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  26 <a name="boost.numeric.odeint.runge_ku_idm45806988848144"></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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.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_ku_idm45806988848144.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_ku_idm45806988848144.html#boost.numeric.odeint.runge_ku_idm45806988848144construct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_ku_idm45806988848144.html#idm45806988793760-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_ku_idm45806988848144.html#idm45806988828176-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_ku_idm45806988848144.html#idm45806988827616-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_ku_idm45806988848144.html#idm45806988811344-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_ku_idm45806988848144.html#idm45806988797536-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_ku_idm45806988848144.html#idm45806988790464-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_ku_idm45806988848144.html#idm45806988789888-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="idm46278815091216"></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="idm46278815088768"></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="idm46278815058480"></a><h3>
 109 <a name="boost.numeric.odeint.runge_ku_idm45806988848144construct-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="idm45806988793760-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_ku_idm45806988848144.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="idm46278815043360"></a><h3>
 138 <a name="idm45806988828176-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">
 141 <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>
 142          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 143   <span class="keyword">void</span> <a name="idm45806988827616-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>
 144                     <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>This method performs one step. The derivative <code class="computeroutput">dxdt</code> of <code class="computeroutput">in</code> at the time <code class="computeroutput">t</code> is passed to the method. <p>The result is updated out-of-place, hence the input is in <code class="computeroutput">in</code> and the output in <code class="computeroutput">out</code>. Futhermore, an estimation of the error is stored in <code class="computeroutput">xerr</code>. Access to this step functionality is provided by explicit_error_stepper_base and <code class="computeroutput">do_step_impl</code> should not be called directly.</p>
 145 <p>
 146 </p>
 147 <div class="variablelist"><table border="0" class="variablelist compact">
 148 <colgroup>
 149 <col align="left" valign="top">
 150 <col>
 151 </colgroup>
 152 <tbody><tr>
 153 <td><p><span class="term">Parameters:</span></p></td>
 154 <td><div class="variablelist"><table border="0" class="variablelist compact">
 155 <colgroup>
 156 <col align="left" valign="top">
 157 <col>
 158 </colgroup>
 159 <tbody>
 160 <tr>
 161 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 162 <td><p>The step size. </p></td>
 163 </tr>
 164 <tr>
 165 <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td>
 166 <td><p>The derivative of x at t. </p></td>
 167 </tr>
 168 <tr>
 169 <td><p><span class="term"><code class="computeroutput">in</code></span></p></td>
 170 <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td>
 171 </tr>
 172 <tr>
 173 <td><p><span class="term"><code class="computeroutput">out</code></span></p></td>
 174 <td><p>The result of the step is written in out. </p></td>
 175 </tr>
 176 <tr>
 177 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 178 <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td>
 179 </tr>
 180 <tr>
 181 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 182 <td><p>The value of the time, at which the step should be performed. </p></td>
 183 </tr>
 184 <tr>
 185 <td><p><span class="term"><code class="computeroutput">xerr</code></span></p></td>
 186 <td><p>The result of the error estimation is written in xerr. </p></td>
 187 </tr>
 188 </tbody>
 189 </table></div></td>
 190 </tr></tbody>
 191 </table></div>
 192 </li>
 193 <li class="listitem">
 194 <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>
 195          <span class="keyword">typename</span> StateOut<span class="special">&gt;</span>
 196   <span class="keyword">void</span> <a name="idm45806988811344-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>
 197                     <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_error_stepper_base and <code class="computeroutput">do_step_impl</code> should not be called directly. <p>
 198 </p>
 199 <div class="variablelist"><table border="0" class="variablelist compact">
 200 <colgroup>
 201 <col align="left" valign="top">
 202 <col>
 203 </colgroup>
 204 <tbody><tr>
 205 <td><p><span class="term">Parameters:</span></p></td>
 206 <td><div class="variablelist"><table border="0" class="variablelist compact">
 207 <colgroup>
 208 <col align="left" valign="top">
 209 <col>
 210 </colgroup>
 211 <tbody>
 212 <tr>
 213 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
 214 <td><p>The step size. </p></td>
 215 </tr>
 216 <tr>
 217 <td><p><span class="term"><code class="computeroutput">dxdt</code></span></p></td>
 218 <td><p>The derivative of x at t. </p></td>
 219 </tr>
 220 <tr>
 221 <td><p><span class="term"><code class="computeroutput">in</code></span></p></td>
 222 <td><p>The state of the ODE which should be solved. in is not modified in this method </p></td>
 223 </tr>
 224 <tr>
 225 <td><p><span class="term"><code class="computeroutput">out</code></span></p></td>
 226 <td><p>The result of the step is written in out. </p></td>
 227 </tr>
 228 <tr>
 229 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
 230 <td><p>The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept. </p></td>
 231 </tr>
 232 <tr>
 233 <td><p><span class="term"><code class="computeroutput">t</code></span></p></td>
 234 <td><p>The value of the time, at which the step should be performed. </p></td>
 235 </tr>
 236 </tbody>
 237 </table></div></td>
 238 </tr></tbody>
 239 </table></div>
 240 </li>
 241 <li class="listitem">
 242 <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="idm45806988797536-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>
 243 </p>
 244 <div class="variablelist"><table border="0" class="variablelist compact">
 245 <colgroup>
 246 <col align="left" valign="top">
 247 <col>
 248 </colgroup>
 249 <tbody><tr>
 250 <td><p><span class="term">Parameters:</span></p></td>
 251 <td><div class="variablelist"><table border="0" class="variablelist compact">
 252 <colgroup>
 253 <col align="left" valign="top">
 254 <col>
 255 </colgroup>
 256 <tbody><tr>
 257 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 258 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 259 </tr></tbody>
 260 </table></div></td>
 261 </tr></tbody>
 262 </table></div>
 263 </li>
 264 </ol></div>
 265 </div>
 266 <div class="refsect2">
 267 <a name="idm46278814951344"></a><h3>
 268 <a name="idm45806988790464-bb"></a><code class="computeroutput">runge_kutta_cash_karp54_classic</code> private member functions</h3>
 269 <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="idm45806988789888-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>
 270 </div>
 271 </div>
 272 </div>
 273 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 274 <td align="left"></td>
 275 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 276         Distributed under the Boost Software License, Version 1.0. (See accompanying
 277         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>)
 278       </p>
 279 </div></td>
 280 </tr></table>
 281 <hr>
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