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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.explicit_generic_rk"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template explicit_generic_rk</span></h2>
  29 <p>boost::numeric::odeint::explicit_generic_rk &#8212; A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers. </p>
  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/explicit_generic_rk_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/explicit_generic_rk.hpp&gt;">boost/numeric/odeint/stepper/explicit_generic_rk.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="identifier">size_t</span> StageCount<span class="special">,</span> <span class="identifier">size_t</span> Order<span class="special">,</span> <span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value<span class="special">,</span>
  35          <span class="keyword">typename</span> Deriv<span class="special">,</span> <span class="keyword">typename</span> Time<span class="special">,</span> <span class="keyword">typename</span> Algebra<span class="special">,</span> <span class="keyword">typename</span> Operations<span class="special">,</span>
  36          <span class="keyword">typename</span> Resizer<span class="special">&gt;</span>
  37 <span class="keyword">class</span> <a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">explicit_stepper_base</span> <span class="special">{</span>
  38 <span class="keyword">public</span><span class="special">:</span>
  39   <span class="comment">// types</span>
  40   <span class="keyword">typedef</span> <span class="identifier">explicit_stepper_base</span><span class="special">&lt;</span> <span class="special">...</span> <span class="special">&gt;</span>          <a name="boost.numeric.odeint.explicit_generic_rk.stepper_base_type"></a><span class="identifier">stepper_base_type</span><span class="special">;</span>
  41   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">state_type</span>         <a name="boost.numeric.odeint.explicit_generic_rk.state_type"></a><span class="identifier">state_type</span><span class="special">;</span>
  42   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">wrapped_state_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.wrapped_state_type"></a><span class="identifier">wrapped_state_type</span><span class="special">;</span>
  43   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">value_type</span>         <a name="boost.numeric.odeint.explicit_generic_rk.value_type"></a><span class="identifier">value_type</span><span class="special">;</span>
  44   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">deriv_type</span>         <a name="boost.numeric.odeint.explicit_generic_rk.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span>
  45   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">wrapped_deriv_type</span> <a name="boost.numeric.odeint.explicit_generic_rk.wrapped_deriv_type"></a><span class="identifier">wrapped_deriv_type</span><span class="special">;</span>
  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.explicit_generic_rk.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.explicit_generic_rk.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.explicit_generic_rk.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.explicit_generic_rk.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50   <span class="keyword">typedef</span> <span class="emphasis"><em><span class="identifier">unspecified</span></em></span>                           <a name="boost.numeric.odeint.explicit_generic_rk.rk_algorithm_type"></a><span class="identifier">rk_algorithm_type</span><span class="special">;</span>
  51   <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_a_type</span>        <a name="boost.numeric.odeint.explicit_generic_rk.coef_a_type"></a><span class="identifier">coef_a_type</span><span class="special">;</span>
  52   <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_b_type</span>        <a name="boost.numeric.odeint.explicit_generic_rk.coef_b_type"></a><span class="identifier">coef_b_type</span><span class="special">;</span>
  53   <span class="keyword">typedef</span> <span class="identifier">rk_algorithm_type</span><span class="special">::</span><span class="identifier">coef_c_type</span>        <a name="boost.numeric.odeint.explicit_generic_rk.coef_c_type"></a><span class="identifier">coef_c_type</span><span class="special">;</span>
  54
  55   <span class="comment">// <a class="link" href="explicit_generic_rk.html#boost.numeric.odeint.explicit_generic_rkconstruct-copy-destruct">construct/copy/destruct</a></span>
  56   <a class="link" href="explicit_generic_rk.html#idm45853739288352-bb"><span class="identifier">explicit_generic_rk</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">coef_a_type</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&amp;</span><span class="special">,</span>
  57                       <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&amp;</span><span class="special">,</span>
  58                       <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>
  59
  60   <span class="comment">// <a class="link" href="explicit_generic_rk.html#idm45853739306496-bb">public member functions</a></span>
  61   <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>
  62            <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
  63     <span class="keyword">void</span> <a class="link" href="explicit_generic_rk.html#idm45853739305936-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>
  64                       <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>
  65   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="explicit_generic_rk.html#idm45853739292128-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>
  66
  67   <span class="comment">// <a class="link" href="explicit_generic_rk.html#idm45853739281696-bb">private member functions</a></span>
  68   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="explicit_generic_rk.html#idm45853739281120-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>
  69 <span class="special">}</span><span class="special">;</span></pre></div>
  70 <div class="refsect1">
  71 <a name="idm45221359245488"></a><h2>Description</h2>
  72 <p>This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!</p>
  73 <p>This class derives explicit_stepper_base which provides the stepper interface.</p>
  74 <p>
  75 </p>
  76 <div class="refsect2">
  77 <a name="idm45221359244032"></a><h3>Template Parameters</h3>
  78 <div class="orderedlist"><ol class="orderedlist" type="1">
  79 <li class="listitem">
  80 <pre class="literallayout"><span class="identifier">size_t</span> StageCount</pre>
  81 <p>The number of stages of the Runge-Kutta algorithm. </p>
  82 </li>
  83 <li class="listitem">
  84 <pre class="literallayout"><span class="identifier">size_t</span> Order</pre>
  85 <p>The order of the stepper. </p>
  86 </li>
  87 <li class="listitem">
  88 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  89 <p>The type representing the state of the ODE. </p>
  90 </li>
  91 <li class="listitem">
  92 <pre class="literallayout"><span class="keyword">typename</span> Value</pre>
  93 <p>The floating point type which is used in the computations. </p>
  94 </li>
  95 <li class="listitem"><pre class="literallayout"><span class="keyword">typename</span> Deriv</pre></li>
  96 <li class="listitem">
  97 <pre class="literallayout"><span class="keyword">typename</span> Time</pre>
  98 <p>The type representing the independent variable - the time - of the ODE. </p>
  99 </li>
 100 <li class="listitem">
 101 <pre class="literallayout"><span class="keyword">typename</span> Algebra</pre>
 102 <p>The algebra type. </p>
 103 </li>
 104 <li class="listitem">
 105 <pre class="literallayout"><span class="keyword">typename</span> Operations</pre>
 106 <p>The operations type. </p>
 107 </li>
 108 <li class="listitem">
 109 <pre class="literallayout"><span class="keyword">typename</span> Resizer</pre>
 110 <p>The resizer policy type. </p>
 111 </li>
 112 </ol></div>
 113 </div>
 114 <div class="refsect2">
 115 <a name="idm45221359224576"></a><h3>
 116 <a name="boost.numeric.odeint.explicit_generic_rkconstruct-copy-destruct"></a><code class="computeroutput">explicit_generic_rk</code>
 117         public
 118        construct/copy/destruct</h3>
 119 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 120 <pre class="literallayout"><a name="idm45853739288352-bb"></a><span class="identifier">explicit_generic_rk</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">coef_a_type</span> <span class="special">&amp;</span> a<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">coef_b_type</span> <span class="special">&amp;</span> b<span class="special">,</span>
 121                     <span class="keyword">const</span> <span class="identifier">coef_c_type</span> <span class="special">&amp;</span> c<span class="special">,</span>
 122                     <span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> algebra <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="explicit_generic_rk.html" title="Class template explicit_generic_rk">explicit_generic_rk</a></code> class. See examples section for details on the coefficients. <p>
 123 </p>
 124 <div class="variablelist"><table border="0" class="variablelist compact">
 125 <colgroup>
 126 <col align="left" valign="top">
 127 <col>
 128 </colgroup>
 129 <tbody><tr>
 130 <td><p><span class="term">Parameters:</span></p></td>
 131 <td><div class="variablelist"><table border="0" class="variablelist compact">
 132 <colgroup>
 133 <col align="left" valign="top">
 134 <col>
 135 </colgroup>
 136 <tbody>
 137 <tr>
 138 <td><p><span class="term"><code class="computeroutput">a</code></span></p></td>
 139 <td><p>Triangular matrix of parameters b in the Butcher tableau. </p></td>
 140 </tr>
 141 <tr>
 142 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 143 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 144 </tr>
 145 <tr>
 146 <td><p><span class="term"><code class="computeroutput">b</code></span></p></td>
 147 <td><p>Last row of the butcher tableau. </p></td>
 148 </tr>
 149 <tr>
 150 <td><p><span class="term"><code class="computeroutput">c</code></span></p></td>
 151 <td><p>Parameters to calculate the time points in the Butcher tableau. </p></td>
 152 </tr>
 153 </tbody>
 154 </table></div></td>
 155 </tr></tbody>
 156 </table></div>
 157 </li></ol></div>
 158 </div>
 159 <div class="refsect2">
 160 <a name="idm45221359197616"></a><h3>
 161 <a name="idm45853739306496-bb"></a><code class="computeroutput">explicit_generic_rk</code> public member functions</h3>
 162 <div class="orderedlist"><ol class="orderedlist" type="1">
 163 <li class="listitem">
 164 <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>
 165          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 166   <span class="keyword">void</span> <a name="idm45853739305936-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>
 167                     <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>
 168 </p>
 169 <div class="variablelist"><table border="0" class="variablelist compact">
 170 <colgroup>
 171 <col align="left" valign="top">
 172 <col>
 173 </colgroup>
 174 <tbody><tr>
 175 <td><p><span class="term">Parameters:</span></p></td>
 176 <td><div class="variablelist"><table border="0" class="variablelist compact">
 177 <colgroup>
 178 <col align="left" valign="top">
 179 <col>
 180 </colgroup>
 181 <tbody>
 182 <tr>
 183 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 184 <td><p>The step size. </p></td>
 185 </tr>
 186 <tr>
 187 <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td>
 188 <td><p>The derivative of x at t. </p></td>
 189 </tr>
 190 <tr>
 191 <td><p><span class="term"><code class="computeroutput">in</code></span></p></td>
 192 <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td>
 193 </tr>
 194 <tr>
 195 <td><p><span class="term"><code class="computeroutput">out</code></span></p></td>
 196 <td><p>The result of the step is written in out. </p></td>
 197 </tr>
 198 <tr>
 199 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 200 <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td>
 201 </tr>
 202 <tr>
 203 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 204 <td><p>The value of the time, at which the step should be performed. </p></td>
 205 </tr>
 206 </tbody>
 207 </table></div></td>
 208 </tr></tbody>
 209 </table></div>
 210 </li>
 211 <li class="listitem">
 212 <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="idm45853739292128-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>
 213 </p>
 214 <div class="variablelist"><table border="0" class="variablelist compact">
 215 <colgroup>
 216 <col align="left" valign="top">
 217 <col>
 218 </colgroup>
 219 <tbody><tr>
 220 <td><p><span class="term">Parameters:</span></p></td>
 221 <td><div class="variablelist"><table border="0" class="variablelist compact">
 222 <colgroup>
 223 <col align="left" valign="top">
 224 <col>
 225 </colgroup>
 226 <tbody><tr>
 227 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 228 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 229 </tr></tbody>
 230 </table></div></td>
 231 </tr></tbody>
 232 </table></div>
 233 </li>
 234 </ol></div>
 235 </div>
 236 <div class="refsect2">
 237 <a name="idm45221359147120"></a><h3>
 238 <a name="idm45853739281696-bb"></a><code class="computeroutput">explicit_generic_rk</code> private member functions</h3>
 239 <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="idm45853739281120-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>
 240 </div>
 241 </div>
 242 </div>
 243 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 244 <td align="left"></td>
 245 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 246         Distributed under the Boost Software License, Version 1.0. (See accompanying
 247         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>)
 248       </p>
 249 </div></td>
 250 </tr></table>
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