code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/detail/functors.hpp

 [begin_description]
 some functors for the iterator based integrate routines
 [end_description]

 Copyright 2009-2013 Karsten Ahnert
 Copyright 2009-2013 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED

#include <utility>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

template< class Observer >
struct obs_caller {

    size_t &m_n;
    Observer m_obs;

    obs_caller( size_t &m , Observer &obs ) : m_n(m) , m_obs( obs ) {}

    template< class State , class Time >
    void operator()( std::pair< const State & , const Time & > x )
    {
        typedef typename odeint::unwrap_reference< Observer >::type observer_type;
        observer_type &obs = m_obs;
        obs( x.first , x.second );
        m_n++;
    }
};

template< class Observer , class Time >
struct obs_caller_time {

    Time &m_t;
    Observer m_obs;

    obs_caller_time( Time &t , Observer &obs ) : m_t(t) , m_obs( obs ) {}

    template< class State >
    void operator()( std::pair< const State & , const Time & > x )
    {
        typedef typename odeint::unwrap_reference< Observer >::type observer_type;
        observer_type &obs = m_obs;
        obs( x.first , x.second );
        m_t = x.second;
    }
};

} // namespace detail
} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_FUNCTORS_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp

 [begin_description]
 Default Integrate adaptive implementation.
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2015 Mario Mulansky
 Copyright 2012 Christoph Koke

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED

#include <stdexcept>

#include <boost/throw_exception.hpp>

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
#include <boost/numeric/odeint/integrate/max_step_checker.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_const.hpp>
#include <boost/numeric/odeint/util/bind.hpp>
#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/util/copy.hpp>

#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>

#include <iostream>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

// forward declaration
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_const(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , stepper_tag );

/*
 * integrate_adaptive for simple stepper is basically an integrate_const + some last step
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , stepper_tag
)
{
    size_t steps = detail::integrate_const( stepper , system , start_state , start_time ,
                                            end_time , dt , observer , stepper_tag() );
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    Time end = start_time + dt*steps;
    if( less_with_sign( end , end_time , dt ) )
    {   //make a last step to end exactly at end_time
        st.do_step( system , start_state , end , end_time - end );
        steps++;
        obs( start_state , end_time );
    }
    return steps;
}

/*
 * integrate adaptive for controlled stepper
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time &start_time , Time end_time , Time &dt ,
        Observer observer , controlled_stepper_tag
)
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    failed_step_checker fail_checker;  // to throw a runtime_error if step size adjustment fails
    size_t count = 0;
    while( less_with_sign( start_time , end_time , dt ) )
    {
        obs( start_state , start_time );
        if( less_with_sign( end_time , static_cast<Time>(start_time + dt) , dt ) )
        {
            dt = end_time - start_time;
        }

        controlled_step_result res;
        do
        {
            res = st.try_step( system , start_state , start_time , dt );
            fail_checker();  // check number of failed steps
        }
        while( res == fail );
        fail_checker.reset();  // if we reach here, the step was successful -> reset fail checker

        ++count;
    }
    obs( start_state , start_time );
    return count;
}

/*
 * integrate adaptive for dense output steppers
 *
 * step size control is used if the stepper supports it
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , dense_output_stepper_tag )
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    size_t count = 0;
    st.initialize( start_state , start_time , dt );

    while( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
    {
        while( less_eq_with_sign( static_cast<Time>(st.current_time() + st.current_time_step()) ,
               end_time ,
               st.current_time_step() ) )
        {   //make sure we don't go beyond the end_time
            obs( st.current_state() , st.current_time() );
            st.do_step( system );
            ++count;
        }
        // calculate time step to arrive exactly at end time
        st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
    }
    obs( st.current_state() , st.current_time() );
    // overwrite start_state with the final point
    boost::numeric::odeint::copy( st.current_state() , start_state );
    return count;
}

} // namespace detail
} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED

license: mit


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/detail/integrate_const.hpp

 [begin_description]
 integrate const implementation
 [end_description]

 Copyright 2012-2015 Mario Mulansky
 Copyright 2012 Christoph Koke
 Copyright 2012 Karsten Ahnert

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_CONST_HPP_INCLUDED

#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/util/unit_helper.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>

#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

// forward declaration
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time &start_time , Time end_time , Time &dt ,
        Observer observer , controlled_stepper_tag
);

template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_const(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , stepper_tag
)
{

    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    Time time = start_time;
    int step = 0;
    // cast time+dt explicitely in case of expression templates (e.g. multiprecision)
    while( less_eq_with_sign( static_cast<Time>(time+dt) , end_time , dt ) )
    {
        obs( start_state , time );
        st.do_step( system , start_state , time , dt );
        // direct computation of the time avoids error propagation happening when using time += dt
        // we need clumsy type analysis to get boost units working here
        ++step;
        time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * dt;
    }
    obs( start_state , time );

    return step;
}

template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_const(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , controlled_stepper_tag
)
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;

    Time time = start_time;
    const Time time_step = dt;
    int real_steps = 0;
    int step = 0;

    while( less_eq_with_sign( static_cast<Time>(time+time_step) , end_time , dt ) )
    {
        obs( start_state , time );
        // integrate_adaptive_checked uses the given checker to throw if an overflow occurs
        real_steps += detail::integrate_adaptive(stepper, system, start_state, time,
                                                 static_cast<Time>(time + time_step), dt,
                                                 null_observer(), controlled_stepper_tag());
        // direct computation of the time avoids error propagation happening when using time += dt
        // we need clumsy type analysis to get boost units working here
        step++;
        time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * time_step;
    }
    obs( start_state , time );

    return real_steps;
}

template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_const(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer , dense_output_stepper_tag
)
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    Time time = start_time;

    st.initialize( start_state , time , dt );
    obs( start_state , time );
    time += dt;

    int obs_step( 1 );
    int real_step( 0 );

    while( less_eq_with_sign( static_cast<Time>(time+dt) , end_time , dt ) )
    {
        while( less_eq_with_sign( time , st.current_time() , dt ) )
        {
            st.calc_state( time , start_state );
            obs( start_state , time );
            ++obs_step;
            // direct computation of the time avoids error propagation happening when using time += dt
            // we need clumsy type analysis to get boost units working here
            time = start_time + static_cast< typename unit_value_type<Time>::type >(obs_step) * dt;
        }
        // we have not reached the end, do another real step
        if( less_with_sign( static_cast<Time>(st.current_time()+st.current_time_step()) ,
                            end_time ,
                            st.current_time_step() ) )
        {
            while( less_eq_with_sign( st.current_time() , time , dt ) )
            {
                st.do_step( system );
                ++real_step;
            }
        }
        else if( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
        { // do the last step ending exactly on the end point
            st.initialize( st.current_state() , st.current_time() , end_time - st.current_time() );
            st.do_step( system );
            ++real_step;
        }

    }
    // last observation, if we are still in observation interval
    // might happen due to finite precision problems when computing the the time
    if( less_eq_with_sign( time , end_time , dt ) )
    {
        st.calc_state( time , start_state );
        obs( start_state , time );
    }

    return real_step;
}

} } } }

#endif


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp

 [begin_description]
 integrate steps implementation
 [end_description]

 Copyright 2012-2015 Mario Mulansky
 Copyright 2012 Christoph Koke
 Copyright 2012 Karsten Ahnert

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED

#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>
#include <boost/numeric/odeint/util/unit_helper.hpp>

#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

// forward declaration
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive_checked(
        Stepper stepper , System system , State &start_state ,
        Time &start_time , Time end_time , Time &dt ,
        Observer observer, controlled_stepper_tag
);

/* basic version */
template< class Stepper , class System , class State , class Time , class Observer>
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps ,
        Observer observer , stepper_tag )
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    Time time = start_time;

    for( size_t step = 0; step < num_of_steps ; ++step )
    {
        obs( start_state , time );
        st.do_step( system , start_state , time , dt );
        // direct computation of the time avoids error propagation happening when using time += dt
        // we need clumsy type analysis to get boost units working here
        time = start_time + static_cast< typename unit_value_type<Time>::type >( step+1 ) * dt;
    }
    obs( start_state , time );

    return time;
}

/* controlled version */
template< class Stepper , class System , class State , class Time , class Observer >
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps ,
        Observer observer , controlled_stepper_tag )
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;

    Time time = start_time;
    Time time_step = dt;

    for( size_t step = 0; step < num_of_steps ; ++step )
    {
        obs( start_state , time );
        // integrate_adaptive_checked uses the given checker to throw if an overflow occurs
        detail::integrate_adaptive(stepper, system, start_state, time, static_cast<Time>(time + time_step), dt,
                                   null_observer(), controlled_stepper_tag());
        // direct computation of the time avoids error propagation happening when using time += dt
        // we need clumsy type analysis to get boost units working here
        time = start_time + static_cast< typename unit_value_type<Time>::type >(step+1) * time_step;
    }
    obs( start_state , time );

    return time;
}

/* dense output version */
template< class Stepper , class System , class State , class Time , class Observer >
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps ,
        Observer observer , dense_output_stepper_tag )
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    Time time = start_time;
    const Time end_time = start_time + static_cast< typename unit_value_type<Time>::type >(num_of_steps) * dt;

    st.initialize( start_state , time , dt );

    size_t step = 0;

    while( step < num_of_steps )
    {
        while( less_with_sign( time , st.current_time() , st.current_time_step() ) )
        {
            st.calc_state( time , start_state );
            obs( start_state , time );
            ++step;
            // direct computation of the time avoids error propagation happening when using time += dt
            // we need clumsy type analysis to get boost units working here
            time = start_time + static_cast< typename unit_value_type<Time>::type >(step) * dt;
        }

        // we have not reached the end, do another real step
        if( less_with_sign( static_cast<Time>(st.current_time()+st.current_time_step()) ,
                            end_time ,
                            st.current_time_step() ) )
        {
            st.do_step( system );
        }
        else if( less_with_sign( st.current_time() , end_time , st.current_time_step() ) )
        { // do the last step ending exactly on the end point
            st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
            st.do_step( system );
        }
    }

    // make sure we really end exactly where we should end
    while( st.current_time() < end_time )
    {
        if( less_with_sign( end_time ,
                            static_cast<Time>(st.current_time()+st.current_time_step()) ,
                            st.current_time_step() ) )
            st.initialize( st.current_state() , st.current_time() , static_cast<Time>(end_time - st.current_time()) );
        st.do_step( system );
    }

    // observation at final point
    obs( st.current_state() , end_time );

    return time;
}

}
}
}
}

#endif /* BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_N_STEPS_HPP_INCLUDED */


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/detail/integrate_times.hpp

 [begin_description]
 Default integrate times implementation.
 [end_description]

 Copyright 2011-2015 Mario Mulansky
 Copyright 2012 Karsten Ahnert
 Copyright 2012 Christoph Koke

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_TIMES_HPP_INCLUDED

#include <stdexcept>

#include <boost/config.hpp>
#include <boost/throw_exception.hpp>
#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
#include <boost/numeric/odeint/integrate/max_step_checker.hpp>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

/*
 * integrate_times for simple stepper
 */
template<class Stepper, class System, class State, class TimeIterator, class Time, class Observer>
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        TimeIterator start_time , TimeIterator end_time , Time dt ,
        Observer observer , stepper_tag
)
{
    typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
    typedef typename odeint::unwrap_reference< Observer >::type observer_type;

    stepper_type &st = stepper;
    observer_type &obs = observer;
    typedef typename unit_value_type<Time>::type time_type;

    size_t steps = 0;
    Time current_dt = dt;
    while( true )
    {
        Time current_time = *start_time++;
        obs( start_state , current_time );
        if( start_time == end_time )
            break;
        while( less_with_sign( current_time , static_cast<time_type>(*start_time) , current_dt ) )
        {
            current_dt = min_abs( dt , *start_time - current_time );
            st.do_step( system , start_state , current_time , current_dt );
            current_time += current_dt;
            steps++;
        }
    }
    return steps;
}

/*
 * integrate_times for controlled stepper
 */
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        TimeIterator start_time , TimeIterator end_time , Time dt ,
        Observer observer , controlled_stepper_tag
)
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;
    typedef typename unit_value_type<Time>::type time_type;

    failed_step_checker fail_checker;  // to throw a runtime_error if step size adjustment fails
    size_t steps = 0;
    while( true )
    {
        Time current_time = *start_time++;
        obs( start_state , current_time );
        if( start_time == end_time )
            break;
        while( less_with_sign( current_time , static_cast<time_type>(*start_time) , dt ) )
        {
            // adjust stepsize to end up exactly at the observation point
            Time current_dt = min_abs( dt , *start_time - current_time );
            if( st.try_step( system , start_state , current_time , current_dt ) == success )
            {
                ++steps;
                // successful step -> reset the fail counter, see #173
                fail_checker.reset();
                // continue with the original step size if dt was reduced due to observation
                dt = max_abs( dt , current_dt );
            }
            else
            {
                fail_checker();  // check for possible overflow of failed steps in step size adjustment
                dt = current_dt;
            }
        }
    }
    return steps;
}

/*
 * integrate_times for dense output stepper
 */
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        TimeIterator start_time , TimeIterator end_time , Time dt ,
        Observer observer , dense_output_stepper_tag
)
{
    typename odeint::unwrap_reference< Observer >::type &obs = observer;
    typename odeint::unwrap_reference< Stepper >::type &st = stepper;

    typedef typename unit_value_type<Time>::type time_type;

    if( start_time == end_time )
        return 0;

    TimeIterator last_time_iterator = end_time;
    --last_time_iterator;
    Time last_time_point = static_cast<time_type>(*last_time_iterator);

    st.initialize( start_state , *start_time , dt );
    obs( start_state , *start_time++ );

    size_t count = 0;
    while( start_time != end_time )
    {
        while( ( start_time != end_time ) && less_eq_with_sign( static_cast<time_type>(*start_time) , st.current_time() , st.current_time_step() ) )
        {
            st.calc_state( *start_time , start_state );
            obs( start_state , *start_time );
            start_time++;
        }

        // we have not reached the end, do another real step
        if( less_eq_with_sign( st.current_time() + st.current_time_step() ,
                               last_time_point ,
                               st.current_time_step() ) )
        {
            st.do_step( system );
            ++count;
        }
        else if( start_time != end_time )
        { // do the last step ending exactly on the end point
            st.initialize( st.current_state() , st.current_time() , last_time_point - st.current_time() );
            st.do_step( system );
            ++count;
        }
    }
    return count;
}

} // namespace detail
} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_DETAIL_INTEGRATE_ADAPTIVE_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/integrate.hpp

 [begin_description]
 Convenience methods which choose the stepper for the current ODE.
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2012 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED

#include <boost/utility/enable_if.hpp>

#include <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp>
#include <boost/numeric/odeint/stepper/controlled_runge_kutta.hpp>
#include <boost/numeric/odeint/integrate/null_observer.hpp>
#include <boost/numeric/odeint/integrate/integrate_adaptive.hpp>

// for has_value_type trait
#include <boost/numeric/odeint/algebra/detail/extract_value_type.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/*
 * ToDo :
 *
 * determine type of dxdt for units
 *
 */
template< class System , class State , class Time , class Observer >
typename boost::enable_if< typename has_value_type<State>::type , size_t >::type
integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
{
    typedef controlled_runge_kutta< runge_kutta_dopri5< State , typename State::value_type , State , Time > > stepper_type;
    return integrate_adaptive( stepper_type() , system , start_state , start_time , end_time , dt , observer );
}

template< class Value , class System , class State , class Time , class Observer >
size_t
integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
{
    typedef controlled_runge_kutta< runge_kutta_dopri5< State , Value , State , Time > > stepper_type;
    return integrate_adaptive( stepper_type() , system , start_state , start_time , end_time , dt , observer );
}

/*
 * the two overloads are needed in order to solve the forwarding problem
 */
template< class System , class State , class Time >
size_t integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
{
    return integrate( system , start_state , start_time , end_time , dt , null_observer() );
}

template< class Value , class System , class State , class Time >
size_t integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
{
    return integrate< Value >( system , start_state , start_time , end_time , dt , null_observer() );
}

/**
 * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
 * \brief Integrates the ODE.
 *
 * Integrates the ODE given by system from start_time to end_time starting
 * with start_state as initial condition and dt as initial time step.
 * This function uses a dense output dopri5 stepper and performs an adaptive
 * integration with step size control, thus dt changes during the integration.
 * This method uses standard error bounds of 1E-6.
 * After each step, the observer is called.
 *
 * \attention A second version of this function template exists which explicitly
 * expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs );
 *
 * \param system The system function to solve, hence the r.h.s. of the
 * ordinary differential equation.
 * \param start_state The initial state.
 * \param start_time Start time of the integration.
 * \param end_time End time of the integration.
 * \param dt Initial step size, will be adjusted during the integration.
 * \param observer Observer that will be called after each time step.
 * \return The number of steps performed.
 */

/**
 * \fn integrate( System system , State &start_state , Time start_time , Time end_time , Time dt )
 * \brief Integrates the ODE without observer calls.
 *
 * Integrates the ODE given by system from start_time to end_time starting
 * with start_state as initial condition and dt as initial time step.
 * This function uses a dense output dopri5 stepper and performs an adaptive
 * integration with step size control, thus dt changes during the integration.
 * This method uses standard error bounds of 1E-6.
 * No observer is called.
 *
 * \attention A second version of this function template exists which explicitly
 * expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt );
 *
 * \param system The system function to solve, hence the r.h.s. of the
 * ordinary differential equation.
 * \param start_state The initial state.
 * \param start_time Start time of the integration.
 * \param end_time End time of the integration.
 * \param dt Initial step size, will be adjusted during the integration.
 * \return The number of steps performed.
 */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/integrate_adaptive.hpp

 [begin_description]
 Adaptive integration of ODEs.
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2015 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED

#include <boost/type_traits/is_same.hpp>

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/integrate/null_observer.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/*
 * the two overloads are needed in order to solve the forwarding problem
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer )
{
    typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
    return detail::integrate_adaptive(
            stepper , system , start_state ,
            start_time , end_time , dt ,
            observer , stepper_category() );

    /*
     * Suggestion for a new extendable version:
     *
     * integrator_adaptive< Stepper , System, State , Time , Observer , typename Stepper::stepper_category > integrator;
     * return integrator.run( stepper , system , start_state , start_time , end_time , dt , observer );
     */
}

/**
 * \brief Second version to solve the forwarding problem,
 * can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class Time , class Observer >
size_t integrate_adaptive(
        Stepper stepper , System system , const State &start_state ,
        Time start_time , Time end_time , Time dt ,
        Observer observer )
{
    typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
    return detail::integrate_adaptive(
            stepper , system , start_state ,
            start_time , end_time , dt ,
            observer , stepper_category() );
}

/**
 * \brief integrate_adaptive without an observer.
 */
template< class Stepper , class System , class State , class Time >
size_t integrate_adaptive(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time end_time , Time dt )
{
    return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
}

/**
 * \brief Second version to solve the forwarding problem,
 * can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class Time >
size_t integrate_adaptive(
        Stepper stepper , System system , const State &start_state ,
        Time start_time , Time end_time , Time dt )
{
    return integrate_adaptive( stepper , system , start_state , start_time , end_time , dt , null_observer() );
}

/************* DOXYGEN ************/

    /**
     * \fn integrate_adaptive( Stepper stepper , System system , State &start_state , Time start_time , Time end_time , Time dt , Observer observer )
     * \brief Integrates the ODE with adaptive step size.
     *
     * This function integrates the ODE given by system with the given stepper.
     * The observer is called after each step. If the stepper has no error
     * control, the step size remains constant and the observer is called at
     * equidistant time points t0+n*dt. If the stepper is a ControlledStepper,
     * the step size is adjusted and the observer is called in non-equidistant
     * intervals.
     *
     * \param stepper The stepper to be used for numerical integration.
     * \param system Function/Functor defining the rhs of the ODE.
     * \param start_state The initial condition x0.
     * \param start_time The initial time t0.
     * \param end_time The final integration time tend.
     * \param dt The time step between observer calls, _not_ necessarily the
     * time step of the integration.
     * \param observer Function/Functor called at equidistant time intervals.
     * \return The number of steps performed.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_ADAPTIVE_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/integrate_const.hpp

 [begin_description]
 Constant integration of ODEs, meaning that the state of the ODE is observed on constant time intervals.
 The routines makes full use of adaptive and dense-output methods.
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2015 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED

#include <boost/type_traits/is_same.hpp>

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/integrate/null_observer.hpp>
#include <boost/numeric/odeint/integrate/check_adapter.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_const.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_adaptive.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/*
 * Integrates with constant time step dt.
 */
template<class Stepper, class System, class State, class Time, class Observer, class StepOverflowChecker>
size_t integrate_const(
        Stepper stepper, System system, State &start_state,
        Time start_time, Time end_time, Time dt,
        Observer observer, StepOverflowChecker checker
) {
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
    // we want to get as fast as possible to the end
    // no overflow checks needed
    if (boost::is_same<null_observer, Observer>::value) {
        return detail::integrate_adaptive(
                stepper, system, start_state,
                start_time, end_time, dt,
                observer, stepper_category());
    }
    else {
        // unwrap references
        typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
        typedef typename odeint::unwrap_reference< Observer >::type observer_type;
        typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;

        return detail::integrate_const(checked_stepper<stepper_type, checker_type>(stepper, checker),
                                       system, start_state,
                                       start_time, end_time, dt,
                                       checked_observer<observer_type, checker_type>(observer, checker),
                                       stepper_category());
    }
}

/**
* \brief Second version to solve the forwarding problem,
* can be called with Boost.Range as start_state.
*/
template<class Stepper, class System, class State, class Time, class Observer, class StepOverflowChecker >
size_t integrate_const(
        Stepper stepper, System system, const State &start_state,
        Time start_time, Time end_time, Time dt,
        Observer observer, StepOverflowChecker checker
) {
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
    // we want to get as fast as possible to the end

    if (boost::is_same<null_observer, Observer>::value) {
        return detail::integrate_adaptive(
                stepper, system, start_state,
                start_time, end_time, dt,
                observer, stepper_category());
    }
    else {
        typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
        typedef typename odeint::unwrap_reference< Observer >::type observer_type;
        typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;

        return detail::integrate_const(checked_stepper<stepper_type, checker_type>(stepper, checker),
                                       system, start_state,
                                       start_time, end_time, dt,
                                       checked_observer<observer_type, checker_type>(observer, checker),
                                       stepper_category());
    }
}

/**
* \brief integrate_const without step overflow checker
*/
template<class Stepper, class System, class State, class Time, class Observer>
size_t integrate_const(
        Stepper stepper, System system, State &start_state,
        Time start_time, Time end_time, Time dt, Observer observer)
{
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
    return detail::integrate_const(stepper, system, start_state,
                                   start_time, end_time, dt, observer, stepper_category());
}

/**
* \brief Second version to solve the forwarding problem,
* can be called with Boost.Range as start_state.
*/
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
) {
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;
    return detail::integrate_const(stepper, system, start_state,
                                   start_time, end_time, dt, observer, stepper_category());
}

/**
* \brief integrate_const without observer calls
*/
template<class Stepper, class System, class State, class Time>
size_t integrate_const(
        Stepper stepper, System system, State &start_state,
        Time start_time, Time end_time, Time dt
) {
    return integrate_const(stepper, system, start_state, start_time, end_time, dt, null_observer());
}

/**
* \brief Second version to solve the forwarding problem,
* can be called with Boost.Range as start_state.
*/
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, null_observer());
}

/********* DOXYGEN *********/
/**
 * \fn integrate_const( Stepper stepper , System system , State &start_state , Time start_time ,
 *                      Time end_time , Time dt , Observer observer , StepOverflowChecker checker )
 * \brief Integrates the ODE with constant step size.
 *
 * Integrates the ODE defined by system using the given stepper.
 * This method ensures that the observer is called at constant intervals dt.
 * If the Stepper is a normal stepper without step size control, dt is also
 * used for the numerical scheme. If a ControlledStepper is provided, the
 * algorithm might reduce the step size to meet the error bounds, but it is
 * ensured that the observer is always called at equidistant time points
 * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
 * and the dense output is used to call the observer at equidistant time
 * points.
 * If a max_step_checker is provided as StepOverflowChecker, a
 * no_progress_error is thrown if too many steps (default: 500) are performed
 * without progress, i.e. in between observer calls. If no checker is provided,
 * no such overflow check is performed.
 *
 * \param stepper The stepper to be used for numerical integration.
 * \param system Function/Functor defining the rhs of the ODE.
 * \param start_state The initial condition x0.
 * \param start_time The initial time t0.
 * \param end_time The final integration time tend.
 * \param dt The time step between observer calls, _not_ necessarily the
 * time step of the integration.
 * \param observer [optional] Function/Functor called at equidistant time intervals.
 * \param checker [optional] Functor to check for step count overflows, if no
 * checker is provided, no exception is thrown.
 * \return The number of steps performed.
 */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_CONST_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/integrate_n_steps.hpp

 [begin_description]
 Integration of n steps with constant time size. Adaptive and dense-output methods are fully supported.
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2015 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED

#include <boost/type_traits/is_same.hpp>

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/integrate/null_observer.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_n_steps.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/*
 * Integrates n steps
 *
 * the two overloads are needed in order to solve the forwarding problem
 */
template< class Stepper , class System , class State , class Time , class Observer , class StepOverflowChecker >
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps ,
        Observer observer , StepOverflowChecker checker )
{
    // unwrap references
    typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
    typedef typename odeint::unwrap_reference< Observer >::type observer_type;
    typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
    typedef typename stepper_type::stepper_category stepper_category;

    return detail::integrate_n_steps(
                checked_stepper<stepper_type, checker_type>(stepper, checker),
                system , start_state ,
                start_time , dt , num_of_steps ,
                checked_observer<observer_type, checker_type>(observer, checker),
                stepper_category() );
}

/**
 * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class Time , class Observer , class StepOverflowChecker >
Time integrate_n_steps(
        Stepper stepper , System system , const State &start_state ,
        Time start_time , Time dt , size_t num_of_steps ,
        Observer observer , StepOverflowChecker checker )
{
    typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
    typedef typename odeint::unwrap_reference< Observer >::type observer_type;
    typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
    typedef typename stepper_type::stepper_category stepper_category;

    return detail::integrate_n_steps(
            checked_stepper<stepper_type, checker_type>(stepper, checker),
            system , start_state ,
            start_time , dt , num_of_steps ,
            checked_observer<observer_type, checker_type>(observer, checker),
            stepper_category() );
}

/**
* \brief The same function as above, but without checker.
*/
template< class Stepper , class System , class State , class Time , class Observer >
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps , Observer observer )
{
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;

    return detail::integrate_n_steps(
            stepper , system , start_state ,
            start_time , dt , num_of_steps ,
            observer , stepper_category() );
}

/**
* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
*/
template< class Stepper , class System , class State , class Time , class Observer >
Time integrate_n_steps(
        Stepper stepper , System system , const State &start_state ,
        Time start_time , Time dt , size_t num_of_steps , Observer observer )
{
    typedef typename odeint::unwrap_reference<Stepper>::type::stepper_category stepper_category;

    return detail::integrate_n_steps(
            stepper , system , start_state ,
            start_time , dt , num_of_steps ,
            observer , stepper_category() );
}

/**
 * \brief The same function as above, but without observer calls.
 */
template< class Stepper , class System , class State , class Time >
Time integrate_n_steps(
        Stepper stepper , System system , State &start_state ,
        Time start_time , Time dt , size_t num_of_steps )
{
    return integrate_n_steps(stepper, system, start_state, start_time,
                             dt, num_of_steps, null_observer());
}

/**
 * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class Time >
Time integrate_n_steps(
        Stepper stepper , System system , const State &start_state ,
        Time start_time , Time dt , size_t num_of_steps )
{
    return integrate_n_steps(stepper, system, start_state, start_time,
                             dt, num_of_steps, null_observer());
}

/************* DOXYGEN *************/
    /**
     * \fn Time integrate_n_steps( Stepper stepper , System system , State &start_state , Time start_time , Time dt , size_t num_of_steps , Observer observer )
     * \brief Integrates the ODE with constant step size.
     *
     * This function is similar to integrate_const. The observer is called at
     * equidistant time intervals t0 + n*dt.
     * If the Stepper is a normal stepper without step size control, dt is also
     * used for the numerical scheme. If a ControlledStepper is provided, the
     * algorithm might reduce the step size to meet the error bounds, but it is
     * ensured that the observer is always called at equidistant time points
     * t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary
     * and the dense output is used to call the observer at equidistant time
     * points. The final integration time is always t0 + num_of_steps*dt.
     * If a max_step_checker is provided as StepOverflowChecker, a
     * no_progress_errror is thrown if too many steps (default: 500) are
     * performed without progress, i.e. in between observer calls. If no
     * checker is provided, no such overflow check is performed.

     *
     * \param stepper The stepper to be used for numerical integration.
     * \param system Function/Functor defining the rhs of the ODE.
     * \param start_state The initial condition x0.
     * \param start_time The initial time t0.
     * \param dt The time step between observer calls, _not_ necessarily the
     * time step of the integration.
     * \param num_of_steps Number of steps to be performed
     * \param observer Function/Functor called at equidistant time intervals.
     * \param checker [optional] Functor to check for step count overflows, if no
     * checker is provided, no exception is thrown.
     * \return The number of steps performed.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_N_STEPS_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/integrate_times.hpp

 [begin_description]
 Integration of ODEs with observation at user defined points
 [end_description]

 Copyright 2011-2013 Karsten Ahnert
 Copyright 2011-2015 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED

#include <boost/type_traits/is_same.hpp>

#include <boost/range.hpp>

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/integrate/null_observer.hpp>
#include <boost/numeric/odeint/integrate/check_adapter.hpp>
#include <boost/numeric/odeint/integrate/detail/integrate_times.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/*
 * \brief Integrates while calling the observer at the time points given by sequence [times_start, time_end)
 * the two overloads are needed in order to solve the forwarding problem
 */
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer , class StepOverflowChecker >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        TimeIterator times_start , TimeIterator times_end , Time dt ,
        Observer observer , StepOverflowChecker checker )
{
    // unwrap references
    typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
    typedef typename odeint::unwrap_reference< Observer >::type observer_type;
    typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
    typedef typename stepper_type::stepper_category stepper_category;

    // pass on checked stepper and observer
    // checked_stepper/observer use references internally, so passing by value is fine
    return detail::integrate_times(
            checked_stepper<stepper_type, checker_type>(stepper, checker) ,
            system , start_state ,
            times_start , times_end , dt ,
            checked_observer<observer_type, checker_type>(observer, checker),
            stepper_category() );
}

/**
 * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer , class StepOverflowChecker >
size_t integrate_times(
        Stepper stepper , System system , const State &start_state ,
        TimeIterator times_start , TimeIterator times_end , Time dt ,
        Observer observer , StepOverflowChecker checker )
{
    typedef typename odeint::unwrap_reference< Stepper >::type stepper_type;
    typedef typename odeint::unwrap_reference< Observer >::type observer_type;
    typedef typename odeint::unwrap_reference< StepOverflowChecker >::type checker_type;
    typedef typename stepper_type::stepper_category stepper_category;

    stepper_type &st = stepper;
    observer_type &obs = observer;
    checker_type &chk = checker;

    return detail::integrate_times(
            checked_stepper<stepper_type, checker_type>(stepper, checker) ,
            system , start_state ,
            times_start , times_end , dt ,
            checked_observer<observer_type, checker_type>(observer, checker),
            stepper_category() );
}

/**
 * \brief The same function as above, but with the observation times given as range.
 */
template< class Stepper , class System , class State , class TimeRange , class Time , class Observer , class StepOverflowChecker >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        const TimeRange &times , Time dt ,
        Observer observer , StepOverflowChecker checker )
{
    return integrate_times(
            stepper , system , start_state ,
            boost::begin( times ) , boost::end( times ) , dt , observer , checker );
}

/**
 * \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
 */
template< class Stepper , class System , class State , class TimeRange , class Time , class Observer , class StepOverflowChecker >
size_t integrate_times(
        Stepper stepper , System system , const State &start_state ,
        const TimeRange &times , Time dt ,
        Observer observer , StepOverflowChecker checker )
{
    return integrate_times(
            stepper , system , start_state ,
            boost::begin( times ) , boost::end( times ) , dt , observer , checker );
}

/*
* The same functions as above, but without a StepOverflowChecker
*/
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        TimeIterator times_start , TimeIterator times_end , Time dt ,
        Observer observer )
{
    typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
    // simply don't use checked_* adapters
    return detail::integrate_times(
            stepper , system , start_state ,
            times_start , times_end , dt ,
            observer , stepper_category() );
}

/**
* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
*/
template< class Stepper , class System , class State , class TimeIterator , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , const State &start_state ,
        TimeIterator times_start , TimeIterator times_end , Time dt ,
        Observer observer )
{
    typedef typename odeint::unwrap_reference< Stepper >::type::stepper_category stepper_category;
    return detail::integrate_times(
            stepper , system , start_state ,
            times_start , times_end , dt ,
            observer , stepper_category() );
}

/**
* \brief The same function as above, but with the observation times given as range.
*/
template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , State &start_state ,
        const TimeRange &times , Time dt ,
        Observer observer )
{
    return integrate_times(
            stepper , system , start_state ,
            boost::begin( times ) , boost::end( times ) , dt , observer );
}

/**
* \brief Solves the forwarding problem, can be called with Boost.Range as start_state.
*/
template< class Stepper , class System , class State , class TimeRange , class Time , class Observer >
size_t integrate_times(
        Stepper stepper , System system , const State &start_state ,
        const TimeRange &times , Time dt ,
        Observer observer )
{
    return integrate_times(
            stepper , system , start_state ,
            boost::begin( times ) , boost::end( times ) , dt , observer);
}

/********* DOXYGEN ***********/

    /**
     * \fn size_t integrate_times( Stepper stepper , System system , State &start_state , TimeIterator times_start , TimeIterator times_end , Time dt , Observer observer )
     * \brief Integrates the ODE with observer calls at given time points.
     *
     * Integrates the ODE given by system using the given stepper. This function
     * does observer calls at the subsequent time points given by the range
     * times_start, times_end. If the stepper has not step size control, the
     * step size might be reduced occasionally to ensure observer calls exactly
     * at the time points from the given sequence. If the stepper is a
     * ControlledStepper, the step size is adjusted to meet the error bounds,
     * but also might be reduced occasionally to ensure correct observer calls.
     * If a DenseOutputStepper is provided, the dense output functionality is
     * used to call the observer at the given times. The end time of the
     * integration is always *(end_time-1).
     * If a max_step_checker is provided as StepOverflowChecker, a
     * no_progress_error is thrown if too many steps (default: 500) are
     * performed without progress, i.e. in between observer calls. If no
     * checker is provided, no such overflow check is performed.
     *
     * \param stepper The stepper to be used for numerical integration.
     * \param system Function/Functor defining the rhs of the ODE.
     * \param start_state The initial condition x0.
     * \param times_start Iterator to the start time
     * \param times_end Iterator to the end time
     * \param dt The time step between observer calls, _not_ necessarily the
     * time step of the integration.
     * \param observer Function/Functor called at equidistant time intervals.
     * \param checker [optional] Functor to check for step count overflows, if no
     * checker is provided, no exception is thrown.
     * \return The number of steps performed.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_INTEGRATE_TIMES_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/max_step_checker.hpp

 [begin_description]
 Throws exception if too many steps are performed.
 [end_description]

 Copyright 2015 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_MAX_STEP_CHECKER_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_MAX_STEP_CHECKER_HPP_INCLUDED

#include <stdexcept>
#include <cstdio>

#include <boost/throw_exception.hpp>
#include <boost/numeric/odeint/util/odeint_error.hpp>

namespace boost {
namespace numeric {
namespace odeint {

/**
 * \brief A class for performing overflow checks on the step count in integrate functions.
 *
 * Provide an instance of this class to integrate functions if you want to throw a runtime error if
 * too many steps are performed without progress during the integrate routine.
 */
class max_step_checker
{
public:

protected:
    const int m_max_steps;
    int m_steps;

public:
    /**
     * \brief Construct the max_step_checker.
     * max_steps is the maximal number of iterations allowed before runtime_error is thrown.
     */
    max_step_checker(const int max_steps = 500)
        : m_max_steps(max_steps)
    {
        reset();
    }

    /**
     * \brief Resets the max_step_checker by setting the internal counter to 0.
     */
    void reset()
    {
        m_steps = 0;
    }

    /**
     * \brief Increases the counter and performs the iteration check
     */
    void operator()(void)
    {
        if( m_steps++ >= m_max_steps )
        {
            char error_msg[200];
            sprintf(error_msg, "Max number of iterations exceeded (%d).", m_max_steps);
            BOOST_THROW_EXCEPTION( no_progress_error(error_msg) );
        }
    }
};

/**
 * \brief A class for performing overflow checks on the failed step count in step size adjustments.
 *
 * Used internally within the dense output stepper and integrate routines.
 */
class failed_step_checker : public max_step_checker
{

public:
    /**
     * \brief Construct the failed_step_checker.
     * max_steps is the maximal number of iterations allowed before runtime_error is thrown.
     */
    failed_step_checker(const int max_steps = 500)
            : max_step_checker(max_steps)
    {}

    /**
     * \brief Increases the counter and performs the iteration check
     */
    void operator()(void)
    {
        if( m_steps++ >= m_max_steps )
        {
            char error_msg[200];
            sprintf(error_msg, "Max number of iterations exceeded (%d). A new step size was not found.", m_max_steps);
            BOOST_THROW_EXCEPTION( step_adjustment_error(error_msg) );
        }
    }
};

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/null_observer.hpp

 [begin_description]
 null_observer
 [end_description]

 Copyright 2011-2012 Karsten Ahnert
 Copyright 2011-2012 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED

namespace boost {
namespace numeric {
namespace odeint {

struct null_observer
{
    template< class State , class Time >
    void operator()( const State& /* x */ , Time /* t */ ) const
    {

    }
};

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_NULL_OBSERVER_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/integrate/observer_collection.hpp

 [begin_description]
 Collection of observers, which are all called during the evolution of the ODE.
 [end_description]

 Copyright 2011-2012 Karsten Ahnert
 Copyright 2011-2012 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED

#include <vector>

#include <boost/function.hpp>

namespace boost {
namespace numeric {
namespace odeint {

template< class State , class Time >
class observer_collection
{
public:

    typedef boost::function< void( const State& , const Time& ) > observer_type;
    typedef std::vector< observer_type > collection_type;

    void operator()( const State& x , Time t )
    {
        for( size_t i=0 ; i<m_observers.size() ; ++i )
            m_observers[i]( x , t );
    }

    collection_type& observers( void ) { return m_observers; }
    const collection_type& observers( void ) const { return m_observers; }

private:

    collection_type m_observers;
};

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_INTEGRATE_OBSERVER_COLLECTION_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/iterator/adaptive_iterator.hpp

 [begin_description]
 Iterator for iterating throught the solution of an ODE with adaptive step size. The dereferenced types containes also the time.
 [end_description]

 Copyright 2012-2013 Karsten Ahnert
 Copyright 2012 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED

#include <boost/numeric/odeint/util/stepper_traits.hpp>
#include <boost/numeric/odeint/util/unit_helper.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
#include <boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp>

namespace boost {
namespace numeric {
namespace odeint {

    /* use the adaptive_iterator_impl with the right tags */
    template< class Stepper , class System , class State
#ifndef DOXYGEN_SKIP
        , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
#endif
    >
    class adaptive_iterator : public adaptive_iterator_impl<
            adaptive_iterator< Stepper , System , State , StepperTag > ,
            Stepper , System , State , detail::ode_state_iterator_tag , StepperTag
        >
    {
        typedef typename traits::time_type< Stepper >::type time_type;
        typedef adaptive_iterator< Stepper , System , State , StepperTag > iterator_type;

    public:
        adaptive_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
            : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
        {}

        adaptive_iterator( Stepper stepper , System sys , State &s )
            : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
        {}
    };

    template< class Stepper , class System , class State >
    adaptive_iterator< Stepper , System , State > make_adaptive_iterator_begin(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return adaptive_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
    }

    template< class Stepper , class System , class State >
    adaptive_iterator< Stepper , System , State > make_adaptive_iterator_end(
        Stepper stepper ,
        System system ,
        State &x )
    {
        return adaptive_iterator< Stepper , System , State >( stepper , system , x );
    }

    template< class Stepper , class System , class State >
    std::pair< adaptive_iterator< Stepper , System , State > , adaptive_iterator< Stepper , System , State > >
    make_adaptive_range(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return std::make_pair(
            adaptive_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
            adaptive_iterator< Stepper , System , State >( stepper , system , x )
            );
    }

    /**
     * \class adaptive_iterator
     *
     * \brief ODE Iterator with adaptive step size. The value type of this iterator is the state type of the stepper.
     *
     * Implements an iterator representing the solution of an ODE from t_start
     * to t_end evaluated at steps with an adaptive step size dt.
     * After each iteration the iterator dereferences to the state x at the next
     * time t+dt where dt is controlled by the stepper.
     * This iterator can be used with ControlledSteppers and
     * DenseOutputSteppers and it always makes use of the all the given steppers
     * capabilities. A for_each over such an iterator range behaves similar to
     * the integrate_adaptive routine.
     *
     * adaptive_iterator is a model of single-pass iterator.
     *
     * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
     *
     * \tparam Stepper The stepper type which should be used during the iteration.
     * \tparam System The type of the system function (ODE) which should be solved.
     * \tparam State The state type of the ODE.
     */

    /**
     * \fn make_adaptive_iterator_begin( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function for adaptive_iterator. Constructs a begin iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The adaptive iterator.
     */

    /**
     * \fn make_adaptive_iterator_end( Stepper stepper , System system , State &x )
     * \brief Factory function for adaptive_iterator. Constructs a end iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state.
     * \returns The adaptive iterator.
     */

    /**
     * \fn make_adaptive_range( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function to construct a single pass range of adaptive iterators. A range is here a pair of adaptive_iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The adaptive range.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_ITERATOR_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/iterator/adaptive_time_iterator.hpp

 [begin_description]
 Iterator for iterating throught the solution of an ODE with adaptive step size. The dereferenced types containes also the time.
 [end_description]

 Copyright 2012-2013 Karsten Ahnert
 Copyright 2012-2013 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/util/stepper_traits.hpp>
#include <boost/numeric/odeint/iterator/impl/adaptive_iterator_impl.hpp>

namespace boost {
namespace numeric {
namespace odeint {

    /* use the adaptive_iterator_impl with the right tags */
    template< class Stepper , class System , class State
#ifndef DOXYGEN_SKIP
        , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
#endif
    >
    class adaptive_time_iterator : public adaptive_iterator_impl<
            adaptive_time_iterator< Stepper , System , State , StepperTag > ,
            Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag
        >
    {
        typedef typename traits::time_type< Stepper >::type time_type;
        typedef adaptive_time_iterator< Stepper , System , State , StepperTag > iterator_type;

    public:
        adaptive_time_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
            : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
        {}

        adaptive_time_iterator( Stepper stepper , System sys , State &s )
            : adaptive_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
        {}
    };

    template< class Stepper , class System , class State >
    adaptive_time_iterator< Stepper , System , State > make_adaptive_time_iterator_begin(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return adaptive_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
    }

    template< class Stepper , class System , class State >
    adaptive_time_iterator< Stepper , System , State > make_adaptive_time_iterator_end(
        Stepper stepper ,
        System system ,
        State &x )
    {
        return adaptive_time_iterator< Stepper , System , State >( stepper , system , x );
    }

    template< class Stepper , class System , class State >
    std::pair< adaptive_time_iterator< Stepper , System , State > , adaptive_time_iterator< Stepper , System , State > >
    make_adaptive_time_range(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return std::make_pair(
            adaptive_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
            adaptive_time_iterator< Stepper , System , State >( stepper , system , x ) );
    }

    /**
     * \class adaptive_time_iterator
     *
     * \brief ODE Iterator with adaptive step size. The value type of this iterator is a std::pair containing state and time.
     *
     * Implements an iterator representing the solution of an ODE from t_start
     * to t_end evaluated at steps with an adaptive step size dt.
     * After each iteration the iterator dereferences to a pair containing state
     * and time at the next time point t+dt where dt is controlled by the stepper.
     * This iterator can be used with ControlledSteppers and
     * DenseOutputSteppers and it always makes use of the all the given steppers
     * capabilities. A for_each over such an iterator range behaves similar to
     * the integrate_adaptive routine.
     *
     * adaptive_iterator is a model of single-pass iterator.
     *
     * The value type of this iterator is a std::pair of  state and time of the stepper.
     *
     * \tparam Stepper The stepper type which should be used during the iteration.
     * \tparam System The type of the system function (ODE) which should be solved.
     * \tparam State The state type of the ODE.
     */

    /**
     * \fn make_adaptive_time_iterator_begin( Stepper stepper , System system , State &x ,
         typename traits::time_type< Stepper >::type t_start ,
         typename traits::time_type< Stepper >::type t_end ,
         typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function for adaptive_time_iterator. Constructs a begin iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The adaptive time iterator.
     */

    /**
     * \fn make_adaptive_time_iterator_end( Stepper stepper , System system , State &x )
     * \brief Factory function for adaptive_time_iterator. Constructs a end iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
     * \returns The adaptive time iterator.
     */

    /**
     * \fn make_adaptive_time_range( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function to construct a single pass range of adaptive time iterators. A range is here a pair of adaptive_time_iterators.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The adaptive time range.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_ITERATOR_ADAPTIVE_TIME_ITERATOR_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/iterator/const_step_iterator.hpp

 [begin_description]
 Iterator for iterating through the solution of an ODE with constant step size.
 [end_description]

 Copyright 2012-2013 Karsten Ahnert
 Copyright 2013 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED

#include <boost/numeric/odeint/util/stepper_traits.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
#include <boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp>

namespace boost {
namespace numeric {
namespace odeint {

    /* use the const_step_iterator_impl with the right tags */
    template< class Stepper , class System , class State
#ifndef DOXYGEN_SKIP
    , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
#endif
    >
    class const_step_iterator : public const_step_iterator_impl<
            const_step_iterator< Stepper , System , State , StepperTag > ,
            Stepper , System , State , detail::ode_state_iterator_tag , StepperTag
        >
    {
        typedef typename traits::time_type< Stepper >::type time_type;
        typedef const_step_iterator< Stepper , System , State , StepperTag > iterator_type;

    public:
        const_step_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
            : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
        {}

        const_step_iterator( Stepper stepper , System sys , State &s )
            : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_iterator_tag , StepperTag >( stepper , sys , s )
        {}
    };

    /* make functions */

    template< class Stepper , class System , class State >
    const_step_iterator< Stepper , System, State > make_const_step_iterator_begin(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return const_step_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
    }

    template< class Stepper , class System , class State >
    const_step_iterator< Stepper , System , State > make_const_step_iterator_end(
        Stepper stepper ,
        System system ,
        State &x )
    {
        return const_step_iterator< Stepper , System , State >( stepper , system , x );
    }

    template< class Stepper , class System , class State >
    std::pair< const_step_iterator< Stepper , System , State > , const_step_iterator< Stepper , System , State > >
    make_const_step_range(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return std::make_pair(
            const_step_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
            const_step_iterator< Stepper , System , State >( stepper , system , x )
            );
    }

    /**
     * \class const_step_iterator
     *
     * \brief ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.
     *
     * Implements an iterator representing the solution of an ODE from t_start
     * to t_end evaluated at steps with constant step size dt.
     * After each iteration the iterator dereferences to the state x at the next
     * time t+dt.
     * This iterator can be used with Steppers and
     * DenseOutputSteppers and it always makes use of the all the given steppers
     * capabilities. A for_each over such an iterator range behaves similar to
     * the integrate_const routine.
     *
     * const_step_iterator is a model of single-pass iterator.
     *
     * The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.
     *
     * \tparam Stepper The stepper type which should be used during the iteration.
     * \tparam System The type of the system function (ODE) which should be solved.
     * \tparam State The state type of the ODE.
     */

    /**
     * \fn make_const_step_iterator_begin(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function for const_step_iterator. Constructs a begin iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The const step iterator.
     */

    /**
     * \fn make_const_step_iterator_end( Stepper stepper , System system , State &x )
     * \brief Factory function for const_step_iterator. Constructs a end iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.
     * \returns The const_step_iterator.
     */

    /**
     * \fn make_const_step_range( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function to construct a single pass range of const step iterators. A range is here a pair
     * of const_step_iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_iterator store a reference of s and changes its value during the iteration.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The const step range.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

//#include <boost/numeric/odeint/iterator/impl/const_step_iterator_dense_output_impl.hpp>

#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_ODE_ITERATOR_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/iterator/const_step_time_iterator.hpp

 [begin_description]
 Iterator for iterating throught the solution of an ODE with constant step size. The dereferences types containes also the time.
 [end_description]

 Copyright 2012-2013 Karsten Ahnert
 Copyright 2013 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED

#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
#include <boost/numeric/odeint/util/stepper_traits.hpp>
#include <boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp>
#include <boost/numeric/odeint/iterator/impl/const_step_iterator_impl.hpp>

namespace boost {
namespace numeric {
namespace odeint {

    /* use the const_step_iterator_impl with the right tags */
    template< class Stepper , class System , class State
#ifndef DOXYGEN_SKIP
        , class StepperTag = typename base_tag< typename traits::stepper_category< Stepper >::type >::type
#endif
    >
    class const_step_time_iterator : public const_step_iterator_impl<
            const_step_time_iterator< Stepper , System , State , StepperTag > ,
            Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag
        >
    {
        typedef typename traits::time_type< Stepper >::type time_type;
        typedef const_step_time_iterator< Stepper , System , State , StepperTag > iterator_type;

    public:
        const_step_time_iterator( Stepper stepper , System sys , State &s , time_type t_start , time_type t_end , time_type dt )
            : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s , t_start , t_end , dt )
        {}

        const_step_time_iterator( Stepper stepper , System sys , State &s )
            : const_step_iterator_impl< iterator_type , Stepper , System , State , detail::ode_state_time_iterator_tag , StepperTag >( stepper , sys , s )
        {}
    };

    template< class Stepper , class System , class State >
    const_step_time_iterator< Stepper , System , State > make_const_step_time_iterator_begin(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return const_step_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt );
    }

    template< class Stepper , class System , class State >
    const_step_time_iterator< Stepper , System , State > make_const_step_time_iterator_end(
        Stepper stepper ,
        System system ,
        State &x )
    {
        return const_step_time_iterator< Stepper , System , State >( stepper , system , x );
    }

    template< class Stepper , class System , class State >
    std::pair< const_step_time_iterator< Stepper , System , State > , const_step_time_iterator< Stepper , System , State > >
    make_const_step_time_range(
        Stepper stepper ,
        System system ,
        State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
    {
        return std::make_pair(
            const_step_time_iterator< Stepper , System , State >( stepper , system , x , t_start , t_end , dt ) ,
            const_step_time_iterator< Stepper , System , State >( stepper , system , x ) );
    }

    /**
     * \class const_step_time_iterator
     *
     * \brief ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time.
     *
     * Implements an iterator representing the solution of an ODE from t_start
     * to t_end evaluated at steps with constant step size dt.
     * After each iteration the iterator dereferences to a pair containing
     * state and time at the next time point t+dt..
     * This iterator can be used with Steppers and
     * DenseOutputSteppers and it always makes use of the all the given steppers
     * capabilities. A for_each over such an iterator range behaves similar to
     * the integrate_const routine.
     *
     * const_step_time_iterator is a model of single-pass iterator.
     *
     * The value type of this iterator is a pair with the state type and time type of the stepper.
     *
     * \tparam Stepper The stepper type which should be used during the iteration.
     * \tparam System The type of the system function (ODE) which should be solved.
     * \tparam State The state type of the ODE.
     */

    /**
     * \fn make_const_step_time_iterator_begin( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt )
     *
     * \brief Factory function for const_step_time_iterator. Constructs a begin iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.
     * \param t_start The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The const step time iterator.
     */

    /**
     * \fn make_const_step_time_iterator_end( Stepper stepper , System system , State &x )
     * \brief Factory function for const_step_time_iterator. Constructs a end iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_time_iterator store a reference of s and changes its value during the iteration.
     * \returns The const step time iterator.
     */

    /**
     * \fn make_const_step_time_range( Stepper stepper , System system , State &x ,
        typename traits::time_type< Stepper >::type t_start ,
        typename traits::time_type< Stepper >::type t_end ,
        typename traits::time_type< Stepper >::type dt)
     *
     * \brief Factory function to construct a single pass range of const_step_time_iterator. A range is here a pair of const_step_time_iterator.
     *
     * \param stepper The stepper to use during the iteration.
     * \param system The system function (ODE) to solve.
     * \param x The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.
     * \param t The initial time.
     * \param t_end The end time, at which the iteration should stop.
     * \param dt The initial time step.
     * \returns The const step time range.
     */

} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_ITERATOR_CONST_STEP_TIME_ITERATOR_HPP_INCLUDED


code:
/*
 [auto_generated]
 boost/numeric/odeint/iterator/detail/ode_iterator_base.hpp

 [begin_description]
 Base class for const_step_iterator and adaptive_iterator.
 [end_description]

 Copyright 2012-2013 Karsten Ahnert
 Copyright 2012-2013 Mario Mulansky

 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 BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED

#include <boost/iterator/iterator_facade.hpp>

#include <boost/numeric/odeint/util/unwrap_reference.hpp>
#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>

namespace boost {
namespace numeric {
namespace odeint {
namespace detail {

    struct ode_state_iterator_tag {};
    struct ode_state_time_iterator_tag {};

    template< class Iterator , class Stepper , class System , class State , typename Tag >
    class ode_iterator_base;

    /* Specialization for the state iterator that has only state_type as its value_type */
    template< class Iterator , class Stepper , class System , class State >
    class ode_iterator_base< Iterator , Stepper , System , State , ode_state_iterator_tag >
        : public boost::iterator_facade
          <
              Iterator ,
              typename traits::state_type< Stepper >::type const ,
              boost::single_pass_traversal_tag
          >
    {
    private:

        typedef Stepper stepper_type;
        typedef System system_type;
        typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
        typedef State state_type;
        typedef typename unwrapped_stepper_type::time_type time_type;
        typedef typename unwrapped_stepper_type::value_type ode_value_type;

    public:

        ode_iterator_base( stepper_type stepper , system_type sys , time_type t , time_type dt )
            : m_stepper( stepper ) , m_system( sys ) ,
              m_t( t ) , m_dt( dt ) , m_at_end( false )
        { }

        ode_iterator_base( stepper_type stepper , system_type sys )
            : m_stepper( stepper ) , m_system( sys ) ,
              m_t() , m_dt() , m_at_end( true )
        { }

        // this function is only for testing
        bool same( const ode_iterator_base &iter ) const
        {
            return (
                //( static_cast<Iterator>(*this).get_state() ==
                //  static_cast<Iterator>(iter).get_state ) &&
                ( m_t == iter.m_t ) &&
                ( m_dt == iter.m_dt ) &&
                ( m_at_end == iter.m_at_end )
                );
        }

    protected:

        friend class boost::iterator_core_access;

        bool equal( ode_iterator_base const& other ) const
        {
            if( m_at_end == other.m_at_end )
            {
                return true;
            }
            else
            {
                return false;
            }
        }

        const state_type& dereference() const
        {
            return static_cast<const Iterator*>(this)->get_state();
        }

    protected:

        stepper_type m_stepper;
        system_type m_system;
        time_type m_t;
        time_type m_dt;
        bool m_at_end;
    };

    /* Specialization for the state-time iterator that has pair<state_type,time_type> as its value_type */

    template< class Iterator , class Stepper , class System , class State >
    class ode_iterator_base< Iterator , Stepper , System , State , ode_state_time_iterator_tag >
        : public boost::iterator_facade
          <
              Iterator ,
              std::pair< const State , const typename traits::time_type< Stepper >::type > ,
              boost::single_pass_traversal_tag ,
              std::pair< const State& , const typename traits::time_type< Stepper >::type& >
          >
    {
    private:

        typedef Stepper stepper_type;
        typedef System system_type;
        typedef typename boost::numeric::odeint::unwrap_reference< stepper_type >::type unwrapped_stepper_type;
        typedef State state_type;
        typedef typename unwrapped_stepper_type::time_type time_type;
        typedef typename unwrapped_stepper_type::value_type ode_value_type;

    public:

        ode_iterator_base( stepper_type stepper , system_type sys ,
                           time_type t , time_type dt )
            : m_stepper( stepper ) , m_system( sys ) ,
              m_t( t ) , m_dt( dt ) , m_at_end( false )
        { }

        ode_iterator_base( stepper_type stepper , system_type sys )
            : m_stepper( stepper ) , m_system( sys ) , m_at_end( true )
        { }

        bool same( ode_iterator_base const& iter )
        {
            return (
                //( static_cast<Iterator>(*this).get_state() ==
                //  static_cast<Iterator>(iter).get_state ) &&
                ( m_t == iter.m_t ) &&
                ( m_dt == iter.m_dt ) &&
                ( m_at_end == iter.m_at_end )
                );
        }

    protected:

        friend class boost::iterator_core_access;

        bool equal( ode_iterator_base const& other ) const
        {
            if( m_at_end == other.m_at_end )
            {
                return true;
            }
            else
            {
                return false;
            }
        }

        std::pair< const state_type& , const time_type& > dereference() const
        {
            return std::pair< const state_type & , const time_type & >(
                    static_cast<const Iterator*>(this)->get_state() , m_t );
        }

        stepper_type m_stepper;
        system_type m_system;
        time_type m_t;
        time_type m_dt;
        bool m_at_end;

    };

} // namespace detail
} // namespace odeint
} // namespace numeric
} // namespace boost

#endif // BOOST_NUMERIC_ODEINT_ITERATOR_DETAIL_ODE_ITERATOR_BASE_HPP_INCLUDED