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<div class="section">
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<div class="titlepage"><div><div><h3 class="title">
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<a name="boost_numeric_odeint.concepts.controlled_stepper"></a><a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled
|
||||
Stepper</a>
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||||
</h3></div></div></div>
|
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<p>
|
||||
This concept specifies the interface a controlled stepper has to fulfill
|
||||
to be used within <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate
|
||||
functions</a>.
|
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</p>
|
||||
<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h0"></a>
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||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.description"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
A controlled stepper following this Controlled Stepper concept provides the
|
||||
possibility to perform 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>
|
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with a given step-size <span class="emphasis"><em>dt</em></span>. Depending on an error estimate
|
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of the solution the step might be rejected and a smaller step-size is suggested.
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</p>
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<h5>
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h1"></a>
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<span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.associated_types"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.associated_types">Associated
|
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types</a>
|
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</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
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<li class="listitem">
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<p><span class="bold"><strong>state_type</strong></span></p>
|
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">state_type</span></code></p>
|
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<p>The
|
||||
type characterizing the state of the ODE, hence <span class="emphasis"><em>x</em></span>.</p>
|
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</li>
|
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<li class="listitem">
|
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<p><span class="bold"><strong>deriv_type</strong></span></p>
|
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<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>
|
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<li class="listitem">
|
||||
<p><span class="bold"><strong>time_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">time_type</span></code></p>
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<p>The
|
||||
type characterizing the dependent variable of the ODE, hence the time
|
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<span class="emphasis"><em>t</em></span>.</p>
|
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</li>
|
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<li class="listitem">
|
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<p><span class="bold"><strong>value_type</strong></span></p>
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">value_type</span></code></p>
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<p>The
|
||||
numerical data type which is used within the stepper, something like
|
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<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">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p>
|
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</li>
|
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<li class="listitem">
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<p><span class="bold"><strong>stepper_category</strong></span></p>
|
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<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p>
|
||||
<p>A
|
||||
tag type characterizing the category of the stepper. This type must be
|
||||
convertible to <code class="computeroutput"><span class="identifier">controlled_stepper_tag</span></code>.</p>
|
||||
</li>
|
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</ul></div>
|
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<h5>
|
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<a name="boost_numeric_odeint.concepts.controlled_stepper.h2"></a>
|
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<span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.notation"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.notation">Notation</a>
|
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</h5>
|
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<div class="variablelist">
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<p class="title"><b></b></p>
|
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<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">ControlledStepper</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of Controlled 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">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">ControlledStepper</span></code>
|
||||
</p></dd>
|
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<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">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 <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.controlled_stepper.h3"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.valid_expressions"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_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>
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||||
<tbody><tr>
|
||||
<td>
|
||||
<p>
|
||||
Do step
|
||||
</p>
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</td>
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<td>
|
||||
<p>
|
||||
</p>
|
||||
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">try_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></pre>
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||||
<p>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">controlled_step_result</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Tries one step of step size <code class="computeroutput"><span class="identifier">dt</span></code>.
|
||||
If the step was successful, <code class="computeroutput"><span class="identifier">success</span></code>
|
||||
is returned, the resulting state is written to <code class="computeroutput"><span class="identifier">x</span></code>,
|
||||
the new time is stored in <code class="computeroutput"><span class="identifier">t</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
|
||||
a new (possibly larger) step-size for the next step. If the error
|
||||
was too big, <code class="computeroutput"><span class="identifier">rejected</span></code>
|
||||
is returned and the results are neglected - <code class="computeroutput"><span class="identifier">x</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">t</span></code> are unchanged
|
||||
and <code class="computeroutput"><span class="identifier">dt</span></code> now contains
|
||||
a reduced step-size to be used for the next try.
|
||||
</p>
|
||||
</td>
|
||||
</tr></tbody>
|
||||
</table></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.controlled_stepper.h4"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.controlled_stepper.models"></a></span><a class="link" href="controlled_stepper.html#boost_numeric_odeint.concepts.controlled_stepper.models">Models</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_cash_karp54</span>
|
||||
<span class="special">></span></code>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><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 class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">runge_kutta_fehlberg78</span>
|
||||
<span class="special">></span></code>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">rosenbrock4_controller</span></code>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">bulirsch_stoer</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 © 2009-2015 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>
|
||||
<hr>
|
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<div class="spirit-nav">
|
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<a accesskey="p" href="error_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="dense_output_stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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@@ -0,0 +1,341 @@
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>Dense Output Stepper</title>
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<a accesskey="p" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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</div>
|
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<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_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 output 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>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.dense_output_stepper.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.description"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
A dense output 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>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.dense_output_stepper.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.associated_types"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.associated_types">Associated
|
||||
types</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-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">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</span><span class="identifier">gt</span><span class="special">;</span></code>.</p>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<p><span class="bold"><strong>stepper_category</strong></span></p>
|
||||
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p>
|
||||
<p>A
|
||||
tag type characterizing the category of the stepper. This type must be
|
||||
convertible to <code class="computeroutput"><span class="identifier">dense_output_stepper_tag</span></code>.</p>
|
||||
</li>
|
||||
</ul></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.dense_output_stepper.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.notation"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<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>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.dense_output_stepper.h3"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.valid_expressions"></a></span><a class="link" href="dense_output_stepper.html#boost_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 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="keyword">const</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>
|
||||
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="keyword">const</span> <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>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Get current time step
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">stepper</span><span class="special">.</span><span class="identifier">current_time_step</span><span class="special">()</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">const</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>
|
||||
Returns the current step size of the stepper, that is <span class="emphasis"><em>dt</em></span>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.dense_output_stepper.h4"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.dense_output_stepper.models"></a></span><a class="link" href="dense_output_stepper.html#boost_numeric_odeint.concepts.dense_output_stepper.models">Models</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<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 class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">bulirsch_stoer_dense_out</span></code>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">rosenbrock4_dense_output</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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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||||
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|
||||
</body>
|
||||
</html>
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||||
@@ -0,0 +1,369 @@
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||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>Error Stepper</title>
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||||
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
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||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
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||||
<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="stepper.html" title="Stepper">
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||||
<link rel="next" href="controlled_stepper.html" title="Controlled Stepper">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
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<hr>
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<div class="spirit-nav">
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<a accesskey="p" href="stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section">
|
||||
<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 fulfill
|
||||
the stepper concept. This can trivially implemented by
|
||||
</p>
|
||||
<p>
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">System</span> <span class="special">></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">&</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 class="phrase"><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 class="phrase"><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" style="list-style-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 class="phrase"><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" style="list-style-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">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</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>
|
||||
<li class="listitem">
|
||||
<p><span class="bold"><strong>stepper_category</strong></span></p>
|
||||
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p>
|
||||
<p>A
|
||||
tag type characterizing the category of the stepper. This type must be
|
||||
convertible to <code class="computeroutput"><span class="identifier">error_stepper_tag</span></code>.</p>
|
||||
</li>
|
||||
</ul></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.error_stepper.h3"></a>
|
||||
<span class="phrase"><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 class="variablelist">
|
||||
<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 class="phrase"><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 class="phrase"><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" style="list-style-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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="controlled_stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="up" href="../concepts.html" title="Concepts">
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<link rel="prev" href="simple_symplectic_system.html" title="Simple Symplectic System">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
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<a accesskey="p" href="simple_symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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</div>
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||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.implicit_system"></a><a class="link" href="implicit_system.html" title="Implicit System">Implicit
|
||||
System</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.implicit_system.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.implicit_system.description"></a></span><a class="link" href="implicit_system.html#boost_numeric_odeint.concepts.implicit_system.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
This concept describes how to define a ODE that can be solved by an implicit
|
||||
routine. Implicit routines need not only the function <span class="emphasis"><em>f(x,t)</em></span>
|
||||
but also the Jacobian <span class="emphasis"><em>df/dx = A(x,t)</em></span>. <span class="emphasis"><em>A</em></span>
|
||||
is a matrix and implicit routines need to solve the linear problem <span class="emphasis"><em>Ax
|
||||
= b</em></span>. In odeint this is implemented with use of <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.uBLAS</a>,
|
||||
therefore, the <span class="emphasis"><em>state_type</em></span> implicit routines is <span class="emphasis"><em>ublas::vector</em></span>
|
||||
and the matrix is defined as <span class="emphasis"><em>ublas::matrix</em></span>.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.implicit_system.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.implicit_system.notation"></a></span><a class="link" href="implicit_system.html#boost_numeric_odeint.concepts.implicit_system.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of <code class="computeroutput"><span class="identifier">Implicit</span>
|
||||
<span class="identifier">System</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 of the ODE
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
|
||||
<dd><p>
|
||||
An object of type <code class="computeroutput"><span class="identifier">System</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type ublas::vector
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">dxdt</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type ublas::vector
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">jacobi</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type ublas::matrix
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Time</span></code>
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.implicit_system.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.implicit_system.valid_expressions"></a></span><a class="link" href="implicit_system.html#boost_numeric_odeint.concepts.implicit_system.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>
|
||||
Calculate <span class="emphasis"><em>dx/dt := f(x,t)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">.</span><span class="identifier">first</span><span class="special">(</span>
|
||||
<span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">dxdt</span> <span class="special">,</span>
|
||||
<span class="identifier">t</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <code class="computeroutput"><span class="identifier">f</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">t</span><span class="special">)</span></code>,
|
||||
the result is stored into dxdt
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Calculate <span class="emphasis"><em>A := df/dx (x,t)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">.</span><span class="identifier">second</span><span class="special">(</span>
|
||||
<span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">jacobi</span> <span class="special">,</span>
|
||||
<span class="identifier">t</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates the Jacobian of <span class="emphasis"><em>f</em></span> at <span class="emphasis"><em>x</em></span>,<span class="emphasis"><em>t</em></span>,
|
||||
the result is stored into <code class="computeroutput"><span class="identifier">jacobi</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="simple_symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,168 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
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|
||||
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|
||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
|
||||
<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="system.html" title="System">
|
||||
<link rel="next" href="symplectic_system.html" title="Symplectic System">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
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<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
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|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.second_order_system"></a><a class="link" href="second_order_system.html" title="Second Order System">Second
|
||||
Order System</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.second_order_system.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.description"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
The Second Order System concept models the algorithmic implementation of
|
||||
the rhs for steppers requirering the second order derivative, hence the r.h.s.
|
||||
of the ODE <span class="emphasis"><em>x'' = f(x,x',t)</em></span>. The only requirement for
|
||||
this concept is that it should be callable with a specific parameter syntax
|
||||
(see below). A Second Order System is typically implemented as a function
|
||||
or a functor. Systems fulfilling this concept are required by the Velocity
|
||||
Verlet method.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.second_order_system.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.notation"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of Second Order System
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Space</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">Velocity</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type representing the derivative <span class="emphasis"><em>x'</em></span> of the ODE
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Acceleration</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type representing the second order derivative <span class="emphasis"><em>x''</em></span>
|
||||
of the ODE
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type representing the time
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
|
||||
<dd><p>
|
||||
An object of type <code class="computeroutput"><span class="identifier">System</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">Space</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">v</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Velocity</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">a</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Acceleration</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Time</span></code>
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.second_order_system.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.valid_expressions"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.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>
|
||||
Calculate <span class="emphasis"><em>x'' := f(x,x',t)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span>
|
||||
<span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">v</span> <span class="special">,</span>
|
||||
<span class="identifier">a</span> <span class="special">,</span>
|
||||
<span class="identifier">t</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates f(x,x',t), the result is stored into a.
|
||||
</p>
|
||||
</td>
|
||||
</tr></tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
+187
@@ -0,0 +1,187 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>Simple Symplectic System</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
|
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<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="symplectic_system.html" title="Symplectic System">
|
||||
<link rel="next" href="implicit_system.html" title="Implicit System">
|
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|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="implicit_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.simple_symplectic_system"></a><a class="link" href="simple_symplectic_system.html" title="Simple Symplectic System">Simple
|
||||
Symplectic System</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.description"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
In most Hamiltonian systems the kinetic term is a quadratic term in the momentum
|
||||
<span class="emphasis"><em>H<sub>kin</sub> = p^2 / 2m</em></span> and in many cases it is possible to rescale
|
||||
coordinates and set <span class="emphasis"><em>m=1</em></span> which leads to a trivial equation
|
||||
of motion:
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>q'(t) = f(p) = p. </em></span>
|
||||
</p>
|
||||
<p>
|
||||
while for <span class="emphasis"><em>p'</em></span> we still have the general form
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>p'(t) = g(q) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
As this case is very frequent we introduced a concept where only the nontrivial
|
||||
equation for <span class="emphasis"><em>p'</em></span> has to be provided to the symplectic
|
||||
stepper. We call this concept <span class="emphasis"><em>SimpleSymplecticSystem</em></span>
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.notation"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term">System</span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of SimpleSymplecticSystem
|
||||
</p></dd>
|
||||
<dt><span class="term">Coor</span></dt>
|
||||
<dd><p>
|
||||
The type of the coordinate <span class="emphasis"><em>q</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term">MomentumDeriv</span></dt>
|
||||
<dd><p>
|
||||
The type of the derivative of momentum <span class="emphasis"><em>p'</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term">sys</span></dt>
|
||||
<dd><p>
|
||||
An object that models System
|
||||
</p></dd>
|
||||
<dt><span class="term">q</span></dt>
|
||||
<dd><p>
|
||||
Object of type Coor
|
||||
</p></dd>
|
||||
<dt><span class="term">dpdt</span></dt>
|
||||
<dd><p>
|
||||
Object of type MomentumDeriv
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.simple_symplectic_system.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.simple_symplectic_system.valid_expressions"></a></span><a class="link" href="simple_symplectic_system.html#boost_numeric_odeint.concepts.simple_symplectic_system.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>
|
||||
Check for pair
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_pair</span><span class="special"><</span>
|
||||
<span class="identifier">System</span> <span class="special">>::</span><span class="identifier">type</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Check if System is a pair, should be evaluated to false in this
|
||||
case.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Calculate <span class="emphasis"><em>dp/dt = g(q)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span>
|
||||
<span class="identifier">q</span> <span class="special">,</span>
|
||||
<span class="identifier">dpdt</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <span class="emphasis"><em>g(q)</em></span>, the result is stored into
|
||||
<code class="computeroutput"><span class="identifier">dpdt</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="symplectic_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="implicit_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
+882
@@ -0,0 +1,882 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>State Algebra Operations</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
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||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
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||||
<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="dense_output_stepper.html" title="Dense Output Stepper">
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||||
<link rel="next" href="state_wrapper.html" title="State Wrapper">
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||||
</head>
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||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr>
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||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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||||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
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||||
<hr>
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||||
<div class="spirit-nav">
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||||
<a accesskey="p" href="dense_output_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_wrapper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations"></a><a class="link" href="state_algebra_operations.html" title="State Algebra Operations">State
|
||||
Algebra Operations</a>
|
||||
</h3></div></div></div>
|
||||
<div class="toc"><dl class="toc">
|
||||
<dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations">Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra">Algebra</a></span></dt>
|
||||
<dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations">Pre-Defined
|
||||
implementations</a></span></dt>
|
||||
<dt><span class="section"><a href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.example_expressions">Example
|
||||
expressions</a></span></dt>
|
||||
</dl></div>
|
||||
<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>
|
||||
The following does not apply to implicit steppers like implicit_euler or
|
||||
Rosenbrock 4 as there the <code class="computeroutput"><span class="identifier">state_type</span></code>
|
||||
can not be changed from <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code>
|
||||
and no algebra/operations are used.
|
||||
</p></td></tr>
|
||||
</table></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.description"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
The <code class="computeroutput"><span class="identifier">State</span></code>, <code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code>
|
||||
together define a concept describing how the mathematical vector operations
|
||||
required for the stepper algorithms are performed. The typical vector operation
|
||||
done within steppers is
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em><span class="bold"><strong>y</strong></span> = Σ α<sub>i</sub> <span class="bold"><strong>x<sub>i</sub></strong></span></em></span>.
|
||||
</p>
|
||||
<p>
|
||||
The <code class="computeroutput"><span class="identifier">State</span></code> represents the
|
||||
state variable of an ODE, usually denoted with <span class="emphasis"><em>x</em></span>. Algorithmically,
|
||||
the state is often realized as a <code class="computeroutput"><span class="identifier">vector</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span></code> or <code class="computeroutput"><span class="identifier">array</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">,</span> <span class="identifier">N</span> <span class="special">></span></code>,
|
||||
however, the genericity of odeint enables you to basically use anything as
|
||||
a state type. The algorithmic counterpart of such mathematical expressions
|
||||
is divided into two parts. First, the <code class="computeroutput"><span class="identifier">Algebra</span></code>
|
||||
is used to account for the vector character of the equation. In the case
|
||||
of a <code class="computeroutput"><span class="identifier">vector</span></code> as state type
|
||||
this means the <code class="computeroutput"><span class="identifier">Algebra</span></code> is
|
||||
responsible for iteration over all vector elements. Second, the <code class="computeroutput"><span class="identifier">Operations</span></code> are used to represent the actual
|
||||
operation applied to each of the vector elements. So the <code class="computeroutput"><span class="identifier">Algebra</span></code>
|
||||
iterates over all elements of the <code class="computeroutput"><span class="identifier">State</span></code>s
|
||||
and calls an operation taken from the <code class="computeroutput"><span class="identifier">Operations</span></code>
|
||||
for each element. This is where <code class="computeroutput"><span class="identifier">State</span></code>,
|
||||
<code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code> have to work together to make
|
||||
odeint running. Please have a look at the <code class="computeroutput"><span class="identifier">range_algebra</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">default_operations</span></code> to
|
||||
see an example how this is implemented.
|
||||
</p>
|
||||
<p>
|
||||
In the following we describe how <code class="computeroutput"><span class="identifier">State</span></code>,
|
||||
<code class="computeroutput"><span class="identifier">Algebra</span></code> and <code class="computeroutput"><span class="identifier">Operations</span></code> are used together within the
|
||||
stepper implementations.
|
||||
</p>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.operations"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations" title="Operations">Operations</a>
|
||||
</h4></div></div></div>
|
||||
<h6>
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.notation"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations.notation">Notation</a>
|
||||
</h6>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Operations</span></code></span></dt>
|
||||
<dd><p>
|
||||
The operations type
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Value1</span></code>, ... ,
|
||||
<code class="computeroutput"><span class="identifier">ValueN</span></code></span></dt>
|
||||
<dd><p>
|
||||
Types representing the value or time type of stepper
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Scale</span></code></span></dt>
|
||||
<dd><p>
|
||||
Type of the scale operation
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">scale</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Scale</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code></span></dt>
|
||||
<dd><p>
|
||||
Type that represents a general scale_sum operation, <code class="literal"><span class="emphasis"><em>N</em></span></code>
|
||||
should be replaced by a number from 1 to 14.
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="literal">scale_sum<span class="emphasis"><em>N</em></span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>,
|
||||
<code class="literal"><span class="emphasis"><em>N</em></span></code> should be replaced by a
|
||||
number from 1 to 14.
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code></span></dt>
|
||||
<dd><p>
|
||||
Type of the scale sum swap operation
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">scale_sum_swap2</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">a1</span><span class="special">,</span>
|
||||
<span class="identifier">a2</span><span class="special">,</span>
|
||||
<span class="special">...</span></code></span></dt>
|
||||
<dd><p>
|
||||
Objects of type <code class="computeroutput"><span class="identifier">Value1</span></code>,
|
||||
<code class="computeroutput"><span class="identifier">Value2</span></code>, ...
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">y</span><span class="special">,</span>
|
||||
<span class="identifier">x1</span><span class="special">,</span>
|
||||
<span class="identifier">x2</span><span class="special">,</span>
|
||||
<span class="special">...</span></code></span></dt>
|
||||
<dd><p>
|
||||
Objects of <code class="computeroutput"><span class="identifier">State</span></code>'s
|
||||
value type
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h6>
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.operations.valid_expressions"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.operations.valid_expressions">Valid
|
||||
Expressions</a>
|
||||
</h6>
|
||||
<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 scale operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale</span><span class="special"><</span>
|
||||
<span class="identifier">Value</span> <span class="special">></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Scale</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Get <code class="computeroutput"><span class="identifier">Scale</span></code> from
|
||||
<code class="computeroutput"><span class="identifier">Operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Scale</span></code> constructor
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Scale</span><span class="special"><</span>
|
||||
<span class="identifier">Value</span> <span class="special">>(</span>
|
||||
<span class="identifier">a</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Scale</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Constructs a <code class="computeroutput"><span class="identifier">Scale</span></code>
|
||||
object
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Scale</span></code> operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">scale</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>
|
||||
Calculates <code class="computeroutput"><span class="identifier">x</span> <span class="special">*=</span> <span class="identifier">a</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Get general <code class="computeroutput"><span class="identifier">scale_sum</span></code>
|
||||
operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">Operations::scale_sum<span class="emphasis"><em>N</em></span>< Value1
|
||||
, ... , ValueN ></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Get the <code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code> type
|
||||
from <code class="computeroutput"><span class="identifier">Operations</span></code>,
|
||||
<code class="literal"><span class="emphasis"><em>N</em></span></code> should be replaced
|
||||
by a number from 1 to 14.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">scale_sum</span></code> constructor
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">ScaleSum<span class="emphasis"><em>N</em></span>< Value1 , ... , ValueN
|
||||
>( a1 , ... , aN )</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">ScaleSum<span class="emphasis"><em>N</em></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Constructs a <code class="computeroutput"><span class="identifier">scale_sum</span></code>
|
||||
object given <code class="literal"><span class="emphasis"><em>N</em></span></code> parameter
|
||||
values with <code class="literal"><span class="emphasis"><em>N</em></span></code> between
|
||||
1 and 14.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">scale_sum</span></code> operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">scale_sum<span class="emphasis"><em>N</em></span>( y , x1 , ... , xN )</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <code class="computeroutput"><span class="identifier">y</span> <span class="special">=</span> <span class="identifier">a1</span><span class="special">*</span><span class="identifier">x1</span>
|
||||
<span class="special">+</span> <span class="identifier">a2</span><span class="special">*</span><span class="identifier">x2</span>
|
||||
<span class="special">+</span> <span class="special">...</span>
|
||||
<span class="special">+</span> <span class="identifier">aN</span><span class="special">*</span><span class="identifier">xN</span></code>.
|
||||
Note that this is an <code class="literal"><span class="emphasis"><em>N</em></span>+1</code>-ary
|
||||
function call.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Get scale sum swap operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale_sum_swap2</span><span class="special"><</span>
|
||||
<span class="identifier">Value1</span> <span class="special">,</span>
|
||||
<span class="identifier">Value2</span> <span class="special">></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Get scale sum swap from operations
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
|
||||
constructor
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">ScaleSumSwap2</span><span class="special"><</span> <span class="identifier">Value1</span>
|
||||
<span class="special">,</span> <span class="identifier">Value2</span>
|
||||
<span class="special">>(</span> <span class="identifier">a1</span>
|
||||
<span class="special">,</span> <span class="identifier">a2</span>
|
||||
<span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Constructor
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">ScaleSumSwap2</span></code>
|
||||
operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">scale_sum_swap2</span><span class="special">(</span> <span class="identifier">x1</span>
|
||||
<span class="special">,</span> <span class="identifier">x2</span>
|
||||
<span class="special">,</span> <span class="identifier">x3</span>
|
||||
<span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <code class="computeroutput"><span class="identifier">tmp</span> <span class="special">=</span> <span class="identifier">x1</span></code>,
|
||||
<code class="computeroutput"><span class="identifier">x1</span> <span class="special">=</span>
|
||||
<span class="identifier">a1</span><span class="special">*</span><span class="identifier">x2</span> <span class="special">+</span>
|
||||
<span class="identifier">a2</span><span class="special">*</span><span class="identifier">x3</span></code> and <code class="computeroutput"><span class="identifier">x2</span>
|
||||
<span class="special">=</span> <span class="identifier">tmp</span></code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra" title="Algebra">Algebra</a>
|
||||
</h4></div></div></div>
|
||||
<h6>
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.notation"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra.notation">Notation</a>
|
||||
</h6>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
|
||||
<dd><p>
|
||||
The state type
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Algebra</span></code></span></dt>
|
||||
<dd><p>
|
||||
The algebra type
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="literal">Operation<span class="emphasis"><em>N</em></span></code></span></dt>
|
||||
<dd><p>
|
||||
An <code class="literal"><span class="emphasis"><em>N</em></span></code>-ary operation type,
|
||||
<code class="literal"><span class="emphasis"><em>N</em></span></code> should be a number from
|
||||
1 to 14.
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">algebra</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Algebra</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="literal">operation<span class="emphasis"><em>N</em></span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="literal">Operation<span class="emphasis"><em>N</em></span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">y</span><span class="special">,</span>
|
||||
<span class="identifier">x1</span><span class="special">,</span>
|
||||
<span class="identifier">x2</span><span class="special">,</span>
|
||||
<span class="special">...</span></code></span></dt>
|
||||
<dd><p>
|
||||
Objects of type <code class="computeroutput"><span class="identifier">State</span></code>
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h6>
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_algebra_operations.algebra.valid_expressions"></a></span><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.algebra.valid_expressions">Valid
|
||||
Expressions</a>
|
||||
</h6>
|
||||
<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>
|
||||
Vector Operation with arity 2
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each2</span><span class="special">(</span>
|
||||
<span class="identifier">y</span> <span class="special">,</span>
|
||||
<span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">operation2</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
void
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calls <code class="computeroutput"><span class="identifier">operation2</span><span class="special">(</span> <span class="identifier">y_i</span>
|
||||
<span class="special">,</span> <span class="identifier">x_i</span>
|
||||
<span class="special">)</span></code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code> of <code class="computeroutput"><span class="identifier">y</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">x_i</span></code> of <code class="computeroutput"><span class="identifier">x</span></code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Vector Operation with arity 3
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each3</span><span class="special">(</span>
|
||||
<span class="identifier">y</span> <span class="special">,</span>
|
||||
<span class="identifier">x1</span> <span class="special">,</span>
|
||||
<span class="identifier">x2</span> <span class="special">,</span>
|
||||
<span class="identifier">operation3</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
void
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calls <code class="computeroutput"><span class="identifier">operation3</span><span class="special">(</span> <span class="identifier">y_i</span>
|
||||
<span class="special">,</span> <span class="identifier">x1_i</span>
|
||||
<span class="special">,</span> <span class="identifier">x2_i</span>
|
||||
<span class="special">)</span></code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code> of <code class="computeroutput"><span class="identifier">y</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">x1_i</span></code> of
|
||||
<code class="computeroutput"><span class="identifier">x1</span></code> and <code class="computeroutput"><span class="identifier">x2_i</span></code> of <code class="computeroutput"><span class="identifier">x2</span></code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Vector Operation with arity <code class="literal"><span class="emphasis"><em>N</em></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="literal">algebra.for_each<span class="emphasis"><em>N</em></span>( y , x1 , ...
|
||||
, xN , operation<span class="emphasis"><em>N</em></span> )</code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
void
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calls <code class="literal">operation<span class="emphasis"><em>N</em></span>( y_i , x1_i ,
|
||||
... , xN_i )</code> for each element <code class="computeroutput"><span class="identifier">y_i</span></code>
|
||||
of <code class="computeroutput"><span class="identifier">y</span></code> and <code class="computeroutput"><span class="identifier">x1_i</span></code> of <code class="computeroutput"><span class="identifier">x1</span></code>
|
||||
and so on. <code class="literal"><span class="emphasis"><em>N</em></span></code> should be
|
||||
replaced by a number between 1 and 14.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.pre_defined_implementations" title="Pre-Defined implementations">Pre-Defined
|
||||
implementations</a>
|
||||
</h4></div></div></div>
|
||||
<p>
|
||||
As standard configuration odeint uses the <code class="computeroutput"><span class="identifier">range_algebra</span></code>
|
||||
and <code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
which suffices most situations. However, a few more possibilities exist
|
||||
either to gain better performance or to ensure interoperability with other
|
||||
libraries. In the following we list the existing <code class="computeroutput"><span class="identifier">Algebra</span></code>/<code class="computeroutput"><span class="identifier">Operations</span></code> configurations that can be
|
||||
used in the steppers.
|
||||
</p>
|
||||
<div class="informaltable"><table class="table">
|
||||
<colgroup>
|
||||
<col>
|
||||
<col>
|
||||
<col>
|
||||
<col>
|
||||
</colgroup>
|
||||
<thead><tr>
|
||||
<th>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">State</span></code>
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Algebra</span></code>
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">Operations</span></code>
|
||||
</p>
|
||||
</th>
|
||||
<th>
|
||||
<p>
|
||||
Remarks
|
||||
</p>
|
||||
</th>
|
||||
</tr></thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Anything supporting <a href="http://www.boost.org/doc/libs/release/libs/range/" target="_top">Boost.Range</a>,
|
||||
like <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span></code>, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">list</span></code>,
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code>,... based on a <code class="computeroutput"><span class="identifier">value_type</span></code> that supports operators
|
||||
+,* (typically <code class="computeroutput"><span class="keyword">double</span></code>)
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">range_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Standard implementation, applicable for most typical situations.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code> based on a <code class="computeroutput"><span class="identifier">value_type</span></code> that supports operators
|
||||
+,*
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">array_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Special implementation for boost::array with better performance
|
||||
than <code class="computeroutput"><span class="identifier">range_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Anything that defines operators + within itself and * with scalar
|
||||
(Mathematically spoken, anything that is a vector space).
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">vector_space_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
For the use of <a class="link" href="controlled_stepper.html" title="Controlled Stepper">Controlled
|
||||
Stepper</a>, the template <code class="computeroutput"><span class="identifier">vector_space_reduce</span></code>
|
||||
has to be instantiated.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">thrust</span><span class="special">::</span><span class="identifier">device_vector</span></code>, <code class="computeroutput"><span class="identifier">thrust</span><span class="special">::</span><span class="identifier">host_vector</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">thrust_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">thrust_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
For running odeint on CUDA devices by using <a href="http://code.google.com/p/thrust/" target="_top">Thrust</a>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Any RandomAccessRange
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">openmp_range_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
OpenMP-parallelised range algebra
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">openmp_state</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">openmp_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">default_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
OpenMP-parallelised algebra for split data
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code> or anything which allocates
|
||||
the elements in a C-like manner
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">vector_space_algebra</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">mkl_operations</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Using the <a href="http://software.intel.com/en-us/articles/intel-mkl/" target="_top">Intel
|
||||
Math Kernel Library</a> in odeint for maximum performance.
|
||||
Currently, only the RK4 stepper is supported.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h4 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_algebra_operations.example_expressions"></a><a class="link" href="state_algebra_operations.html#boost_numeric_odeint.concepts.state_algebra_operations.example_expressions" title="Example expressions">Example
|
||||
expressions</a>
|
||||
</h4></div></div></div>
|
||||
<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>
|
||||
Vector operation
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">algebra</span><span class="special">.</span><span class="identifier">for_each3</span><span class="special">(</span>
|
||||
<span class="identifier">y</span> <span class="special">,</span>
|
||||
<span class="identifier">x1</span> <span class="special">,</span>
|
||||
<span class="identifier">x2</span> <span class="special">,</span>
|
||||
<span class="identifier">Operations</span><span class="special">::</span><span class="identifier">scale_sum2</span><span class="special"><</span>
|
||||
<span class="identifier">Value1</span> <span class="special">,</span>
|
||||
<span class="identifier">Value2</span> <span class="special">>(</span>
|
||||
<span class="identifier">a1</span> <span class="special">,</span>
|
||||
<span class="identifier">a2</span> <span class="special">)</span>
|
||||
<span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
void
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <span class="emphasis"><em><span class="bold"><strong>y</strong></span> = a1
|
||||
<span class="bold"><strong>x1</strong></span> + a2 <span class="bold"><strong>x2</strong></span></em></span>
|
||||
</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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="dense_output_stepper.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="state_wrapper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,233 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>State Wrapper</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
|
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<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="state_algebra_operations.html" title="State Algebra Operations">
|
||||
<link rel="next" href="../literature.html" title="Literature">
|
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../literature.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.state_wrapper"></a><a class="link" href="state_wrapper.html" title="State Wrapper">State Wrapper</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.state_wrapper.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_wrapper.description"></a></span><a class="link" href="state_wrapper.html#boost_numeric_odeint.concepts.state_wrapper.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
The <code class="computeroutput"><span class="identifier">State</span> <span class="identifier">Wrapper</span></code>
|
||||
concept describes the way odeint creates temporary state objects to store
|
||||
intermediate results within the stepper's <code class="computeroutput"><span class="identifier">do_step</span></code>
|
||||
methods.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.state_wrapper.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_wrapper.notation"></a></span><a class="link" href="state_wrapper.html#boost_numeric_odeint.concepts.state_wrapper.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">State</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is the <code class="computeroutput"><span class="identifier">state_type</span></code>
|
||||
of the ODE
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">WrappedState</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of State Wrapper for the state type <code class="computeroutput"><span class="identifier">State</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">w</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.state_wrapper.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.state_wrapper.valid_expressions"></a></span><a class="link" href="state_wrapper.html#boost_numeric_odeint.concepts.state_wrapper.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 resizeability
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">is_resizeable</span><span class="special"><</span>
|
||||
<span class="identifier">State</span> <span class="special">></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">false_type</span></code> or <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">true_type</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">true_type</span></code> if the <code class="computeroutput"><span class="identifier">State</span></code> is resizeable, <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">false_type</span></code> otherwise.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Create <code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
type
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">state_wrapper</span><span class="special"><</span>
|
||||
<span class="identifier">State</span> <span class="special">></span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Creates the type for a <code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
for the state type <code class="computeroutput"><span class="identifier">State</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Constructor
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">WrappedState</span><span class="special">()</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Constructs a state wrapper with an empty state
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Copy Constructor
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">WrappedState</span><span class="special">(</span>
|
||||
<span class="identifier">w</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">WrappedState</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Constructs a state wrapper with a state of the same size as the
|
||||
state in <code class="computeroutput"><span class="identifier">w</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Get state
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">w</span><span class="special">.</span><span class="identifier">m_v</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">State</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns the <code class="computeroutput"><span class="identifier">State</span></code>
|
||||
object of this state wrapper.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="state_algebra_operations.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../literature.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,279 @@
|
||||
<html>
|
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<head>
|
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
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<title>Stepper</title>
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<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
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<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
|
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|
||||
<link rel="prev" href="implicit_system.html" title="Implicit System">
|
||||
<link rel="next" href="error_stepper.html" title="Error Stepper">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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<td align="center"><a href="../../../../../../../index.html">Home</a></td>
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||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="implicit_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="error_stepper.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.stepper"></a><a class="link" href="stepper.html" title="Stepper">Stepper</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
This concepts specifies the interface a simple stepper has to fulfill to
|
||||
be used within the <a class="link" href="../odeint_in_detail/integrate_functions.html" title="Integrate functions">integrate
|
||||
functions</a>.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.description"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
The basic stepper concept. A basic stepper following this Stepper concept
|
||||
is able 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> using a given step size
|
||||
<span class="emphasis"><em>dt</em></span>. Basic steppers can be Runge-Kutta steppers, symplectic
|
||||
steppers as well as implicit steppers. Depending on the actual stepper, 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>. Note that all error steppers are also basic steppers.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.refinement_of"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.refinement_of">Refinement
|
||||
of</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
DefaultConstructable
|
||||
</li>
|
||||
<li class="listitem">
|
||||
CopyConstructable
|
||||
</li>
|
||||
</ul></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.associated_types"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.associated_types">Associated
|
||||
types</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-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">&</span><span class="identifier">lt</span><span class="special">;</span> <span class="keyword">double</span> <span class="special">&</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>
|
||||
<li class="listitem">
|
||||
<p><span class="bold"><strong>stepper_category</strong></span></p>
|
||||
<p><code class="computeroutput"><span class="identifier">Stepper</span><span class="special">::</span><span class="identifier">stepper_category</span></code></p>
|
||||
<p>A
|
||||
tag type characterizing the category of the stepper. This type must be
|
||||
convertible to <code class="computeroutput"><span class="identifier">stepper_tag</span></code>.</p>
|
||||
</li>
|
||||
</ul></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h3"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.notation"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Stepper</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of 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">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">Stepper</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">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. Depending on the Stepper this might 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>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h4"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.valid_expressions"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.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 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.
|
||||
</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 in <code class="computeroutput"><span class="identifier">x</span></code>.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.stepper.h5"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.stepper.models"></a></span><a class="link" href="stepper.html#boost_numeric_odeint.concepts.stepper.models">Models</a>
|
||||
</h5>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">runge_kutta4</span></code>
|
||||
</li>
|
||||
<li class="listitem">
|
||||
<code class="computeroutput"><span class="identifier">euler</span></code>
|
||||
</li>
|
||||
<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">modified_midpoint</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 © 2009-2015 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>
|
||||
<hr>
|
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<div class="spirit-nav">
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<a accesskey="p" href="second_order_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="simple_symplectic_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.symplectic_system"></a><a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic
|
||||
System</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.symplectic_system.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.symplectic_system.description"></a></span><a class="link" href="symplectic_system.html#boost_numeric_odeint.concepts.symplectic_system.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
This concept describes how to define a symplectic system written with generalized
|
||||
coordinate <code class="computeroutput"><span class="identifier">q</span></code> and generalized
|
||||
momentum <code class="computeroutput"><span class="identifier">p</span></code>:
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>q'(t) = f(p) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>p'(t) = g(q) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
Such a situation is typically found for Hamiltonian systems with a separable
|
||||
Hamiltonian:
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>H(p,q) = H<sub>kin</sub>(p) + V(q) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
which gives the equations of motion:
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>q'(t) = dH<sub>kin</sub> / dp = f(p) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
<span class="emphasis"><em>p'(t) = dV / dq = g(q) </em></span>
|
||||
</p>
|
||||
<p>
|
||||
The algorithmic implementation of this situation is described by a pair of
|
||||
callable objects for <span class="emphasis"><em>f</em></span> and <span class="emphasis"><em>g</em></span> with
|
||||
a specific parameter signature. Such a system should be implemented as a
|
||||
std::pair of functions or a functors. Symplectic systems are used in symplectic
|
||||
steppers like <code class="computeroutput"><span class="identifier">symplectic_rkn_sb3a_mclachlan</span></code>.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.symplectic_system.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.symplectic_system.notation"></a></span><a class="link" href="symplectic_system.html#boost_numeric_odeint.concepts.symplectic_system.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of SymplecticSystem
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Coor</span></code></span></dt>
|
||||
<dd><p>
|
||||
The type of the coordinate <span class="emphasis"><em>q</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Momentum</span></code></span></dt>
|
||||
<dd><p>
|
||||
The type of the momentum <span class="emphasis"><em>p</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">CoorDeriv</span></code></span></dt>
|
||||
<dd><p>
|
||||
The type of the derivative of coordinate <span class="emphasis"><em>q'</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">MomentumDeriv</span></code></span></dt>
|
||||
<dd><p>
|
||||
The type of the derivative of momentum <span class="emphasis"><em>p'</em></span>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
|
||||
<dd><p>
|
||||
An object of the type <code class="computeroutput"><span class="identifier">System</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">q</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type Coor
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">p</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type Momentum
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">dqdt</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type CoorDeriv
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">dpdt</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type MomentumDeriv
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.symplectic_system.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.symplectic_system.valid_expressions"></a></span><a class="link" href="symplectic_system.html#boost_numeric_odeint.concepts.symplectic_system.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>
|
||||
Check for pair
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_pair</span><span class="special"><</span>
|
||||
<span class="identifier">System</span> <span class="special">>::</span><span class="identifier">type</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Check if System is a pair
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Calculate <span class="emphasis"><em>dq/dt = f(p)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">.</span><span class="identifier">first</span><span class="special">(</span>
|
||||
<span class="identifier">p</span> <span class="special">,</span>
|
||||
<span class="identifier">dqdt</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <span class="emphasis"><em>f(p)</em></span>, the result is stored into
|
||||
<code class="computeroutput"><span class="identifier">dqdt</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Calculate <span class="emphasis"><em>dp/dt = g(q)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">.</span><span class="identifier">second</span><span class="special">(</span>
|
||||
<span class="identifier">q</span> <span class="special">,</span>
|
||||
<span class="identifier">dpdt</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates <span class="emphasis"><em>g(q)</em></span>, the result is stored into
|
||||
<code class="computeroutput"><span class="identifier">dpdt</span></code>
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="second_order_system.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="simple_symplectic_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
@@ -0,0 +1,158 @@
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>System</title>
|
||||
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
|
||||
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
||||
<link rel="home" href="../../index.html" title="Chapter 1. Boost.Numeric.Odeint">
|
||||
<link rel="up" href="../concepts.html" title="Concepts">
|
||||
<link rel="prev" href="../concepts.html" title="Concepts">
|
||||
<link rel="next" href="second_order_system.html" title="Second Order System">
|
||||
</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
|
||||
<table cellpadding="2" width="100%"><tr>
|
||||
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../logo.jpg"></td>
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||||
<td align="center"><a href="../../../../../../../index.html">Home</a></td>
|
||||
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
|
||||
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
|
||||
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../concepts.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="second_order_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_numeric_odeint.concepts.system"></a><a class="link" href="system.html" title="System">System</a>
|
||||
</h3></div></div></div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.system.h0"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.system.description"></a></span><a class="link" href="system.html#boost_numeric_odeint.concepts.system.description">Description</a>
|
||||
</h5>
|
||||
<p>
|
||||
The System concept models the algorithmic implementation of the rhs. of the
|
||||
ODE <span class="emphasis"><em>x' = f(x,t)</em></span>. The only requirement for this concept
|
||||
is that it should be callable with a specific parameter syntax (see below).
|
||||
A System is typically implemented as a function or a functor. Systems fulfilling
|
||||
this concept are required by all Runge-Kutta steppers as well as the Bulirsch-Stoer
|
||||
steppers. However, symplectic and implicit steppers work with other system
|
||||
concepts, see <a class="link" href="symplectic_system.html" title="Symplectic System">Symplectic
|
||||
System</a> and <a class="link" href="implicit_system.html" title="Implicit System">Implicit
|
||||
System</a>.
|
||||
</p>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.system.h1"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.system.notation"></a></span><a class="link" href="system.html#boost_numeric_odeint.concepts.system.notation">Notation</a>
|
||||
</h5>
|
||||
<div class="variablelist">
|
||||
<p class="title"><b></b></p>
|
||||
<dl class="variablelist">
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type that is a model of System
|
||||
</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">Deriv</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type representing the derivative <span class="emphasis"><em>x'</em></span> of the ODE
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
|
||||
<dd><p>
|
||||
A type representing the time
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
|
||||
<dd><p>
|
||||
An object of type <code class="computeroutput"><span class="identifier">System</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">dxdt</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Deriv</span></code>
|
||||
</p></dd>
|
||||
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt>
|
||||
<dd><p>
|
||||
Object of type <code class="computeroutput"><span class="identifier">Time</span></code>
|
||||
</p></dd>
|
||||
</dl>
|
||||
</div>
|
||||
<h5>
|
||||
<a name="boost_numeric_odeint.concepts.system.h2"></a>
|
||||
<span class="phrase"><a name="boost_numeric_odeint.concepts.system.valid_expressions"></a></span><a class="link" href="system.html#boost_numeric_odeint.concepts.system.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>
|
||||
Calculate <span class="emphasis"><em>dx/dt := f(x,t)</em></span>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span>
|
||||
<span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">dxdt</span> <span class="special">,</span>
|
||||
<span class="identifier">t</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Calculates f(x,t), the result is stored into dxdt
|
||||
</p>
|
||||
</td>
|
||||
</tr></tbody>
|
||||
</table></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 © 2009-2015 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>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../concepts.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../concepts.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="second_order_system.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user