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<title>Dense Output Stepper</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper"></a><a class="link" href="dense_output_stepper.html" title="Dense Output Stepper">Dense
Output Stepper</a>
</h3></div></div></div>
<p>
This concept specifies the interface a dense ouput stepper has to fulfill
to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate
functions</a>.
</p>
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper.description"></a><h5>
<a name="id614806"></a>
<a class="link" href="dense_output_stepper.html#boost_sandbox_numeric_odeint.concepts.dense_output_stepper.description">Description</a>
</h5>
<p>
A dense ouput stepper following this Dense Output Stepper concept provides
the possibility to perform a single step of the solution <span class="emphasis"><em>x(t)</em></span>
of an ODE to obtain <span class="emphasis"><em>x(t+dt)</em></span>. The step-size <code class="computeroutput"><span class="identifier">dt</span></code> might be adjusted automatically due
to error control. Dense output steppers also can interpolate the solution
to calculate the state <span class="emphasis"><em>x(t')</em></span> at any point <span class="emphasis"><em>t
<= t' <= t+dt</em></span>.
</p>
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper.associated_types"></a><h5>
<a name="id614857"></a>
<a class="link" href="dense_output_stepper.html#boost_sandbox_numeric_odeint.concepts.dense_output_stepper.associated_types">Associated
types</a>
</h5>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></span></dt>
<dd><p>
A type representing the state <span class="emphasis"><em>x</em></span> of the system
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></span></dt>
<dd><p>
A type representing the time <span class="emphasis"><em>t</em></span> of the system
</p></dd>
</dl>
</div>
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper.notation"></a><h5>
<a name="id614951"></a>
<a class="link" href="dense_output_stepper.html#boost_sandbox_numeric_odeint.concepts.dense_output_stepper.notation">Notation</a>
</h5>
<div class="variablelist">
<p class="title"><b></b></p>
<dl>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span></code></span></dt>
<dd><p>
A type that is a model of Dense Output Stepper
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
<dd><p>
A type representing the state <span class="emphasis"><em>x</em></span> of the ODE
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">stepper</span></code></span></dt>
<dd><p>
An object of type <code class="computeroutput"><span class="identifier">Stepper</span></code>
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">x0</span></code>, <code class="computeroutput"><span class="identifier">x</span></code></span></dt>
<dd><p>
Object of type <code class="computeroutput"><span class="identifier">State</span></code>
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">t0</span></code>, <code class="computeroutput"><span class="identifier">dt0</span></code>, <code class="computeroutput"><span class="identifier">t</span></code></span></dt>
<dd><p>
Objects of type <code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code>
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
<dd><p>
An object defining the ODE, should be a model of <a class="link" href="system.html" title="System">System</a>,
<a class="link" href="symplectic_system.html" title="Symplectic_System">Symplectic_System</a>,
<a class="link" href="simple_symplectic_system.html" title="Simple_Symplectic_System">Simple_Symplectic_System</a>
or <a class="link" href="implicit_system.html" title="Implicit_System">Implicit_System</a>.
</p></dd>
</dl>
</div>
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper.valid_expressions"></a><h5>
<a name="id615208"></a>
<a class="link" href="dense_output_stepper.html#boost_sandbox_numeric_odeint.concepts.dense_output_stepper.valid_expressions">Valid
Expressions</a>
</h5>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Name
</p>
</th>
<th>
<p>
Expression
</p>
</th>
<th>
<p>
Type
</p>
</th>
<th>
<p>
Semantics
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Initialize integration
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">initialize</span><span class="special">(</span>
<span class="identifier">x0</span> <span class="special">,</span>
<span class="identifier">t0</span> <span class="special">,</span>
<span class="identifier">dt0</span> <span class="special">)</span></code>
</p>
</td>
<td>
<p>
void
</p>
</td>
<td>
<p>
Initializes the stepper with initial values <code class="computeroutput"><span class="identifier">x0</span></code>,
<code class="computeroutput"><span class="identifier">t0</span></code> and <code class="computeroutput"><span class="identifier">dt0</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
Do step
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span>
<span class="identifier">sys</span> <span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span>
<span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">,</span>
<span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code>
</p>
</td>
<td>
<p>
Performs one step using the ODE defined by <code class="computeroutput"><span class="identifier">sys</span></code>.
The step-size might be changed internally due to error control.
This function returns a pair containing <code class="computeroutput"><span class="identifier">t</span></code>
and <code class="computeroutput"><span class="identifier">t</span><span class="special">+</span><span class="identifier">dt</span></code> representing the interval
for which interpolation can be performed.
</p>
</td>
</tr>
<tr>
<td>
<p>
Do step with reference
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">(</span>
<span class="identifier">sys</span> <span class="special">)</span>
<span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span>
<span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">,</span>
<span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span> <span class="special">></span></code>
</p>
</td>
<td>
<p>
Same as above with <code class="computeroutput"><span class="identifier">System</span></code>
as reference
</p>
</td>
</tr>
<tr>
<td>
<p>
Do interpolation
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">calc_state</span><span class="special">(</span>
<span class="identifier">t_inter</span> <span class="special">,</span>
<span class="identifier">x</span> <span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
Performs the interpolation to calculate /x(t<sub>inter</sub>/) where /t <=
t<sub>inter</sub> <= t+dt/.
</p>
</td>
</tr>
<tr>
<td>
<p>
Get current time
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span><span class="special">&</span></code>
</p>
</td>
<td>
<p>
Returns the current time <span class="emphasis"><em>t+dt</em></span> of the stepper,
that is the end time of the last step and the starting time for
the next call of <code class="computeroutput"><span class="identifier">do_step</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
Get current state
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_state</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span><span class="special">&</span></code>
</p>
</td>
<td>
<p>
Returns the current state of the stepper, that is <span class="emphasis"><em>x(t+dt)</em></span>,
the state at the time returned by <code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time</span><span class="special">()</span></code>
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="boost_sandbox_numeric_odeint.concepts.dense_output_stepper.models"></a><h5>
<a name="id616021"></a>
<a class="link" href="dense_output_stepper.html#boost_sandbox_numeric_odeint.concepts.dense_output_stepper.models">Models</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<code class="computeroutput"><span class="identifier">dense_output_controlled_explicit_fsal</span><span class="special"><</span> <span class="identifier">controlled_error_stepper_fsal</span><span class="special"><</span> <span class="identifier">runge_kutta_dopri5</span>
<span class="special">></span></code>
</li>
<li>
<code class="computeroutput"><span class="identifier">bulirsch_stoer_dense_out</span></code>
</li>
</ul></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 © 2009 -2011 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>
</tr></table>
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