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Subject: [Boost-commit] svn:boost r70391 - in sandbox/odeint/branches/karsten/libs/numeric/odeint: doc doc/html doc/html/boost_sandbox_numeric_odeint examples
From: karsten.ahnert_at_[hidden]
Date: 2011-03-22 13:28:33

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Author: karsten
Date: 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
New Revision: 70391
URL: http://svn.boost.org/trac/boost/changeset/70391

Log:
documentation
Added:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_stiff_systems.qbk (contents, props changed)
Text files modified:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html | 275 ++++++++++++++++++---------------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/extend_odeint.html | 4
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html | 48 +++++-
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/reference.html | 6
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html | 206 +++++++++++++++++++++++++++--
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html | 8
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial.qbk | 6
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/Jamfile | 1
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/stiff_system.cpp | 155 +++++++++++++++-------
   9 files changed, 469 insertions(+), 240 deletions(-)

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/concepts.html 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -13,7 +13,7 @@
<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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -59,8 +59,12 @@
</colgroup>
<thead><tr>
<th>
+ 
+ 
 </th>
<th>
+ 
+ 
 </th>
<th>
 
@@ -145,25 +149,23 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <code class="computeroutput">Stepper()</code>
- Constructor.
- </li>
-<li>
- <code class="computeroutput">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>
- <code class="computeroutput">void do_step( DynamicalSystem
- &system
- , container_type
- &x
- , time_type
- t ,
- time_type dt
- )</code>
- </li>
+<code class="computeroutput">Stepper()</code>
+ Constructor.
+ </li>
+<li>
+<code class="computeroutput">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><code class="computeroutput">void do_step( DynamicalSystem
+ &system
+ , container_type
+ &x
+ , time_type
+ t ,
+ time_type dt
+ )</code></li>
</ul></div>

 Executes one timestep with the given parameters:
@@ -266,16 +268,14 @@
 The result of this method is the (approximate) state of the system x(t+dt) and is stored in the variable <code class="computeroutput">x</code> (in-place). Note, that the time <code class="computeroutput">t</code> is not automatically increased by this
 method.
 
-<div class="itemizedlist"><ul type="disc"><li>
- <code class="computeroutput">void do_step( DynamicalSystem
- &system
- , container_type
- &x
- , const
- container_type &dxdt , time_type t
- , time_type
- dt )</code>
- </li></ul></div>
+<div class="itemizedlist"><ul type="disc"><li><code class="computeroutput">void do_step( DynamicalSystem
+ &system
+ , container_type
+ &x
+ , const
+ container_type &dxdt , time_type t
+ , time_type
+ dt )</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)
@@ -283,33 +283,26 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <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>
- <code class="computeroutput">order_type order_step()</code> Returns the order of the algorithm.
- If n is the order of a method, then
- the result of one iteration with the timestep dt
- is accurate up to dt^n. That means the
- error made by the time discretization is of order dt^(n+1).
- </li>
+<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>
+<code class="computeroutput">order_type order_step()</code> Returns the order of the algorithm. If
+ n is the order of a method, then the result
+ of one iteration with the timestep dt
+ is accurate up to dt^n. That means the
+ error made by the time discretization is of order dt^(n+1).
+ </li>
</ul></div>

 Stepper that model this concept
 
<div class="itemizedlist"><ul type="disc">
-<li>
- <code class="computeroutput">stepper_euler</code>
- </li>
-<li>
- <code class="computeroutput">stepper_rk4</code>
- </li>
-<li>
- <code class="computeroutput">stepper_rk78_fehlberg</code>
- </li>
+<li><code class="computeroutput">stepper_euler</code></li>
+<li><code class="computeroutput">stepper_rk4</code></li>
+<li><code class="computeroutput">stepper_rk78_fehlberg</code></li>
</ul></div>
</div>
<div class="section" lang="en">
@@ -339,26 +332,24 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <code class="computeroutput">Error_Stepper()</code>
- Constructor.
- </li>
-<li>
- <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>
- <code class="computeroutput">void do_step( DynamicalSystem
- &system
- , container_type
- &x
- , time_type
- t ,
- time_type dt
- , container_type
- &xerr)</code>
- </li>
+<code class="computeroutput">Error_Stepper()</code>
+ Constructor.
+ </li>
+<li>
+<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><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:
@@ -480,17 +471,15 @@
 Note, that the time <code class="computeroutput">t</code> is
 not automatically increased by this method.
 
-<div class="itemizedlist"><ul type="disc"><li>
- <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>
+<div class="itemizedlist"><ul type="disc"><li><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)
@@ -498,33 +487,26 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <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>
- <code class="computeroutput">order_type order_error_step()</code> Returns the order of the result x(t+dt) of the algorithm.
- </li>
-<li>
- <code class="computeroutput">order_type order_error()</code> Returns the order of the error estimation
- of the algorithm.
- </li>
+<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>
+<code class="computeroutput">order_type order_error_step()</code> Returns the order of the result x(t+dt) of the algorithm.
+ </li>
+<li>
+<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 type="disc">
-<li>
- <code class="computeroutput">stepper_rk5_ck</code>
- </li>
-<li>
- <code class="computeroutput">stepper_rk78_fehlberg</code>
- </li>
-<li>
- <code class="computeroutput">stepper_half_step</code>
- </li>
+<li><code class="computeroutput">stepper_rk5_ck</code></li>
+<li><code class="computeroutput">stepper_rk78_fehlberg</code></li>
+<li><code class="computeroutput">stepper_half_step</code></li>
</ul></div>
</div>
<div class="section" lang="en">
@@ -547,13 +529,11 @@

 Methods
 
-<div class="itemizedlist"><ul type="disc"><li>
- <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>
+<div class="itemizedlist"><ul type="disc"><li><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
@@ -574,18 +554,20 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <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>
- <code class="computeroutput">controlled_step_result try_step(
- DynamicalSystem &system, container_type &x, time_type &t, time_type &dt )</code>
- </li>
+<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><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
@@ -700,37 +682,30 @@
 
<div class="itemizedlist"><ul type="disc">
<li>
- <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>
- <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>
+<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>
+<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>
- <code class="computeroutput">order_type order_error_step()</code> Returns the order of the result x(t+dt) of the algorithm.
- </li>
+<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 type="disc">
-<li>
- <code class="computeroutput">controlled_stepper_standard</code>
- </li>
-<li>
- <code class="computeroutput">controlled_stepper_bs</code>
- </li>
+<li><code class="computeroutput">controlled_stepper_standard</code></li>
+<li><code class="computeroutput">controlled_stepper_bs</code></li>
</ul></div>
</div>
<div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title">
@@ -758,7 +733,7 @@
</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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</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 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -13,7 +13,7 @@
<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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -60,7 +60,7 @@
</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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -13,7 +13,7 @@
<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>
+<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -52,7 +52,7 @@
 algorithms are implemented:
 
<div class="table">
-<a name="id518246"></a>Table 1.1. Stepper Algorithms
+<a name="id326539"></a>Table 1.1. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -369,7 +369,9 @@
 = (x,p):
 

-
+ 
+
+

<pre class="programlisting">/* The type of container used to hold the state vector */
typedef std::vector< double > state_type;
@@ -384,6 +386,8 @@
}
</pre>

+ 
+
 

 Here we chose <code class="computeroutput">vector<double></code>
@@ -399,13 +403,17 @@
 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>
@@ -414,12 +422,16 @@
 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
@@ -435,7 +447,9 @@
 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 {
@@ -453,18 +467,24 @@
};
</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
@@ -473,7 +493,9 @@
 to provide a reasonable observer. An example is
 

-
+ 
+
+

<pre class="programlisting">struct push_back_state_and_time
{
@@ -491,13 +513,17 @@
};
</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;
@@ -513,6 +539,8 @@
}
</pre>

+ 
+
 

 That is all. Of course, you can use functional libraries like Boost.Lambda
@@ -534,7 +562,7 @@
</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>
+<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</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 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -12,7 +12,7 @@
<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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -33,7 +33,7 @@
classes</a>
</h3></div></div></div>
<div class="table">
-<a name="id568603"></a>Table 1.3. Stepper Algorithms
+<a name="id378666"></a>Table 1.3. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -241,7 +241,7 @@
</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.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
</div>
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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 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -13,7 +13,7 @@
<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="getting_started.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -71,7 +71,9 @@
 to just define a function, e.g:
 

-
+ 
+
+

<pre class="programlisting">/* The type of container used to hold the state vector */
typedef std::vector< double > state_type;
@@ -86,6 +88,8 @@
}
</pre>

+ 
+
 

 The parameters of the function must follow the example above where <code class="computeroutput">x</code> is the current state, <code class="computeroutput">dxdt</code> is the derivative x'
@@ -98,7 +102,9 @@
 parameter structure as above:
 

-
+ 
+
+

<pre class="programlisting">/* The rhs of x' = f(x) defined as a class */
class harm_osc {
@@ -116,6 +122,8 @@
};
</pre>

+ 
+
 

 odeint can deal with instances of such classes instead of pure functions
@@ -139,7 +147,7 @@
 choose:
 
<div class="table">
-<a name="id561513"></a>Table 1.2. Stepper Algorithms
+<a name="id370055"></a>Table 1.2. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -434,12 +442,16 @@
 )</code> function from odeint:
 

-
+ 
+
+

<pre class="programlisting">explicit_rk4< state_type > stepper;
integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
</pre>

+ 
+
 

 This call integrates the system defined by <code class="computeroutput">harmonic_oscillator</code>
@@ -451,13 +463,17 @@
 method which can used directly. So, you write down the above example as
 

-
+ 
+
+

<pre class="programlisting">const double dt = 0.01;
for( double t=0.0 ; t<10.0 ; t+= dt )
 stepper.do_step( harmonic_oscillator , x , t , dt );
</pre>

+ 
+
 
</div>
<div class="section" lang="en">
@@ -475,12 +491,16 @@
 with 4th order error estimation and coefficients introduced by Cash-Karp.
 

-
+ 
+
+

<pre class="programlisting">typedef explicit_error_rk54_ck< state_type > error_stepper_type;
error_stepper_type rk54;
</pre>

+ 
+
 

 Given the error stepper, one still needs an instance that checks the error
@@ -504,13 +524,17 @@
 stepper create by <code class="computeroutput">make_controlled_stepper_standard</code>.
 

-
+ 
+
+

<pre class="programlisting">typedef controlled_error_stepper< error_stepper_type > controlled_stepper_type;
controlled_stepper_type controlled_stepper;
integrate_adaptive( controlled_stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
</pre>

+ 
+
 

 As above, this integrates the system defined by <code class="computeroutput">harmonic_oscillator</code>
@@ -616,7 +640,9 @@
 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 >
@@ -647,6 +673,8 @@
// more operators
</pre>

+ 
+
 

 The next step is to define a container type storing the values of q
@@ -654,7 +682,9 @@
 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;
@@ -664,6 +694,8 @@
typedef std::tr1::array< double , n > mass_type;
</pre>

+ 
+
 

 The <code class="computeroutput">container_type</code> is different
@@ -677,7 +709,9 @@
 As system function we have to provide f(p) and f(q):
 

-
+ 
+
+

<pre class="programlisting">const double gravitational_constant = 2.95912208286e-4;

@@ -695,9 +729,13 @@
};
</pre>

+ 
+
 

-
+ 
+
+

<pre class="programlisting">struct solar_system_momentum
{
@@ -725,6 +763,8 @@
};
</pre>

+ 
+
 

 In general a three body-system is chaotic, hence we can not expect that
@@ -739,7 +779,9 @@
 apply here:
 

-
+ 
+
+

<pre class="programlisting">typedef symplectic_rkn_sb3a_mclachlan< container_type > stepper_type;
const double dt = 100.0;
@@ -751,6 +793,8 @@
 0.0 , 200000.0 , dt , streaming_observer( cout ) );
</pre>

+ 
+
 

 These integration routine was used to produce the above sketch of the solar
@@ -763,7 +807,9 @@
 is also passed, but this is not a problem at all:
 

-
+ 
+
+

<pre class="programlisting">struct streaming_observer
{
@@ -782,6 +828,8 @@
};
</pre>

+ 
+
 

 The full example can be found here: ../../examples/solar_system.cpp
@@ -803,7 +851,133 @@
 systems</a>
</h3></div></div></div>

- blah blah
+ 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">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;
+
+vector_type x( 3 , 1.0 ) , xerr( 3 );
+
+size_t num_of_steps = integrate_const( controlled_stepper_type() ,
+ make_pair( stiff_system() , stiff_system_jacobi() ) ,
+ x , 0.0 , 50.0 , 0.01 );
+</pre>
+
+ 
+
+ 
+
+ During the integration approximately XX 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 ca.
+ XX steps.
+ 
+
+ The full example can be found here: ../../examples/stiff_system.cpp
 
</div>
<div class="section" lang="en">
@@ -1018,7 +1192,7 @@
</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="getting_started.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
</div>
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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 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -10,7 +10,7 @@
<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/getting_started.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
<div class="chapter" lang="en">
<div class="titlepage"><div>
<div><h2 class="title">
@@ -23,7 +23,7 @@
</h3></div></div>
<div>Copyright © 2009 -2011 Karsten Ahnert and Mario Mulansky</div>
<div><div class="legalnotice">
-<a name="id549573"></a>
+<a name="id358081"></a>
 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)
 
@@ -93,10 +93,10 @@
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left">Last revised: March 18, 2011 at 17:07:57 GMT</td>
+<td align="left">Last revised: March 22, 2011 at 17:34:59 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/getting_started.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial.qbk 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -10,11 +10,7 @@

[endsect]

-[section Stiff systems]
-
-blah blah
-
-[endsect]
+[include tutorial_stiff_systems.qbk]

[section Odeint in detail]

Added: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_stiff_systems.qbk
==============================================================================
--- (empty file)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_stiff_systems.qbk 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -0,0 +1,37 @@
+[section Stiff systems]
+
+[import ../examples/stiff_system.cpp]
+
+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 f[subl i] / d x[subl j]]
+
+is needed. Here is the definition of the above example
+
+[stiff_system_definition]
+
+The state type has to be a `ublas::vector` and the matrix type must by a `ublas::matrix` 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 `operator()`:
+
+[stiff_system_alternative_definition]
+
+Now you can use `stiff_system` in combination with `std::vector` or `std::tr1::array`. In the example the explicit time derivative of ['f(x,t)] is introduced separately in the Jacobian. If ['df / dt = 0] simply fill `dfdt` 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:
+
+[integrate_stiff_system]
+
+During the integration approximately XX 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 ca. XX steps.
+
+
+The full example can be found here: [@../../examples/stiff_system.cpp]
+
+
+[endsect]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/Jamfile
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/Jamfile (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/Jamfile 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -14,5 +14,4 @@

exe harmonic_oscillator : harmonic_oscillator.cpp ;
exe solar_system : solar_system.cpp ;
-
exe stiff_system : stiff_system.cpp ;
\ No newline at end of file

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/stiff_system.cpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/stiff_system.cpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/stiff_system.cpp 2011-03-22 13:28:29 EDT (Tue, 22 Mar 2011)
@@ -1,70 +1,127 @@
-/* Boost implicit_euler.cpp example file
-
- Copyright 2010 Karsten Ahnert
- Copyright 2010 Mario Mulansky
-
- This file shows the use of the implicit euler stepper
-
- 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)
-*/
+/*
+ * rosenbrock4.cpp
+ *
+ * Created on: Jan 9, 2011
+ * Author: karsten
+ */

#include <iostream>
+#include <fstream>
#include <utility>
+#include <tr1/array>

#include <boost/numeric/odeint.hpp>
-#include <boost/numeric/odeint/stepper/implicit_euler.hpp>
-#include <boost/numeric/odeint/algebra/vector_space_algebra.hpp>
-
-#include <boost/numeric/ublas/vector.hpp>
-#include <boost/numeric/ublas/matrix.hpp>

-#define tab '\t'
+using namespace std;
+using namespace boost::numeric::odeint;

-typedef double value_type;
-typedef boost::numeric::ublas::vector< value_type > state_type;
-typedef boost::numeric::ublas::matrix< value_type > matrix_type;
+//[ stiff_system_definition
+typedef boost::numeric::ublas::vector< double > vector_type;
+typedef boost::numeric::ublas::matrix< double > matrix_type;

-void stiff_system( state_type &x , state_type &dxdt , value_type t )
+struct stiff_system
{
- dxdt( 0 ) = -101.0 * x( 0 ) - 100.0 * x( 1 );
- dxdt( 1 ) = x( 0 );
-}
+ 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 ];
+ }
+};

-void jacobi( state_type &x , matrix_type &jacobi , value_type t )
+struct stiff_system_jacobi
{
- jacobi( 0 , 0 ) = -101.0;
- jacobi( 0 , 1 ) = -100.0;
- jacobi( 1 , 0 ) = 1.0;
- jacobi( 1 , 1 ) = 0.0;
-}
+ 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;
+ }
+};
+//]

-using namespace std;
-using namespace boost::numeric::odeint;

-int main( void )
+/*
+//[ stiff_system_alternative_definition
+struct stiff_system
{
- explicit_euler< state_type , value_type /*, vector_space_algebra */> expl_euler;
- implicit_euler< value_type > impl_euler;
+ 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 )
+ {
+ ...
+ }
+};
+//]
+*/
+

- state_type x1( 2 );
- x1( 0 ) = 1.0; x1( 1 ) = 0.0;
- state_type x2( x1 );

- const value_type dt = 0.01; // for dt >= 0.01 the euler method gets unstable
- const size_t steps = 1000;

- value_type t = 0.0;
- for( size_t step = 0 ; step < steps ; ++step , t+=dt )
- {
- clog << step << " of " << steps << endl;
- cout << t << tab << x1( 0 ) << tab << x1( 1 ) << tab << x2( 0 ) << tab << x2( 1 ) << tab;
- cout << 1.0 / 99.0 * exp( -100.0 * t ) * ( 100.0 - exp( 99.0 * t ) ) << tab;
- cout << 1.0 / 99.0 * exp( -100.0 * t ) * ( -1.0 + exp( 99.0 * t ) ) << endl;

- expl_euler.do_step( stiff_system , x1 , t , dt );
- impl_euler.do_step( make_pair( stiff_system , jacobi ) , x2 , t , dt );
+void rk54_ck_controlled_with_stiff_system( void )
+{
+ typedef explicit_error_rk54_ck< vector_type > stepper_type;
+ typedef controlled_error_stepper< stepper_type > controlled_stepper_type;
+ controlled_stepper_type stepper;
+
+ vector_type x( 3 , 1.0 );
+ double t = 0.0 , dt = 0.00001;
+ ofstream fout( "rk54_ck_controller_stiff.dat" );
+ size_t count = 0;
+ while( t < 50.0 )
+ {
+ fout << t << "\t" << dt << "\t" << stepper.last_error() << "\t";
+ fout << x[0] << "\t" << x[1] << "\t" << x[2] << "\t";
+ fout <<std::endl;
+
+ size_t trials = 0;
+ while( trials < 100 )
+ {
+ if( stepper.try_step( stiff_system() , x , t , dt ) != step_size_decreased )
+ break;
+ ++trials;
+ }
+ if( trials == 100 )
+ {
+ cerr << "Error : stepper did not converge! " << endl;
+ break;
+ }
+ ++count;
}
+ clog << "RK 54 : " << count << endl;
+}
+
+
+
+
+
+
+int main( int argc , char **argv )
+{
+//[ integrate_stiff_system
+ typedef rosenbrock4< double > stepper_type;
+ typedef rosenbrock4_controller< stepper_type > controlled_stepper_type;
+
+ vector_type x( 3 , 1.0 ) , xerr( 3 );
+
+ size_t num_of_steps = integrate_const( controlled_stepper_type() ,
+ make_pair( stiff_system() , stiff_system_jacobi() ) ,
+ x , 0.0 , 50.0 , 0.01 );
+//]
+ clog << num_of_steps << endl;
+
+ rk54_ck_controlled_with_stiff_system();

+ return 0;
}

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