 165 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 166 </tr></tbody>
 167 </table></div></td>
 168 </tr></tbody>
 169 </table></div>
 170 </li>
 171 </ol></div>
 172 </div>
 173 <div class="refsect2">
 174 <a name="idp99490000"></a><h3>
 175 <a name="idp61818240-bb"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</code> private member functions</h3>
 176 <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="idp61818816-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>
 177 </div>
 178 </div>
 179 </div>
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 183         Distributed under the Boost Software License, Version 1.0. (See accompanying
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