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  26 <a name="boost.numeric.odeint.integrat_idm45853741306272"></a><div class="titlepage"></div>
  27 <div class="refnamediv">
  28 <h2><span class="refentrytitle">Function template integrate</span></h2>
  29 <p>boost::numeric::odeint::integrate &#8212; Integrates the ODE. </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/integrate/integrate_hpp.html" title="Header &lt;boost/numeric/odeint/integrate/integrate.hpp&gt;">boost/numeric/odeint/integrate/integrate.hpp</a>&gt;
  33
  34 </span>
  35 <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> State<span class="special">,</span> <span class="keyword">typename</span> Time<span class="special">,</span> <span class="keyword">typename</span> Observer<span class="special">&gt;</span>
  36   <span class="identifier">boost</span><span class="special">::</span><span class="identifier">enable_if</span><span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">has_value_type</span><span class="special">&lt;</span> <span class="identifier">State</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span>
  37   <span class="identifier">integrate</span><span class="special">(</span><span class="identifier">System</span> system<span class="special">,</span> <span class="identifier">State</span> <span class="special">&amp;</span> start_state<span class="special">,</span> <span class="identifier">Time</span> start_time<span class="special">,</span>
  38             <span class="identifier">Time</span> end_time<span class="special">,</span> <span class="identifier">Time</span> dt<span class="special">,</span> <span class="identifier">Observer</span> observer<span class="special">)</span><span class="special">;</span></pre></div>
  39 <div class="refsect1">
  40 <a name="idm45221370010768"></a><h2>Description</h2>
  41 <p>Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. After each step, the observer is called.</p>
  42 <div class="note"><table border="0" summary="Note">
  43 <tr>
  44 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
  45 <th align="left">Note</th>
  46 </tr>
  47 <tr><td align="left" valign="top"><p>A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate&lt; double &gt;( sys , x , t0 , t1 , dt , obs );</p></td></tr>
  48 </table></div>
  49 <p>
  50
  51
  52 </p>
  53 <div class="variablelist"><table border="0" class="variablelist compact">
  54 <colgroup>
  55 <col align="left" valign="top">
  56 <col>
  57 </colgroup>
  58 <tbody>
  59 <tr>
  60 <td><p><span class="term">Parameters:</span></p></td>
  61 <td><div class="variablelist"><table border="0" class="variablelist compact">
  62 <colgroup>
  63 <col align="left" valign="top">
  64 <col>
  65 </colgroup>
  66 <tbody>
  67 <tr>
  68 <td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
  69 <td><p>Initial step size, will be adjusted during the integration. </p></td>
  70 </tr>
  71 <tr>
  72 <td><p><span class="term"><code class="computeroutput">end_time</code></span></p></td>
  73 <td><p>End time of the integration. </p></td>
  74 </tr>
  75 <tr>
  76 <td><p><span class="term"><code class="computeroutput">observer</code></span></p></td>
  77 <td><p>Observer that will be called after each time step. </p></td>
  78 </tr>
  79 <tr>
  80 <td><p><span class="term"><code class="computeroutput">start_state</code></span></p></td>
  81 <td><p>The initial state. </p></td>
  82 </tr>
  83 <tr>
  84 <td><p><span class="term"><code class="computeroutput">start_time</code></span></p></td>
  85 <td><p>Start time of the integration. </p></td>
  86 </tr>
  87 <tr>
  88 <td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
  89 <td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. </p></td>
  90 </tr>
  91 </tbody>
  92 </table></div></td>
  93 </tr>
  94 <tr>
  95 <td><p><span class="term">Returns:</span></p></td>
  96 <td><p>The number of steps performed. </p></td>
  97 </tr>
  98 </tbody>
  99 </table></div>
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