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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>Adapt your own state types</title>
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<link rel="stylesheet" href="../../boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="home" href="../../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
|
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<link rel="up" href="../extend_odeint.html" title="Extend odeint">
|
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<link rel="prev" href="../extend_odeint.html" title="Extend odeint">
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<link rel="next" href="write_own_steppers.html" title="Write own steppers">
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</head>
|
||||
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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||||
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../extend_odeint.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../extend_odeint.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="write_own_steppers.html"><img src="../../images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
<div class="section">
|
||||
<div class="titlepage"><div><div><h3 class="title">
|
||||
<a name="boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_state_types"></a><a class="link" href="adapt_your_own_state_types.html" title="Adapt your own state types">Adapt
|
||||
your own state types</a>
|
||||
</h3></div></div></div>
|
||||
<p>
|
||||
One of the main goals of odeint is to provide algorithms independent from
|
||||
the underlying state type. The state type is a type representing the state
|
||||
of the ODE, that is the variable x. As we usually deal with systems of ODEs,
|
||||
the state type is represented by some sort of container. Most often, the
|
||||
value type of the container is simply <code class="computeroutput"><span class="keyword">double</span></code>,
|
||||
as usually ODEs are defined as systems of real variables. However, it is
|
||||
also possible to use complex types (<code class="computeroutput"><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>) as underlying value type. Moreover,
|
||||
you can even adopt odeint to work with <span class="underline">any</span>
|
||||
value type as long as the required operations are defined. However, in the
|
||||
following I will describe how your own state types can be used to run with
|
||||
odeint. I will assume that the state type is some sort of container aggregating
|
||||
a number of values representing state of the ODE. As odeint also takes care
|
||||
for the memory management of where intermediate results are stored, it first
|
||||
of all needs to know how to construct/destruct and possibly resize the state
|
||||
type. Additionally, it requires to be told how basic algebraic operations
|
||||
are to be performed on state types. So when introducing new state types to
|
||||
odeint, the following points have to be considered:
|
||||
</p>
|
||||
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
|
||||
<li class="listitem">
|
||||
construction/destruction
|
||||
</li>
|
||||
<li class="listitem">
|
||||
resizing (if possible/required)
|
||||
</li>
|
||||
<li class="listitem">
|
||||
algebraic operations
|
||||
</li>
|
||||
</ul></div>
|
||||
<p>
|
||||
Of course, odeint already provides basic interfaces for most of the usual
|
||||
state types. So if you use a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span></code>,
|
||||
or a <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span></code> as state type no additional work
|
||||
is required, they just work out of the box.
|
||||
</p>
|
||||
<p>
|
||||
We distinguish between two basic state types: fixed sized and dynamically
|
||||
sized. For fixed size state types the default constructor <code class="computeroutput"><span class="identifier">state_type</span><span class="special">()</span></code> already allocates the required memory,
|
||||
prominent example is <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">N</span><span class="special">></span></code>.
|
||||
Dynamically sized types have to be resized to make sure enough memory is
|
||||
allocated, the standard constructor does not take care of the resizing. Examples
|
||||
for this are the STL containers like <code class="computeroutput"><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>.
|
||||
</p>
|
||||
<p>
|
||||
The most easy way of getting your own state type to work with odeint is to
|
||||
use a fixed size state, base calculations on the range_algebra and provide
|
||||
the following functionality:
|
||||
</p>
|
||||
<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>
|
||||
Construct State
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">State</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>
|
||||
Creates an instance of <code class="computeroutput"><span class="identifier">State</span></code>
|
||||
and allocates memory.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Begin of the sequence
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
boost::begin(x)
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Iterator
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns an iterator pointing to the begin of the sequence
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
End of the sequence
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
boost::end(x)
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Iterator
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns an iterator pointing to the end of the sequence
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<div class="caution"><table border="0" summary="Caution">
|
||||
<tr>
|
||||
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../images/caution.png"></td>
|
||||
<th align="left">Caution</th>
|
||||
</tr>
|
||||
<tr><td align="left" valign="top"><p>
|
||||
If your state type does not allocate memory by default construction, you
|
||||
<span class="bold"><strong>must define it as resizeable</strong></span> and provide
|
||||
resize functionality. Otherwise segmentation faults will occur.
|
||||
</p></td></tr>
|
||||
</table></div>
|
||||
<p>
|
||||
So fixed sized arrays supported by <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>
|
||||
immediately work with odeint. For dynamically sized arrays one has to additionally
|
||||
supply the resize functionality. First, the state has to be tagged as resizeable
|
||||
by specializing the struct <code class="computeroutput"><span class="identifier">is_resizeable</span></code>
|
||||
which consists of one typedef and one bool value:
|
||||
</p>
|
||||
<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>
|
||||
Resizability
|
||||
</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><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">true_type</span></code> or <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">false_type</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Determines resizeability of the state type, returns <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">true_type</span></code> if the state is resizeable.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Resizability
|
||||
</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><span class="identifier">value</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">bool</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Same as above, but with <code class="computeroutput"><span class="keyword">bool</span></code>
|
||||
value.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
This tells odeint that your state is resizeable. By default, odeint now expects
|
||||
the support of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">size</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code> and a <code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">resize</span><span class="special">(</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">size</span><span class="special">(</span><span class="identifier">y</span><span class="special">)</span>
|
||||
<span class="special">)</span></code> member function for resizing:
|
||||
</p>
|
||||
<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 size
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">size</span><span class="special">(</span>
|
||||
<span class="identifier">x</span> <span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">size_type</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns the current size of x.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Resize
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">x</span><span class="special">.</span><span class="identifier">resize</span><span class="special">(</span>
|
||||
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">size</span><span class="special">(</span>
|
||||
<span class="identifier">y</span> <span class="special">)</span>
|
||||
<span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Resizes x to have the same size as y.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
As an example of the above we will adopt <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code>
|
||||
from <a href="http://www.boost.org/doc/libs/release/libs/numeric/ublas/index.html" target="_top">Boost.UBlas</a>
|
||||
to work as a state type in odeint. This is particularily easy because <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code> supports <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>,
|
||||
including <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">size</span></code>. It also has a resize member function
|
||||
so all that has to be done in this case is to declare resizability:
|
||||
</p>
|
||||
<p>
|
||||
|
||||
</p>
|
||||
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">state_type</span><span class="special">;</span>
|
||||
|
||||
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">odeint</span> <span class="special">{</span>
|
||||
|
||||
<span class="keyword">template</span><span class="special"><></span>
|
||||
<span class="keyword">struct</span> <span class="identifier">is_resizeable</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span>
|
||||
<span class="special">{</span>
|
||||
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">true_type</span> <span class="identifier">type</span><span class="special">;</span>
|
||||
<span class="keyword">const</span> <span class="keyword">static</span> <span class="keyword">bool</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">type</span><span class="special">::</span><span class="identifier">value</span><span class="special">;</span>
|
||||
<span class="special">};</span>
|
||||
|
||||
<span class="special">}</span> <span class="special">}</span> <span class="special">}</span>
|
||||
</pre>
|
||||
<p>
|
||||
</p>
|
||||
<p>
|
||||
This immediately makes <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code>
|
||||
working with odeint as all other requirements are fullfilled by default in
|
||||
this case. You can find the full example in <a href="https://github.com/headmyshoulder/odeint-v2/tree/master/libs/numeric/odeint/examples/ublas/lorenz_ublas.cpp" target="_top">lorenz_ublas.cpp</a>.
|
||||
</p>
|
||||
<p>
|
||||
If your state type does work with <a href="http://www.boost.org/doc/libs/release/libs/range/index.html" target="_top">Boost.Range</a>,
|
||||
but handles resizing differently you are required to specialize two implementations
|
||||
used by odeint to check a state's size and to resize:
|
||||
</p>
|
||||
<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 size
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">same_size_impl</span><span class="special"><</span><span class="identifier">State</span><span class="special">,</span><span class="identifier">State</span><span class="special">>::</span><span class="identifier">same_size</span><span class="special">(</span><span class="identifier">x</span>
|
||||
<span class="special">,</span> <span class="identifier">y</span><span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">bool</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Returns true if the size of x equals the size of y.
|
||||
</p>
|
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</td>
|
||||
</tr>
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||||
<tr>
|
||||
<td>
|
||||
<p>
|
||||
Resize
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="identifier">resize_impl</span><span class="special"><</span><span class="identifier">State</span><span class="special">,</span><span class="identifier">State</span><span class="special">>::</span><span class="identifier">resize</span><span class="special">(</span><span class="identifier">x</span> <span class="special">,</span>
|
||||
<span class="identifier">y</span><span class="special">)</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
<code class="computeroutput"><span class="keyword">void</span></code>
|
||||
</p>
|
||||
</td>
|
||||
<td>
|
||||
<p>
|
||||
Resizes x to have the same size as y.
|
||||
</p>
|
||||
</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table></div>
|
||||
<p>
|
||||
gsl_vector, gsl_matrix, ublas::matrix, blitz::matrix, thrust
|
||||
</p>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"></td>
|
||||
<td align="right"><div class="copyright-footer">Copyright © 2009-2011 Karsten Ahnert
|
||||
and Mario Mulansky<p>
|
||||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||||
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
|
||||
</p>
|
||||
</div></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav">
|
||||
<a accesskey="p" href="../extend_odeint.html"><img src="../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../extend_odeint.html"><img src="../../images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../images/home.png" alt="Home"></a><a accesskey="n" href="write_own_steppers.html"><img src="../../images/next.png" alt="Next"></a>
|
||||
</div>
|
||||
</body>
|
||||
</html>
|
||||
1737
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<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
||||
<title>Chapter 1. boost.sandbox.numeric.odeint</title>
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<link rel="stylesheet" href="boostbook.css" type="text/css">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="next" href="boost_sandbox_numeric_odeint/getting_started.html" title="Getting started">
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</head>
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<hr>
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<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
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<div class="chapter">
|
||||
<div class="titlepage"><div>
|
||||
<div><h2 class="title">
|
||||
<a name="odeint"></a>Chapter 1. boost.sandbox.numeric.odeint</h2></div>
|
||||
<div><div class="author"><h3 class="author">
|
||||
<span class="firstname">Karsten</span> <span class="surname">Ahnert</span>
|
||||
</h3></div></div>
|
||||
<div><div class="author"><h3 class="author">
|
||||
<span class="firstname">Mario</span> <span class="surname">Mulansky</span>
|
||||
</h3></div></div>
|
||||
<div><p class="copyright">Copyright © 2009-2011 Karsten Ahnert
|
||||
and Mario Mulansky</p></div>
|
||||
<div><div class="legalnotice">
|
||||
<a name="id605478"></a><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></div>
|
||||
</div></div>
|
||||
<div class="toc">
|
||||
<p><b>Table of Contents</b></p>
|
||||
<dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/getting_started.html">Getting started</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/getting_started/overview.html">Overview</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/getting_started/usage__compilation__headers.html">Usage,
|
||||
Compilation, Headers</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/getting_started/short_example.html">Short
|
||||
Example</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial.html">Tutorial</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/harmonic_oscillator.html">Harmonic
|
||||
oscillator</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/solar_system.html">Solar
|
||||
system</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html">Chaotic
|
||||
systems and Lyapunov exponents</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/stiff_systems.html">Stiff
|
||||
systems</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/special_topics.html">Special
|
||||
topics</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/using_cuda_and_thrust.html">Using
|
||||
Cuda and Thrust</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/all_examples.html">All
|
||||
examples</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/tutorial/references.html">References</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail.html">Odeint in
|
||||
detail</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/steppers.html">Steppers</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/generation_functions.html">Generation
|
||||
functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/integrate_functions.html">Integrate
|
||||
functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/algebras_and_operations.html">Algebras
|
||||
and operations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__ref.html">Using
|
||||
boost::ref</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/odeint_in_detail/using_boost__range.html">Using
|
||||
boost::range</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/extend_odeint.html">Extend odeint</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_state_types.html">Adapt
|
||||
your own state types</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/extend_odeint/write_own_steppers.html">Write
|
||||
own steppers</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html">Adapt
|
||||
your own operations</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts.html">Concepts</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/system.html">System</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/symplectic_system.html">Symplectic
|
||||
System</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/simple_symplectic_system.html">Simple
|
||||
Symplectic System</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/implicit_system.html">Implicit
|
||||
System</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/observer.html">Observer</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/stepper.html">Stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/error_stepper.html">Error
|
||||
Stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/controlled_stepper.html">Controlled
|
||||
Stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/dense_output_stepper.html">Dense
|
||||
Output Stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/state_algebra_operations.html">State
|
||||
Algebra Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/concepts/state_wrapper.html">State
|
||||
Wrapper</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="odeint/reference.html">Reference</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts.html">Old Concepts</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/basic_stepper.html">Basic
|
||||
stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/error_stepper.html">Error
|
||||
stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/controlled_stepper.html">Controlled
|
||||
stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/dense_ouput_stepper.html">Dense
|
||||
ouput stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/size_adjusting_stepper.html">Size
|
||||
adjusting stepper</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_concepts/compositestepper.html">CompositeStepper</a></span></dt>
|
||||
</dl></dd>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference.html">Old Reference</a></span></dt>
|
||||
<dd><dl>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference/stepper_classes.html">Stepper
|
||||
classes</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference/integration_functions.html">Integration
|
||||
functions</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference/algebras.html">Algebras</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference/operations.html">Operations</a></span></dt>
|
||||
<dt><span class="section"><a href="boost_sandbox_numeric_odeint/old_reference/resizing.html">Resizing</a></span></dt>
|
||||
</dl></dd>
|
||||
</dl>
|
||||
</div>
|
||||
</div>
|
||||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||||
<td align="left"><p><small>Last revised: November 16, 2011 at 20:59:19 GMT</small></p></td>
|
||||
<td align="right"><div class="copyright-footer"></div></td>
|
||||
</tr></table>
|
||||
<hr>
|
||||
<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user