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Subject: [Boost-commit] svn:boost r71200 - in sandbox/odeint/branches/karsten/libs/numeric/odeint: doc doc/html doc/html/boost_sandbox_numeric_odeint examples
From: karsten.ahnert_at_[hidden]
Date: 2011-04-12 10:12:45

Author: karsten
Date: 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
New Revision: 71200
URL: http://svn.boost.org/trac/boost/changeset/71200

Log:
chaotic system example finalized
Added:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmidt.hpp (contents, props changed)
      - copied, changed from r71199, /sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp
Removed:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp
Text files modified:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html | 325 +++++++++++++++++++++------------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html | 16
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html | 60 +-----
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html | 26 +-
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html | 243 ++++++++++------------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html | 14
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk | 3
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_chaotic_system.qbk | 29 +-
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/chaotic_system.cpp | 4
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmidt.hpp | 2
   10 files changed, 329 insertions(+), 393 deletions(-)

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Concepts</title>
<link rel="stylesheet" href="../boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="up" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="prev" href="extend_odeint.html" title="Extend odeint">
<link rel="next" href="reference.html" title="Reference">
@@ -13,9 +13,9 @@
<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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="extend_odeint.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="reference.html"><img src="../images/next.png" alt="Next"></a>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_sandbox_numeric_odeint.concepts"></a><a class="link" href="concepts.html" title="Concepts">Concepts</a>
</h2></div></div></div>
@@ -35,7 +35,7 @@
<p>
       The odeint library defines three concepts for stepping objects.
     </p>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.basic_stepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.basic_stepper" title="Basic stepper">Basic
       stepper</a>
@@ -59,12 +59,8 @@
</colgroup>
<thead><tr>
<th>
- <p>
- </p>
               </th>
<th>
- <p>
- </p>
               </th>
<th>
                 <p>
@@ -147,25 +143,27 @@
<p>
         <span class="bold"><strong>Methods</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">()</span></code>
- Constructor.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">Stepper</span><span class="special">(</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code> Constructor
- that allocates internal memory to store intermediate results of the same
- size as <code class="computeroutput"><span class="identifier">x</span></code>.
- </li>
-<li><code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
- <span class="special">&</span><span class="identifier">system</span>
- <span class="special">,</span> <span class="identifier">container_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></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">Stepper</span><span class="special">()</span></code>
+ Constructor.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">Stepper</span><span class="special">(</span>
+ <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
+ Constructor that allocates internal memory to store intermediate results
+ of the same size as <code class="computeroutput"><span class="identifier">x</span></code>.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
+ <span class="special">&</span><span class="identifier">system</span>
+ <span class="special">,</span> <span class="identifier">container_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></code>
+ </li>
</ul></div>
<p>
         Executes one timestep with the given parameters:
@@ -268,44 +266,53 @@
         The result of this method is the (approximate) state of the system <span class="bold"><strong>x(t+dt)</strong></span> and is stored in the variable <code class="computeroutput"><span class="identifier">x</span></code> (in-place). Note, that the time <code class="computeroutput"><span class="identifier">t</span></code> is not automatically increased by this
         method.
       </p>
-<div class="itemizedlist"><ul type="disc"><li><code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
- <span class="special">&</span><span class="identifier">system</span>
- <span class="special">,</span> <span class="identifier">container_type</span>
- <span class="special">&</span><span class="identifier">x</span>
- <span class="special">,</span> <span class="keyword">const</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</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></code></li></ul></div>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
+ <span class="special">&</span><span class="identifier">system</span>
+ <span class="special">,</span> <span class="identifier">container_type</span>
+ <span class="special">&</span><span class="identifier">x</span>
+ <span class="special">,</span> <span class="keyword">const</span>
+ <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</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></code>
+ </li></ul></div>
<p>
         The same as above but with the additional parameter <code class="computeroutput"><span class="identifier">dxdt</span></code>
         that represents the derivative <span class="bold"><strong>x'(t) = f(x,t)</strong></span>
         at the time <span class="bold"><strong>t</strong></span>.
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code> Adjusts
- the internal memory to store intermediate results of the same size as
- <code class="computeroutput"><span class="identifier">x</span></code>. This function <span class="emphasis"><em>must</em></span>
- be called whenever the system size changes during the integration.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_step</span><span class="special">()</span></code> Returns the order of the algorithm. If
- <span class="bold"><strong>n</strong></span> is the order of a method, then the result
- of one iteration with the timestep <span class="bold"><strong>dt</strong></span>
- is accurate up to <span class="bold"><strong>dt^n</strong></span>. That means the
- error made by the time discretization is of order <span class="bold"><strong>dt^(n+1)</strong></span>.
- </li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
+ Adjusts the internal memory to store intermediate results of the same
+ size as <code class="computeroutput"><span class="identifier">x</span></code>. This function
+ <span class="emphasis"><em>must</em></span> be called whenever the system size changes
+ during the integration.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_step</span><span class="special">()</span></code> Returns the order of the algorithm.
+ If <span class="bold"><strong>n</strong></span> is the order of a method, then
+ the result of one iteration with the timestep <span class="bold"><strong>dt</strong></span>
+ is accurate up to <span class="bold"><strong>dt^n</strong></span>. That means the
+ error made by the time discretization is of order <span class="bold"><strong>dt^(n+1)</strong></span>.
+ </li>
</ul></div>
<p>
         <span class="bold"><strong>Stepper that model this concept</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li><code class="computeroutput"><span class="identifier">stepper_euler</span></code></li>
-<li><code class="computeroutput"><span class="identifier">stepper_rk4</span></code></li>
-<li><code class="computeroutput"><span class="identifier">stepper_rk78_fehlberg</span></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_euler</span></code>
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_rk4</span></code>
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_rk78_fehlberg</span></code>
+ </li>
</ul></div>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.error_stepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.error_stepper" title="Error stepper">Error
       stepper</a>
@@ -330,26 +337,28 @@
<p>
         <span class="bold"><strong>Methods</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="identifier">Error_Stepper</span><span class="special">()</span></code>
- Constructor.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">Error_Stepper</span><span class="special">(</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code> Constructor
- that allocates internal memory to store intermediate results of the same
- size as <code class="computeroutput"><span class="identifier">x</span></code>.
- </li>
-<li><code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
- <span class="special">&</span><span class="identifier">system</span>
- <span class="special">,</span> <span class="identifier">container_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="identifier">container_type</span>
- <span class="special">&</span><span class="identifier">xerr</span><span class="special">)</span></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">Error_Stepper</span><span class="special">()</span></code>
+ Constructor.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">Error_Stepper</span><span class="special">(</span>
+ <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
+ Constructor that allocates internal memory to store intermediate results
+ of the same size as <code class="computeroutput"><span class="identifier">x</span></code>.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
+ <span class="special">&</span><span class="identifier">system</span>
+ <span class="special">,</span> <span class="identifier">container_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="identifier">container_type</span>
+ <span class="special">&</span><span class="identifier">xerr</span><span class="special">)</span></code>
+ </li>
</ul></div>
<p>
         Executes one timestep with the given parameters:
@@ -471,45 +480,54 @@
         Note, that the time <code class="computeroutput"><span class="identifier">t</span></code> is
         not automatically increased by this method.
       </p>
-<div class="itemizedlist"><ul type="disc"><li><code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
- <span class="special">&</span><span class="identifier">system</span>
- <span class="special">,</span> <span class="identifier">container_type</span>
- <span class="special">&</span><span class="identifier">x</span>
- <span class="special">,</span> <span class="keyword">const</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</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="identifier">container_type</span> <span class="special">&</span><span class="identifier">xerr</span><span class="special">)</span></code></li></ul></div>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span>
+ <span class="special">&</span><span class="identifier">system</span>
+ <span class="special">,</span> <span class="identifier">container_type</span>
+ <span class="special">&</span><span class="identifier">x</span>
+ <span class="special">,</span> <span class="keyword">const</span>
+ <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</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="identifier">container_type</span> <span class="special">&</span><span class="identifier">xerr</span><span class="special">)</span></code>
+ </li></ul></div>
<p>
         The same as above but with the additional parameter <code class="computeroutput"><span class="identifier">dxdt</span></code>
         that represents the derivative <span class="bold"><strong>x'(t) = f(x,t)</strong></span>
         at the time <span class="bold"><strong>t</strong></span>.
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code> Adjusts
- the internal memory to store intermediate results of the same size as
- <code class="computeroutput"><span class="identifier">x</span></code>. This function <span class="emphasis"><em>must</em></span>
- be called whenever the system size changes during the integration.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error_step</span><span class="special">()</span></code> Returns the order of the result <span class="bold"><strong>x(t+dt)</strong></span> of the algorithm.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error</span><span class="special">()</span></code> Returns the order of the error estimation
- of the algorithm.
- </li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
+ Adjusts the internal memory to store intermediate results of the same
+ size as <code class="computeroutput"><span class="identifier">x</span></code>. This function
+ <span class="emphasis"><em>must</em></span> be called whenever the system size changes
+ during the integration.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error_step</span><span class="special">()</span></code> Returns the order of the result <span class="bold"><strong>x(t+dt)</strong></span> of the algorithm.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error</span><span class="special">()</span></code> Returns the order of the error estimation
+ of the algorithm.
+ </li>
</ul></div>
<p>
         <span class="bold"><strong>Stepper that model this concept</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li><code class="computeroutput"><span class="identifier">stepper_rk5_ck</span></code></li>
-<li><code class="computeroutput"><span class="identifier">stepper_rk78_fehlberg</span></code></li>
-<li><code class="computeroutput"><span class="identifier">stepper_half_step</span></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_rk5_ck</span></code>
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_rk78_fehlberg</span></code>
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">stepper_half_step</span></code>
+ </li>
</ul></div>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.controlled_stepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper" title="Controlled stepper">Controlled
       stepper</a>
@@ -529,11 +547,13 @@
<p>
         <span class="bold"><strong>Methods</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc"><li><code class="computeroutput"><span class="identifier">Controlled_Stepper</span><span class="special">(</span>
- <span class="identifier">time_type</span> <span class="identifier">abs_err</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="identifier">rel_err</span><span class="special">,</span>
- <span class="identifier">time_type</span> <span class="identifier">factor_x</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="identifier">factor_dxdt</span> <span class="special">)</span></code></li></ul></div>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
+ <code class="computeroutput"><span class="identifier">Controlled_Stepper</span><span class="special">(</span>
+ <span class="identifier">time_type</span> <span class="identifier">abs_err</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="identifier">rel_err</span><span class="special">,</span>
+ <span class="identifier">time_type</span> <span class="identifier">factor_x</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="identifier">factor_dxdt</span> <span class="special">)</span></code>
+ </li></ul></div>
<p>
         Constructor that initializes the controlled stepper with several parameters
         of the error control. The controlled stepper assures that the error done
@@ -552,22 +572,20 @@
         If the estimated error is less than half of the desired error, an increased
         stepsize will be suggested.
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="identifier">Controlled_Stepper</span><span class="special">(</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="identifier">abs_err</span><span class="special">,</span>
- <span class="identifier">time_type</span> <span class="identifier">rel_err</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="identifier">factor_x</span><span class="special">,</span>
- <span class="identifier">time_type</span> <span class="identifier">factor_dxdt</span>
- <span class="special">)</span></code> Same as above, but with additional
- allocation of the internal memory to store intermediate results of the
- same size as <code class="computeroutput"><span class="identifier">x</span></code>.
- </li>
-<li><code class="computeroutput"><span class="identifier">controlled_step_result</span> <span class="identifier">try_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span> <span class="special">&</span><span class="identifier">system</span><span class="special">,</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="special">&</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="special">&</span><span class="identifier">dt</span>
- <span class="special">)</span></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">Controlled_Stepper</span><span class="special">(</span>
+ <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="identifier">abs_err</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="identifier">rel_err</span><span class="special">,</span>
+ <span class="identifier">time_type</span> <span class="identifier">factor_x</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="identifier">factor_dxdt</span> <span class="special">)</span></code>
+ Same as above, but with additional allocation of the internal memory
+ to store intermediate results of the same size as <code class="computeroutput"><span class="identifier">x</span></code>.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">controlled_step_result</span> <span class="identifier">try_step</span><span class="special">(</span>
+ <span class="identifier">DynamicalSystem</span> <span class="special">&</span><span class="identifier">system</span><span class="special">,</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="identifier">dt</span> <span class="special">)</span></code>
+ </li>
</ul></div>
<p>
         Tries one timestep with the given parameters
@@ -680,43 +698,50 @@
         <code class="computeroutput"><span class="identifier">dt</span></code> now containes the suggested
         reduced stepsize that should give an error below the desired level.
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li>
-<code class="computeroutput"><span class="identifier">controlled_step_result</span> <span class="identifier">try_step</span><span class="special">(</span> <span class="identifier">DynamicalSystem</span> <span class="special">&</span><span class="identifier">system</span><span class="special">,</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span>
- <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">time_type</span> <span class="special">&</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">time_type</span>
- <span class="special">&</span><span class="identifier">dt</span>
- <span class="special">)</span></code> Same as above but with the additional
- parameter <code class="computeroutput"><span class="identifier">dxdt</span></code> that that
- represents the derivative <span class="bold"><strong>x'(t) = f(x,t)</strong></span>
- at the time <span class="bold"><strong>t</strong></span>.
- </li>
-<li>
-<code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code> Adjusts
- the internal memory to store intermediate results of the same size as
- <code class="computeroutput"><span class="identifier">x</span></code>. This function <span class="emphasis"><em>must</em></span>
- be called whenever the system size changes during the integration.
- </li>
-<li>
-<code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error_step</span><span class="special">()</span></code> Returns the order of the result <span class="bold"><strong>x(t+dt)</strong></span> of the algorithm.
- </li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">controlled_step_result</span> <span class="identifier">try_step</span><span class="special">(</span>
+ <span class="identifier">DynamicalSystem</span> <span class="special">&</span><span class="identifier">system</span><span class="special">,</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">container_type</span>
+ <span class="special">&</span><span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="special">&</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">time_type</span>
+ <span class="special">&</span><span class="identifier">dt</span>
+ <span class="special">)</span></code> Same as above but with the additional
+ parameter <code class="computeroutput"><span class="identifier">dxdt</span></code> that that
+ represents the derivative <span class="bold"><strong>x'(t) = f(x,t)</strong></span>
+ at the time <span class="bold"><strong>t</strong></span>.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="keyword">void</span> <span class="identifier">adjust_size</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">container_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">)</span></code>
+ Adjusts the internal memory to store intermediate results of the same
+ size as <code class="computeroutput"><span class="identifier">x</span></code>. This function
+ <span class="emphasis"><em>must</em></span> be called whenever the system size changes
+ during the integration.
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">order_type</span> <span class="identifier">order_error_step</span><span class="special">()</span></code> Returns the order of the result <span class="bold"><strong>x(t+dt)</strong></span> of the algorithm.
+ </li>
</ul></div>
<p>
         <span class="bold"><strong>Stepper that model this concept</strong></span>
       </p>
-<div class="itemizedlist"><ul type="disc">
-<li><code class="computeroutput"><span class="identifier">controlled_stepper_standard</span></code></li>
-<li><code class="computeroutput"><span class="identifier">controlled_stepper_bs</span></code></li>
+<div class="itemizedlist"><ul class="itemizedlist" type="disc">
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">controlled_stepper_standard</span></code>
+ </li>
+<li class="listitem">
+ <code class="computeroutput"><span class="identifier">controlled_stepper_bs</span></code>
+ </li>
</ul></div>
</div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.dense_ouput_stepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.dense_ouput_stepper" title="Dense ouput stepper">Dense
       ouput stepper</a>
</h3></div></div></div></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.size_adjusting_stepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.size_adjusting_stepper" title="Size adjusting stepper">Size
       adjusting stepper</a>
</h3></div></div></div></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.concepts.compositestepper"></a><a class="link" href="concepts.html#boost_sandbox_numeric_odeint.concepts.compositestepper" title="CompositeStepper">CompositeStepper</a>
</h3></div></div></div></div>
<p>
@@ -733,7 +758,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="extend_odeint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="extend_odeint.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="reference.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extend odeint</title>
<link rel="stylesheet" href="../boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="up" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="prev" href="tutorial.html" title="Tutorial">
<link rel="next" href="concepts.html" title="Concepts">
@@ -13,9 +13,9 @@
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="tutorial.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="concepts.html"><img src="../images/next.png" alt="Next"></a>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_sandbox_numeric_odeint.extend_odeint"></a><a class="link" href="extend_odeint.html" title="Extend odeint">Extend odeint</a>
</h2></div></div></div>
@@ -27,11 +27,11 @@
<dt><span class="section"><a href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_operations">Adapt
       your own operations</a></span></dt>
</dl></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.extend_odeint.write_own_steppers"></a><a class="link" href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.write_own_steppers" title="Write own steppers">Write
       own steppers</a>
</h3></div></div></div></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_containers"></a><a class="link" href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_containers" title="Adapt your own containers">Adapt
       your own containers</a>
@@ -40,7 +40,7 @@
         gsl_vector, gsl_matrix, ublas::matrix, blitz::matrix, thrust
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_operations"></a><a class="link" href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_operations" title="Adapt your own operations">Adapt
       your own operations</a>
@@ -60,7 +60,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="tutorial.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="concepts.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Getting started</title>
<link rel="stylesheet" href="../boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="up" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="prev" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="next" href="tutorial.html" title="Tutorial">
@@ -13,9 +13,9 @@
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="tutorial.html"><img src="../images/next.png" alt="Next"></a>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_sandbox_numeric_odeint.getting_started"></a><a class="link" href="getting_started.html" title="Getting started">Getting started</a>
</h2></div></div></div>
@@ -26,7 +26,7 @@
<dt><span class="section"><a href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.short_example">Short
       Example</a></span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.getting_started.overview"></a><a class="link" href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.overview" title="Overview">Overview</a>
</h3></div></div></div>
@@ -52,7 +52,7 @@
         algorithms are implemented:
       </p>
<div class="table">
-<a name="id326539"></a><p class="title"><b>Table 1.1. Stepper Algorithms</b></p>
+<a name="id533115"></a><p class="title"><b>Table 1.1. Stepper Algorithms</b></p>
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -331,7 +331,7 @@
         sometimes also refered as lattices ODEs.
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers"></a><a class="link" href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers" title="Usage, Compilation, Headers">Usage,
       Compilation, Headers</a>
@@ -354,7 +354,7 @@
<p>
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.getting_started.short_example"></a><a class="link" href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.short_example" title="Short Example">Short
       Example</a>
@@ -369,9 +369,7 @@
         = (x,p)</em></span>:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">/* The type of container used to hold the state vector */</span>
<span class="keyword">typedef</span> <span class="identifier">std</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>
@@ -386,8 +384,6 @@
<span class="special">}</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         Here we chose <code class="computeroutput"><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>
@@ -403,17 +399,13 @@
         start:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">state_type</span> <span class="identifier">x</span><span class="special">(</span><span class="number">2</span><span class="special">);</span>
<span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> <span class="comment">// start at x=1.0, p=0.0
</span><span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">;</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         For the integration itself we'll use the <code class="computeroutput">integrate</code>
@@ -422,16 +414,12 @@
         stepper (5th order) and uses adaptive stepsize.
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">size_t</span> <span class="identifier">steps</span> <span class="special">=</span> <span class="identifier">integrate</span><span class="special">(</span> <span class="identifier">harmonic_oscillator</span> <span class="special">,</span>
                           <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">0.1</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         The integrate function expects as parameters the rhs of the ode as defined
@@ -447,9 +435,7 @@
         rhs must then be implemented as a functor having defined the ()-operator:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">/* The rhs of x' = f(x) defined as a class */</span>
<span class="keyword">class</span> <span class="identifier">harm_osc</span> <span class="special">{</span>
@@ -467,24 +453,18 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         which can be used via
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">harm_osc</span> <span class="identifier">ho</span><span class="special">(</span><span class="number">0.15</span><span class="special">);</span>
<span class="identifier">steps</span> <span class="special">=</span> <span class="identifier">integrate</span><span class="special">(</span> <span class="identifier">ho</span> <span class="special">,</span>
                    <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">0.1</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         You surely have already noticed that during the integration a lot of steps
@@ -493,9 +473,7 @@
         to provide a reasonable observer. An example is
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">push_back_state_and_time</span>
<span class="special">{</span>
@@ -513,17 +491,13 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         which stores the intermediate steps in a container. Now, you only have to
         pass this container to the integration function:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">vector</span><span class="special"><</span><span class="identifier">state_type</span><span class="special">></span> <span class="identifier">x_vec</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">times</span><span class="special">;</span>
@@ -539,8 +513,6 @@
<span class="special">}</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         That is all. Of course, you can use functional libraries like Boost.Lambda
@@ -562,7 +534,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="tutorial.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Reference</title>
<link rel="stylesheet" href="../boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="up" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="prev" href="concepts.html" title="Concepts">
</head>
@@ -12,9 +12,9 @@
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="concepts.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+<a accesskey="p" href="concepts.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_sandbox_numeric_odeint.reference"></a><a class="link" href="reference.html" title="Reference">Reference</a>
</h2></div></div></div>
@@ -27,13 +27,13 @@
<dt><span class="section">Operations</span></dt>
<dt><span class="section">Resizing</span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.reference.stepper_classes"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.stepper_classes" title="Stepper classes">Stepper
       classes</a>
</h3></div></div></div>
<div class="table">
-<a name="id383946"></a><p class="title"><b>Table 1.4. Stepper Algorithms</b></p>
+<a name="id589793"></a><p class="title"><b>Table 1.4. Stepper Algorithms</b></p>
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -201,7 +201,7 @@
</div>
<br class="table-break">
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.reference.integration_functions"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions" title="Integration functions">Integration
       functions</a>
@@ -212,22 +212,22 @@
<dt><span class="section"><a href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions.adaptive_step_size_functions">Adaptive
         step-size functions</a></span></dt>
</dl></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title">
+<div class="section"><div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.reference.integration_functions.constant_step_size_functions"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions.constant_step_size_functions" title="Constant step-size functions">Constant
         step-size functions</a>
</h4></div></div></div></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title">
+<div class="section"><div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.reference.integration_functions.adaptive_step_size_functions"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions.adaptive_step_size_functions" title="Adaptive step-size functions">Adaptive
         step-size functions</a>
</h4></div></div></div></div>
</div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.reference.algebras"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.algebras" title="Algebras">Algebras</a>
</h3></div></div></div></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.reference.operations"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.operations" title="Operations">Operations</a>
</h3></div></div></div></div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
+<div class="section"><div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.reference.resizing"></a><a class="link" href="reference.html#boost_sandbox_numeric_odeint.reference.resizing" title="Resizing">Resizing</a>
</h3></div></div></div></div>
</div>
@@ -241,7 +241,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="concepts.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+<a accesskey="p" href="concepts.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,8 +3,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Tutorial</title>
<link rel="stylesheet" href="../boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="up" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="prev" href="getting_started.html" title="Getting started">
<link rel="next" href="extend_odeint.html" title="Extend odeint">
@@ -13,9 +13,9 @@
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="getting_started.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="getting_started.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="extend_odeint.html"><img src="../images/next.png" alt="Next"></a>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_sandbox_numeric_odeint.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial">Tutorial</a>
</h2></div></div></div>
@@ -36,7 +36,7 @@
       examples</a></span></dt>
<dt><span class="section">References</span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator" title="Harmonic oscillator">Harmonic
       oscillator</a>
@@ -51,7 +51,7 @@
<dt><span class="section"><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.integration_with_adaptive_step_size">Integration
         with Adaptive Step Size</a></span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.define_the_ode"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.define_the_ode" title="Define the ODE">Define
         the ODE</a>
@@ -73,9 +73,7 @@
           to just define a function, e.g:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">/* The type of container used to hold the state vector */</span>
<span class="keyword">typedef</span> <span class="identifier">std</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>
@@ -90,8 +88,6 @@
<span class="special">}</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           The parameters of the function must follow the example above where <code class="computeroutput"><span class="identifier">x</span></code> is the current state, <code class="computeroutput"><span class="identifier">dxdt</span></code> is the derivative <span class="emphasis"><em>x'</em></span>
@@ -104,9 +100,7 @@
           parameter structure as above:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">/* The rhs of x' = f(x) defined as a class */</span>
<span class="keyword">class</span> <span class="identifier">harm_osc</span> <span class="special">{</span>
@@ -124,15 +118,13 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           odeint can deal with instances of such classes instead of pure functions
           which allows for cleaner code.
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.stepper_types"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.stepper_types" title="Stepper Types">Stepper
         Types</a>
@@ -149,7 +141,7 @@
           choose:
         </p>
<div class="table">
-<a name="id370055"></a><p class="title"><b>Table 1.2. Stepper Algorithms</b></p>
+<a name="id575770"></a><p class="title"><b>Table 1.2. Stepper Algorithms</b></p>
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -426,7 +418,7 @@
           which kind of steppers should be applied.
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.integration_with_constant_step_size"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.integration_with_constant_step_size" title="Integration with Constant Step Size">Integration
         with Constant Step Size</a>
@@ -444,16 +436,12 @@
           <span class="special">)</span></code> function from odeint:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">explicit_rk4</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <span class="identifier">stepper</span><span class="special">;</span>
<span class="identifier">integrate_const</span><span class="special">(</span> <span class="identifier">stepper</span> <span class="special">,</span> <span class="identifier">harmonic_oscillator</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           This call integrates the system defined by <code class="computeroutput"><span class="identifier">harmonic_oscillator</span></code>
@@ -465,20 +453,16 @@
           method which can used directly. So, you write down the above example as
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">dt</span> <span class="special">=</span> <span class="number">0.01</span><span class="special">;</span>
<span class="keyword">for</span><span class="special">(</span> <span class="keyword">double</span> <span class="identifier">t</span><span class="special">=</span><span class="number">0.0</span> <span class="special">;</span> <span class="identifier">t</span><span class="special"><</span><span class="number">10.0</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">stepper</span><span class="special">.</span><span class="identifier">do_step</span><span class="special">(</span> <span class="identifier">harmonic_oscillator</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>
<p>
- </p>
-<p>
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.integration_with_adaptive_step_size"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator.integration_with_adaptive_step_size" title="Integration with Adaptive Step Size">Integration
         with Adaptive Step Size</a>
@@ -493,16 +477,12 @@
           with 4th order error estimation and coefficients introduced by Cash-Karp.
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">explicit_error_rk54_ck</span><span class="special"><</span> <span class="identifier">state_type</span> <span class="special">></span> <span class="identifier">error_stepper_type</span><span class="special">;</span>
<span class="identifier">error_stepper_type</span> <span class="identifier">rk54</span><span class="special">;</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           Given the error stepper, one still needs an instance that checks the error
@@ -526,17 +506,13 @@
           stepper create by <code class="computeroutput"><span class="identifier">make_controlled_stepper_standard</span></code>.
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">error_stepper_type</span> <span class="special">></span> <span class="identifier">controlled_stepper_type</span><span class="special">;</span>
<span class="identifier">controlled_stepper_type</span> <span class="identifier">controlled_stepper</span><span class="special">;</span>
<span class="identifier">integrate_adaptive</span><span class="special">(</span> <span class="identifier">controlled_stepper</span> <span class="special">,</span> <span class="identifier">harmonic_oscillator</span> <span class="special">,</span> <span class="identifier">x</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="number">10.0</span> <span class="special">,</span> <span class="number">0.01</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           As above, this integrates the system defined by <code class="computeroutput"><span class="identifier">harmonic_oscillator</span></code>
@@ -559,7 +535,7 @@
         The full cpp file for this example can be found here: ../../examples/harmonic_oscillator.cpp
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.solar_system"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system" title="Solar system">Solar
       system</a>
@@ -570,7 +546,7 @@
<dt><span class="section"><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system.define_the_system_function">Define
         the system function</a></span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.solar_system.gravitation_and_energy_conservation"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system.gravitation_and_energy_conservation" title="Gravitation and energy conservation">Gravitation
         and energy conservation</a>
@@ -632,7 +608,7 @@
           f( q<sub>i</sub> )</em></span>.
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.solar_system.define_the_system_function"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system.define_the_system_function" title="Define the system function">Define
         the system function</a>
@@ -642,9 +618,7 @@
           space as well as the velocity. Therefore, we use the operators from Boost.Operators:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">/*the point type */</span>
<span class="keyword">template</span><span class="special"><</span> <span class="keyword">class</span> <span class="identifier">T</span> <span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">Dim</span> <span class="special">></span>
@@ -675,8 +649,6 @@
</span><span class="comment">// more operators
</span></pre>
<p>
- </p>
-<p>
         </p>
<p>
           The next step is to define a container type storing the values of <span class="emphasis"><em>q</em></span>
@@ -684,9 +656,7 @@
           type we use <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">array</span></code>
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">// we simulate 5 planets and the sun
</span><span class="keyword">const</span> <span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">6</span><span class="special">;</span>
@@ -696,8 +666,6 @@
<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><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> <span class="identifier">mass_type</span><span class="special">;</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           The <code class="computeroutput"><span class="identifier">container_type</span></code> is different
@@ -711,9 +679,7 @@
           As system function we have to provide <span class="emphasis"><em>f(p)</em></span> and <span class="emphasis"><em>f(q)</em></span>:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">gravitational_constant</span> <span class="special">=</span> <span class="number">2.95912208286e-4</span><span class="special">;</span>

@@ -731,13 +697,9 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">solar_system_momentum</span>
<span class="special">{</span>
@@ -765,8 +727,6 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           In general a three body-system is chaotic, hence we can not expect that
@@ -781,9 +741,7 @@
           apply here:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">symplectic_rkn_sb3a_mclachlan</span><span class="special"><</span> <span class="identifier">container_type</span> <span class="special">></span> <span class="identifier">stepper_type</span><span class="special">;</span>
<span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">dt</span> <span class="special">=</span> <span class="number">100.0</span><span class="special">;</span>
@@ -795,8 +753,6 @@
                 <span class="number">0.0</span> <span class="special">,</span> <span class="number">200000.0</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">,</span> <span class="identifier">streaming_observer</span><span class="special">(</span> <span class="identifier">cout</span> <span class="special">)</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           These integration routine was used to produce the above sketch of the solar
@@ -809,9 +765,7 @@
           is also passed, but this is not a problem at all:
         </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">streaming_observer</span>
<span class="special">{</span>
@@ -830,15 +784,13 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
         </p>
<p>
           The full example can be found here: ../../examples/solar_system.cpp
         </p>
</div>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents" title="Chaotic systems and Lyapunov exponents">Chaotic
       systems and Lyapunov exponents</a>
@@ -852,16 +804,16 @@
         via
       </p>
<p>
- <span class="emphasis"><em>d delta x / dt = J(x) delta x</em></span>
+ <span class="emphasis"><em>d δ x / dt = J(x) δ x</em></span>
       </p>
<p>
         where <span class="emphasis"><em>J</em></span> is the Jacobian of the system under consideration.
- <span class="emphasis"><em>delta x</em></span> cam also be interpreted as a perturbation of
- the original system. In principle <span class="emphasis"><em>n</em></span> of these perturbations
- exit, they form a hypercube and evolve in the time. The Lyapunov exponents
- are then defined as logarithmic growth rates of the perturbations. If one
- Lyapunov exponent is larger then zero nearby trajectories divergy exponentially
- hence they are chaotic. If the largest Lyapunov exponent is zero one is usually
+ <span class="emphasis"><em>δ x</em></span> cam also be interpreted as a perturbation of the original
+ system. In principle <span class="emphasis"><em>n</em></span> of these perturbations exit,
+ they form a hypercube and evolve in the time. The Lyapunov exponents are
+ then defined as logarithmic growth rates of the perturbations. If one Lyapunov
+ exponent is larger then zero nearby trajectories divergy exponentially hence
+ they are chaotic. If the largest Lyapunov exponent is zero one is usually
         faced with periodic motion. In the case of a largest Lyapunov exponent smaller
         then zero the converges the a fixed point. More informations about Lyapunov
         exponents and nonlinear dynamical systems can be found in many textbooks,
@@ -890,7 +842,9 @@
<span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">R</span> <span class="special">=</span> <span class="number">28.0</span><span class="special">;</span>
<span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">8.0</span> <span class="special">/</span> <span class="number">3.0</span><span class="special">;</span>

-<span class="keyword">void</span> <span class="identifier">lorenz</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">state_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">,</span> <span class="identifier">state_type</span> <span class="special">&</span><span class="identifier">dxdt</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span>
+<span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">tr1</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">,</span> <span class="number">3</span> <span class="special">></span> <span class="identifier">lorenz_state_type</span><span class="special">;</span>
+
+<span class="keyword">void</span> <span class="identifier">lorenz</span><span class="special">(</span> <span class="keyword">const</span> <span class="identifier">lorenz_state_type</span> <span class="special">&</span><span class="identifier">x</span> <span class="special">,</span> <span class="identifier">lorenz_state_type</span> <span class="special">&</span><span class="identifier">dxdt</span> <span class="special">,</span> <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
     <span class="identifier">dxdt</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">sigma</span> <span class="special">*</span> <span class="special">(</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">);</span>
     <span class="identifier">dxdt</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">R</span> <span class="special">*</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">[</span><span class="number">1</span><span class="special">]</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">*</span> <span class="identifier">x</span><span class="special">[</span><span class="number">2</span><span class="special">];</span>
@@ -898,11 +852,11 @@
<span class="special">}</span>
</pre>
<p>
- Now, we need also need to integrate the set of the perturbations. This is
- done in parallel to the original system, hence within one system function.
- Of course, we want to use the above defintion of the Lorenz system, hence
- the definition of the system function including the Lorenz system itself
- and the perturbation could look like:
+ We need also need to integrate the set of the perturbations. This is done
+ in parallel to the original system, hence within one system function. Of
+ course, we want to use the above defintion of the Lorenz system, hence the
+ definition of the system function including the Lorenz system itself and
+ the perturbation could look like:
       </p>
<p>

@@ -931,9 +885,10 @@
<p>
       </p>
<p>
- But this approach will not work, since lorenz() and lorenz_with_lyap() have different state type. A simple
- trick to over come this problem is put the Lorenz system inside a functor
- with templatized arguments:
+ The perturbations are stored linearly in the <code class="computeroutput"><span class="identifier">state_type</span></code>
+ behind the state of the Lorenz system. The problem that lorenz() and lorenz_with_lyap() have different
+ state types. A simple trick to over come this problem is put the Lorenz system
+ inside a functor with templatized arguments:
       </p>
<p>

@@ -1007,9 +962,7 @@
         the system ready to work with Boost.Range the system has to by changed:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">lorenz</span>
<span class="special">{</span>
@@ -1026,44 +979,44 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         This is in principle all. Now, we only have to call <code class="computeroutput"><span class="identifier">integrate_n_steps</span></code>
         with an suited range:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="comment">// perform 10000 transient steps
</span><span class="identifier">integrate_n_steps</span><span class="special">(</span> <span class="identifier">rk4</span> <span class="special">,</span> <span class="identifier">lorenz</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">make_pair</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="identifier">n</span> <span class="special">)</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">,</span> <span class="identifier">dt</span> <span class="special">,</span> <span class="number">10000</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         Having integrated a sufficient number of transients steps we are now able
         to calculate the Lyapunov exponents:
       </p>
-<div class="orderedlist"><ol type="1">
-<li>
- First, we initialize the perturbations. They are stored linearly behind
- the state of the Lorenz system. The perturbation are initialized such that
- they fullfill <span class="emphasis"><em>< p <sub>i</sub> , p<sub>j</sub> > = delta <sub>ij</sub> </em></span> where <,>
- is the classical scalar product and delta <sub>ij</sub> is the Kronecker symbol.
- </li>
-<li>
- as
- </li>
+<div class="orderedlist"><ol class="orderedlist" type="1">
+<li class="listitem">
+ We initialize the perturbations. They are stored linearly behind the
+ state of the Lorenz system. The perturbation are initialized such that
+ they fullfill <span class="emphasis"><em>< p <sub>i</sub> , p<sub>j</sub> > = δ <sub>ij</sub> </em></span> where <span class="emphasis"><em><,></em></span>
+ is the classical scalar product and <span class="emphasis"><em>δ <sub>ij</sub></em></span> is the Kronecker
+ symbol.
+ </li>
+<li class="listitem">
+ Integrate 100 steps of the full system with perturbations
+ </li>
+<li class="listitem">
+ Orthonormalize the perturbation using Gram-Schmidt orthonormalization
+ algorithm.
+ </li>
+<li class="listitem">
+ Repeat step 2 and 3. Every 10000 steps write the current Lyapunov exponent.
+ </li>
</ol></div>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="identifier">fill</span><span class="special">(</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">begin</span><span class="special">()+</span><span class="identifier">n</span> <span class="special">,</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">end</span><span class="special">()</span> <span class="special">,</span> <span class="number">0.0</span> <span class="special">);</span>
<span class="keyword">for</span><span class="special">(</span> <span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span> <span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="identifier">num_of_lyap</span> <span class="special">;</span> <span class="special">++</span><span class="identifier">i</span> <span class="special">)</span> <span class="identifier">x</span><span class="special">[</span><span class="identifier">n</span><span class="special">+</span><span class="identifier">n</span><span class="special">*</span><span class="identifier">i</span><span class="special">+</span><span class="identifier">i</span><span class="special">]</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span>
@@ -1086,14 +1039,12 @@
<span class="special">}</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
- gram schmitt
+ The full code can be found here: ../../examples/chaotic_system.cpp
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.stiff_systems"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.stiff_systems" title="Stiff systems">Stiff
       systems</a>
@@ -1121,9 +1072,7 @@
         is needed. Here is the definition of the above example
       </p>
<p>
- </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">vector_type</span><span class="special">;</span>
<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">matrix</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">matrix_type</span><span class="special">;</span>
@@ -1151,8 +1100,6 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         The state type has to be a <code class="computeroutput"><span class="identifier">ublas</span><span class="special">::</span><span class="identifier">vector</span></code>
@@ -1162,9 +1109,7 @@
         just templatize the <code class="computeroutput"><span class="keyword">operator</span><span class="special">()</span></code>:
       </p>
<p>
- </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">vector_type</span><span class="special">;</span>
<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">matrix</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">matrix_type</span><span class="special">;</span>
@@ -1186,8 +1131,6 @@
<span class="special">};</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         Now you can use <code class="computeroutput"><span class="identifier">stiff_system</span></code>
@@ -1202,9 +1145,7 @@
         all the other stepper:
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">rosenbrock4</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">stepper_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">rosenbrock4_controller</span><span class="special"><</span> <span class="identifier">stepper_type</span> <span class="special">></span> <span class="identifier">controlled_stepper_type</span><span class="special">;</span>
@@ -1218,8 +1159,6 @@
                 <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">phoenix</span><span class="special">::</span><span class="identifier">arg_names</span><span class="special">::</span><span class="identifier">arg2</span> <span class="special"><<</span> <span class="string">" "</span> <span class="special"><<</span> <span class="identifier">phoenix</span><span class="special">::</span><span class="identifier">arg_names</span><span class="special">::</span><span class="identifier">arg1</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         During the integration 71 steps have been done. Comparing to a classical
@@ -1227,9 +1166,7 @@
         5 method with step size control and dense output yields 1531 steps.
       </p>
<p>
- </p>
-<p>
-
+
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">explicit_error_dopri5</span><span class="special"><</span> <span class="identifier">vector_type</span> <span class="special">></span> <span class="identifier">dopri5_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">controlled_error_stepper</span><span class="special"><</span> <span class="identifier">dopri5_type</span> <span class="special">></span> <span class="identifier">controlled_dopri5_type</span><span class="special">;</span>
@@ -1242,8 +1179,6 @@
                 <span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">phoenix</span><span class="special">::</span><span class="identifier">arg_names</span><span class="special">::</span><span class="identifier">arg2</span> <span class="special"><<</span> <span class="string">" "</span> <span class="special"><<</span> <span class="identifier">phoenix</span><span class="special">::</span><span class="identifier">arg_names</span><span class="special">::</span><span class="identifier">arg1</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special"><<</span> <span class="string">"\n"</span> <span class="special">);</span>
</pre>
<p>
- </p>
-<p>
       </p>
<p>
         Note, that we have used Boost.Phoenix
@@ -1253,7 +1188,7 @@
         The full example can be found here: ../../examples/stiff_system.cpp
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.odeint_in_detail"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.odeint_in_detail" title="Odeint in detail">Odeint
       in detail</a>
@@ -1280,7 +1215,7 @@
         Overview and table
       </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics" title="Special topics">Special
       topics</a>
@@ -1309,7 +1244,7 @@
<dt><span class="section"><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.self_expanding_lattices">Self
         expanding lattices</a></span></dt>
</dl></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.complex_state_types"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.complex_state_types" title="Complex state types">Complex
         state types</a>
@@ -1324,7 +1259,7 @@
           DNLS
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.lattice_systems"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.lattice_systems" title="Lattice systems">Lattice
         systems</a>
@@ -1333,7 +1268,7 @@
           Fermi-Pasta-Ulam system
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.partial_differential_equations"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.partial_differential_equations" title="Partial differential equations">Partial
         differential equations</a>
@@ -1348,7 +1283,7 @@
           Ginzburg-Landau
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__units"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__units" title="Using boost::units">Using
         boost::units</a>
@@ -1357,7 +1292,7 @@
           blah blah
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.using_cuda_and_thrust"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_cuda_and_thrust" title="Using Cuda and Thrust">Using
         Cuda and Thrust</a>
@@ -1366,7 +1301,7 @@
           blah blah
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.using_matrices_as_state_types"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_matrices_as_state_types" title="Using matrices as state types">Using
         matrices as state types</a>
@@ -1375,11 +1310,11 @@
           Expanding resizing
         </p>
</div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title">
+<div class="section"><div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.ordinary_differential_equations_on_networks"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.ordinary_differential_equations_on_networks" title="Ordinary differential equations on networks">Ordinary
         differential equations on networks</a>
</h4></div></div></div></div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.pass_by_value_or_by_reference"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.pass_by_value_or_by_reference" title="Pass by value or by reference">Pass
         by value or by reference</a>
@@ -1388,7 +1323,7 @@
           blah blah
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__range"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__range" title="Using boost::range">Using
         boost::range</a>
@@ -1397,7 +1332,7 @@
           blah blah
         </p>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.using_arbitrary_precision_floating_point_types"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_arbitrary_precision_floating_point_types" title="Using arbitrary precision floating point types">Using
         arbitrary precision floating point types</a>
@@ -1406,12 +1341,12 @@
           GMP
         </p>
</div>
-<div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title">
+<div class="section"><div class="titlepage"><div><div><h4 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.special_topics.self_expanding_lattices"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.self_expanding_lattices" title="Self expanding lattices">Self
         expanding lattices</a>
</h4></div></div></div></div>
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.all_examples"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.all_examples" title="All examples">All
       examples</a>
@@ -1420,7 +1355,7 @@
         The following table gives an overview over all examples.
       </p>
<div class="table">
-<a name="id380798"></a><p class="title"><b>Table 1.3. Examples Overview</b></p>
+<a name="id586564"></a><p class="title"><b>Table 1.3. Examples Overview</b></p>
<div class="table-contents"><table class="table" summary="Examples Overview">
<colgroup>
<col>
@@ -1494,7 +1429,7 @@
</div>
<br class="table-break">
</div>
-<div class="section" lang="en">
+<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_sandbox_numeric_odeint.tutorial.references"></a><a class="link" href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.references" title="References">References</a>
</h3></div></div></div>
@@ -1551,7 +1486,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="getting_started.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="getting_started.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="extend_odeint.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -3,15 +3,15 @@
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chapter 1. boost.sandbox.numeric.odeint</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
+<link rel="home" href="index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
<link rel="next" href="boost_sandbox_numeric_odeint/getting_started.html" title="Getting started">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
-<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
-<div class="chapter" lang="en">
+<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
+<div class="chapter">
<div class="titlepage"><div>
<div><h2 class="title">
<a name="odeint"></a>Chapter 1. boost.sandbox.numeric.odeint</h2></div>
@@ -23,7 +23,7 @@
</h3></div></div>
<div><p class="copyright">Copyright © 2009 -2011 Karsten Ahnert and Mario Mulansky</p></div>
<div><div class="legalnotice">
-<a name="id358081"></a><p>
+<a name="id563828"></a><p>
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       </p>
@@ -95,10 +95,10 @@
</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: April 12, 2011 at 13:09:10 GMT</small></p></td>
+<td align="left"><p><small>Last revised: April 12, 2011 at 15:11:39 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="../../../../doc/html/images/next.png" alt="Next"></a></div>
+<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>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -29,6 +29,8 @@

[def __alpha '''α''']
+[def __delta '''δ''']
+[def __Delta '''Δ''']
[def __lambda '''λ'''][/lower case]
[def __Lambda '''Λ'''][/upper case]
[def __gamma '''γ''']
@@ -37,6 +39,7 @@
[def __Sigma '''Σ''']
[def __space '''''']

+
[template super[x]'''<superscript>'''[x]'''</superscript>''']
[template sub[x]'''<subscript>'''[x]'''</subscript>''']
[template subl[x]'''<subscript>'''__space[x]'''</subscript>''']

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_chaotic_system.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_chaotic_system.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_chaotic_system.qbk 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -4,9 +4,9 @@

Odeint can easily be used to investigate the properties of chaotic deterministic systems. In mathematical terms chaotic refers to an exponential growth of perturbations. In order to observe this exponential growth one usually solves the equations for the tangential dynamics which is again an ordinary differential equation. These equations are linear but time dependent and can be obtained via

-['d delta x / dt = J(x) delta x]
+['d __delta x / dt = J(x) __delta x]

-where ['J] is the Jacobian of the system under consideration. ['delta x] cam also be interpreted as a perturbation of the original system. In principle ['n] of these perturbations exit, they form a hypercube and evolve in the time. The Lyapunov exponents are then defined as logarithmic growth rates of the perturbations. If one Lyapunov exponent is larger then zero nearby trajectories divergy exponentially hence they are chaotic. If the largest Lyapunov exponent is zero one is usually faced with periodic motion. In the case of a largest Lyapunov exponent smaller then zero the converges the a fixed point. More informations about Lyapunov exponents and nonlinear dynamical systems can be found in many textbooks, see for example .
+where ['J] is the Jacobian of the system under consideration. ['__delta x] cam also be interpreted as a perturbation of the original system. In principle ['n] of these perturbations exit, they form a hypercube and evolve in the time. The Lyapunov exponents are then defined as logarithmic growth rates of the perturbations. If one Lyapunov exponent is larger then zero nearby trajectories divergy exponentially hence they are chaotic. If the largest Lyapunov exponent is zero one is usually faced with periodic motion. In the case of a largest Lyapunov exponent smaller then zero the converges the a fixed point. More informations about Lyapunov exponents and nonlinear dynamical systems can be found in many textbooks, see for example .

To calculate the Lyapunov exponents numerically one usually solves the equations of motion for ['n] perturbations und orthonormalized them every ['k] steps. The Lyapunov exponent is the average the logarithm of the stretching factor of each perturbation.

@@ -19,14 +19,16 @@
const double R = 28.0;
const double b = 8.0 / 3.0;

-void lorenz( const state_type &x , state_type &dxdt , double t )
+typedef std::tr1::array< double , 3 > lorenz_state_type;
+
+void lorenz( const lorenz_state_type &x , lorenz_state_type &dxdt , double t )
{
     dxdt[0] = sigma * ( x[1] - x[0] );
     dxdt[1] = R * x[0] - x[1] - x[0] * x[2];
     dxdt[2] = -b * x[2] + x[0] * x[1];
}
``
-Now, we need also need to integrate the set of the perturbations. This is done in parallel to the original system, hence within one system function. Of course, we want to use the above defintion of the Lorenz system, hence the definition of the system function including the Lorenz system itself and the perturbation could look like:
+We need also need to integrate the set of the perturbations. This is done in parallel to the original system, hence within one system function. Of course, we want to use the above defintion of the Lorenz system, hence the definition of the system function including the Lorenz system itself and the perturbation could look like:

``
const size_t n = 3;
@@ -51,7 +53,8 @@
}
``

-But this approach will not work, since '''lorenz()''' and '''lorenz_with_lyap()''' have different state type. A simple trick to over come this problem is put the Lorenz system inside a functor with templatized arguments:
+The perturbations are stored linearly in the `state_type` behind the state of the Lorenz system.
+The problem that '''lorenz()''' and '''lorenz_with_lyap()''' have different state types. A simple trick to over come this problem is put the Lorenz system inside a functor with templatized arguments:

``
struct lorenz
@@ -111,17 +114,15 @@

Having integrated a sufficient number of transients steps we are now able to calculate the Lyapunov exponents:

-# First, we initialize the perturbations. They are stored linearly behind the state of the Lorenz system. The perturbation are initialized such that they fullfill
-[' < p [subl i] , p[subl j] > = delta [subl ij] ]
-where <,> is the classical scalar product and delta [subl ij] is the Kronecker symbol.
-# as
-
+# We initialize the perturbations. They are stored linearly behind the state of the Lorenz system. The perturbation are initialized such that they fullfill
+[' < p [subl i] , p[subl j] > = __delta [subl ij] ]
+where ['<,>] is the classical scalar product and ['__delta [subl ij]] is the Kronecker symbol.
+# Integrate 100 steps of the full system with perturbations
+# Orthonormalize the perturbation using Gram-Schmidt orthonormalization algorithm.
+# Repeat step 2 and 3. Every 10000 steps write the current Lyapunov exponent.

[lyapunov_full_code]

-
-
-
-gram schmitt
+The full code can be found here: [@../../examples/chaotic_system.cpp]

[endsect]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/chaotic_system.cpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/chaotic_system.cpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/chaotic_system.cpp 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -14,7 +14,7 @@

#include <boost/numeric/odeint.hpp>

-#include "gram_schmitt.hpp"
+#include "gram_schmidt.hpp"

using namespace std;
using namespace boost::numeric::odeint;
@@ -95,7 +95,7 @@
     while( true )
     {
             t = integrate_n_steps( rk4 , lorenz_with_lyap , x , t , dt , 100 );
- gram_schmitt( x , lyap , n , num_of_lyap );
+ gram_schmidt( x , lyap , n , num_of_lyap );
             ++count;

         if( !(count % 100000) )

Copied: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmidt.hpp (from r71199, /sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp)
==============================================================================
--- /sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmidt.hpp 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
@@ -35,7 +35,7 @@
}

template< class StateType , class LyapType >
-void gram_schmitt( StateType &x , LyapType &lyap , size_t n , size_t num_of_lyap )
+void gram_schmidt( StateType &x , LyapType &lyap , size_t n , size_t num_of_lyap )
{
if( !num_of_lyap ) return;
if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )

Deleted: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/gram_schmitt.hpp 2011-04-12 10:12:41 EDT (Tue, 12 Apr 2011)
+++ (empty file)
@@ -1,88 +0,0 @@
-/*
- boost header: numeric/odeint/gram_schmitt.hpp
-
- Copyright 2009 Karsten Ahnert
- Copyright 2009 Mario Mulansky
- Copyright 2009 Andre Bergner
-
- Distributed under the Boost Software License, Version 1.0.
- (See accompanying file LICENSE_1_0.txt or
- copy at http://www.boost.org/LICENSE_1_0.txt)
- */
-
-#ifndef BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
-#define BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED
-
-#include <iterator>
-#include <algorithm>
-#include <numeric>
-
-namespace boost {
-namespace numeric {
-namespace odeint {
-
-template< class Iterator , class T >
-void normalize( Iterator first , Iterator last , T norm )
-{
- while( first != last ) *first++ /= norm;
-}
-
-template< class Iterator , class T >
-void substract_vector( Iterator first1 , Iterator last1 ,
- Iterator first2 , T val )
-{
- while( first1 != last1 ) *first1++ -= val * ( *first2++ );
-}
-
-template< class StateType , class LyapType >
-void gram_schmitt( StateType &x , LyapType &lyap , size_t n , size_t num_of_lyap )
-{
- if( !num_of_lyap ) return;
- if( ptrdiff_t( ( num_of_lyap + 1 ) * n ) != std::distance( x.begin() , x.end() ) )
- throw std::domain_error( "renormalization() : size of state does not match the number of lyapunov exponents." );
-
- typedef typename StateType::value_type value_type;
- typedef typename StateType::iterator iterator;
-
- value_type norm[num_of_lyap] , tmp[num_of_lyap];
- iterator first = x.begin() + n;
- iterator beg1 = first , end1 = first + n ;
-
- std::fill( norm , norm+num_of_lyap , 0.0 );
-
- // normalize first vector
- norm[0] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
- normalize( beg1 , end1 , norm[0] );
-
- beg1 += n;
- end1 += n;
-
- for( size_t j=1 ; j<num_of_lyap ; ++j , beg1+=n , end1+=n )
- {
- for( size_t k=0 ; k<j ; ++k )
- {
- tmp[k] = std::inner_product( beg1 , end1 , first + k*n , 0.0 );
-// clog << j << " " << k << " " << tmp[k] << "\n";
- }
-
-
-
- for( size_t k=0 ; k<j ; ++k )
- substract_vector( beg1 , end1 , first + k*n , tmp[k] );
-
- // nromalize j-th vector
- norm[j] = sqrt( std::inner_product( beg1 , end1 , beg1 , 0.0 ) );
-// clog << j << " " << norm[j] << "\n";
- normalize( beg1 , end1 , norm[j] );
- }
-
- for( size_t j=0 ; j<num_of_lyap ; j++ )
- lyap[j] += log( norm[j] );
-}
-
-
-} // namespace odeint
-} // namespace numeric
-} // namespace boost
-
-#endif //BOOST_NUMERIC_ODEINT_GRAM_SCHMITT_HPP_INCLUDED

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