odeint supports iterators that iterate along an approximate solution of an ordinary differential equation. Iterators offer you an alternative to the integrate functions. Furthermore, many of the standard algorithms in the C++ standard library and Boost.Range can be used with the odeint's iterators.

Several iterator types are provided, in consistence with the integrate functions. Hence there are const_step_iterator, adaptive_step_iterator, n_step_iterator and times_iterator -- each of them in two versions: either with only the state or with a std::pair<state,time> as value type. They are all single pass iterators. In the following, we show a few examples of how to use those iterators together with std algorithms.

runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = std::accumulate( make_const_step_iterator_begin( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) ,
                              make_const_step_iterator_end( stepper , lorenz() , x ) ,
                              0.0 ,
                              []( double sum , const state_type &x ) {
                                  return sum + x[0]; } );
cout << res << endl;

In this example all x-values of the solution are accumulated. Note, how dereferencing the iterator gives the current state x of the ODE (the second argument of the accumulate lambda). The iterator itself does not occur directly in this example but it is generated by the factory functions make_const_step_iterator_begin and make_const_step_iterator_end. odeint also supports Boost.Range, that allows to write the above example in a more compact form with the factory function make_const_step_range, but now using boost::accumulate from __bost_range:

runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::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]; } );
cout << res << endl;

The second iterator type is also a iterator with const step size. But the value type of this iterator consists here of a pair of the time and the state of the solution of the ODE. An example is

runge_kutta4< state_type > stepper;
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_const_step_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
                                []( double sum , const std::pair< const state_type &, double > &x ) {
                                    return sum + x.first[0]; } );
cout << res << endl;

The factory functions are now make_const_step_time_iterator_begin, make_const_step_time_iterator_end and make_const_step_time_range. Note, how the lambda now expects a std::pair as this is the value type of the const_step_time_iterator's.

Next, we discuss the adaptive iterators which are completely analogous to the const step iterators, but are based on adaptive stepper routines and thus adjust the step size during the iteration. Examples are

auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_adaptive_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
                                []( double sum , const state_type& x ) {
                                    return sum + x[0]; } );
cout << res << endl;

auto stepper = make_controlled( 1.0e-6 , 1.0e-6 , runge_kutta_cash_karp54< state_type >() );
state_type x = {{ 10.0 , 10.0 , 10.0 }};
double res = boost::accumulate( make_adaptive_time_range( stepper , lorenz() , x , 0.0 , 1.0 , 0.01 ) , 0.0 ,
                                []( double sum , const pair< const state_type& , double > &x ) {
                                    return sum + x.first[0]; } );
cout << res << endl;

	Note
	'adaptive_iterator and adaptive_time_iterator' can only be used with Controlled Stepper or Dense Output Stepper.

In general one can say that iterating over a range of a const_step_iterator behaves like an integrate_const function call, and similarly for adaptive_iterator and integrate_adaptive, n_step_iterator and integrate_n_steps, and finally times_iterator and integrate_times.

Below we list the most important properties of the exisiting iterators: