On Wed, Jul 11, 2012 at 2:57 PM, Karsten Ahnert <karsten.ahnert@ambrosys.de>wrote:
On 07/11/2012 07:44 PM, Jeffrey Lee Hellrung, Jr. wrote:
On Wed, Jul 11, 2012 at 9:04 AM, Karsten Ahnert <karsten.ahnert@ambrosys.de>wrote:
Hi,
we have posted a review request for odeint (a library for solving ordinary differential equations) on this list some days ago. An ODE is dx/dt = f(x(t)) and one is looking for the solution x(t) which is a function of t. Solving ODEs is usually an iterative task, so one starts with x(0) and iteratively applies a solver to obtain a discretized (and approximated) representation of the solution: x(0) -> x(dt) -> x(2*dt) -> x(3*dt) -> ...
I played around with an iterator which is doing exactly this iterative procedure. For example, it can be used via
odeint::runge_kutta4< state_type > stepper; // ode solver std::array< double , 3 > x = {{ 10.0 , 10.0 , 10.0 }}; // initial state
double res = std::accumulate( // parameters : solver , ode , state , time , time_step make_const_step_iterator_begin(stepper, lorenz(), x, 0.0, 0.01) , make_const_step_iterator_end( stepper, lorenz(), x, 1.0, 0.01) , 0.0 , []( double sum, const state_type &x) { return sum + x[0]; } );
The first iterator increments the time until the time of the second iterator is rearched t=0.0 -> t=0.01 -> t=0.02 -> .. t=1.0 and the first component of the solution is accumulated.
In principle, this approach works quite well, but there are some problems at least semantically. Maybe someone here has some comments or ideas on this:
The defintion of this iterator is:
template< class Stepper , class System , class StepperTag > class const_step_iterator : public boost::iterator_facade < const_step_iterator< Stepper , System , StepperTag > , typename Stepper::state_type const , boost::single_pass_traversal_tag
{ ... };
It is a single pass iterator, so it can only check for equality of two iterators.
[...]
This is problematic since equality here means that the time
(t) of the begin iterator is smaller then the time of the end iterator.
Can you elaborate? I don't understand why this is what equality means.
One needs to implement the != operator (or equal if you use Boost.Iterator). A naive implementation of operator!= (or the equal() if you use boost.iterator) could check that the current time of the ODE is smaller then the time of other iterator:
bool equal( iterator other ) { return this->t < other->t; }
:: confused :: I would think iterator1 op iterator2 is equivalent to time1 op time2. Of course, this is not a check for equality but a check for less_then.
It will also destroy commutativity of the !=operation and will not work in general. So you need somehow introduce which iterator is the first and which one is the last. I have done this with a flag which says if the iterator is the first and which the last such that the operation is now
bool equal( iterator other ) { return ( this->first ) ? ( this->t < other->t ) : ( this->t > other->t ); }
To ensure commutativity of the != or == operation I needed to flag the begin and end iterator explicitly. This is the reason for the two factory functions make_const_step_iterator_begin and make_const_step_iterator_end, which are doing this flagging.
I might understand your reasoning for doing this better if I understood your rationale for equality semantics...sorry, maybe I'm being dense :/
The second semantically problem is that the end iterator in principle does not need to know the stepper as well as the system (lorenz() in the above example). But all algorithms from the standard library and Boost.Range assume that the begin and end iterator are of same type. Therefore you have to put the stepper and the system into the end iterator too.
Ugh, yes, this is an unfortunate consequence of the design of iterator-based, STL-like algorithms. Perhaps it would be better to simply define range-equivalents of your iterators, and encourage use of the Boost.Range algorithms (which, AFAIK, under the hood, use the STL iterator-based algorithms)? That would eliminate a lot of the repetition you're seeing in defining begin and end iterators separately.
Yeah, we already have a factory function returning a range. You could also write the upper example as follows:
double res = boost::range::accumulate( make_const_step_range(stepper, lorenz(), x, 0.0, 1.0 , 0.01 ) , 0.0 , []( double sum, const state_type &x) { return sum + x[0]; } );
But I fear, this does not solve this problem. Boost.Range also expects that begin and end are of the same type.
. The state also encapsulates the end condition, and an end iterator is an uninitialized optional. When incrementing an iterator, if you've reached
Sounds like you want your iterator to be a wrapper around optional< state the end condition, uninitialize (i.e., reset) the underlying optional. == and != on the iterators are equivalent to those on the optionals. Equivalently, if your state is completely external (and you don't need to manage it within the iterator), you can use a state* and use its nullness to distguish end iterators from not-end iterators.
Of course, there are techniques like type erasure which
might solve this problem, but they introduce some run-time overhead which we want to avoid here.
I don't see type erasure solving your problem, but regarding the overhead of type erasure only, it could be minimal relative to the cost of the actual time stepper. But that observation probably isn't relevant to your problem.
With type erasure it is in principle possible to remove the dependency of iterator from the stepper and the system and put this in some member class, maybe something like
template< class State , class StepperTag > class const_step_iterator : public boost::iterator_facade < const_step_iterator< State , StepperTag > , State const , boost::single_pass_traversal_tag
{ public:
template< class Stepper , class System > const_step_iterator( Stepper stepper , System system , State &x , Time t_start , Time dt ) { this->data_ = new DataStepper< Stepper , System >( stepper , system , State , t , dt ); }
template< class Stepper , class System > const_step_iterator( Time t_end ) { this->data_ = new DataTime( t ); }
struct IData { ... };
template< class Stepper , class System > struct DataStepper : public IData { ... };
struct DataTime : public IData { ... };
...
private:
std::unique_ptr< IData > data_; };
I don't see what this buys you relative to the original problem. - Jeff