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  25 <div class="refentry">
  26 <a name="boost.numeric.odeint.runge_kutta_dopri5"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Class template runge_kutta_dopri5</span></h2>
  29 <p>boost::numeric::odeint::runge_kutta_dopri5 &#8212; The Runge-Kutta Dormand-Prince 5 method. </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_dopri5_hpp.html" title="Header &lt;boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp&gt;">boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp</a>&gt;
  33
  34 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> State<span class="special">,</span> <span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span><span class="special">,</span> <span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span><span class="special">,</span>
  35          <span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span><span class="special">,</span>
  36          <span class="keyword">typename</span> Algebra <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">algebra_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">algebra_type</span><span class="special">,</span>
  37          <span class="keyword">typename</span> Operations <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">operations_dispatcher</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">operations_type</span><span class="special">,</span>
  38          <span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span><span class="special">&gt;</span>
  39 <span class="keyword">class</span> <a class="link" href="runge_kutta_dopri5.html" title="Class template runge_kutta_dopri5">runge_kutta_dopri5</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">explicit_error_stepper_fsal_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_fsal_base</span><span class="special">&lt;</span> <a class="link" href="runge_kutta_dopri5.html" title="Class template runge_kutta_dopri5">runge_kutta_dopri5</a><span class="special">&lt;</span> <span class="special">...</span> <span class="special">&gt;</span><span class="special">,</span><span class="special">...</span> <span class="special">&gt;</span> <a name="boost.numeric.odeint.runge_kutta_dopri5.stepper_base_type"></a><span class="identifier">stepper_base_type</span><span class="special">;</span>
  43   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">state_type</span>                                     <a name="boost.numeric.odeint.runge_kutta_dopri5.state_type"></a><span class="identifier">state_type</span><span class="special">;</span>
  44   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">value_type</span>                                     <a name="boost.numeric.odeint.runge_kutta_dopri5.value_type"></a><span class="identifier">value_type</span><span class="special">;</span>
  45   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">deriv_type</span>                                     <a name="boost.numeric.odeint.runge_kutta_dopri5.deriv_type"></a><span class="identifier">deriv_type</span><span class="special">;</span>
  46   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">time_type</span>                                      <a name="boost.numeric.odeint.runge_kutta_dopri5.time_type"></a><span class="identifier">time_type</span><span class="special">;</span>
  47   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">algebra_type</span>                                   <a name="boost.numeric.odeint.runge_kutta_dopri5.algebra_type"></a><span class="identifier">algebra_type</span><span class="special">;</span>
  48   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">operations_type</span>                                <a name="boost.numeric.odeint.runge_kutta_dopri5.operations_type"></a><span class="identifier">operations_type</span><span class="special">;</span>
  49   <span class="keyword">typedef</span> <span class="identifier">stepper_base_type</span><span class="special">::</span><span class="identifier">resizer_type</span>                                   <a name="boost.numeric.odeint.runge_kutta_dopri5.resizer_type"></a><span class="identifier">resizer_type</span><span class="special">;</span>
  50
  51   <span class="comment">// <a class="link" href="runge_kutta_dopri5.html#boost.numeric.odeint.runge_kutta_dopri5construct-copy-destruct">construct/copy/destruct</a></span>
  52   <a class="link" href="runge_kutta_dopri5.html#idp61880560-bb"><span class="identifier">runge_kutta_dopri5</span></a><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span>
  53
  54   <span class="comment">// <a class="link" href="runge_kutta_dopri5.html#idp61844176-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> DerivOut<span class="special">&gt;</span>
  57     <span class="keyword">void</span> <a class="link" href="runge_kutta_dopri5.html#idp61844736-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">DerivOut</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> 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">,</span> <span class="keyword">typename</span> DerivOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
  61     <span class="keyword">void</span> <a class="link" href="runge_kutta_dopri5.html#idp61853488-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">DerivOut</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>
  63   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> StateIn1<span class="special">,</span> <span class="keyword">typename</span> DerivIn1<span class="special">,</span>
  64            <span class="keyword">typename</span> StateIn2<span class="special">,</span> <span class="keyword">typename</span> DerivIn2<span class="special">&gt;</span>
  65     <span class="keyword">void</span> <a class="link" href="runge_kutta_dopri5.html#idp61863488-bb"><span class="identifier">calc_state</span></a><span class="special">(</span><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="keyword">const</span> <span class="identifier">StateIn1</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn1</span> <span class="special">&amp;</span><span class="special">,</span>
  66                     <span class="identifier">time_type</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn2</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn2</span> <span class="special">&amp;</span><span class="special">,</span> <span class="identifier">time_type</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  67   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="runge_kutta_dopri5.html#idp61876784-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>
  68
  69   <span class="comment">// <a class="link" href="runge_kutta_dopri5.html#idp61883840-bb">private member functions</a></span>
  70   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="runge_kutta_dopri5.html#idp61884416-bb"><span class="identifier">resize_k_x_tmp_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>
  71   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateIn<span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="runge_kutta_dopri5.html#idp61886800-bb"><span class="identifier">resize_dxdt_tmp_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>
  72 <span class="special">}</span><span class="special">;</span></pre></div>
  73 <div class="refsect1">
  74 <a name="idp99729744"></a><h2>Description</h2>
  75 <p>The Runge-Kutta Dormand-Prince 5 method is a very popular method for solving ODEs, see <a href="../../../" target="_top"></a>. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is available which make this method favourable for many applications.</p>
  76 <p>This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring template pattern). The method possesses the FSAL (first-same-as-last) property. See explicit_error_stepper_fsal_base for more details.</p>
  77 <p>
  78 </p>
  79 <div class="refsect2">
  80 <a name="idp99731984"></a><h3>Template Parameters</h3>
  81 <div class="orderedlist"><ol class="orderedlist" type="1">
  82 <li class="listitem">
  83 <pre class="literallayout"><span class="keyword">typename</span> State</pre>
  84 <p>The state type. </p>
  85 </li>
  86 <li class="listitem">
  87 <pre class="literallayout"><span class="keyword">typename</span> Value <span class="special">=</span> <span class="keyword">double</span></pre>
  88 <p>The value type. </p>
  89 </li>
  90 <li class="listitem">
  91 <pre class="literallayout"><span class="keyword">typename</span> Deriv <span class="special">=</span> <span class="identifier">State</span></pre>
  92 <p>The type representing the time derivative of the state. </p>
  93 </li>
  94 <li class="listitem">
  95 <pre class="literallayout"><span class="keyword">typename</span> Time <span class="special">=</span> <span class="identifier">Value</span></pre>
  96 <p>The time representing the independent variable - the time. </p>
  97 </li>
  98 <li class="listitem">
  99 <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>
 100 <p>The algebra type. </p>
 101 </li>
 102 <li class="listitem">
 103 <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>
 104 <p>The operations type. </p>
 105 </li>
 106 <li class="listitem">
 107 <pre class="literallayout"><span class="keyword">typename</span> Resizer <span class="special">=</span> <span class="identifier">initially_resizer</span></pre>
 108 <p>The resizer policy type. </p>
 109 </li>
 110 </ol></div>
 111 </div>
 112 <div class="refsect2">
 113 <a name="idp99762352"></a><h3>
 114 <a name="boost.numeric.odeint.runge_kutta_dopri5construct-copy-destruct"></a><code class="computeroutput">runge_kutta_dopri5</code>
 115         public
 116        construct/copy/destruct</h3>
 117 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
 118 <pre class="literallayout"><a name="idp61880560-bb"></a><span class="identifier">runge_kutta_dopri5</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">algebra_type</span> <span class="special">&amp;</span> algebra <span class="special">=</span> <span class="identifier">algebra_type</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span></pre>Constructs the <code class="computeroutput"><a class="link" href="runge_kutta_dopri5.html" title="Class template runge_kutta_dopri5">runge_kutta_dopri5</a></code> class. This constructor can be used as a default constructor if the algebra has a default constructor. <p>
 119 </p>
 120 <div class="variablelist"><table border="0" class="variablelist compact">
 121 <colgroup>
 122 <col align="left" valign="top">
 123 <col>
 124 </colgroup>
 125 <tbody><tr>
 126 <td><p><span class="term">Parameters:</span></p></td>
 127 <td><div class="variablelist"><table border="0" class="variablelist compact">
 128 <colgroup>
 129 <col align="left" valign="top">
 130 <col>
 131 </colgroup>
 132 <tbody><tr>
 133 <td><p><span class="term"><code class="computeroutput">algebra</code></span></p></td>
 134 <td><p>A copy of algebra is made and stored inside explicit_stepper_base. </p></td>
 135 </tr></tbody>
 136 </table></div></td>
 137 </tr></tbody>
 138 </table></div>
 139 </li></ol></div>
 140 </div>
 141 <div class="refsect2">
 142 <a name="idp99777456"></a><h3>
 143 <a name="idp61844176-bb"></a><code class="computeroutput">runge_kutta_dopri5</code> public member functions</h3>
 144 <div class="orderedlist"><ol class="orderedlist" type="1">
 145 <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>
 146          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> DerivOut<span class="special">&gt;</span>
 147   <span class="keyword">void</span> <a name="idp61844736-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>
 148                     <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span> dxdt_in<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>
 149                     <span class="identifier">DerivOut</span> <span class="special">&amp;</span> dxdt_out<span class="special">,</span> <span class="identifier">time_type</span> dt<span class="special">)</span><span class="special">;</span></pre></li>
 150 <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>
 151          <span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> DerivOut<span class="special">,</span> <span class="keyword">typename</span> Err<span class="special">&gt;</span>
 152   <span class="keyword">void</span> <a name="idp61853488-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>
 153                     <span class="keyword">const</span> <span class="identifier">DerivIn</span> <span class="special">&amp;</span> dxdt_in<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>
 154                     <span class="identifier">DerivOut</span> <span class="special">&amp;</span> dxdt_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>
 155 <li class="listitem">
 156 <pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> StateOut<span class="special">,</span> <span class="keyword">typename</span> StateIn1<span class="special">,</span> <span class="keyword">typename</span> DerivIn1<span class="special">,</span>
 157          <span class="keyword">typename</span> StateIn2<span class="special">,</span> <span class="keyword">typename</span> DerivIn2<span class="special">&gt;</span>
 158   <span class="keyword">void</span> <a name="idp61863488-bb"></a><span class="identifier">calc_state</span><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> x<span class="special">,</span> <span class="keyword">const</span> <span class="identifier">StateIn1</span> <span class="special">&amp;</span> x_old<span class="special">,</span>
 159                   <span class="keyword">const</span> <span class="identifier">DerivIn1</span> <span class="special">&amp;</span> deriv_old<span class="special">,</span> <span class="identifier">time_type</span> t_old<span class="special">,</span>
 160                   <span class="keyword">const</span> <span class="identifier">StateIn2</span> <span class="special">&amp;</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">DerivIn2</span> <span class="special">&amp;</span> deriv_new<span class="special">,</span>
 161                   <span class="identifier">time_type</span> t_new<span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>This method is used for continuous output and it calculates the state <code class="computeroutput">x</code> at a time <code class="computeroutput">t</code> from the knowledge of two states <code class="computeroutput">old_state</code> and <code class="computeroutput">current_state</code> at time points <code class="computeroutput">t_old</code> and <code class="computeroutput">t_new</code>. It also uses internal variables to calculate the result. Hence this method must be called after two successful <code class="computeroutput">do_step</code> calls. </li>
 162 <li class="listitem">
 163 <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="idp61876784-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>
 164 </p>
 165 <div class="variablelist"><table border="0" class="variablelist compact">
 166 <colgroup>
 167 <col align="left" valign="top">
 168 <col>
 169 </colgroup>
 170 <tbody><tr>
 171 <td><p><span class="term">Parameters:</span></p></td>
 172 <td><div class="variablelist"><table border="0" class="variablelist compact">
 173 <colgroup>
 174 <col align="left" valign="top">
 175 <col>
 176 </colgroup>
 177 <tbody><tr>
 178 <td><p><span class="term"><code class="computeroutput">x</code></span></p></td>
 179 <td><p>A state from which the size of the temporaries to be resized is deduced. </p></td>
 180 </tr></tbody>
 181 </table></div></td>
 182 </tr></tbody>
 183 </table></div>
 184 </li>
 185 </ol></div>
 186 </div>
 187 <div class="refsect2">
 188 <a name="idp99880816"></a><h3>
 189 <a name="idp61883840-bb"></a><code class="computeroutput">runge_kutta_dopri5</code> private member functions</h3>
 190 <div class="orderedlist"><ol class="orderedlist" type="1">
 191 <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="idp61884416-bb"></a><span class="identifier">resize_k_x_tmp_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>
 192 <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="idp61886800-bb"></a><span class="identifier">resize_dxdt_tmp_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>
 193 </ol></div>
 194 </div>
 195 </div>
 196 </div>
 197 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 198 <td align="left"></td>
 199 <td align="right"><div class="copyright-footer">Copyright &#169; 2009-2015 Karsten Ahnert and Mario Mulansky<p>
 200         Distributed under the Boost Software License, Version 1.0. (See accompanying
 201         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>)
 202       </p>
 203 </div></td>
 204 </tr></table>
 205 <hr>
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