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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.runge_kutta4_classic"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template runge_kutta4_classic</span></h2>
  29 <p>boost::numeric::odeint::runge_kutta4_classic &#8212; The classical Runge-Kutta stepper of fourth order. </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_kutta4_classic_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/runge_kutta4_classic.hpp&gt;">boost/numeric/odeint/stepper/runge_kutta4_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_kutta4_classic.html" title="Class template runge_kutta4_classic">runge_kutta4_classic</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">explicit_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_stepper_base</span><span class="special">&lt;</span> <a class="link" href="runge_kutta4_classic.html" title="Class template runge_kutta4_classic">runge_kutta4_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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.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_kutta4_classic.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_kutta4_classic.html#boost.numeric.odeint.runge_kutta4_classicconstruct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_kutta4_classic.html#idp61717616-bb"><span class="identifier">runge_kutta4_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_kutta4_classic.html#idp61699472-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">&gt;</span>
  57     <span class="keyword">void</span> <a class="link" href="runge_kutta4_classic.html#idp61700032-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="special">;</span>
  59   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateType<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="runge_kutta4_classic.html#idp61713840-bb"><span class="identifier">adjust_size</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  60
  61   <span class="comment">// <a class="link" href="runge_kutta4_classic.html#idp61720896-bb">private member functions</a></span>
  62   <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_kutta4_classic.html#idp61721472-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>
  63 <span class="special">}</span><span class="special">;</span></pre></div>
  64 <div class="refsect1">
  65 <a name="idp98803904"></a><h2>Description</h2>
  66 <p>The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also <a href="http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods" target="_top">en.wikipedia.org/wiki/Runge-Kutta_methods</a> The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided. This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.</p>
  67 <p>This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). For more details see explicit_stepper_base.</p>
  68 <p>
  69 </p>
  70 <div class="refsect2">
  71 <a name="idp98806400"></a><h3>Template Parameters</h3>
  72 <div class="orderedlist"><ol class="orderedlist" type="1">
  73 <li class="listitem">
  74 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  75 <p>The state type. </p>
  76 </li>
  77 <li class="listitem">
  78 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
  79 <p>The value type. </p>
  80 </li>
  81 <li class="listitem">
  82 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
  83 <p>The type representing the time derivative of the state. </p>
  84 </li>
  85 <li class="listitem">
  86 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
  87 <p>The time representing the independent variable - the time. </p>
  88 </li>
  89 <li class="listitem">
  90 <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>
  91 <p>The algebra type. </p>
  92 </li>
  93 <li class="listitem">
  94 <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>
  95 <p>The operations type. </p>
  96 </li>
  97 <li class="listitem">
  98 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
  99 <p>The resizer policy type. </p>
 100 </li>
 101 </ol></div>
 102 </div>
 103 <div class="refsect2">
 104 <a name="idp98836768"></a><h3>
 105 <a name="boost.numeric.odeint.runge_kutta4_classicconstruct-copy-destruct"></a><code class="computeroutput">runge_kutta4_classic</code>
 106         public
 107        construct/copy/destruct</h3>
 108 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 109 <pre class="literallayout"><a name="idp61717616-bb"></a><span class="identifier">runge_kutta4_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_kutta4_classic.html" title="Class template runge_kutta4_classic">runge_kutta4_classic</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <p>
 110 </p>
 111 <div class="variablelist"><table border="0" class="variablelist compact">
 112 <colgroup>
 113 <col align="left" valign="top">
 114 <col>
 115 </colgroup>
 116 <tbody><tr>
 117 <td><p><span class="term">Parameters:</span></p></td>
 118 <td><div class="variablelist"><table border="0" class="variablelist compact">
 119 <colgroup>
 120 <col align="left" valign="top">
 121 <col>
 122 </colgroup>
 123 <tbody><tr>
 124 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 125 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 126 </tr></tbody>
 127 </table></div></td>
 128 </tr></tbody>
 129 </table></div>
 130 </li></ol></div>
 131 </div>
 132 <div class="refsect2">
 133 <a name="idp98851904"></a><h3>
 134 <a name="idp61699472-bb"></a><code class="computeroutput">runge_kutta4_classic</code> public member functions</h3>
 135 <div class="orderedlist"><ol class="orderedlist" type="1">
 136 <li class="listitem">
 137 <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>
 138          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 139   <span class="keyword">void</span> <a name="idp61700032-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>
 140                     <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>
 141 </p>
 142 <div class="variablelist"><table border="0" class="variablelist compact">
 143 <colgroup>
 144 <col align="left" valign="top">
 145 <col>
 146 </colgroup>
 147 <tbody><tr>
 148 <td><p><span class="term">Parameters:</span></p></td>
 149 <td><div class="variablelist"><table border="0" class="variablelist compact">
 150 <colgroup>
 151 <col align="left" valign="top">
 152 <col>
 153 </colgroup>
 154 <tbody>
 155 <tr>
 156 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 157 <td><p>The step size. </p></td>
 158 </tr>
 159 <tr>
 160 <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td>
 161 <td><p>The derivative of x at t. </p></td>
 162 </tr>
 163 <tr>
 164 <td><p><span class="term"><code class="computeroutput">in</code></span></p></td>
 165 <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td>
 166 </tr>
 167 <tr>
 168 <td><p><span class="term"><code class="computeroutput">out</code></span></p></td>
 169 <td><p>The result of the step is written in out. </p></td>
 170 </tr>
 171 <tr>
 172 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 173 <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td>
 174 </tr>
 175 <tr>
 176 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 177 <td><p>The value of the time, at which the step should be performed. </p></td>
 178 </tr>
 179 </tbody>
 180 </table></div></td>
 181 </tr></tbody>
 182 </table></div>
 183 </li>
 184 <li class="listitem">
 185 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateType<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idp61713840-bb"></a><span class="identifier">adjust_size</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">StateType</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>
 186 </p>
 187 <div class="variablelist"><table border="0" class="variablelist compact">
 188 <colgroup>
 189 <col align="left" valign="top">
 190 <col>
 191 </colgroup>
 192 <tbody><tr>
 193 <td><p><span class="term">Parameters:</span></p></td>
 194 <td><div class="variablelist"><table border="0" class="variablelist compact">
 195 <colgroup>
 196 <col align="left" valign="top">
 197 <col>
 198 </colgroup>
 199 <tbody><tr>
 200 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 201 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 202 </tr></tbody>
 203 </table></div></td>
 204 </tr></tbody>
 205 </table></div>
 206 </li>
 207 </ol></div>
 208 </div>
 209 <div class="refsect2">
 210 <a name="idp98902400"></a><h3>
 211 <a name="idp61720896-bb"></a><code class="computeroutput">runge_kutta4_classic</code> private member functions</h3>
 212 <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="idp61721472-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>
 213 </div>
 214 </div>
 215 </div>
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