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Subject: [Boost-commit] svn:boost r70132 - in sandbox/odeint/branches/karsten: . boost/numeric boost/numeric/odeint/integrate boost/numeric/odeint/integrate/detail boost/numeric/odeint/stepper/base libs/numeric/odeint/doc libs/numeric/odeint/doc/html libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint libs/numeric/odeint/examples libs/numeric/odeint/regression_test
From: karsten.ahnert_at_[hidden]
Date: 2011-03-18 13:08:19

Author: karsten
Date: 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
New Revision: 70132
URL: http://svn.boost.org/trac/boost/changeset/70132

Log:
documentation and bug fixing
Added:
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/solar_system.jpg (contents, props changed)
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.agr (contents, props changed)
Text files modified:
   sandbox/odeint/branches/karsten/TODO | 9
   sandbox/odeint/branches/karsten/boost/numeric/odeint.hpp | 8
   sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp | 6
   sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_const.hpp | 15
   sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/integrate_const.hpp | 41 ++++
   sandbox/odeint/branches/karsten/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp | 5
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/getting_started.qbk | 25 +
   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 | 221 +++++++++++++----------
   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 | 356 ++++++++++++++++++++++++++++-----------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html | 8
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/odeint.qbk | 27 +++
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/stepper_table.qbk | 1
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_harmonic_oscillator.qbk | 81 +-------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_solar_system.qbk | 77 +++-----
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/Jamfile | 2
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/harmonic_oscillator.cpp | 60 ++++-
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/point_type.hpp | 183 ++++++++++---------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.cpp | 261 ++++++++++++++++------------
   sandbox/odeint/branches/karsten/libs/numeric/odeint/regression_test/integrate_functions.cpp | 2
   22 files changed, 982 insertions(+), 691 deletions(-)

Modified: sandbox/odeint/branches/karsten/TODO
==============================================================================
--- sandbox/odeint/branches/karsten/TODO (original)
+++ sandbox/odeint/branches/karsten/TODO 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -20,11 +20,10 @@
   * documente every file in the preamble
   * check once more, if all contructor, destructors and assign-operators are present
* INTEGRATE FUNCTIONS
- * check forwarding problem
- * check where exactly the observer will be called (before, after each step?)
- * ranges
- * functions without obversers
- * integrate without stepper , intelligent choice of the stepper
+ * check forwarding problem, ranges
+ OK * check where exactly the observer will be called (before, after each step?)
+ OK * functions without obversers
+ OK * integrate without stepper , intelligent choice of the stepper
   OK * check function signatures
   OK * what to throw?
   OK * check lambdas, lambda is broken

Modified: sandbox/odeint/branches/karsten/boost/numeric/odeint.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/boost/numeric/odeint.hpp (original)
+++ sandbox/odeint/branches/karsten/boost/numeric/odeint.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -19,7 +19,6 @@

#include <boost/numeric/odeint/stepper/explicit_euler.hpp>
#include <boost/numeric/odeint/stepper/explicit_rk4.hpp>
-
#include <boost/numeric/odeint/stepper/explicit_error_rk54_ck.hpp>
#include <boost/numeric/odeint/stepper/explicit_error_dopri5.hpp>

@@ -28,6 +27,13 @@
#include <boost/numeric/odeint/stepper/dense_output_explicit.hpp>
#include <boost/numeric/odeint/stepper/dense_output_controlled_explicit_fsal.hpp>

+#include <boost/numeric/odeint/stepper/symplectic_euler.hpp>
+#include <boost/numeric/odeint/stepper/symplectic_rkn_sb3a_mclachlan.hpp>
+
+#include <boost/numeric/odeint/stepper/implicit_euler.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4.hpp>
+#include <boost/numeric/odeint/stepper/rosenbrock4_controller.hpp>
+
/*
* Including this algebra slows down the compilation time
*/

Modified: sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp (original)
+++ sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -50,6 +50,7 @@
 size_t count = 0;
 while( start_time < end_time )
 {
+ observer( start_state , start_time );
 if( ( start_time + dt ) > end_time )
 {
 dt = end_time - start_time;
@@ -65,9 +66,9 @@
 while( ( res == step_size_decreased ) && ( trials < max_attempts ) );
 if( trials == max_attempts ) throw std::overflow_error( error_string );

- observer( start_state , start_time );
 ++count;
 }
+ observer( start_state , start_time );
 return count;
}

@@ -87,10 +88,11 @@
 stepper.initialize( start_state , start_time , dt );
 while( stepper.current_time() < end_time )
 {
- stepper.do_step( system );
 observer( stepper.current_state() , stepper.current_time() );
+ stepper.do_step( system );
 ++count;
 }
+ observer( stepper.current_state() , stepper.current_time() );
 return count;
}

Modified: sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_const.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_const.hpp (original)
+++ sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/detail/integrate_const.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -37,6 +37,7 @@
 start_time += dt;
 ++count;
 }
+ observer( start_state , start_time );
 return count;
}

@@ -57,14 +58,14 @@
 Time time_step = dt;
 while( start_time < end_time )
 {
+ observer( start_state , start_time );
 Time next_time = start_time + time_step;
 if( next_time > end_time ) next_time = end_time;
- detail::integrate_adaptive(
- stepper , system , start_state , start_time , next_time , dt ,
- do_nothing_observer() , controlled_stepper_tag() );
- ++count;
- observer( start_state , start_time );
+ count += detail::integrate_adaptive(
+ stepper , system , start_state , start_time , next_time , dt ,
+ do_nothing_observer() , controlled_stepper_tag() );
 }
+ observer( start_state , start_time );
 return count;
}

@@ -74,8 +75,6 @@
 * integrates with constant time step using a controlled stepper
 *
 * step size control is used if the stepper is a controlled stepper, otherwise not
- *
- * TODO : check the loops for the observers
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_const(
@@ -93,13 +92,13 @@
 stepper.calc_state( start_time , start_state );
 observer( start_state , start_time );
 start_time += dt;
- ++count;
 }

 // we have not reached the end, do another real step
 if( start_time < end_time )
 {
 stepper.do_step( system );
+ ++count;
 }
 }
 return count;

Modified: sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/integrate_const.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/integrate_const.hpp (original)
+++ sandbox/odeint/branches/karsten/boost/numeric/odeint/integrate/integrate_const.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -50,6 +50,37 @@
}

+template< class Stepper , class System , class State , class Time , class Observer >
+size_t integrate_const(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt ,
+ Observer observer
+ )
+{
+ // we want to get as fast as possible to the end
+ if( boost::is_same< do_nothing_observer , Observer >::value )
+ {
+ return detail::integrate_adaptive(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , typename Stepper::stepper_category() );
+ }
+ else
+ {
+ return detail::integrate_const(
+ stepper , system , start_state ,
+ start_time , end_time , dt ,
+ observer , typename Stepper::stepper_category() );
+ }
+}
+
+
+
+
+
+/*
+ * Without observers
+ */
template< class Stepper , class System , class State , class Time >
size_t integrate_const(
Stepper stepper , System system , State &start_state ,
@@ -59,6 +90,16 @@
return integrate_const( stepper , system , start_state , start_time , end_time , dt , do_nothing_observer() );
}

+template< class Stepper , class System , class State , class Time >
+size_t integrate_const(
+ Stepper stepper , System system , const State &start_state ,
+ Time start_time , Time end_time , Time dt
+ )
+{
+ return integrate_const( stepper , system , start_state , start_time , end_time , dt , do_nothing_observer() );
+}
+
+

Modified: sandbox/odeint/branches/karsten/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp (original)
+++ sandbox/odeint/branches/karsten/boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -131,6 +131,8 @@
 /*
 * Version 2 : do_step( system , q , p , t , dt );
 *
+ * For Convenience
+ *
 * The two overloads are needed in order to solve the forwarding problem.
 */
 template< class System , class CoorInOut , class MomentumInOut >
@@ -139,7 +141,6 @@
 do_step( system , std::make_pair( boost::ref( q ) , boost::ref( p ) ) , t , dt );
 }

- // for convenience
 template< class System , class CoorInOut , class MomentumInOut >
 void do_step( System system , const CoorInOut &q , const MomentumInOut &p , const time_type &t , const time_type &dt )
 {
@@ -151,7 +152,7 @@

 /*
- * Version 2 : do_step( system , in , t , out , dt )
+ * Version 3 : do_step( system , in , t , out , dt )
 *
 * The forwarding problem is not solved in this version
 */

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/getting_started.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/getting_started.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/getting_started.qbk 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -2,9 +2,9 @@

[section Overview]

-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 `dxdt` which is also our notation for the derivative in the source code.
+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 `dxdt` 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 ~ dt^2. 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:
+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 ['~ dt[super 2]]. 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:

[include stepper_table.qbk]

@@ -31,7 +31,7 @@

[section Short Example]

-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):
+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)]:

[import ../examples/harmonic_oscillator.cpp]
[rhs_function]
@@ -46,11 +46,7 @@

[integration]

-The integrate function expects as parameters the rhs of the ode as defined above, the initial state x, the start-and end-time of the integration as well as the initial time step. Note, that [funcref boost::numeric::odeint::integrate integrate] 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.
-
-[integrate_observer]
-
-[integrate_observ]
+The integrate function expects as parameters the rhs of the ode as defined above, the initial state `x`, the start-and end-time of the integration as well as the initial time step. Note, that [funcref boost::numeric::odeint::integrate integrate] 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:

@@ -60,6 +56,19 @@

[integration_class]

+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
+
+[integrate_observer]
+
+which stores the intermediate steps in a container. Now, you only have to pass this container to the integration function:
+
+[integrate_observ]
+
+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]
+
+
[endsect]

[endsect]
\ No newline at end of file

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 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="extend_odeint.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -59,12 +59,8 @@
</colgroup>
<thead><tr>
<th>
- 
- 
 </th>
<th>
- 
- 
 </th>
<th>
 
@@ -149,23 +145,25 @@
 
<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:
@@ -268,14 +266,16 @@
 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)
@@ -283,26 +283,33 @@
 
<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">
@@ -332,24 +339,26 @@
 
<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:
@@ -471,15 +480,17 @@
 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)
@@ -487,26 +498,33 @@
 
<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">
@@ -529,11 +547,13 @@

 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
@@ -554,20 +574,18 @@
 
<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
@@ -682,30 +700,37 @@
 
<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">
@@ -733,7 +758,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="extend_odeint.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="extend_odeint.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="reference.html"><img src="../images/next.png" alt="Next"></a>
</div>
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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 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="tutorial.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="tutorial.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="concepts.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/getting_started.html 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -33,22 +33,26 @@

 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 ~ dt^2. 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:
+ 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="id326495"></a>Table 1.1. Stepper Algorithms
+<a name="id518246"></a>Table 1.1. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -283,6 +287,38 @@
 
 </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>
@@ -325,15 +361,15 @@
</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):
+ 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;
@@ -348,8 +384,6 @@
}
</pre>

- 
-
 

 Here we chose <code class="computeroutput">vector<double></code>
@@ -365,17 +399,13 @@
 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>
@@ -384,116 +414,113 @@
 stepper (5th order) and uses adaptive stepsize.
 

- 
-
-
+

<pre class="programlisting">size_t steps = integrate( harmonic_oscillator ,
- x , 0.0 , 10.0 , 0.1
- );
+ 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 x, the start-and end-time of the integration as
- well as the initial time step. Note, that <code class="computeroutput">integrate</code>
+ 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">struct push_back_state_and_time
-{
- vector< state_type >& m_states;
- vector< double >& m_time;
+<pre class="programlisting">/* The rhs of x' = f(x) defined as a class */
+class harm_osc {

- push_back_state_and_time( vector< state_type > &states , vector< double > &times )
- : m_states( states ) , m_times( times ) { }
+ double m_gam;

- void operator()( const state_type &x , double t )
- {
- m_states.push_back( x );
- m_times.push_back( t );
- }
+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">vector<state_type> x_vec;
-vector<double> times;
-
-size_t 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_t_vec[i][0] << '\t' << x_t_vec[i][1] << '\n';
-}
+<pre class="programlisting">harm_osc ho(0.15);
+steps = integrate( ho ,
+ x , 0.0 , 10.0 , 0.1 );
</pre>

- 
-
 

- 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:
+ 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">class harm_osc {
-
- double m_gam;
+<pre class="programlisting">struct push_back_state_and_time
+{
+ std::vector< state_type >& m_states;
+ std::vector< double >& m_times;

-public:
- harm_osc( double gam ) : m_gam(gam) { }
+ 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 , state_type &dxdt , const double t )
- {
- dxdt[0] = x[1];
- dxdt[1] = -x[0] - m_gam*x[1];
- }
+ void operator()( const state_type &x , double t )
+ {
+ m_states.push_back( x );
+ m_times.push_back( t );
+ }
};
</pre>

- 
-
 

- which can be used via
+ which stores the intermediate steps in a container. Now, you only have to
+ pass this container to the integration function:
 

- 
-
-
+

-<pre class="programlisting">harm_osc ho(0.15);
-steps = integrate( ho ,
- x , 0.0 , 10.0 , 0.1
- );
+<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>
@@ -507,7 +534,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="../index.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="tutorial.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
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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 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+<a accesskey="p" href="concepts.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -33,7 +33,7 @@
classes</a>
</h3></div></div></div>
<div class="table">
-<a name="id374081"></a>Table 1.3. Stepper Algorithms
+<a name="id568603"></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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+<a accesskey="p" href="concepts.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/boost_sandbox_numeric_odeint/tutorial.html 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="getting_started.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
@@ -56,16 +56,12 @@
</h4></div></div></div>

 First of all, you have to specify the datatype that represents a state
- of your system x. Mathematically, this
- usually is an n-dimensional vector with real numbers or complex numbers
- as scalar objects. For odeint the most natural way is to use <code class="computeroutput">vector<
- double ></code>
- or <code class="computeroutput">vector<
- complex<
- double >
- ></code> to represent the system state.
- However, odeint can deal with other container types as well, e.g. <code class="computeroutput">tr1::array< double , N ></code>
- as long as it is fullfils some requirements defined below.
+ of your system x. Mathematically, this usually is
+ an n-dimensional vector with real numbers or complex numbers as scalar
+ objects. For odeint the most natural way is to use <code class="computeroutput">vector< double ></code> or <code class="computeroutput">vector< complex< double > ></code>
+ to represent the system state. However, odeint can deal with other container
+ types as well, e.g. <code class="computeroutput">tr1::array< double , N ></code> as long as it is fullfils some requirements
+ defined below.
 

 To integrate a differential equation numerically, one has to define the
@@ -75,9 +71,7 @@
 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;
@@ -92,14 +86,11 @@
}
</pre>

- 
-
 

- The parameters of the function must follow the example above where x is the current state, dxdt
- is the derivative x' and should be filled by the function
- with f(x) and t is
- the current time.
+ 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'
+ and should be filled by the function with f(x) and
+ <code class="computeroutput">t</code> is the current time.
 

 A more sophisticated approach is to implement the system as a class where
@@ -107,11 +98,10 @@
 parameter structure as above:
 

- 
-
-
+

-<pre class="programlisting">class harm_osc {
+<pre class="programlisting">/* The rhs of x' = f(x) defined as a class */
+class harm_osc {

 double m_gam;

@@ -126,8 +116,6 @@
};
</pre>

- 
-
 

 odeint can deal with instances of such classes instead of pure functions
@@ -145,13 +133,13 @@
 to obtain the approximate state x(t+dt). There exist
 many different methods to perform such a timestep each of which has a certain
 order q. If the order of a method is q
- than it is accurate up to term ~dt^q that means the
- error in x made by such a step is ~dt^(q+1).
+ than it is accurate up to term ~dtq that means the
+ error in x made by such a step is ~dtq+1.
 odeint provides several steppers of different orders from which you can
 choose:
 
<div class="table">
-<a name="id369858"></a>Table 1.2. Stepper Algorithms
+<a name="id561513"></a>Table 1.2. Stepper Algorithms
<div class="table-contents"><table class="table" summary="Stepper Algorithms">
<colgroup>
<col>
@@ -386,6 +374,38 @@
 
 </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>
@@ -403,7 +423,7 @@
</h4></div></div></div>

 The basic stepper just performs one timestep and doesn't give you any information
- about the error that was made (except that you know it is of order q+1).
+ about the error that was made (except that you know it is of order q+1).
 Such steppers are used with constant step size that should be chosen small
 enough to have reasonable small errors. However, you should apply some
 sort of validity check of your results (such as observing conserved quantities)
@@ -414,37 +434,30 @@
 )</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>
- using the rk4 method from t=0 to 10 with a stepsize dt=0.01 and the initial
- condition given in <code class="computeroutput">x</code>. The
- result, x(t=10) is stored in <code class="computeroutput">x</code>
+ using the RK4 method from t=0 to 10
+ with a stepsize dt=0.01 and the initial condition
+ given in <code class="computeroutput">x</code>. The result,
+ x(t=10) is stored in <code class="computeroutput">x</code>
 (in-place). Each stepper defines a <code class="computeroutput">do_step</code>
 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">
@@ -458,20 +471,16 @@
 control is realized via stepper algorithms that additionally provide an
 error estimation of the applied step. Odeint provides a number of such
 ErrorSteppers and we will show their usage
- on the example of stepper_rk5_ck -- a 5th order Runge-Kutta method with
- 4th order error estimation and coefficients introduced by Cash-Karp.
+ on the example of `explicit_error_rk54_ck? -- a 5th order Runge-Kutta method
+ 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
@@ -485,9 +494,9 @@
 as parameter and four values defining the maximal absolute and relative
 error allowed for one integration step. The standard controlled stepper
 created by this method ensures that the error err
- of the solution fulfills err < eps_abs + eps_rel * ( a_x *
- |x| + a_dxdt * dt * |dxdt| ) by decreasesing the step size.
- Note, that the stepsize is also increased if the error gets too small compared
+ of the solution fulfills err < eps_abs + eps_rel * ( ax * |x|
+ + adxdt * dt * |dxdt| ) by decreasesing the step size. Note,
+ that the stepsize is also increased if the error gets too small compared
 to the rhs of the above relation. Now we have everything needed to integrate
 the harmonic oscillator using an adaptive step size method. Similar to
 the case with constant step size above, there exists a <code class="computeroutput">integrate_adaptive</code>
@@ -495,23 +504,20 @@
 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>
- using an adaptive step size method based on the rk5_ck scheme from t=0
- to 10 with an initial step size of dt=0.01 (will be adjusted) and the initial
- condition given in x. The result, x(t=10), will also be stored in x (in-place).
+ using an adaptive step size method based on the rk5_ck scheme from t=0
+ to 10 with an initial step size of dt=0.01
+ (will be adjusted) and the initial condition given in x. The result, [x(t=10)'],
+ will also be stored in x (in-place).
 
</div>

@@ -523,6 +529,9 @@

 Default construction
 
+
+ The full cpp file for this example can be found here: ../../examples/harmonic_oscillator.cpp
+ 
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h3 class="title">
@@ -541,53 +550,60 @@
 and energy conservation</a>
</h4></div></div></div>

- The next example in this tutorial is a simulation of the solar system.
- In the solar system each planet, and of course also the sun will be represented
- by mass points. The interaction force between each object is the gravitational
- force which can be written as
+ 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">
 

- F_ij = -gamma m_i m_j (q_i-q_j)/|q_i-q_j|^3
+ 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
 

- where gamma is the gravitational constant, m_i and m_j are the masses and
- q_i and q_j are the locations of the two objects. The equations of motion
- are then
+ Fij = -γ mi mj ( qi - qj ) / | qi - qj | 3
 

- dq_i/dt = p_i dp_i/dt = 1/m_i sum_ji F_ij
+ 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
 

- where pi is the momenta of object i. The equations of motion can also be
- derived from the Hamiltonian
+ dqi / dt = pi
 

- H = sum_i p_i^2/(2m_i) + sum_j V( qi , qj )
+ dpi / dt = 1 / mi Σji Fij
 

- with the interaction potential V(q_i,q_j). The Hamiltonian equations give
- the equations of motion
+ where pi is the momenta of object i.
+ The equations of motion can also be derived from the Hamiltonian
 

- dq_i/dt = dH/dp_i
+ H = Σi pi2 / ( 2 mi ) + Σj V( qi , qj )
 

- dp_i = -dH/dq_i.
+ with the interaction potential V(qi,qj). The Hamiltonian
+ equations give the equations of motion
 

- In time independent Hamiltonian system the energy is conserved and special
- integration methods have to be applied in order to ensure energy conservation.
- The odeint library provides classes for Hamiltonian systems, which are
- separable and can be written in the form H = sum p_i^2/2m_i + Hq(q), where
- Hq(q) only depends on the coordinates.
+ dqi / dt = dH / dpi
 

- hamiltonian_stepper_euler hamiltonian_stepper_rk
+ dpi = -dH / dqi
 

- 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=mi pi dpi=f(qi).
+ 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" lang="en">
@@ -597,29 +613,118 @@
</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/operator.hpp>:
+ space as well as the velocity. Therefore, we use the operators from Boost.Operators:
 

- [point_type]
+
+
+<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 systems (derivative) functions. As container type we use
- std::tr1::array and the state type is then simply
+ 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>
 

- [state_type_definition]
+
+
+<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>
+
 

- and represents all space coordinates q or all momenta coordinates p. As
- system function we have to provide f(p) = dq and f(q) = -dp, which acts
- only on p or q:
+ 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.
 

- [momentum_function]
+ As system function we have to provide f(p) and f(q):
 

- [coordinate_function]
+
+
+<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
@@ -628,13 +733,58 @@
 conditions, which are taken from the book of Hairer, Wannier, Lubich.
 

- Now, we use the rk stepper to integrate the solar system. To visualize
- the motion we save the trajectory of each planet in a circular buffer.
- The output can be piped directly into gnuplot and a very nice visualization
- of the motion appears.
+ 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>
+
 

- [integration_solar_system]
+ The full example can be found here: ../../examples/solar_system.cpp
 
</div>
</div>
@@ -868,7 +1018,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
-<a accesskey="p" href="getting_started.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+<a accesskey="p" href="getting_started.html"><img src="../images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../images/home.png" alt="Home"></a><a accesskey="n" href="extend_odeint.html"><img src="../images/next.png" alt="Next"></a>
</div>
</body>
</html>

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/index.html 2011-03-18 13:08:14 EDT (Fri, 18 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="../../../../doc/html/images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
<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="id358081"></a>
+<a name="id549573"></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 09:58:43 GMT</td>
+<td align="left">Last revised: March 18, 2011 at 17:07:57 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="../../../../doc/html/images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="boost_sandbox_numeric_odeint/getting_started.html"><img src="images/next.png" alt="Next"></a></div>
</body>
</html>

Added: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/html/solar_system.jpg
==============================================================================
Binary file. No diff available.

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 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -15,6 +15,33 @@
]
]

+[def __boost_lambda
+ [@http://www.boost.org/doc/libs/release/doc/html/lambda.html Boost.Lambda]]
+[def __boost_phoenix
+ [@http://www.boost.org/doc/libs/1_46_1/libs/spirit/phoenix/doc/html/index.html Boost.Phoenix]]
+[def __boost_operators
+ [@http://www.boost.org/doc/libs/release/doc/html/operators.html Boost.Operators]]
+[def __boost_ref
+ [@http://www.boost.org/doc/libs/release/doc/html/ref.html `boost::ref`]]
+
+
+
+
+[def __alpha '''α''']
+[def __lambda '''λ'''][/lower case]
+[def __Lambda '''Λ'''][/upper case]
+[def __gamma '''γ''']
+[def __Gamma '''Γ''']
+[def __sigma '''σ''']
+[def __Sigma '''Σ''']
+[def __space '''''']
+
+[template super[x]'''<superscript>'''[x]'''</superscript>''']
+[template sub[x]'''<subscript>'''[x]'''</subscript>''']
+[template subl[x]'''<subscript>'''__space[x]'''</subscript>''']
+
+
+
[include getting_started.qbk]

[include tutorial.qbk]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/stepper_table.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/stepper_table.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/stepper_table.qbk 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -6,4 +6,5 @@
   [[Dormand-Prince 5] [explicit_error_dopri5] [5] [Yes (Order 4)] [Yes] [...]]
   [[Implicit Euler] [implicit_euler] [1] [No] [No] [Needs the Jacobian]]
   [[Rosenbrock 4] [rosenbrock4] [4] [Yes] [Yes] [Good for stiff systems]]
+ [[Symplectic Euler] [symplectic_euler] [1] [No] [No] [Symplectic solver for separable Hamiltonian system]]
]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_harmonic_oscillator.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_harmonic_oscillator.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_harmonic_oscillator.qbk 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -2,43 +2,25 @@

[section Define the ODE]

-First of all, you have to specify the datatype that represents a state of your
-system [*x]. Mathematically, this usually is an n-dimensional vector with
-real numbers or complex numbers as scalar objects. For odeint the most natural
-way is to use `vector< double >` or `vector< complex< double > >` to represent
-the system state. However, odeint can deal with other container types as well, e.g. `tr1::array< double , N >` as long as it is fullfils some requirements defined below.
-
-To integrate a differential equation numerically, one has to define the rhs of
-the equation ['x' = f(x)]. In odeint you supply this function in terms of
-an object that implements the ()-operator with a certain parameter structure.
-Hence, the straight forward way would be to just define a function, e.g:
+First of all, you have to specify the datatype that represents a state of your system ['x]. Mathematically, this usually is an n-dimensional vector with real numbers or complex numbers as scalar objects. For odeint the most natural way is to use `vector< double >` or `vector< complex< double > >` to represent the system state. However, odeint can deal with other container types as well, e.g. `tr1::array< double , N >` as long as it is fullfils some requirements defined below.
+
+To integrate a differential equation numerically, one has to define the rhs of the equation ['x' = f(x)]. In odeint you supply this function in terms of an object that implements the ()-operator with a certain parameter structure. Hence, the straight forward way would be to just define a function, e.g:

[rhs_function]

-The parameters of the function must follow the example above where [*x] is the
-current state, [*dxdt] is the derivative ['x'] and should be filled by the
-function with ['f(x)] and [*t] is the current time.
-
-A more sophisticated approach is to implement the system as a class where the
-rhs function is defined as the ()-operator of the class with the same parameter
-structure as above:
+The parameters of the function must follow the example above where `x` is the current state, `dxdt` is the derivative ['x'] and should be filled by the function with ['f(x)] and `t` is the current time.
+
+A more sophisticated approach is to implement the system as a class where the rhs function is defined as the ()-operator of the class with the same parameter structure as above:

[rhs_class]

-odeint can deal with instances of such classes instead of pure functions which
-allows for cleaner code.
+odeint can deal with instances of such classes instead of pure functions which allows for cleaner code.

[endsect]

[section Stepper Types]

-Numerical integration works iteratively, that means you start at a state ['x(t)]
-and perform a timestep of length ['dt] to obtain the approximate state
-['x(t+dt)]. There exist many different methods to perform such a timestep each
-of which has a certain order ['q]. If the order of a method is ['q] than it is
-accurate up to term ['~dt^q] that means the error in ['x] made by such a step
-is ['~dt^(q+1)]. odeint provides several steppers of different orders from which
-you can choose:
+Numerical integration works iteratively, that means you start at a state ['x(t)] and perform a timestep of length ['dt] to obtain the approximate state ['x(t+dt)]. There exist many different methods to perform such a timestep each of which has a certain order ['q]. If the order of a method is ['q] than it is accurate up to term ['~dt[super q]] that means the error in ['x] made by such a step is ['~dt[super q+1]]. odeint provides several steppers of different orders from which you can choose:

[include stepper_table.qbk]

@@ -48,21 +30,11 @@

[section Integration with Constant Step Size]

-The basic stepper just performs one timestep and doesn't give you any
-information about the error that was made (except that you know it is of order
-q+1). Such steppers are used with constant step size that should be chosen small
-enough to have reasonable small errors. However, you should apply some sort of
-validity check of your results (such as observing conserved quantities) becasue
-you have no other control of the error. The following example defines a basic
-stepper based on the classical Runge-Kutta scheme of 4th order. The declaration of the stepper requires the state type as template parameter.
-The integration can now be done by using the `integrate_const( Stepper, System,
- state, start_time, end_time, step_size )` function from odeint:
+The basic stepper just performs one timestep and doesn't give you any information about the error that was made (except that you know it is of order ['q+1]). Such steppers are used with constant step size that should be chosen small enough to have reasonable small errors. However, you should apply some sort of validity check of your results (such as observing conserved quantities) becasue you have no other control of the error. The following example defines a basic stepper based on the classical Runge-Kutta scheme of 4th order. The declaration of the stepper requires the state type as template parameter. The integration can now be done by using the `integrate_const( Stepper, System, state, start_time, end_time, step_size )` function from odeint:

[define_const_stepper]

-This call integrates the system defined by `harmonic_oscillator` using the rk4
-method from t=0 to 10 with a stepsize dt=0.01 and the initial condition given
-in `x`. The result, ['x(t=10)] is stored in `x` (in-place). Each stepper defines a `do_step` method which can used directly. So, you write down the above example as
+This call integrates the system defined by `harmonic_oscillator` using the RK4 method from ['t=0] to ['10] with a stepsize ['dt=0.01] and the initial condition given in `x`. The result, ['x(t=10)] is stored in `x` (in-place). Each stepper defines a `do_step` method which can used directly. So, you write down the above example as

[integrate_const_loop]

@@ -70,40 +42,15 @@

[section Integration with Adaptive Step Size]

-To improve the numerical results and additionally minimize the computational
-effort, the application of a step size control is advisable.
-Step size control is realized via stepper algorithms that additionally provide an
-error estimation of the applied step.
-Odeint provides a number of such *ErrorSteppers* and we will show their usage on
-the example of stepper_rk5_ck -- a 5th order Runge-Kutta method with 4th order
-error estimation and coefficients introduced by Cash-Karp.
+To improve the numerical results and additionally minimize the computational effort, the application of a step size control is advisable. Step size control is realized via stepper algorithms that additionally provide an error estimation of the applied step. Odeint provides a number of such *ErrorSteppers* and we will show their usage on the example of `explicit_error_rk54_ck? -- a 5th order Runge-Kutta method with 4th order error estimation and coefficients introduced by Cash-Karp.

[define_adapt_stepper]

-Given the error stepper, one still needs an instance that checks the error and
-adjusts the step size accordingly.
-In odeint, this is done by *ControlledSteppers*.
-The usual way to create a controlled stepper is via the
-`make_controlled_stepper_standard( ErrorStepper , eps_abs , eps_rel , a_x , a_dxdt )`
-function that takes an error stepper as parameter and four values defining the maximal
-absolute and relative error allowed for one integration step.
-The standard controlled stepper created by this method ensures that the error ['err]
-of the solution fulfills
-['err < eps_abs + eps_rel * ( a_x * |x| + a_dxdt * dt * |dxdt| ) ]
-by decreasesing the step size. Note, that the stepsize is also increased if the error
-gets too small compared to the rhs of the above relation.
-Now we have everything needed to integrate the harmonic oscillator using an adaptive
-step size method.
-Similar to the case with constant step size above, there exists a `integrate_adaptive`
-function with a similar parameter structure, but it requires the controlled stepper
-create by `make_controlled_stepper_standard`.
+Given the error stepper, one still needs an instance that checks the error and adjusts the step size accordingly. In odeint, this is done by *ControlledSteppers*. The usual way to create a controlled stepper is via the `make_controlled_stepper_standard( ErrorStepper , eps_abs , eps_rel , a_x , a_dxdt )` function that takes an error stepper as parameter and four values defining the maximal absolute and relative error allowed for one integration step. The standard controlled stepper created by this method ensures that the error ['err] of the solution fulfills ['err < eps_abs + eps_rel * ( a[sub x] * |x| + a[sub dxdt] * dt * |dxdt| ) ] by decreasesing the step size. Note, that the stepsize is also increased if the error gets too small compared to the rhs of the above relation. Now we have everything needed to integrate the harmonic oscillator using an adaptive step size method. Similar to the case with constant step size above, there exists a `integrate_adaptive` function with a similar parameter structure, bu
t it requires the controlled stepper create by `make_controlled_stepper_standard`.

[integrate_adapt]

-As above, this integrates the system defined by `harmonic_oscillator` using an adaptive
-step size method based on the rk5_ck scheme from t=0 to 10 with an initial step size of
-dt=0.01 (will be adjusted) and the initial condition given in x. The result, x(t=10), will
-also be stored in x (in-place).
+As above, this integrates the system defined by `harmonic_oscillator` using an adaptive step size method based on the rk5_ck scheme from ['t=0] to ['10] with an initial step size of ['dt=0.01] (will be adjusted) and the initial condition given in x. The result, [x(t=10)'], will also be stored in x (in-place).

[endsect]

@@ -113,4 +60,6 @@

Default construction

+The full cpp file for this example can be found here: [@../../examples/harmonic_oscillator.cpp]
+
[endsect]

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_solar_system.qbk
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_solar_system.qbk (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/doc/tutorial_solar_system.qbk 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -2,84 +2,69 @@

[section Gravitation and energy conservation]

-The next example in this tutorial is a simulation of the solar system. In the
-solar system each planet, and of course also the sun will be represented by
-mass points. The interaction force between each object is the gravitational
-force which can be written as
+The next example in this tutorial is a simulation of the outer solar system, consisting of the sun, Jupiter, Saturn, Uranus, Neptune and Pluto.

-F_ij = -gamma m_i m_j (q_i-q_j)/|q_i-q_j|^3
+[$solar_system.jpg]

-where gamma is the gravitational constant, m_i and m_j are the masses and q_i
-and q_j are the locations of the two objects. The equations of motion are then
+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

-dq_i/dt = p_i
-dp_i/dt = 1/m_i sum_ji F_ij
+['F[subl ij] = -__gamma m[subl i] m[subl j] ( q[subl i] - q[subl j] ) / | q[subl i] - q[subl j] | [super 3]]

-where pi is the momenta of object i. The equations of motion can also be
-derived from the Hamiltonian
+where [' __gamma] is the gravitational constant, ['m[subl i]] and ['m[subl j]] are the masses and ['q[subl i]] and ['q[subl j]] are the locations of the two objects. The equations of motion are then

-H = sum_i p_i^2/(2m_i) + sum_j V( qi , qj )
+['dq[subl i] / dt = p[subl i]]

-with the interaction potential V(q_i,q_j). The Hamiltonian equations give the
+['dp[subl i] / dt = 1 / m[subl i] __Sigma[subl ji] F[subl ij]]
+
+where ['p[subl i]] is the momenta of object ['i]. The equations of motion can also be derived from the Hamiltonian
+
+['H = __Sigma[subl i] p[subl i][super 2] / ( 2 m[subl i] ) + __Sigma[subl j] V( q[subl i] , q[subl j] )]
+
+with the interaction potential ['V(q[subl i],q[subl j])]. The Hamiltonian equations give the
equations of motion

-dq_i/dt = dH/dp_i
+['dq[subl i] / dt = dH / dp[subl i]]

-dp_i = -dH/dq_i.
+['dp[subl i] = -dH / dq[subl i]]

-In time independent Hamiltonian system the energy is conserved and special
-integration methods have to be applied in order to ensure energy
-conservation. The odeint library provides classes for Hamiltonian
-systems, which are separable and can be written in the form H = sum p_i^2/2m_i +
-Hq(q), where Hq(q) only depends on the coordinates.
-
-hamiltonian_stepper_euler
-hamiltonian_stepper_rk
-
-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=mi pi dpi=f(qi).
+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 = __Sigma p[subl i][super 2] / (2m[subl i]) + H[subl q](q)], where ['H[subl q](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 ['dq[subl i] / dt = p[subl i]] / m[subl i] , ['dp[subl i] / dt = f( q[subl i] )].

[endsect]

[section Define the system function]

-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/operator.hpp>:
+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:

[import ../examples/point_type.hpp]
[point_type]

-The next step is to define a container type storing the values of q and p and
-to define systems (derivative) functions. As container type we use
-std::tr1::array and the state type is then simply
+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 `std::tr1::array`

[import ../examples/solar_system.cpp]
-[state_type_definition]
+[container_type_definition]

-and represents all space coordinates q or all momenta coordinates p. As system
-function we have to provide f(p) = dq and f(q) = -dp, which acts only on p or q:
+The `container_type` is different from the state type of the ODE. The state type of the ode is simply a `pair< container_type , container_type >` since it needs the informations about the coordinates and the momenta.

+As system function we have to provide ['f(p)] and ['f(q)]:
+
+[coordinate_function]

[momentum_function]

-[coordinate_function]
+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.

-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.
-
-Now, we use the rk stepper to integrate the solar system. To visualize the
-motion we save the trajectory of each planet in a circular buffer. The output
-can be piped directly into gnuplot and a very nice visualization of the motion
-appears.
+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:

[integration_solar_system]

+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 `container_type` but a pair of `container_type`. 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 `container_type`. The reference wrapper is also passed, but this is not a problem at all:
+
+[streaming_observer]
+
+The full example can be found here: [@../../examples/solar_system.cpp]
+
[endsect]

[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 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -13,6 +13,6 @@

exe harmonic_oscillator : harmonic_oscillator.cpp ;
-# exe solar_system : solar_system.cpp point_type.hpp ;
+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/harmonic_oscillator.cpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/harmonic_oscillator.cpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/harmonic_oscillator.cpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -1,7 +1,10 @@
#include <iostream>
+#include <vector>

#include <boost/numeric/odeint.hpp>

+
+
//[ rhs_function
/* The type of container used to hold the state vector */
typedef std::vector< double > state_type;
@@ -16,7 +19,12 @@
}
//]

+
+
+
+
//[ rhs_class
+/* The rhs of x' = f(x) defined as a class */
class harm_osc {

 double m_gam;
@@ -33,13 +41,16 @@
//]

+
+
+
//[ integrate_observer
struct push_back_state_and_time
{
- vector< state_type >& m_states;
- vector< double >& m_time;
+ std::vector< state_type >& m_states;
+ std::vector< double >& m_times;

- push_back_state_and_time( vector< state_type > &states , vector< double > &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 )
@@ -56,6 +67,7 @@
 using namespace std;
 using namespace boost::numeric::odeint;

+
 //[ state_initialization
 state_type x(2);
 x[0] = 1.0; // start at x=1.0, p=0.0
@@ -63,35 +75,42 @@
 //]

+
 //[ integration
 size_t steps = integrate( harmonic_oscillator ,
- x , 0.0 , 10.0 , 0.1
- );
+ x , 0.0 , 10.0 , 0.1 );
+ //]
+
+
+
+ //[ integration_class
+ harm_osc ho(0.15);
+ steps = integrate( ho ,
+ x , 0.0 , 10.0 , 0.1 );
 //]

+
+
+
+
 //[ integrate_observ
 vector<state_type> x_vec;
 vector<double> times;

- size_t steps = integrate( harmonic_oscillator ,
- x , 0.0 , 10.0 , 0.1 ,
- push_back_state_and_time( x_vec , times )
- );
+ steps = integrate( harmonic_oscillator ,
+ x , 0.0 , 10.0 , 0.1 ,
+ push_back_state_and_time( x_vec , times ) );

- // output
+ /* output */
 for( size_t i=0; i<=steps; i++ )
 {
- cout << times[i] << '\t' << x_t_vec[i][0] << '\t' << x_t_vec[i][1] << '\n';
+ cout << times[i] << '\t' << x_vec[i][0] << '\t' << x_vec[i][1] << '\n';
 }
 //]

- //[ integration_class
- harm_osc ho(0.15);
- steps = integrate( ho ,
- x , 0.0 , 10.0 , 0.1
- );
- //]
+
+

@@ -100,6 +119,9 @@
 integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 );
 //]

+
+
+
 //[ integrate_const_loop
 const double dt = 0.01;
 for( double t=0.0 ; t<10.0 ; t+= dt )
@@ -107,11 +129,15 @@
 //]

+
+
 //[ define_adapt_stepper
 typedef explicit_error_rk54_ck< state_type > error_stepper_type;
 error_stepper_type rk54;
 //]

+
+
 //[ integrate_adapt
 typedef controlled_error_stepper< error_stepper_type > controlled_stepper_type;
 controlled_stepper_type controlled_stepper;

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/point_type.hpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/point_type.hpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/point_type.hpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -8,7 +8,7 @@
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or
copy at http://www.boost.org/LICENSE_1_0.txt)
-*/
+ */

#ifndef POINT_TYPE_HPP_INCLUDED
#define POINT_TYPE_HPP_INCLUDED
@@ -18,89 +18,100 @@
#include <ostream>

-//
-// the point type
-//
+//[ point_type
+/*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
- > > >
+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;
-
- point( void )
- {
- for( size_t i=0 ; i<dim ; ++i ) m_val[i] = 0.0;
- }
- point( value_type val )
- {
- for( size_t i=0 ; i<dim ; ++i ) m_val[i] = val;
- }
- point( value_type x , value_type y , value_type z = 0.0 )
- {
- if( dim > 0 ) m_val[0] = x;
- if( dim > 1 ) m_val[1] = y;
- if( dim > 2 ) m_val[2] = z;
- }
-
- T operator[]( size_t i ) const { return m_val[i]; }
- T& operator[]( size_t i ) { return m_val[i]; }
-
-
-
- point_type& operator+=( const point_type& p )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] += p[i];
- return *this;
- }
-
- point_type& operator-=( const point_type& p )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] -= p[i];
- return *this;
- }
-
- point_type& operator+=( const value_type& val )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] += val;
- return *this;
- }
-
- point_type& operator-=( const value_type& val )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] -= val;
- return *this;
- }
-
- point_type& operator*=( const value_type &val )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] *= val;
- return *this;
- }
-
- point_type& operator/=( const value_type &val )
- {
- for( size_t i=0 ; i<dim ; ++i )
- m_val[i] /= val;
- return *this;
- }
+ const static size_t dim = Dim;
+ typedef T value_type;
+ typedef point< value_type , dim > point_type;
+
+ // ...
+ // constructors
+ //<-
+ point( void )
+ {
+ for( size_t i=0 ; i<dim ; ++i ) m_val[i] = 0.0;
+ }
+
+ point( value_type val )
+ {
+ for( size_t i=0 ; i<dim ; ++i ) m_val[i] = val;
+ }
+
+ point( value_type x , value_type y , value_type z = 0.0 )
+ {
+ if( dim > 0 ) m_val[0] = x;
+ if( dim > 1 ) m_val[1] = y;
+ if( dim > 2 ) m_val[2] = z;
+ }
+ //->
+
+ // ...
+ // operators
+ //<-
+ T operator[]( size_t i ) const { return m_val[i]; }
+ T& operator[]( size_t i ) { return m_val[i]; }
+
+ point_type& operator+=( const point_type& p )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] += p[i];
+ return *this;
+ }
+
+ point_type& operator-=( const point_type& p )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] -= p[i];
+ return *this;
+ }
+
+ point_type& operator+=( const value_type& val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] += val;
+ return *this;
+ }
+
+ point_type& operator-=( const value_type& val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] -= val;
+ return *this;
+ }
+
+ point_type& operator*=( const value_type &val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] *= val;
+ return *this;
+ }
+
+ point_type& operator/=( const value_type &val )
+ {
+ for( size_t i=0 ; i<dim ; ++i )
+ m_val[i] /= val;
+ return *this;
+ }
+
+ //->

private:

- T m_val[dim];
+ T m_val[dim];
};

+//...
+// more operators
+//]

//
// the - operator
@@ -108,22 +119,20 @@
template< class T , size_t Dim >
point< T , Dim > operator-( const point< T , Dim > &p )
{
- point< T , Dim > tmp;
- for( size_t i=0 ; i<Dim ; ++i ) tmp[i] = -p[i];
- return tmp;
+ point< T , Dim > tmp;
+ for( size_t i=0 ; i<Dim ; ++i ) tmp[i] = -p[i];
+ return tmp;
}

-
-
//
// scalar product
//
template< class T , size_t Dim >
T scalar_prod( const point< T , Dim > &p1 , const point< T , Dim > &p2 )
{
- T tmp = 0.0;
- for( size_t i=0 ; i<Dim ; ++i ) tmp += p1[i] * p2[i];
- return tmp;
+ T tmp = 0.0;
+ for( size_t i=0 ; i<Dim ; ++i ) tmp += p1[i] * p2[i];
+ return tmp;
}

@@ -134,7 +143,7 @@
template< class T , size_t Dim >
T norm( const point< T , Dim > &p1 )
{
- return scalar_prod( p1 , p1 );
+ return scalar_prod( p1 , p1 );
}

@@ -146,7 +155,7 @@
template< class T , size_t Dim >
T abs( const point< T , Dim > &p1 )
{
- return sqrt( norm( p1 ) );
+ return sqrt( norm( p1 ) );
}

@@ -158,9 +167,9 @@
template< class T , size_t Dim >
std::ostream& operator<<( std::ostream &out , const point< T , Dim > &p )
{
- if( Dim > 0 ) out << p[0];
- for( size_t i=1 ; i<Dim ; ++i ) out << " " << p[i];
- return out;
+ if( Dim > 0 ) out << p[0];
+ for( size_t i=1 ; i<Dim ; ++i ) out << " " << p[i];
+ return out;
}

Added: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.agr
==============================================================================
--- (empty file)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.agr 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -0,0 +1,12672 @@
+# Grace project file
+#
+@version 50122
+@page size 792, 612
+@page scroll 5%
+@page inout 5%
+@link page off
+@map font 0 to "Times-Roman", "Times-Roman"
+@map font 1 to "Times-Italic", "Times-Italic"
+@map font 2 to "Times-Bold", "Times-Bold"
+@map font 3 to "Times-BoldItalic", "Times-BoldItalic"
+@map font 4 to "Helvetica", "Helvetica"
+@map font 5 to "Helvetica-Oblique", "Helvetica-Oblique"
+@map font 6 to "Helvetica-Bold", "Helvetica-Bold"
+@map font 7 to "Helvetica-BoldOblique", "Helvetica-BoldOblique"
+@map font 8 to "Courier", "Courier"
+@map font 9 to "Courier-Oblique", "Courier-Oblique"
+@map font 10 to "Courier-Bold", "Courier-Bold"
+@map font 11 to "Courier-BoldOblique", "Courier-BoldOblique"
+@map font 12 to "Symbol", "Symbol"
+@map font 13 to "ZapfDingbats", "ZapfDingbats"
+@map color 0 to (255, 255, 255), "white"
+@map color 1 to (0, 0, 0), "black"
+@map color 2 to (255, 0, 0), "red"
+@map color 3 to (0, 255, 0), "green"
+@map color 4 to (0, 0, 255), "blue"
+@map color 5 to (255, 255, 0), "yellow"
+@map color 6 to (188, 143, 143), "brown"
+@map color 7 to (220, 220, 220), "grey"
+@map color 8 to (148, 0, 211), "violet"
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+35.3316 -13.2741
+&

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.cpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.cpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/examples/solar_system.cpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -8,158 +8,193 @@
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)
-*/
+ */

-#include <bits/stdc++.h>
-#include <bits/stdtr1c++.h>
+#include <iostream>
+#include <tr1/array>

-#include <boost/circular_buffer.hpp>
-#include <boost/ref.hpp>
#include <boost/numeric/odeint.hpp>

#include "point_type.hpp"

-#define tab "\t"
-
-using namespace std;
-using namespace boost::numeric::odeint;
-
+//[ container_type_definition
// 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 > state_type;
+typedef std::tr1::array< point_type , n > container_type;
typedef std::tr1::array< double , n > mass_type;
-typedef hamiltonian_stepper_euler< state_type > stepper_type;
+//]
+
+
+
+

+
+//[ coordinate_function
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];
+ }
+};
+//]
+

-ostream& operator<<( ostream &out , const state_type &x )
+//[ momentum_function
+struct solar_system_momentum
{
- typedef state_type::value_type value_type;
- copy( x.begin() , x.end() ,
- ostream_iterator< value_type >( out , "\n" ) );
- return out;
-}
+ 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;
+
+ }
+ }
+ }
+};
+//]
+
+

-point_type center_of_mass( const state_type &x , const mass_type &m )
+
+
+
+//[ some_helpers
+point_type center_of_mass( const container_type &x , const mass_type &m )
{
- double overall_mass = 0.0;
- point_type mean( 0.0 );
- for( size_t i=0 ; i<x.size() ; ++i )
- {
- overall_mass += m[i];
- mean += m[i] * x[i];
- }
- if( x.size() != 0 ) mean /= overall_mass;
- return mean;
+ double overall_mass = 0.0;
+ point_type mean( 0.0 );
+ for( size_t i=0 ; i<x.size() ; ++i )
+ {
+ overall_mass += m[i];
+ mean += m[i] * x[i];
+ }
+ if( !x.empty() ) mean /= overall_mass;
+ return mean;
}

-double energy( const state_type &q , const state_type &p ,
- const mass_type &masses )
+double energy( const container_type &q , const container_type &p , const mass_type &masses )
{
- const size_t n = q.size();
- double en = 0.0;
- for( size_t i=0 ; i<n ; ++i )
- {
- en += 0.5 * norm( p[i] ) / masses[i];
- for( size_t j=0 ; j<i ; ++j )
- {
- double diff = abs( q[i] - q[j] );
- en -= gravitational_constant * masses[j] * masses[i] / diff;
- }
- }
- return en;
+ const size_t n = q.size();
+ double en = 0.0;
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ en += 0.5 * norm( p[i] ) / masses[i];
+ for( size_t j=0 ; j<i ; ++j )
+ {
+ double diff = abs( q[i] - q[j] );
+ en -= gravitational_constant * masses[j] * masses[i] / diff;
+ }
+ }
+ return en;
}
+//]

-struct solar_system
+
+//[ streaming_observer
+struct streaming_observer
{
- mass_type &m_masses;
+ std::ostream& m_out;

- solar_system( mass_type &masses ) : m_masses( masses ) { }
+ streaming_observer( std::ostream &out ) : m_out( out ) { }

- void operator()( const state_type &q , state_type &dpdt )
- {
- const size_t n = q.size();
- fill( dpdt.begin() , dpdt.end() , 0.0 );
- for( size_t i=0 ; i<n ; ++i )
- {
- for( size_t j=i+1 ; j<n ; ++j )
- {
- point_type diff = q[j] - q[i];
- double d = abs( diff );
- diff = gravitational_constant * diff / d / d / d;
- dpdt[i] += diff * m_masses[j];
- dpdt[j] -= diff * m_masses[i];
- }
- }
- }
+ 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";
+ }
};
+//]

int main( int argc , char **argv )
{
- mass_type masses = {{
- 1.00000597682 , // sun
- 0.000954786104043 , // jupiter
- 0.000285583733151 , // saturn
- 0.0000437273164546 , // uranus
- 0.0000517759138449 , // neptune
- 1.0 / ( 1.3e8 ) // pluto
- }};
-
- state_type q = {{
- point_type( 0.0 , 0.0 , 0.0 ) , // sun
- point_type( -3.5023653 , -3.8169847 , -1.5507963 ) , // jupiter
- point_type( 9.0755314 , -3.0458353 , -1.6483708 ) , // saturn
- point_type( 8.3101420 , -16.2901086 , -7.2521278 ) , // uranus
- point_type( 11.4707666 , -25.7294829 , -10.8169456 ) , // neptune
- point_type( -15.5387357 , -25.2225594 , -3.1902382 ) // pluto
- }};
-
- state_type p = {{
- point_type( 0.0 , 0.0 , 0.0 ) , // sun
- point_type( 0.00565429 , -0.00412490 , -0.00190589 ) , // jupiter
- point_type( 0.00168318 , 0.00483525 , 0.00192462 ) , // saturn
- point_type( 0.00354178 , 0.00137102 , 0.00055029 ) , // uranus
- point_type( 0.00288930 , 0.00114527 , 0.00039677 ) , // neptune
- point_type( 0.00276725 , -0.00170702 , -0.00136504 ) // pluto
- }};
-
-
- point_type qmean = center_of_mass( q , masses );
- point_type pmean = center_of_mass( p , masses );
- for( size_t i=0 ; i<n ; ++i ) { q[i] -= qmean ; p[i] -= pmean; }
-
- stepper_type stepper;
-
- const double dt = 100.0;
- double t = 0.0;
- while( t < 10000000.0 )
- {
- clog << t << tab << energy( q , p , masses ) << tab;
- clog << center_of_mass( q , masses ) << tab;
- clog << center_of_mass( p , masses ) << endl;
-
- cout << t;
- for( size_t i=0 ; i<n ; ++i ) cout << tab << q[i];
- cout << endl;
-
- for( size_t i=0 ; i<1 ; ++i,t+=dt )
- stepper.do_step( solar_system( masses ) , q , p , dt );
- t += dt;
- }

- return 0;
+ using namespace std;
+ using namespace boost::numeric::odeint;
+
+ mass_type masses = {{
+ 1.00000597682 , // sun
+ 0.000954786104043 , // jupiter
+ 0.000285583733151 , // saturn
+ 0.0000437273164546 , // uranus
+ 0.0000517759138449 , // neptune
+ 1.0 / ( 1.3e8 ) // pluto
+ }};
+
+ container_type q = {{
+ point_type( 0.0 , 0.0 , 0.0 ) , // sun
+ point_type( -3.5023653 , -3.8169847 , -1.5507963 ) , // jupiter
+ point_type( 9.0755314 , -3.0458353 , -1.6483708 ) , // saturn
+ point_type( 8.3101420 , -16.2901086 , -7.2521278 ) , // uranus
+ point_type( 11.4707666 , -25.7294829 , -10.8169456 ) , // neptune
+ point_type( -15.5387357 , -25.2225594 , -3.1902382 ) // pluto
+ }};
+
+ container_type p = {{
+ point_type( 0.0 , 0.0 , 0.0 ) , // sun
+ point_type( 0.00565429 , -0.00412490 , -0.00190589 ) , // jupiter
+ point_type( 0.00168318 , 0.00483525 , 0.00192462 ) , // saturn
+ point_type( 0.00354178 , 0.00137102 , 0.00055029 ) , // uranus
+ point_type( 0.00288930 , 0.00114527 , 0.00039677 ) , // neptune
+ point_type( 0.00276725 , -0.00170702 , -0.00136504 ) // pluto
+ }};
+
+ point_type qmean = center_of_mass( q , masses );
+ point_type pmean = center_of_mass( p , masses );
+ for( size_t i=0 ; i<n ; ++i )
+ {
+ q[i] -= qmean ;
+ p[i] -= pmean;
+ }
+
+ for( size_t i=0 ; i<n ; ++i ) p[i] *= masses[i];
+
+ //[ integration_solar_system
+ 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 ) );
+ //]
+
+ return 0;
}

/*
Plot with gnuplot:
p "solar_system.dat" u 2:4 w l,"solar_system.dat" u 5:7 w l,"solar_system.dat" u 8:10 w l,"solar_system.dat" u 11:13 w l,"solar_system.dat" u 14:16 w l,"solar_system.dat" u 17:19 w l
-*/
+ */

Modified: sandbox/odeint/branches/karsten/libs/numeric/odeint/regression_test/integrate_functions.cpp
==============================================================================
--- sandbox/odeint/branches/karsten/libs/numeric/odeint/regression_test/integrate_functions.cpp (original)
+++ sandbox/odeint/branches/karsten/libs/numeric/odeint/regression_test/integrate_functions.cpp 2011-03-18 13:08:14 EDT (Fri, 18 Mar 2011)
@@ -95,7 +95,7 @@
 template< class T1 , class T2 >
 void operator()( const T1 &t1 , const T2 &t2 ) const
 {
-// m_out << t2 << " " << t1 << "\n";
+ m_out << t2 << " " << t1 << "\n";
 }
};

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