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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.extrapolation_stepper"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template extrapolation_stepper</span></h2>
  29 <p>boost::numeric::odeint::extrapolation_stepper &#8212; Extrapolation stepper with configurable order, and error estimation. </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/extrapolation_stepper_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/extrapolation_stepper.hpp&gt;">boost/numeric/odeint/stepper/extrapolation_stepper.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">short</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">double</span><span class="special">,</span>
  35          <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>
  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="extrapolation_stepper.html" title="Class template extrapolation_stepper">extrapolation_stepper</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="extrapolation_stepper.html" title="Class template extrapolation_stepper">extrapolation_stepper</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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.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.extrapolation_stepper.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50   <span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span>                                                  <a name="boost.numeric.odeint.extrapolation_stepper.order_type"></a><span class="identifier">order_type</span><span class="special">;</span>
  51
  52   <span class="comment">// <a class="link" href="extrapolation_stepper.html#boost.numeric.odeint.extrapolation_stepperconstruct-copy-destruct">construct/copy/destruct</a></span>
  53   <a class="link" href="extrapolation_stepper.html#idm45853739192848-bb"><span class="identifier">extrapolation_stepper</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>
  54
  55   <span class="comment">// <a class="link" href="extrapolation_stepper.html#idm45853739251808-bb">private member functions</a></span>
  56    <a class="link" href="extrapolation_stepper.html#idm45853739251232-bb"><span class="identifier">BOOST_STATIC_ASSERT_MSG</span></a><span class="special">(</span><span class="special">(</span><span class="special">(</span><span class="identifier">Order</span> <span class="special">%</span> <span class="number">2</span><span class="special">)</span><span class="special">==</span><span class="number">0</span><span class="special">)</span> <span class="special">&amp;&amp;</span><span class="special">(</span><span class="identifier">Order</span> <span class="special">&gt;</span> <span class="number">2</span><span class="special">)</span><span class="special">,</span>
  57                            <span class="string">"extrapolation_stepper requires even Order larger than 2"</span><span class="special">)</span><span class="special">;</span>
  58   <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="extrapolation_stepper.html#idm45853739249104-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>
  59   <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="extrapolation_stepper.html#idm45853739246720-bb"><span class="identifier">resize_m_xout</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>
  60   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
  61     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739244336-bb"><span class="identifier">extrapolate</span></a><span class="special">(</span><span class="identifier">size_t</span><span class="special">,</span> <span class="identifier">state_table_type</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">value_matrix</span> <span class="special">&amp;</span><span class="special">,</span>
  62                      <span class="identifier">StateInOut</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  63
  64   <span class="comment">// <a class="link" href="extrapolation_stepper.html#idm45853739239728-bb">public member functions</a></span>
  65   <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>
  66            <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
  67     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739239168-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>
  68                       <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>
  69   <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span>
  70            <span class="keyword">typename</span> Err<span class="special">&gt;</span>
  71     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739230416-bb"><span class="identifier">do_step_impl_io</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</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>
  72                          <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>
  73   <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>
  74            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  75     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739222912-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>
  76                       <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>
  77   <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">&gt;</span>
  78     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739215408-bb"><span class="identifier">do_step_impl_io</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</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>
  79                          <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  80   <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">&gt;</span>
  81     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739209152-bb"><span class="identifier">do_step_dxdt_impl</span></a><span class="special">(</span><span class="identifier">System</span><span class="special">,</span> <span class="identifier">StateInOut</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>
  82                            <span class="identifier">time_type</span><span class="special">)</span><span class="special">;</span>
  83   <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>
  84            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  85     <span class="keyword">void</span> <a class="link" href="extrapolation_stepper.html#idm45853739202896-bb"><span class="identifier">do_step_dxdt_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>
  86                            <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>
  87   <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="extrapolation_stepper.html#idm45853739195392-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>
  88
  89   <span class="comment">// public data members</span>
  90   <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">order_type</span> <span class="identifier">order_value</span><span class="special">;</span>
  91   <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">order_type</span> <span class="identifier">stepper_order_value</span><span class="special">;</span>
  92   <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">order_type</span> <span class="identifier">error_order_value</span><span class="special">;</span>
  93   <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">size_t</span> <span class="identifier">m_k_max</span><span class="special">;</span>
  94 <span class="special">}</span><span class="special">;</span></pre></div>
  95 <div class="refsect1">
  96 <a name="idm45221358821040"></a><h2>Description</h2>
  97 <p>The extrapolation stepper is a stepper with error estimation and configurable order. The order is given as template parameter and needs to be an <span class="emphasis"><em>odd</em></span> number. The stepper is based on several executions of the modified midpoint method and a Richardson extrapolation. This is essentially the same technique as for <a class="link" href="bulirsch_stoer.html" title="Class template bulirsch_stoer">bulirsch_stoer</a>, but without the variable order.</p>
  98 <div class="note"><table border="0" summary="Note">
  99 <tr>
 100 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
 101 <th align="left">Note</th>
 102 </tr>
 103 <tr><td align="left" valign="top"><p>The Order parameter has to be an even number greater 2. </p></td></tr>
 104 </table></div>
 105 <p>
 106 </p>
 107 <div class="refsect2">
 108 <a name="idm45221358817920"></a><h3>
 109 <a name="boost.numeric.odeint.extrapolation_stepperconstruct-copy-destruct"></a><code class="computeroutput">extrapolation_stepper</code>
 110         public
 111        construct/copy/destruct</h3>
 112 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><a name="idm45853739192848-bb"></a><span class="identifier">extrapolation_stepper</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></li></ol></div>
 113 </div>
 114 <div class="refsect2">
 115 <a name="idm45221358807504"></a><h3>
 116 <a name="idm45853739251808-bb"></a><code class="computeroutput">extrapolation_stepper</code> private member functions</h3>
 117 <div class="orderedlist"><ol class="orderedlist" type="1">
 118 <li class="listitem"><pre class="literallayout"> <a name="idm45853739251232-bb"></a><span class="identifier">BOOST_STATIC_ASSERT_MSG</span><span class="special">(</span><span class="special">(</span><span class="special">(</span><span class="identifier">Order</span> <span class="special">%</span> <span class="number">2</span><span class="special">)</span><span class="special">==</span><span class="number">0</span><span class="special">)</span> <span class="special">&amp;&amp;</span><span class="special">(</span><span class="identifier">Order</span> <span class="special">&gt;</span> <span class="number">2</span><span class="special">)</span><span class="special">,</span>
 119                          <span class="string">"extrapolation_stepper requires even Order larger than 2"</span><span class="special">)</span><span class="special">;</span></pre></li>
 120 <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="idm45853739249104-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>
 121 <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="idm45853739246720-bb"></a><span class="identifier">resize_m_xout</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>
 122 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateInOut<span class="special">&gt;</span>
 123   <span class="keyword">void</span> <a name="idm45853739244336-bb"></a><span class="identifier">extrapolate</span><span class="special">(</span><span class="identifier">size_t</span> k<span class="special">,</span> <span class="identifier">state_table_type</span> <span class="special">&amp;</span> table<span class="special">,</span>
 124                    <span class="keyword">const</span> <span class="identifier">value_matrix</span> <span class="special">&amp;</span> coeff<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</span> xest<span class="special">)</span><span class="special">;</span></pre></li>
 125 </ol></div>
 126 </div>
 127 <div class="refsect2">
 128 <a name="idm45221358759472"></a><h3>
 129 <a name="idm45853739239728-bb"></a><code class="computeroutput">extrapolation_stepper</code> public member functions</h3>
 130 <div class="orderedlist"><ol class="orderedlist" type="1">
 131 <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>
 132          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 133   <span class="keyword">void</span> <a name="idm45853739239168-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>
 134                     <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>
 135 <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 136   <span class="keyword">void</span> <a name="idm45853739230416-bb"></a><span class="identifier">do_step_impl_io</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</span> inout<span class="special">,</span>
 137                        <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">time_type</span> dt<span class="special">,</span>
 138                        <span class="identifier">Err</span> <span class="special">&amp;</span> xerr<span class="special">)</span><span class="special">;</span></pre></li>
 139 <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>
 140          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 141   <span class="keyword">void</span> <a name="idm45853739222912-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>
 142                     <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>
 143 <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">&gt;</span>
 144   <span class="keyword">void</span> <a name="idm45853739215408-bb"></a><span class="identifier">do_step_impl_io</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</span> inout<span class="special">,</span>
 145                        <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">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li>
 146 <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> StateInOut<span class="special">,</span> <span class="keyword">typename</span> DerivIn<span class="special">&gt;</span>
 147   <span class="keyword">void</span> <a name="idm45853739209152-bb"></a><span class="identifier">do_step_dxdt_impl</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">StateInOut</span> <span class="special">&amp;</span> x<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span> dxdt<span class="special">,</span>
 148                          <span class="identifier">time_type</span> t<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li>
 149 <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>
 150          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 151   <span class="keyword">void</span> <a name="idm45853739202896-bb"></a><span class="identifier">do_step_dxdt_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>
 152                          <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>
 153                          <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li>
 154 <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="idm45853739195392-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></li>
 155 </ol></div>
 156 </div>
 157 </div>
 158 </div>
 159 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 160 <td align="left"></td>
 161 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 162         Distributed under the Boost Software License, Version 1.0. (See accompanying
 163         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>)
 164       </p>
 165 </div></td>
 166 </tr></table>
 167 <hr>
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