Re: [Yanl-develop] my thoughts about current development state

[Karsten A. <kar...@gm...>]

Hello everybody,

First of all, it is nice that we started a very constructive discussion.
In my eyes it goes in the right direction.

I would suggest that we write and discuss here some minimal code which
is then implemented. I would also suggest that we use the euler steper
as the basis for discussion, because its the most simple one and we drop
any discussion about names, const, ... to a later point, until main
points have been clarified.

My suggestion for a minimal stepper design is the following (avoiding
any discussion about autonomous and non-autonomous systems)

template<class ContainerType>
class ode_step_euler
{

     ContainerType dxdt;


 public:

     template<class CallMethod, class Iterator>
     void do_step(
	CallMethod derivative ,
	double dt ,
	Iterator start ,
	Iterater end )
     {
         ContainerType::iterator dxdtiter = dxdt.begin();
         derivative( start , dxdtiter );
         while( start != end )
             *start++ += dt * (*dxdtiter++);
     }

    template< class CallMethod , class StateContainer >
    void do_step(
        CallMethod derivative ,
	double dt ,
	StateContainer state )
    {
        do_step( derivative , dt , state.begin() , state.end() );
    }
};

I think this design has all we need and is very flexible:
* no virtual functions are used anymode
* One can use the iterator and the container version
* CallMethod can be a function or a class, whatever one likes.


What we have to do now is, define how dxdt is created, which is indeed
not trivial.

> Concerning the current discussion:
> If the standard C-like usage (via functions) is not supported, as
> currently discussed and which is also my position, I would recommend to
> put the
> system's state definition (the ContainerType) into the dynamical_system
> class (or some derivation of it) as I did it in my
> lib. This is less error prone, since the user must not care about what
> kind of variable (s)he has to create for storing the state.
> In Mario's example with the harmonic oscillator the user has to provide
> the state-container-type twice, once to the stepper and to the system.
> The latter seems to be kind of redundant and should be part of the
> system and not the user's choice.

You are right, with the above approach this is possible but not necessary...

> In stepper:
> The current time point  't'  should, if needed (as for non-autonomous
> systems), be part of the system's state and being integrated by the
> system using dt.

This is not possible, the time has to be a parameter. It will not work
in RK4 or others for the intermediate points.

Bye, Karsten