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<title>Error Stepper</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numeric_odeint.concepts.error_stepper"></a><a class="link" href="error_stepper.html" title="Error Stepper">Error Stepper</a>
</h3></div></div></div>
<p>
This concepts specifies the interface an error stepper has to fulfill to
be used within a ControlledErrorStepper. An error stepper must always fullfil
the stepper concept. This can trivially implemented by
</p>
<p>
</p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span> <span class="keyword">class</span> <span class="identifier">System</span> <span class="special">&gt;</span>
<span class="identifier">error_stepper</span><span class="special">::</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">System</span> <span class="identifier">sys</span> <span class="special">,</span> <span class="identifier">state_type</span> <span class="special">&amp;</span><span class="identifier">x</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">time_type</span> <span class="identifier">dt</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">state_type</span> <span class="identifier">xerr</span><span class="special">;</span>
<span class="comment">// allocate xerr</span>
<span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">sys</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="identifier">t</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">,</span> <span class="identifier">xerr</span> <span class="special">);</span>
<span class="special">}</span>
</pre>
<p>
</p>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h0"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.description"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_stepper.description">Description</a>
</h5>
<p>
An error stepper following this Error Stepper concept is capable of doing
one step of the solution <span class="emphasis"><em>x(t)</em></span> of an ODE with step-size
<span class="emphasis"><em>dt</em></span> to obtain <span class="emphasis"><em>x(t+dt)</em></span> and also computing
an error estimate <span class="emphasis"><em>x<sub>err</sub></em></span> of the result. Error Steppers
can be Runge Kutta steppers, symplectic steppers as well as implicit steppers.
Based on the stepper type, the ODE is defined as <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>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h1"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.refinement_of"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_stepper.refinement_of">Refinement
of</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
DefaultConstructable
</li>
<li class="listitem">
CopyConstructable
</li>
<li class="listitem">
Stepper
</li>
</ul></div>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h2"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.associated_types"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_stepper.associated_types">Associated
types</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<p><span class="bold"><strong>state_type</strong></span></p>
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p>
<p>The
type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p>
</li>
<li class="listitem">
<p><span class="bold"><strong>deriv_type</strong></span></p>
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">deriv_type</span></code></p>
<p>The
type characterizing the derivative of the ODE, hence <span class="emphasis"><em>d x/dt</em></span>.</p>
</li>
<li class="listitem">
<p><span class="bold"><strong>time_type</strong></span></p>
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p>
<p>The
type characterizing the dependent variable of the ODE, hence the time
<span class="emphasis"><em>t</em></span>.</p>
</li>
<li class="listitem">
<p><span class="bold"><strong>value_type</strong></span></p>
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p>
<p>The
numerical data type which is used within the stepper, something like
<code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code>,
<code class="computeroutput"><span class="identifier">complex</span><span class="special">&amp;</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&amp;</span><span class="identifier">gt</span><span class="special">;</span></code>.</p>
</li>
<li class="listitem">
<p><span class="bold"><strong>order_type</strong></span></p>
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">order_type</span></code></p>
<p>The
type characterizing the order of the ODE, typically <code class="computeroutput"><span class="keyword">unsigned</span>
<span class="keyword">short</span></code>.</p>
</li>
</ul></div>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h3"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.notation"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_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">ErrorStepper</span></code></span></dt>
<dd><p>
A type that is a model of Error 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">Error</span></code></span></dt>
<dd><p>
A type representing the error calculated by the stepper, usually same
as <code class="computeroutput"><span class="identifier">State</span></code>
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
<dd><p>
A type representing the time <span class="emphasis"><em>t</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">ErrorStepper</span></code>
</p></dd>
<dt><span class="term"><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">xerr</span></code></span></dt>
<dd><p>
Object of type <code class="computeroutput"><span class="identifier">Error</span></code>
</p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code>, <code class="computeroutput"><span class="identifier">dt</span></code></span></dt>
<dd><p>
Objects of type <code class="computeroutput"><span class="identifier">Time</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 either <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>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h4"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.valid_expressions"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_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>
Get the stepper order
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">order</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">order_type</span></code>
</p>
</td>
<td>
<p>
Returns the order of the stepper for one step without error estimation.
</p>
</td>
</tr>
<tr>
<td>
<p>
Get the stepper order
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">stepper_order</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">order_type</span></code>
</p>
</td>
<td>
<p>
Returns the order of the stepper for one error estimation step
which is used for error calculation.
</p>
</td>
</tr>
<tr>
<td>
<p>
Get the error order
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">errorr_order</span><span class="special">()</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">order_type</span></code>
</p>
</td>
<td>
<p>
Returns the order of the error step which is used for error calculation.
</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>
<span class="identifier">x</span> <span class="special">,</span>
<span class="identifier">t</span> <span class="special">,</span>
<span class="identifier">dt</span> <span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
Performs one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>.
The newly obtained state is written in-place to <code class="computeroutput"><span class="identifier">x</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
Do step with error estimation
</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>
<span class="identifier">x</span> <span class="special">,</span>
<span class="identifier">t</span> <span class="special">,</span>
<span class="identifier">dt</span> <span class="special">,</span>
<span class="identifier">xerr</span> <span class="special">)</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="keyword">void</span></code>
</p>
</td>
<td>
<p>
Performs one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>
with error estimation. The newly obtained state is written in-place
to <code class="computeroutput"><span class="identifier">x</span></code> and the estimated
error to <code class="computeroutput"><span class="identifier">xerr</span></code>.
</p>
</td>
</tr>
</tbody>
</table></div>
<h5>
<a name="boost_numeric_odeint.concepts.error_stepper.h5"></a>
<span><a name="boost_numeric_odeint.concepts.error_stepper.models"></a></span><a class="link" href="error_stepper.html#boost_numeric_odeint.concepts.error_stepper.models">Models</a>
</h5>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<code class="computeroutput"><span class="identifier">runge_kutta_cash_karp54</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">runge_kutta_dopri5</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">runge_kutta_fehlberg78</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">rosenbrock4</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 &#169; 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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