Boost-Commit :

Date view	Thread view	Subject view	Author view

Subject: [Boost-commit] svn:boost r71914 - in sandbox/odeint/branches/karsten/libs/numeric/odeint/doc: . html html/boost_sandbox_numeric_odeint
From: karsten.ahnert_at_[hidden]
Date: 2011-05-13 06:21:58

Author: karsten
Date: 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
New Revision: 71914
URL: http://svn.boost.org/trac/boost/changeset/71914

Log:
chunk the first section
Removed:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html
Text files modified:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/Jamfile | 4
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html | 450 ------------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html | 30
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html | 46 -
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html | 964 ---------------------------------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html | 565 ++++++++++++++++++++++-
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk | 3
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/reference.qbk | 1
   8 files changed, 575 insertions(+), 1488 deletions(-)

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/Jamfile
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/Jamfile (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/Jamfile 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -18,8 +18,8 @@
 :
 <xsl:param>navig.graphics=1
 <xsl:param>boost.root=../../../..
- <xsl:param>chunk.section.depth=1
- <xsl:param>chunk.first.sections=1
+ <xsl:param>chunk.section.depth=2
+ <xsl:param>chunk.first.sections=0
 <xsl:param>toc.section.depth=2
 <xsl:param>toc.max.depth=2
 <xsl:param>generate.section.toc.level=3

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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -6,14 +6,14 @@
<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">
+<link rel="prev" href="extend_odeint/adapt_your_own_operations.html" title="Adapt your own operations">
+<link rel="next" href="concepts/error_stepper.html" title="Error stepper">
</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="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>
+<a accesskey="p" href="extend_odeint/adapt_your_own_operations.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/error_stepper.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -22,15 +22,15 @@
<div class="toc"><dl>
<dt><a href="concepts.html#boost_sandbox_numeric_odeint.concepts.basic_stepper">Basic
 stepper</a></dt>
-<dt><a href="concepts.html#boost_sandbox_numeric_odeint.concepts.error_stepper">Error
+<dt><a href="concepts/error_stepper.html">Error
 stepper</a></dt>
-<dt><a href="concepts.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper">Controlled
+<dt><a href="concepts/controlled_stepper.html">Controlled
 stepper</a></dt>
-<dt><a href="concepts.html#boost_sandbox_numeric_odeint.concepts.dense_ouput_stepper">Dense
+<dt><a href="concepts/dense_ouput_stepper.html">Dense
 ouput stepper</a></dt>
-<dt><a href="concepts.html#boost_sandbox_numeric_odeint.concepts.size_adjusting_stepper">Size
+<dt><a href="concepts/size_adjusting_stepper.html">Size
 adjusting stepper</a></dt>
-<dt>CompositeStepper</dt>
+<dt>CompositeStepper</dt>
</dl></div>

 The odeint library defines three concepts for stepping objects.
@@ -312,438 +312,6 @@
 </li>
</ul></div>
</div>
-<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>
-</h3></div></div></div>
-
- Error steppers execute one timestep of a specific order with a given stepsize.
- Additionally, an error estimation of the obtained result is computed that
- can be used to control the error introduced by the time discretization. Like
- the basic steppers, error steppers usually allocate internal memory to store
- intermediate function call results. If state types with variable size are
- used (e.g. <code class="computeroutput">vector</code>), it has
- to be assured that the stepper gets informed about any change of the state
- size by calling its <code class="computeroutput">adjust_size</code>
- method.
- 
-
- Associated Types
- 
-
- Same as for basic steppers above.
- 
-
- Methods
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">Error_Stepper()</code>
- Constructor.
- </li>
-<li class="listitem">
- <code class="computeroutput">Error_Stepper(
- container_type &x )</code>
- Constructor that allocates internal memory to store intermediate results
- of the same size as <code class="computeroutput">x</code>.
- </li>
-<li class="listitem">
- <code class="computeroutput">void do_step( DynamicalSystem
- &system
- , container_type
- &x
- , time_type
- t ,
- time_type dt
- , container_type
- &xerr)</code>
- </li>
-</ul></div>
-
- Executes one timestep with the given parameters:
- 
-<div class="informaltable"><table class="table">
-<colgroup>
-<col>
-<col>
-<col>
-</colgroup>
-<thead><tr>
-<th>
- 
- Parameter
- 
- </th>
-<th>
- 
- Type
- 
- </th>
-<th>
- 
- Description
- 
- </th>
-</tr></thead>
-<tbody>
-<tr>
-<td>
- 
- system
- 
- </td>
-<td>
- 
- DynamicalSystem
- 
- </td>
-<td>
- 
- Function (callable object) that computes the rhs of the ode
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- x
- 
- </td>
-<td>
- 
- container_type
- 
- </td>
-<td>
- 
- The current state of the system x(t)
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- t
- 
- </td>
-<td>
- 
- time_type
- 
- </td>
-<td>
- 
- The current time t
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- dt
- 
- </td>
-<td>
- 
- time_type
- 
- </td>
-<td>
- 
- Length of the timestep to be executed
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- xerr
- 
- </td>
-<td>
- 
- container_type
- 
- </td>
-<td>
- 
- Used by the method to return the error estimation of this computation
- 
- </td>
-</tr>
-</tbody>
-</table></div>
-
- The result of this method is the (approximate) state of the system x(t+dt), which is returned in the variable <code class="computeroutput">x</code> (in-place), and the corresponding error
- estimation returned in <code class="computeroutput">xerr</code>.
- Note, that the time <code class="computeroutput">t</code> is
- not automatically increased by this method.
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
- <code class="computeroutput">void do_step( DynamicalSystem
- &system
- , container_type
- &x
- , const
- container_type &dxdt , time_type t
- , time_type
- dt ,
- container_type &xerr)</code>
- </li></ul></div>
-
- The same as above but with the additional parameter <code class="computeroutput">dxdt</code>
- that represents the derivative x'(t) = f(x,t)
- at the time t.
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">void adjust_size( const container_type &x )</code>
- Adjusts the internal memory to store intermediate results of the same
- size as <code class="computeroutput">x</code>. This function
- must be called whenever the system size changes
- during the integration.
- </li>
-<li class="listitem">
- <code class="computeroutput">order_type order_error_step()</code> Returns the order of the result x(t+dt) of the algorithm.
- </li>
-<li class="listitem">
- <code class="computeroutput">order_type order_error()</code> Returns the order of the error estimation
- of the algorithm.
- </li>
-</ul></div>
-
- Stepper that model this concept
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">stepper_rk5_ck</code>
- </li>
-<li class="listitem">
- <code class="computeroutput">stepper_rk78_fehlberg</code>
- </li>
-<li class="listitem">
- <code class="computeroutput">stepper_half_step</code>
- </li>
-</ul></div>
-</div>
-<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>
-</h3></div></div></div>
-
- Controlled steppers try to execute a timestep with a given error threshold.
- If the estimated error of the obtained solution is too big, the result is
- rejected and a new stepsize is proposed. If the error is small enough the
- timestep is accepted and possibly an increased stepsize is proposed.
- 
-
- Associated Types
- 
-
- Same as for basic steppers above.
- 
-
- Methods
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
- <code class="computeroutput">Controlled_Stepper(
- time_type abs_err, time_type
- rel_err,
- time_type factor_x, time_type
- factor_dxdt )</code>
- </li></ul></div>
-
- Constructor that initializes the controlled stepper with several parameters
- of the error control. The controlled stepper assures that the error done
- by each individual timestep yields:
- 
-
- xerr < 1.1 ( eps_abs + eps_rel * (factor_x |x| +
- factor_dxdt h |x'|) ) 
- 
-
- The factor 1.1 is for safety to avoid unnecessary many stepsize adjustings.
- The above inequality should be understand to hold for all
- components of the possibly more dimensional vectors x,
- x' and xerr.
- If the estimated error is too large, a reduced stepsize will be suggested.
- If the estimated error is less than half of the desired error, an increased
- stepsize will be suggested.
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">Controlled_Stepper(
- container_type &x, time_type abs_err, time_type
- rel_err,
- time_type factor_x, time_type
- factor_dxdt )</code>
- Same as above, but with additional allocation of the internal memory
- to store intermediate results of the same size as <code class="computeroutput">x</code>.
- </li>
-<li class="listitem">
- <code class="computeroutput">controlled_step_result try_step(
- DynamicalSystem &system, container_type &x, time_type &t, time_type &dt )</code>
- </li>
-</ul></div>
-
- Tries one timestep with the given parameters
- 
-<div class="informaltable"><table class="table">
-<colgroup>
-<col>
-<col>
-<col>
-</colgroup>
-<thead><tr>
-<th>
- 
- Parameter
- 
- </th>
-<th>
- 
- Type
- 
- </th>
-<th>
- 
- Description
- 
- </th>
-</tr></thead>
-<tbody>
-<tr>
-<td>
- 
- system
- 
- </td>
-<td>
- 
- DynamicalSystem
- 
- </td>
-<td>
- 
- Function (callable object) that computes the rhs of the ode
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- x
- 
- </td>
-<td>
- 
- container_type
- 
- </td>
-<td>
- 
- The current state of the system x(t)
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- t
- 
- </td>
-<td>
- 
- time_type
- 
- </td>
-<td>
- 
- The current time t
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- dt
- 
- </td>
-<td>
- 
- time_type
- 
- </td>
-<td>
- 
- Length of the timestep to be executed
- 
- </td>
-</tr>
-</tbody>
-</table></div>
-
- This method has three possible outcomes represented by the returned value
- <code class="computeroutput">result</code>: If <code class="computeroutput">result = success</code> the step has been applied and x
- contains the new state x(t) where the time
- has also been increased t += dt. If <code class="computeroutput">result = step_size_increased</code> the step has also been
- accomplished, but the estimated error was so small that a new stepsize is
- proposed in the variable <code class="computeroutput">dt</code>.
- If <code class="computeroutput">result =
- step_size_decreased</code> the step has
- been rejected due to a too big error. <code class="computeroutput">x</code>
- and <code class="computeroutput">t</code> remain unchanged and
- <code class="computeroutput">dt</code> now containes the suggested
- reduced stepsize that should give an error below the desired level.
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">controlled_step_result try_step(
- DynamicalSystem &system, container_type &x, const container_type
- &dxdt, time_type
- &t, time_type
- &dt
- )</code> Same as above but with the additional
- parameter <code class="computeroutput">dxdt</code> that that
- represents the derivative x'(t) = f(x,t)
- at the time t.
- </li>
-<li class="listitem">
- <code class="computeroutput">void adjust_size( const container_type &x )</code>
- Adjusts the internal memory to store intermediate results of the same
- size as <code class="computeroutput">x</code>. This function
- must be called whenever the system size changes
- during the integration.
- </li>
-<li class="listitem">
- <code class="computeroutput">order_type order_error_step()</code> Returns the order of the result x(t+dt) of the algorithm.
- </li>
-</ul></div>
-
- Stepper that model this concept
- 
-<div class="itemizedlist"><ul class="itemizedlist" type="disc">
-<li class="listitem">
- <code class="computeroutput">controlled_stepper_standard</code>
- </li>
-<li class="listitem">
- <code class="computeroutput">controlled_stepper_bs</code>
- </li>
-</ul></div>
-</div>
-<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"><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"><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>

 see the wiki
 
@@ -758,7 +326,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="extend_odeint.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../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>
+<a accesskey="p" href="extend_odeint/adapt_your_own_operations.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/error_stepper.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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -6,14 +6,14 @@
<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">
+<link rel="prev" href="tutorial/references.html" title="References">
+<link rel="next" href="extend_odeint/adapt_your_own_containers.html" title="Adapt your own containers">
</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="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>
+<a accesskey="p" href="tutorial/references.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/adapt_your_own_containers.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -22,33 +22,15 @@
<div class="toc"><dl>
<dt><a href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.write_own_steppers">Write
 own steppers</a></dt>
-<dt><a href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_containers">Adapt
+<dt><a href="extend_odeint/adapt_your_own_containers.html">Adapt
 your own containers</a></dt>
-<dt><a href="extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_operations">Adapt
+<dt><a href="extend_odeint/adapt_your_own_operations.html">Adapt
 your own operations</a></dt>
</dl></div>
<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">
-<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>
-</h3></div></div></div>
-
- gsl_vector, gsl_matrix, ublas::matrix, blitz::matrix, thrust
- 
-</div>
-<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>
-</h3></div></div></div>
-
- gsl_complex, complex, thrust
- 
-</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
@@ -60,7 +42,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<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>
+<a accesskey="p" href="tutorial/references.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/adapt_your_own_containers.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Deleted: 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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
+++ (empty file)
@@ -1,549 +0,0 @@
-<html>
-<head>
-<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 V1.75.2">
-<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">
-</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="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">
-<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>
-<div class="toc"><dl>
-<dt>Overview</dt>
-<dt><a href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers">Usage,
- Compilation, Headers</a></dt>
-<dt><a href="getting_started.html#boost_sandbox_numeric_odeint.getting_started.short_example">Short
- Example</a></dt>
-</dl></div>
-<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>
-<div class="caution"><table border="0" summary="Caution">
-<tr>
-<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../images/caution.png"></td>
-<th align="left">Caution</th>
-</tr>
-<tr><td align="left" valign="top">
- Boost.Odeint is not an official boost library!
- </td></tr>
-</table></div>
-
- Odeint is a library for solving initial value problems (IVP) of ordinary
- differential equations. Mathematically, these problems are formulated as
- follows: x'(t) = f(x,t), x(0) = x0.
- x and f can be vectors and the
- solution is some function x(t) fullfilling both equations
- above. In the following we will refer to x'(t) also
- <code class="computeroutput">dxdt</code> which is also our notation
- for the derivative in the source code.
- 
-
- Numerical approximations for the solution x(t) are calculated
- iteratively. The easiest algorithm is the Euler-Scheme, where starting at
- x(0) one finds x(dt) = x(0) + dt f(x(0),0).
- Now one can use x(dt) and obtain x(2dt)
- in a similar way and so on. The Euler method is of order 1, that means the
- error at each step is ~ dt2. This is, of course, not
- very satisfying, which is why the Euler method is merely used for real life
- problems and serves just as illustrative example. In odeint, the following
- algorithms are implemented:
- 
-<div class="table">
-<a name="id532034"></a>Table 1.1. Stepper Algorithms
-<div class="table-contents"><table class="table" summary="Stepper Algorithms">
-<colgroup>
-<col>
-<col>
-<col>
-<col>
-<col>
-<col>
-</colgroup>
-<thead><tr>
-<th>
- 
- Method
- 
- </th>
-<th>
- 
- Class
- 
- </th>
-<th>
- 
- Order
- 
- </th>
-<th>
- 
- Error Estimation
- 
- </th>
-<th>
- 
- Dense Output
- 
- </th>
-<th>
- 
- Remarks
- 
- </th>
-</tr></thead>
-<tbody>
-<tr>
-<td>
- 
- Explicit Euler
- 
- </td>
-<td>
- 
- explicit_euler
- 
- </td>
-<td>
- 
- 1
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- Yes
- 
- </td>
-<td>
- 
- Very simple, only for demonstrating purposes
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Runge-Kutta 4
- 
- </td>
-<td>
- 
- explicit_rkrk4
- 
- </td>
-<td>
- 
- 4
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- Good default method
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Runge-Kutta Cash-Karp
- 
- </td>
-<td>
- 
- explicit_error_rk54_ck
- 
- </td>
-<td>
- 
- 5
- 
- </td>
-<td>
- 
- Yes (Order 4)
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- ...
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Dormand-Prince 5
- 
- </td>
-<td>
- 
- explicit_error_dopri5
- 
- </td>
-<td>
- 
- 5
- 
- </td>
-<td>
- 
- Yes (Order 4)
- 
- </td>
-<td>
- 
- Yes
- 
- </td>
-<td>
- 
- ...
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Implicit Euler
- 
- </td>
-<td>
- 
- implicit_euler
- 
- </td>
-<td>
- 
- 1
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- Needs the Jacobian
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Rosenbrock 4
- 
- </td>
-<td>
- 
- rosenbrock4
- 
- </td>
-<td>
- 
- 4
- 
- </td>
-<td>
- 
- Yes
- 
- </td>
-<td>
- 
- Yes
- 
- </td>
-<td>
- 
- Good for stiff systems
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- Symplectic Euler
- 
- </td>
-<td>
- 
- symplectic_euler
- 
- </td>
-<td>
- 
- 1
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- No
- 
- </td>
-<td>
- 
- Symplectic solver for separable Hamiltonian system
- 
- </td>
-</tr>
-</tbody>
-</table></div>
-</div>
- 
- Ordinary differential equations occur nearly everywhere in natural sciences.
- For example, the whole Newtonian mechanics are described by second order
- differential equations. Be sure, you will find them in every discipline.
- They also occur if partial differential equations (PDEs) are discretized
- in one coordinate. Then, a system of coupled ordinary differential occurs,
- sometimes also refered as lattices ODEs.
- 
-</div>
-<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>
-</h3></div></div></div>
-
- Odeint is completely header-only, meaning that you do not link against any
- library. It can be include by
- 
-
-
-
-<pre class="programlisting">#include <boost/numeric/odeint.hpp>
-</pre>
-
- which includes all headers in the library. All functions and classes from
- odeint live in the namespace
-
-<pre class="programlisting">using namespace boost::numeric::odeint;
-</pre>
-
- 
-</div>
-<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>
-</h3></div></div></div>
-
- Image, you want to numerically integrate a harmonic oscillator with friction.
- The equations of motion are given by x'' = -x + gamma x'.
- This can be transformed to a system of two coupled first-order differential
- equations with new variables x and p=x'.
- To apply numerical integration one first has to design the right hand side
- of the equation w' = f(w) where in this case w
- = (x,p):
- 
-
-
-
-<pre class="programlisting">/* The type of container used to hold the state vector */
-typedef std::vector< double > state_type;
-
-const double gam = 0.15;
-
-/* The rhs of x' = f(x) */
-void harmonic_oscillator( const state_type &x , state_type &dxdt , const double t )
-{
- dxdt[0] = x[1];
- dxdt[1] = -x[0] - gam*x[1];
-}
-</pre>
-
- 
-
- Here we chose <code class="computeroutput">vector<double></code>
- as the state type, but others are also possible, for example <code class="computeroutput">tr1::array<double,2></code>.
- Odeint is designed in such a way that you can easily use your own state types.
- Next, we define the ODE which is in this case a simple function. The parameter
- signature of this function is crucial: the integration methods will always
- call them in the form <code class="computeroutput">f(x, dxdt, t)</code>.
- So, even if there is no explicit time dependence, one has to define <code class="computeroutput">t</code> as a function parameter.
- 
-
- Now, we have to define the initial state from which the integration should
- start:
- 
-
-
-
-<pre class="programlisting">state_type x(2);
-x[0] = 1.0; // start at x=1.0, p=0.0
-x[1] = 0.0;
-</pre>
-
- 
-
- For the integration itself we'll use the <code class="computeroutput">integrate</code>
- function, which is a convenient way to get quick results. It is based on
- the error-controlled <code class="computeroutput">runge_kutta_rk5_ck</code>
- stepper (5th order) and uses adaptive stepsize.
- 
-
-
-
-<pre class="programlisting">size_t steps = integrate( harmonic_oscillator ,
- x , 0.0 , 10.0 , 0.1 );
-</pre>
-
- 
-
- The integrate function expects as parameters the rhs of the ode as defined
- above, the initial state <code class="computeroutput">x</code>,
- the start-and end-time of the integration as well as the initial time step.
- Note, that <code class="computeroutput">integrate</code>
- uses an adaptive stepsize during the integration steps so the time points
- will not be equally spaced. The integration returns the number of steps that
- were applied.
- 
-
- It is, of course, also possible to implement the ode system as a class. The
- rhs must then be implemented as a functor having defined the ()-operator:
- 
-
-
-
-<pre class="programlisting">/* The rhs of x' = f(x) defined as a class */
-class harm_osc {
-
- double m_gam;
-
-public:
- harm_osc( double gam ) : m_gam(gam) { }
-
- void operator() ( const state_type &x , state_type &dxdt , const double t )
- {
- dxdt[0] = x[1];
- dxdt[1] = -x[0] - m_gam*x[1];
- }
-};
-</pre>
-
- 
-
- which can be used via
- 
-
-
-
-<pre class="programlisting">harm_osc ho(0.15);
-steps = integrate( ho ,
- x , 0.0 , 10.0 , 0.1 );
-</pre>
-
- 
-
- You surely have already noticed that during the integration a lot of steps
- have been done. You might wonder if you could access them do observe the
- solution during the iteration. Yes, you can do that. All you have to do is
- to provide a reasonable observer. An example is
- 
-
-
-
-<pre class="programlisting">struct push_back_state_and_time
-{
- std::vector< state_type >& m_states;
- std::vector< double >& m_times;
-
- push_back_state_and_time( std::vector< state_type > &states , std::vector< double > &times )
- : m_states( states ) , m_times( times ) { }
-
- void operator()( const state_type &x , double t )
- {
- m_states.push_back( x );
- m_times.push_back( t );
- }
-};
-</pre>
-
- 
-
- which stores the intermediate steps in a container. Now, you only have to
- pass this container to the integration function:
- 
-
-
-
-<pre class="programlisting">vector<state_type> x_vec;
-vector<double> times;
-
-steps = integrate( harmonic_oscillator ,
- x , 0.0 , 10.0 , 0.1 ,
- push_back_state_and_time( x_vec , times ) );
-
-/* output */
-for( size_t i=0; i<=steps; i++ )
-{
- cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
-}
-</pre>
-
- 
-
- That is all. Of course, you can use functional libraries like Boost.Lambda
- or Boost.Phoenix
- to ease the creation of observer functions.
- 
-
- The full cpp file for this example can be found here: ../../examples/harmonic_oscillator.cpp
- 
-</div>
-</div>
-<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left"></td>
-<td align="right"><div class="copyright-footer">Copyright © 2009 -2011 Karsten Ahnert and Mario Mulansky
- 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)
- 
-</div></td>
-</tr></table>
-<hr>
-<div class="spirit-nav">
-<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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -6,13 +6,14 @@
<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">
+<link rel="prev" href="concepts/compositestepper.html" title="CompositeStepper">
+<link rel="next" href="reference/integration_functions.html" title="Integration functions">
</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="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>
+<a accesskey="p" href="concepts/compositestepper.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/integration_functions.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -21,11 +22,11 @@
<div class="toc"><dl>
<dt><a href="reference.html#boost_sandbox_numeric_odeint.reference.stepper_classes">Stepper
 classes</a></dt>
-<dt><a href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions">Integration
+<dt><a href="reference/integration_functions.html">Integration
 functions</a></dt>
-<dt>Algebras</dt>
-<dt>Operations</dt>
-<dt>Resizing</dt>
+<dt>Algebras</dt>
+<dt>Operations</dt>
+<dt>Resizing</dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
@@ -33,7 +34,7 @@
 classes</a>
</h3></div></div></div>
<div class="table">
-<a name="id589875"></a>Table 1.4. Stepper Algorithms
+<a name="id589799"></a>Table 1.4. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -201,35 +202,6 @@
</div>
 
</div>
-<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>
-</h3></div></div></div>
-<div class="toc"><dl>
-<dt><a href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions.constant_step_size_functions">Constant
- step-size functions</a></dt>
-<dt><a href="reference.html#boost_sandbox_numeric_odeint.reference.integration_functions.adaptive_step_size_functions">Adaptive
- step-size functions</a></dt>
-</dl></div>
-<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"><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"><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"><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"><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>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
@@ -241,7 +213,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<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>
+<a accesskey="p" href="concepts/compositestepper.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/integration_functions.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/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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -6,14 +6,14 @@
<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">
+<link rel="prev" href="../index.html" title="Chapter 1. boost.sandbox.numeric.odeint">
+<link rel="next" href="tutorial/solar_system.html" title="Solar system">
</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="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>
+<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/solar_system.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -22,19 +22,19 @@
<div class="toc"><dl>
<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator">Harmonic
 oscillator</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system">Solar
+<dt><a href="tutorial/solar_system.html">Solar
 system</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents">Chaotic
+<dt><a href="tutorial/chaotic_systems_and_lyapunov_exponents.html">Chaotic
 systems and Lyapunov exponents</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.stiff_systems">Stiff
+<dt><a href="tutorial/stiff_systems.html">Stiff
 systems</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.odeint_in_detail">Odeint
+<dt><a href="tutorial/odeint_in_detail.html">Odeint
 in detail</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics">Special
+<dt><a href="tutorial/special_topics.html">Special
 topics</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.all_examples">All
+<dt><a href="tutorial/all_examples.html">All
 examples</a></dt>
-<dt>References</dt>
+<dt>References</dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
@@ -141,7 +141,7 @@
 choose:
 
<div class="table">
-<a name="id575784"></a>Table 1.2. Stepper Algorithms
+<a name="id575777"></a>Table 1.2. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -535,946 +535,6 @@
 The full cpp file for this example can be found here: ../../examples/harmonic_oscillator.cpp
 
</div>
-<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>
-</h3></div></div></div>
-<div class="toc"><dl>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system.gravitation_and_energy_conservation">Gravitation
- and energy conservation</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system.define_the_system_function">Define
- the system function</a></dt>
-</dl></div>
-<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>
-</h4></div></div></div>
-
- The next example in this tutorial is a simulation of the outer solar system,
- consisting of the sun, Jupiter, Saturn, Uranus, Neptune and Pluto.
- 
-
- <img src="../solar_system.jpg" alt="solar_system">
- 
-
- Each planet and of course the sun will be represented by mass points. The
- interaction force between each object is the gravitational force which
- can be written as
- 
-
- Fij = -γ mi mj ( qi - qj ) / | qi - qj | 3
- 
-
- where γ is the gravitational constant, mi
- and mj are the masses and qi
- and qj are the locations of the two objects. The equations
- of motion are then
- 
-
- dqi / dt = pi
- 
-
- dpboost_1_46_1.tari / dt = 1 / mi Σji Fij
- 
-
- where pi is the momenta of object i.
- The equations of motion can also be derived from the Hamiltonian
- 
-
- H = Σi pi2 / ( 2 mi ) + Σj V( qi , qj )
- 
-
- with the interaction potential V(qi,qj). The Hamiltonian
- equations give the equations of motion
- 
-
- dqi / dt = dH / dpi
- 
-
- dpi = -dH / dqi
- 
-
- In time independent Hamiltonian system the energy and the phase space volume
- are conserved and special integration methods have to be applied in order
- to ensure these conservation laws. The odeint library provides classes
- for separable Hamiltonian systems, which can be written in the form H
- = Σ pi2 / (2mi) + Hq(q), where Hq(q) only
- depends on the coordinates. Alltough this functional form might look a
- bit arbitrary it covers nearly all classical mechanical systems with inertia
- and without dissipation, or where the equations of motion can be written
- in the form dqi / dt = pi / mi , dpi / dt =
- f( qi ).
- 
-</div>
-<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>
-</h4></div></div></div>
-
- To implement this system we define a point type which will represent the
- space as well as the velocity. Therefore, we use the operators from Boost.Operators:
- 
-
-
-
-<pre class="programlisting">/*the point type */
-template< class T , size_t Dim >
-class point :
-boost::additive1< point< T , Dim > ,
-boost::additive2< point< T , Dim > , T ,
-boost::multiplicative2< point< T , Dim > , T
-> > >
-{
-public:
-
- const static size_t dim = Dim;
- typedef T value_type;
- typedef point< value_type , dim > point_type;
-
- // ...
- // constructors
-
- // ...
- // operators
-
-private:
-
- T m_val[dim];
-};
-
-//...
-// more operators
-</pre>
-
- 
-
- The next step is to define a container type storing the values of q
- and p and to define system functions. As container
- type we use <code class="computeroutput">std::tr1::array</code>
- 
-
-
-
-<pre class="programlisting">// we simulate 5 planets and the sun
-const size_t n = 6;
-
-typedef point< double , 3 > point_type;
-typedef std::tr1::array< point_type , n > container_type;
-typedef std::tr1::array< double , n > mass_type;
-</pre>
-
- 
-
- The <code class="computeroutput">container_type</code> is different
- from the state type of the ODE. The state type of the ode is simply a
- <code class="computeroutput">pair<
- container_type ,
- container_type ></code>
- since it needs the informations about the coordinates and the momenta.
- 
-
- As system function we have to provide f(p) and f(q):
- 
-
-
-
-<pre class="programlisting">const double gravitational_constant = 2.95912208286e-4;
-
-struct solar_system_coor
-{
- const mass_type &m_masses;
-
- solar_system_coor( const mass_type &masses ) : m_masses( masses ) { }
-
- void operator()( const container_type &p , container_type &dqdt ) const
- {
- for( size_t i=0 ; i<n ; ++i )
- dqdt[i] = p[i] / m_masses[i];
- }
-};
-</pre>
-
- 
-
-
-
-<pre class="programlisting">struct solar_system_momentum
-{
- const mass_type &m_masses;
-
- solar_system_momentum( const mass_type &masses ) : m_masses( masses ) { }
-
- void operator()( const container_type &q , container_type &dpdt ) const
- {
- const size_t n = q.size();
- for( size_t i=0 ; i<n ; ++i )
- {
- dpdt[i] = 0.0;
- for( size_t j=0 ; j<i ; ++j )
- {
- point_type diff = q[j] - q[i];
- double d = abs( diff );
- diff *= ( gravitational_constant * m_masses[i] * m_masses[j] / d / d / d );
- dpdt[i] += diff;
- dpdt[j] -= diff;
-
- }
- }
- }
-};
-</pre>
-
- 
-
- In general a three body-system is chaotic, hence we can not expect that
- arbitray initial conditions of the system will lead to a dynamic which
- is comparable with the solar system. That is we have to define proper initial
- conditions, which are taken from the book of Hairer, Wannier, Lubich.
- 
-
- As mentioned above, we need to use some special integrators in order to
- conserve phase space volume and energy. There is a well known family of
- such integrators, the so-called Runge-Kutta-Nystroem solvers, which we
- apply here:
- 
-
-
-
-<pre class="programlisting">typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
-const double dt = 100.0;
-
-integrate_const(
- stepper_type() ,
- make_pair( solar_system_coor( masses ) , solar_system_momentum( masses ) ) ,
- make_pair( boost::ref( q ) , boost::ref( p ) ) ,
- 0.0 , 200000.0 , dt , streaming_observer( cout ) );
-</pre>
-
- 
-
- These integration routine was used to produce the above sketch of the solar
- system. Note, that there are two particularities in this example. First,
- the state of the symplectic stepper is not <code class="computeroutput">container_type</code>
- but a pair of <code class="computeroutput">container_type</code>.
- Hence, we must pass such a pair to the integrate function. Since, we want
- to pass them as references we can simply pack them into boost::ref. The second point is the
- observer, which is called with a state type, hence a pair of <code class="computeroutput">container_type</code>. The reference wrapper
- is also passed, but this is not a problem at all:
- 
-
-
-
-<pre class="programlisting">struct streaming_observer
-{
- std::ostream& m_out;
-
- streaming_observer( std::ostream &out ) : m_out( out ) { }
-
- template< class State >
- void operator()( const State &x , double t ) const
- {
- container_type &q = x.first;
- m_out << t;
- for( size_t i=0 ; i<q.size() ; ++i ) m_out << "\t" << q[i];
- m_out << "\n";
- }
-};
-</pre>
-
- 
-
- The full example can be found here: ../../examples/solar_system.cpp
- 
-</div>
-</div>
-<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>
-</h3></div></div></div>
-
- 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 δ x / dt = J(x) δ x
- 
-
- where J is the Jacobian of the system under consideration.
- δ 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.
- 
-
- To demonstrate how one can use odeint to determine the Lyapunov exponents
- we choose the Lorenz system. It is one of the most studied dynamical systems
- in the nonlinear dynamics community. For the standard parameters is possesses
- a strange attractor with non-integer dimension. The Lyapunov exponents take
- values of approximately 0.9, 0 and -12.
- 
-
- The implementation of the Lorenz system is
- 
-
-
-
-<pre class="programlisting">const double sigma = 10.0;
-const double R = 28.0;
-const double b = 8.0 / 3.0;
-
-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];
-}
-</pre>
-
- 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:
- 
-
-
-
-<pre class="programlisting">const size_t n = 3;
-const size_t num_of_lyap = 3;
-const size_t N = n + n*num_of_lyap;
-
-typedef std::tr1::array< double , N > state_type;
-typedef std::tr1::array< double , num_of_lyap > lyap_type;
-
-void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
-{
- lorenz( x , dxdt , t );
-
- for( size_t l=0 ; l<num_of_lyap ; ++l )
- {
- const double *pert = x.begin() + 3 + l * 3;
- double *dpert = dxdt.begin() + 3 + l * 3;
- dpert[0] = - sigma * pert[0] + 10.0 * pert[1];
- dpert[1] = ( R - x[2] ) * pert[0] - pert[1] - x[0] * pert[2];
- dpert[2] = x[1] * pert[0] + x[0] * pert[1] - b * pert[2];
- }
-}
-</pre>
-
- 
-
- The perturbations are stored linearly in the <code class="computeroutput">state_type</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:
- 
-
-
-
-<pre class="programlisting">struct lorenz
-{
- template< class StateIn , class StateOut , class Value >
- void operator()( const StateIn &x , StateOut &dxdt , Value 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];
- }
-};
-
-void lorenz_with_lyap( const state_type &x , state_type &dxdt , double t )
-{
- lorenz()( x , dxdt , t );
- ...
-}
-
-</pre>
-
- This works fine and <code class="computeroutput">lorenz_with_lyap</code>
- can be used for example via
-
-<pre class="programlisting">state_type x;
-// initialize x
-explicit_rk4< state_type > rk4;
-integrate_n_steps( rk4 , lorenz_with_lyap , x , 0.0 , 0.01 , 1000 );
-</pre>
-
- This code snippet performs 1000 steps with constant step size 0.01.
- 
-
- A real world use case for the calculation of the Lyapunov exponents of Lorenz
- system would always include some transient steps, just to ensure that the
- current state lies on the attractor, hence it would look like
- 
-
-
-
-<pre class="programlisting">state_type x;
-// initialize x
-explicit_rk4< state_type > rk4;
-integrate_n_steps( rk4 , lorenz , x , 0.0 , 0.01 , 1000 );
-</pre>
-
- The problem is now, that <code class="computeroutput">x</code>
- is the full state containing also the perturbations and <code class="computeroutput">integrate_n_steps</code>
- does not know that it should only use 3 element. In detail, odeint and its
- steppers determine the length of the system under consideration be determing
- the length of the state. In the classical solvers from the problem was solved
- by pointer to the state and an appropriate length, something similar to
- 
-
-
-
-<pre class="programlisting">void lorenz( double* x , double *dxdt , double t, void* params )
-{
- ...
-}
-
-int system_length = 3;
-rk4( x , system_length , t , dt , lorenz );
-</pre>
-
- 
-
- But odeint supports a similar and much more sophisticated concept: Boost.Range. To make the steppers and
- the system ready to work with Boost.Range the system has to by changed:
- 
-
-
-
-<pre class="programlisting">struct lorenz
-{
- template< class State , class Deriv >
- void operator()( const State &x_ , Deriv &dxdt_ , double t ) const
- {
- typename boost::range_iterator< const State >::type x = boost::begin( x_ );
- typename boost::range_iterator< Deriv >::type dxdt = boost::begin( dxdt_ );
-
- 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];
- }
-};
-</pre>
-
- 
-
- This is in principle all. Now, we only have to call <code class="computeroutput">integrate_n_steps</code>
- with an suited range:
- 
-
-
-
-<pre class="programlisting">// perform 10000 transient steps
-integrate_n_steps( rk4 , lorenz() , std::make_pair( x.begin() , x.begin() + n ) , 0.0 , dt , 10000 );
-</pre>
-
- 
-
- Having integrated a sufficient number of transients steps we are now able
- to calculate the Lyapunov exponents:
- 
-<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 i , pj > = δ ij where <,>
- is the classical scalar product and δ ij 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>
-
-
-
-<pre class="programlisting">fill( x.begin()+n , x.end() , 0.0 );
-for( size_t i=0 ; i<num_of_lyap ; ++i ) x[n+n*i+i] = 1.0;
-fill( lyap.begin() , lyap.end() , 0.0 );
-
-double t = 0.0;
-size_t count = 0;
-while( true )
-{
- t = integrate_n_steps( rk4 , lorenz_with_lyap , x , t , dt , 100 );
- gram_schmidt( x , lyap , n , num_of_lyap );
- ++count;
-
- if( !(count % 100000) )
- {
- cout << t;
- for( size_t i=0 ; i<num_of_lyap ; ++i ) cout << "\t" << lyap[i] / t ;
- cout << endl;
- }
-}
-</pre>
-
- 
-
- The full code can be found here: ../../examples/chaotic_system.cpp
- 
-</div>
-<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>
-</h3></div></div></div>
-
- An important class of ordinary differential equations are so called stiff
- system which are characterized by two or more time scales of different order.
- 
-
- what are stiff systems?
- 
-
- examples
- 
-
- applications
- 
-
- To solve stiff systems numerically the Jacobian
- 
-
- J = d fi / d xj
- 
-
- is needed. Here is the definition of the above example
- 
-
-
-
-<pre class="programlisting">typedef boost::numeric::ublas::vector< double > vector_type;
-typedef boost::numeric::ublas::matrix< double > matrix_type;
-
-struct stiff_system
-{
- void operator()( const vector_type &x , vector_type &dxdt , double t )
- {
- dxdt[ 0 ] = -101.0 * x[ 0 ] - 100.0 * x[ 1 ];
- dxdt[ 1 ] = x[ 0 ];
- }
-};
-
-struct stiff_system_jacobi
-{
- void operator()( const vector_type &x , matrix_type &J , const double &t , vector_type &dfdt )
- {
- J( 0 , 0 ) = -101.0;
- J( 0 , 1 ) = -100.0;
- J( 1 , 0 ) = 1.0;
- J( 1 , 1 ) = 0.0;
- dfdt[0] = 0.0;
- dfdt[1] = 0.0;
- }
-};
-</pre>
-
- 
-
- The state type has to be a <code class="computeroutput">ublas::vector</code>
- and the matrix type must by a <code class="computeroutput">ublas::matrix</code>
- since the stiff integrator only accepts these types. With a little trick
- you can simply make this functions valid for other state and matrix types,
- just templatize the <code class="computeroutput">operator()</code>:
- 
-
-
-
-<pre class="programlisting">typedef boost::numeric::ublas::vector< double > vector_type;
-typedef boost::numeric::ublas::matrix< double > matrix_type;
-
-struct stiff_system
-{
- template< class State >
- void operator()( const State &x , State &dxdt , double t )
- {
- }
-};
-
-struct stiff_system_jacobi
-{
- template< class State , class Matrix >
- void operator()( const State &x , Matrix &J , const double &t , State &dfdt )
- {
- }
-};
-</pre>
-
- 
-
- Now you can use <code class="computeroutput">stiff_system</code>
- in combination with <code class="computeroutput">std::vector</code> or <code class="computeroutput">std::tr1::array</code>. In the example the explicit time
- derivative of f(x,t) is introduced separately in the
- Jacobian. If df / dt = 0 simply fill <code class="computeroutput">dfdt</code>
- with zeros.
- 
-
- A well know solver for stiff systems is the so called Rosenbrock method.
- It has a step size control and dense output facilities and can be used like
- all the other stepper:
- 
-
-
-
-<pre class="programlisting">typedef rosenbrock4< double > stepper_type;
-typedef rosenbrock4_controller< stepper_type > controlled_stepper_type;
-typedef rosenbrock4_dense_output< controlled_stepper_type > dense_output_type;
-
-vector_type x( 3 , 1.0 );
-
-size_t num_of_steps = integrate_const( dense_output_type() ,
- make_pair( stiff_system() , stiff_system_jacobi() ) ,
- x , 0.0 , 50.0 , 0.01 ,
- cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
-</pre>
-
- 
-
- During the integration 71 steps have been done. Comparing to a classical
- Runge-Kutta solver this is a very good result. For example the Dormand-Prince
- 5 method with step size control and dense output yields 1531 steps.
- 
-
-
-
-<pre class="programlisting">typedef explicit_error_dopri5< vector_type > dopri5_type;
-typedef controlled_error_stepper< dopri5_type > controlled_dopri5_type;
-typedef dense_output_controlled_explicit_fsal< controlled_dopri5_type > dense_output_dopri5_type;
-
-vector_type x2( 3 , 1.0 );
-
-size_t num_of_steps2 = integrate_const( dense_output_dopri5_type() ,
- stiff_system() , x2 , 0.0 , 50.0 , 0.01 ,
- cout << phoenix::arg_names::arg2 << " " << phoenix::arg_names::arg1[0] << "\n" );
-</pre>
-
- 
-
- Note, that we have used Boost.Phoenix
- a great functional programming library to create and compose the observer.
- 
-
- The full example can be found here: ../../examples/stiff_system.cpp
- 
-</div>
-<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>
-</h3></div></div></div>
-
- Different steppers
- 
-
- Explicit steppers
- 
-
- Implicit steppers
- 
-
- Step size controll
- 
-
- dense output
- 
-
- Algebras and operations
- 
-
- Overview and table
- 
-</div>
-<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>
-</h3></div></div></div>
-<div class="toc"><dl>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.complex_state_types">Complex
- state types</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.lattice_systems">Lattice
- systems</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.partial_differential_equations">Partial
- differential equations</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__units">Using
- boost::units</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_cuda_and_thrust">Using
- Cuda and Thrust</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_matrices_as_state_types">Using
- matrices as state types</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.ordinary_differential_equations_on_networks">Ordinary
- differential equations on networks</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.pass_by_value_or_by_reference">Pass
- by value or by reference</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_boost__range">Using
- boost::range</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.using_arbitrary_precision_floating_point_types">Using
- arbitrary precision floating point types</a></dt>
-<dt><a href="tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics.self_expanding_lattices">Self
- expanding lattices</a></dt>
-</dl></div>
-<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>
-</h4></div></div></div>
-
- typedef vector< complex< double > > state_type;
- 
-
- Stuart landau
- 
-
- DNLS
- 
-</div>
-<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>
-</h4></div></div></div>
-
- Fermi-Pasta-Ulam system
- 
-</div>
-<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>
-</h4></div></div></div>
-
- Wave equation
- 
-
- KdV
- 
-
- Ginzburg-Landau
- 
-</div>
-<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>
-</h4></div></div></div>
-
- blah blah
- 
-</div>
-<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>
-</h4></div></div></div>
-
- blah blah
- 
-</div>
-<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>
-</h4></div></div></div>
-
- Expanding resizing
- 
-</div>
-<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">
-<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>
-</h4></div></div></div>
-
- blah blah
- 
-</div>
-<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>
-</h4></div></div></div>
-
- blah blah
- 
-</div>
-<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>
-</h4></div></div></div>
-
- GMP
- 
-</div>
-<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">
-<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>
-</h3></div></div></div>
-
- The following table gives an overview over all examples.
- 
-<div class="table">
-<a name="id586646"></a>Table 1.3. Examples Overview
-<div class="table-contents"><table class="table" summary="Examples Overview">
-<colgroup>
-<col>
-<col>
-</colgroup>
-<thead><tr>
-<th>
- 
- File
- 
- </th>
-<th>
- 
- Brief Description
- 
- </th>
-</tr></thead>
-<tbody>
-<tr>
-<td>
- 
- ../../examples/harmonic_oscillator.cpp
- 
- </td>
-<td>
- 
- The harmonic oscillator examples gives a brief introduction to
- odeint and shows the usage of the classical Runge-Kutta-solvers.
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- ../../examples/solar_system.cpp
- 
- </td>
-<td>
- 
- The solar system example shows the usage of the symplectic solvers.
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- ../../examples/stiff_system.cpp
- 
- </td>
-<td>
- 
- The stiff system example shows the usage of the stiff solvers using
- the Jacobian of the system function.
- 
- </td>
-</tr>
-<tr>
-<td>
- 
- ../../examples/thrust/phase_osc_chain.cu
- 
- </td>
-<td>
- 
- tba.
- 
- </td>
-</tr>
-</tbody>
-</table></div>
-</div>
- 
-</div>
-<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>
-
- General informations about numerical integration of
- ordinary differential equations:
- 
-
- [1] Press William H et al., Numerical Recipes 3rd Edition: The Art of Scientific
- Computing, 3rd ed. (Cambridge University Press, 2007).
- 
-
- [2] Ernst Hairer, Syvert P. Nørsett, and Gerhard Wanner, Solving Ordinary
- Differential Equations I: Nonstiff Problems, 2nd ed. (Springer, Berlin, 2009).
- 
-
- [3] Ernst Hairer and Gerhard Wanner, Solving Ordinary Differential Equations
- II: Stiff and Differential-Algebraic Problems, 2nd ed. (Springer, Berlin,
- 2010).
- 
-
- Symplectic integration of numerical integration:
- 
-
- [4] Ernst Hairer, Gerhard Wanner, and Christian Lubich, Geometric Numerical
- Integration: Structure-Preserving Algorithms for Ordinary Differential Equations,
- 2nd ed. (Springer-Verlag Gmbh, 2006).
- 
-
- [5] Leimkuhler Benedict and Reich Sebastian, Simulating Hamiltonian Dynamics
- (Cambridge University Press, 2005).
- 
-
- Special symplectic methods:
- 
-
- [6] Haruo Yoshida, “Construction of higher order symplectic integrators,”
- Physics Letters A 150, no. 5 (November 12, 1990): 262-268.
- 
-
- [7] Robert I. McLachlan, “On the numerical integration of ordinary differential
- equations by symmetric composition methods,” SIAM J. Sci. Comput. 16, no.
- 1 (1995): 151-168.
- 
-</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
@@ -1486,7 +546,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<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>
+<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/solar_system.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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -5,12 +5,12 @@
<link rel="stylesheet" href="boostbook.css" type="text/css">
<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">
+<link rel="next" href="boost_sandbox_numeric_odeint/tutorial.html" title="Tutorial">
</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="images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/tutorial.html"><img src="images/next.png" alt="Next"></a></div>
<div class="chapter">
<div class="titlepage"><div>
<div><h2 class="title">
@@ -32,82 +32,591 @@
<div class="toc">
Table of Contents
<dl>
-<dt>Getting started</dt>
+<dt>Getting started</dt>
<dd><dl>
-<dt>Overview</dt>
-<dt><a href="boost_sandbox_numeric_odeint/getting_started.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers">Usage,
+<dt>Overview</dt>
+<dt><a href="index.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers">Usage,
 Compilation, Headers</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/getting_started.html#boost_sandbox_numeric_odeint.getting_started.short_example">Short
+<dt><a href="index.html#boost_sandbox_numeric_odeint.getting_started.short_example">Short
 Example</a></dt>
</dl></dd>
<dt>Tutorial</dt>
<dd><dl>
<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.harmonic_oscillator">Harmonic
 oscillator</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.solar_system">Solar
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/solar_system.html">Solar
 system</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.chaotic_systems_and_lyapunov_exponents">Chaotic
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/chaotic_systems_and_lyapunov_exponents.html">Chaotic
 systems and Lyapunov exponents</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.stiff_systems">Stiff
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/stiff_systems.html">Stiff
 systems</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.odeint_in_detail">Odeint
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/odeint_in_detail.html">Odeint
 in detail</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.special_topics">Special
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/special_topics.html">Special
 topics</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/tutorial.html#boost_sandbox_numeric_odeint.tutorial.all_examples">All
+<dt><a href="boost_sandbox_numeric_odeint/tutorial/all_examples.html">All
 examples</a></dt>
-<dt>References</dt>
+<dt>References</dt>
</dl></dd>
<dt>Extend odeint</dt>
<dd><dl>
<dt><a href="boost_sandbox_numeric_odeint/extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.write_own_steppers">Write
 own steppers</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_containers">Adapt
+<dt><a href="boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_containers.html">Adapt
 your own containers</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/extend_odeint.html#boost_sandbox_numeric_odeint.extend_odeint.adapt_your_own_operations">Adapt
+<dt><a href="boost_sandbox_numeric_odeint/extend_odeint/adapt_your_own_operations.html">Adapt
 your own operations</a></dt>
</dl></dd>
<dt>Concepts</dt>
<dd><dl>
<dt><a href="boost_sandbox_numeric_odeint/concepts.html#boost_sandbox_numeric_odeint.concepts.basic_stepper">Basic
 stepper</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/concepts.html#boost_sandbox_numeric_odeint.concepts.error_stepper">Error
+<dt><a href="boost_sandbox_numeric_odeint/concepts/error_stepper.html">Error
 stepper</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/concepts.html#boost_sandbox_numeric_odeint.concepts.controlled_stepper">Controlled
+<dt><a href="boost_sandbox_numeric_odeint/concepts/controlled_stepper.html">Controlled
 stepper</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/concepts.html#boost_sandbox_numeric_odeint.concepts.dense_ouput_stepper">Dense
+<dt><a href="boost_sandbox_numeric_odeint/concepts/dense_ouput_stepper.html">Dense
 ouput stepper</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/concepts.html#boost_sandbox_numeric_odeint.concepts.size_adjusting_stepper">Size
+<dt><a href="boost_sandbox_numeric_odeint/concepts/size_adjusting_stepper.html">Size
 adjusting stepper</a></dt>
-<dt>CompositeStepper</dt>
+<dt>CompositeStepper</dt>
</dl></dd>
<dt>Reference</dt>
<dd><dl>
<dt><a href="boost_sandbox_numeric_odeint/reference.html#boost_sandbox_numeric_odeint.reference.stepper_classes">Stepper
 classes</a></dt>
-<dt><a href="boost_sandbox_numeric_odeint/reference.html#boost_sandbox_numeric_odeint.reference.integration_functions">Integration
+<dt><a href="boost_sandbox_numeric_odeint/reference/integration_functions.html">Integration
 functions</a></dt>
-<dt>Algebras</dt>
-<dt>Operations</dt>
-<dt>Resizing</dt>
+<dt>Algebras</dt>
+<dt>Operations</dt>
+<dt>Resizing</dt>
</dl></dd>
</dl>
</div>
+<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="index.html#boost_sandbox_numeric_odeint.getting_started" title="Getting started">Getting started</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt>Overview</dt>
+<dt><a href="index.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers">Usage,
+ Compilation, Headers</a></dt>
+<dt><a href="index.html#boost_sandbox_numeric_odeint.getting_started.short_example">Short
+ Example</a></dt>
+</dl></div>
+<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="index.html#boost_sandbox_numeric_odeint.getting_started.overview" title="Overview">Overview</a>
+</h3></div></div></div>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="images/caution.png"></td>
<th align="left">Caution</th>
</tr>
<tr><td align="left" valign="top">
- Boost.Odeint is not an official boost library!
- </td></tr>
+ Boost.Odeint is not an official boost library!
+ </td></tr>
</table></div>
+
+ Odeint is a library for solving initial value problems (IVP) of ordinary
+ differential equations. Mathematically, these problems are formulated as
+ follows: x'(t) = f(x,t), x(0) = x0.
+ x and f can be vectors and the
+ solution is some function x(t) fullfilling both equations
+ above. In the following we will refer to x'(t) also
+ <code class="computeroutput">dxdt</code> which is also our notation
+ for the derivative in the source code.
+ 
+
+ Numerical approximations for the solution x(t) are calculated
+ iteratively. The easiest algorithm is the Euler-Scheme, where starting at
+ x(0) one finds x(dt) = x(0) + dt f(x(0),0).
+ Now one can use x(dt) and obtain x(2dt)
+ in a similar way and so on. The Euler method is of order 1, that means the
+ error at each step is ~ dt2. This is, of course, not
+ very satisfying, which is why the Euler method is merely used for real life
+ problems and serves just as illustrative example. In odeint, the following
+ algorithms are implemented:
+ 
+<div class="table">
+<a name="id533122"></a>Table 1.1. Stepper Algorithms
+<div class="table-contents"><table class="table" summary="Stepper Algorithms">
+<colgroup>
+<col>
+<col>
+<col>
+<col>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+ 
+ Method
+ 
+ </th>
+<th>
+ 
+ Class
+ 
+ </th>
+<th>
+ 
+ Order
+ 
+ </th>
+<th>
+ 
+ Error Estimation
+ 
+ </th>
+<th>
+ 
+ Dense Output
+ 
+ </th>
+<th>
+ 
+ Remarks
+ 
+ </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+ 
+ Explicit Euler
+ 
+ </td>
+<td>
+ 
+ explicit_euler
+ 
+ </td>
+<td>
+ 
+ 1
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ Yes
+ 
+ </td>
+<td>
+ 
+ Very simple, only for demonstrating purposes
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Runge-Kutta 4
+ 
+ </td>
+<td>
+ 
+ explicit_rkrk4
+ 
+ </td>
+<td>
+ 
+ 4
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ Good default method
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Runge-Kutta Cash-Karp
+ 
+ </td>
+<td>
+ 
+ explicit_error_rk54_ck
+ 
+ </td>
+<td>
+ 
+ 5
+ 
+ </td>
+<td>
+ 
+ Yes (Order 4)
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ ...
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Dormand-Prince 5
+ 
+ </td>
+<td>
+ 
+ explicit_error_dopri5
+ 
+ </td>
+<td>
+ 
+ 5
+ 
+ </td>
+<td>
+ 
+ Yes (Order 4)
+ 
+ </td>
+<td>
+ 
+ Yes
+ 
+ </td>
+<td>
+ 
+ ...
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Implicit Euler
+ 
+ </td>
+<td>
+ 
+ implicit_euler
+ 
+ </td>
+<td>
+ 
+ 1
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ Needs the Jacobian
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Rosenbrock 4
+ 
+ </td>
+<td>
+ 
+ rosenbrock4
+ 
+ </td>
+<td>
+ 
+ 4
+ 
+ </td>
+<td>
+ 
+ Yes
+ 
+ </td>
+<td>
+ 
+ Yes
+ 
+ </td>
+<td>
+ 
+ Good for stiff systems
+ 
+ </td>
+</tr>
+<tr>
+<td>
+ 
+ Symplectic Euler
+ 
+ </td>
+<td>
+ 
+ symplectic_euler
+ 
+ </td>
+<td>
+ 
+ 1
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ No
+ 
+ </td>
+<td>
+ 
+ Symplectic solver for separable Hamiltonian system
+ 
+ </td>
+</tr>
+</tbody>
+</table></div>
+</div>
+ 
+ Ordinary differential equations occur nearly everywhere in natural sciences.
+ For example, the whole Newtonian mechanics are described by second order
+ differential equations. Be sure, you will find them in every discipline.
+ They also occur if partial differential equations (PDEs) are discretized
+ in one coordinate. Then, a system of coupled ordinary differential occurs,
+ sometimes also refered as lattices ODEs.
+ 
+</div>
+<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="index.html#boost_sandbox_numeric_odeint.getting_started.usage__compilation__headers" title="Usage, Compilation, Headers">Usage,
+ Compilation, Headers</a>
+</h3></div></div></div>
+
+ Odeint is completely header-only, meaning that you do not link against any
+ library. It can be include by
+ 
+
+
+
+<pre class="programlisting">#include <boost/numeric/odeint.hpp>
+</pre>
+
+ which includes all headers in the library. All functions and classes from
+ odeint live in the namespace
+
+<pre class="programlisting">using namespace boost::numeric::odeint;
+</pre>
+
+ 
+</div>
+<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="index.html#boost_sandbox_numeric_odeint.getting_started.short_example" title="Short Example">Short
+ Example</a>
+</h3></div></div></div>
+
+ Image, you want to numerically integrate a harmonic oscillator with friction.
+ The equations of motion are given by x'' = -x + gamma x'.
+ This can be transformed to a system of two coupled first-order differential
+ equations with new variables x and p=x'.
+ To apply numerical integration one first has to design the right hand side
+ of the equation w' = f(w) where in this case w
+ = (x,p):
+ 
+
+
+
+<pre class="programlisting">/* The type of container used to hold the state vector */
+typedef std::vector< double > state_type;
+
+const double gam = 0.15;
+
+/* The rhs of x' = f(x) */
+void harmonic_oscillator( const state_type &x , state_type &dxdt , const double t )
+{
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - gam*x[1];
+}
+</pre>
+
+ 
+
+ Here we chose <code class="computeroutput">vector<double></code>
+ as the state type, but others are also possible, for example <code class="computeroutput">tr1::array<double,2></code>.
+ Odeint is designed in such a way that you can easily use your own state types.
+ Next, we define the ODE which is in this case a simple function. The parameter
+ signature of this function is crucial: the integration methods will always
+ call them in the form <code class="computeroutput">f(x, dxdt, t)</code>.
+ So, even if there is no explicit time dependence, one has to define <code class="computeroutput">t</code> as a function parameter.
+ 
+
+ Now, we have to define the initial state from which the integration should
+ start:
+ 
+
+
+
+<pre class="programlisting">state_type x(2);
+x[0] = 1.0; // start at x=1.0, p=0.0
+x[1] = 0.0;
+</pre>
+
+ 
+
+ For the integration itself we'll use the <code class="computeroutput">integrate</code>
+ function, which is a convenient way to get quick results. It is based on
+ the error-controlled <code class="computeroutput">runge_kutta_rk5_ck</code>
+ stepper (5th order) and uses adaptive stepsize.
+ 
+
+
+
+<pre class="programlisting">size_t steps = integrate( harmonic_oscillator ,
+ x , 0.0 , 10.0 , 0.1 );
+</pre>
+
+ 
+
+ The integrate function expects as parameters the rhs of the ode as defined
+ above, the initial state <code class="computeroutput">x</code>,
+ the start-and end-time of the integration as well as the initial time step.
+ Note, that <code class="computeroutput">integrate</code>
+ uses an adaptive stepsize during the integration steps so the time points
+ will not be equally spaced. The integration returns the number of steps that
+ were applied.
+ 
+
+ It is, of course, also possible to implement the ode system as a class. The
+ rhs must then be implemented as a functor having defined the ()-operator:
+ 
+
+
+
+<pre class="programlisting">/* The rhs of x' = f(x) defined as a class */
+class harm_osc {
+
+ double m_gam;
+
+public:
+ harm_osc( double gam ) : m_gam(gam) { }
+
+ void operator() ( const state_type &x , state_type &dxdt , const double t )
+ {
+ dxdt[0] = x[1];
+ dxdt[1] = -x[0] - m_gam*x[1];
+ }
+};
+</pre>
+
+ 
+
+ which can be used via
+ 
+
+
+
+<pre class="programlisting">harm_osc ho(0.15);
+steps = integrate( ho ,
+ x , 0.0 , 10.0 , 0.1 );
+</pre>
+
+ 
+
+ You surely have already noticed that during the integration a lot of steps
+ have been done. You might wonder if you could access them do observe the
+ solution during the iteration. Yes, you can do that. All you have to do is
+ to provide a reasonable observer. An example is
+ 
+
+
+
+<pre class="programlisting">struct push_back_state_and_time
+{
+ std::vector< state_type >& m_states;
+ std::vector< double >& m_times;
+
+ push_back_state_and_time( std::vector< state_type > &states , std::vector< double > &times )
+ : m_states( states ) , m_times( times ) { }
+
+ void operator()( const state_type &x , double t )
+ {
+ m_states.push_back( x );
+ m_times.push_back( t );
+ }
+};
+</pre>
+
+ 
+
+ which stores the intermediate steps in a container. Now, you only have to
+ pass this container to the integration function:
+ 
+
+
+
+<pre class="programlisting">vector<state_type> x_vec;
+vector<double> times;
+
+steps = integrate( harmonic_oscillator ,
+ x , 0.0 , 10.0 , 0.1 ,
+ push_back_state_and_time( x_vec , times ) );
+
+/* output */
+for( size_t i=0; i<=steps; i++ )
+{
+ cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
+}
+</pre>
+
+ 
+
+ That is all. Of course, you can use functional libraries like Boost.Lambda
+ or Boost.Phoenix
+ to ease the creation of observer functions.
+ 
+
+ The full cpp file for this example can be found here: ../../examples/harmonic_oscillator.cpp
+ 
+</div>
+</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left">Last revised: May 13, 2011 at 10:39:06 GMT</td>
+<td align="left">Last revised: May 13, 2011 at 11:19:54 GMT</td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
-<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/tutorial.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 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -44,9 +44,6 @@
[template sub[x]'''<subscript>'''[x]'''</subscript>''']
[template subl[x]'''<subscript>'''__space[x]'''</subscript>''']

-[caution Boost.Odeint is not an official boost library!]
-
-
[include getting_started.qbk]

[include tutorial.qbk]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/reference.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/reference.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/reference.qbk 2011-05-13 06:21:57 EDT (Fri, 13 May 2011)
@@ -1,6 +1,5 @@
[section Reference]

-
[include reference_steppers.qbk]

[include reference_integrate_functions.qbk]

Date view	Thread view	Subject view	Author view

Boost-Commit list run by bdawes at acm.org, david.abrahams at rcn.com, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk