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+<a name="boost.numeric.odeint.integrate_idp19069360"></a><div class="titlepage"></div>
+<div class="refnamediv">
+<h2><span class="refentrytitle">Function template integrate</span></h2>
+<p>boost::numeric::odeint::integrate &#8212; Integrates the ODE. </p>
+</div>
+<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
+<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;
+
+</span>
+<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>
+ <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>
+ <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>
+ <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>
+<div class="refsect1">
+<a name="idp105333664"></a><h2>Description</h2>
+<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>
+<div class="note"><table border="0" summary="Note">
+<tr>
+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../doc/src/images/note.png"></td>
+<th align="left">Note</th>
+</tr>
+<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>
+</table></div>
+<p>
+
+
+</p>
+<div class="variablelist"><table border="0" class="variablelist compact">
+<colgroup>
+<col align="left" valign="top">
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td><p><span class="term">Parameters:</span></p></td>
+<td><div class="variablelist"><table border="0" class="variablelist compact">
+<colgroup>
+<col align="left" valign="top">
+<col>
+</colgroup>
+<tbody>
+<tr>
+<td><p><span class="term"><code class="computeroutput">dt</code></span></p></td>
+<td><p>Initial step size, will be adjusted during the integration. </p></td>
+</tr>
+<tr>
+<td><p><span class="term"><code class="computeroutput">end_time</code></span></p></td>
+<td><p>End time of the integration. </p></td>
+</tr>
+<tr>
+<td><p><span class="term"><code class="computeroutput">observer</code></span></p></td>
+<td><p>Observer that will be called after each time step. </p></td>
+</tr>
+<tr>
+<td><p><span class="term"><code class="computeroutput">start_state</code></span></p></td>
+<td><p>The initial state. </p></td>
+</tr>
+<tr>
+<td><p><span class="term"><code class="computeroutput">start_time</code></span></p></td>
+<td><p>Start time of the integration. </p></td>
+</tr>
+<tr>
+<td><p><span class="term"><code class="computeroutput">system</code></span></p></td>
+<td><p>The system function to solve, hence the r.h.s. of the ordinary differential equation. </p></td>
+</tr>
+</tbody>
+</table></div></td>
+</tr>
+<tr>
+<td><p><span class="term">Returns:</span></p></td>
+<td><p>The number of steps performed. </p></td>
+</tr>
+</tbody>
+</table></div>
+</div>
+</div>
+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
+<td align="left"></td>
+<td align="right"><div class="copyright-footer">Copyright &#169; 2009-2012 Karsten
+ Ahnert and Mario Mulansky<p>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ 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>)
+ </p>
+</div></td>
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