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/* [auto_generated]
boost/numeric/odeint/stepper/controlled_runge_kutta.hpp
[begin_description]
The default controlled stepper which can be used with all explicit Runge-Kutta error steppers.
[end_description]
Copyright 2010-2013 Karsten Ahnert
Copyright 2010-2015 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_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
#define BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
#include <cmath>
#include <boost/config.hpp>
#include <boost/utility/enable_if.hpp>
#include <boost/type_traits/is_same.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/state_wrapper.hpp>
#include <boost/numeric/odeint/util/is_resizeable.hpp>
#include <boost/numeric/odeint/util/resizer.hpp>
#include <boost/numeric/odeint/util/detail/less_with_sign.hpp>
#include <boost/numeric/odeint/algebra/range_algebra.hpp>
#include <boost/numeric/odeint/algebra/default_operations.hpp>
#include <boost/numeric/odeint/algebra/algebra_dispatcher.hpp>
#include <boost/numeric/odeint/stepper/controlled_step_result.hpp>
#include <boost/numeric/odeint/stepper/stepper_categories.hpp>
namespace boost {
namespace numeric {
namespace odeint {
template
<
class Value ,
class Algebra ,
class Operations
>
class default_error_checker
{
public:
typedef Value value_type;
typedef Algebra algebra_type;
typedef Operations operations_type;
default_error_checker(
value_type eps_abs = static_cast< value_type >( 1.0e-6 ) ,
value_type eps_rel = static_cast< value_type >( 1.0e-6 ) ,
value_type a_x = static_cast< value_type >( 1 ) ,
value_type a_dxdt = static_cast< value_type >( 1 ))
: m_eps_abs( eps_abs ) , m_eps_rel( eps_rel ) , m_a_x( a_x ) , m_a_dxdt( a_dxdt )
{ }
template< class State , class Deriv , class Err, class Time >
value_type error( const State &x_old , const Deriv &dxdt_old , Err &x_err , Time dt ) const
{
return error( algebra_type() , x_old , dxdt_old , x_err , dt );
}
template< class State , class Deriv , class Err, class Time >
value_type error( algebra_type &algebra , const State &x_old , const Deriv &dxdt_old , Err &x_err , Time dt ) const
{
using std::abs;
// this overwrites x_err !
algebra.for_each3( x_err , x_old , dxdt_old ,
typename operations_type::template rel_error< value_type >( m_eps_abs , m_eps_rel , m_a_x , m_a_dxdt * abs(get_unit_value( dt )) ) );
// value_type res = algebra.reduce( x_err ,
// typename operations_type::template maximum< value_type >() , static_cast< value_type >( 0 ) );
return algebra.norm_inf( x_err );
}
private:
value_type m_eps_abs;
value_type m_eps_rel;
value_type m_a_x;
value_type m_a_dxdt;
};
template< typename Value, typename Time >
class default_step_adjuster
{
public:
typedef Time time_type;
typedef Value value_type;
default_step_adjuster(const time_type max_dt=static_cast<time_type>(0))
: m_max_dt(max_dt)
{}
time_type decrease_step(time_type dt, const value_type error, const int error_order) const
{
// returns the decreased time step
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
using std::pow;
dt *= max
BOOST_PREVENT_MACRO_SUBSTITUTION(
static_cast<value_type>( static_cast<value_type>(9) / static_cast<value_type>(10) *
pow(error, static_cast<value_type>(-1) / (error_order - 1))),
static_cast<value_type>( static_cast<value_type>(1) / static_cast<value_type> (5)));
if(m_max_dt != static_cast<time_type >(0))
// limit to maximal stepsize even when decreasing
dt = detail::min_abs(dt, m_max_dt);
return dt;
}
time_type increase_step(time_type dt, value_type error, const int stepper_order) const
{
// returns the increased time step
BOOST_USING_STD_MIN();
BOOST_USING_STD_MAX();
using std::pow;
// adjust the size if dt is smaller than max_dt (providede max_dt is not zero)
if(error < 0.5)
{
// error should be > 0
error = max BOOST_PREVENT_MACRO_SUBSTITUTION (
static_cast<value_type>( pow( static_cast<value_type>(5.0) , -static_cast<value_type>(stepper_order) ) ) ,
error);
time_type dt_old = dt;
//error too small - increase dt and keep the evolution and limit scaling factor to 5.0
dt *= static_cast<value_type>(9)/static_cast<value_type>(10) *
pow(error, static_cast<value_type>(-1) / stepper_order);
if(m_max_dt != static_cast<time_type >(0))
// limit to maximal stepsize
dt = detail::min_abs(dt, m_max_dt);
}
return dt;
}
bool check_step_size_limit(const time_type dt)
{
if(m_max_dt != static_cast<time_type >(0))
return detail::less_eq_with_sign(dt, m_max_dt, dt);
return true;
}
time_type get_max_dt() { return m_max_dt; }
private:
time_type m_max_dt;
};
/*
* error stepper category dispatcher
*/
template<
class ErrorStepper ,
class ErrorChecker = default_error_checker< typename ErrorStepper::value_type ,
typename ErrorStepper::algebra_type ,
typename ErrorStepper::operations_type > ,
class StepAdjuster = default_step_adjuster< typename ErrorStepper::value_type ,
typename ErrorStepper::time_type > ,
class Resizer = typename ErrorStepper::resizer_type ,
class ErrorStepperCategory = typename ErrorStepper::stepper_category
>
class controlled_runge_kutta ;
/*
* explicit stepper version
*
* this class introduces the following try_step overloads
* try_step( sys , x , t , dt )
* try_step( sys , x , dxdt , t , dt )
* try_step( sys , in , t , out , dt )
* try_step( sys , in , dxdt , t , out , dt )
*/
/**
* \brief Implements step size control for Runge-Kutta steppers with error
* estimation.
*
* This class implements the step size control for standard Runge-Kutta
* steppers with error estimation.
*
* \tparam ErrorStepper The stepper type with error estimation, has to fulfill the ErrorStepper concept.
* \tparam ErrorChecker The error checker
* \tparam Resizer The resizer policy type.
*/
template<
class ErrorStepper,
class ErrorChecker,
class StepAdjuster,
class Resizer
>
class controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster, Resizer ,
explicit_error_stepper_tag >
{
public:
typedef ErrorStepper stepper_type;
typedef typename stepper_type::state_type state_type;
typedef typename stepper_type::value_type value_type;
typedef typename stepper_type::deriv_type deriv_type;
typedef typename stepper_type::time_type time_type;
typedef typename stepper_type::algebra_type algebra_type;
typedef typename stepper_type::operations_type operations_type;
typedef Resizer resizer_type;
typedef ErrorChecker error_checker_type;
typedef StepAdjuster step_adjuster_type;
typedef explicit_controlled_stepper_tag stepper_category;
#ifndef DOXYGEN_SKIP
typedef typename stepper_type::wrapped_state_type wrapped_state_type;
typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
typedef controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster ,
Resizer , explicit_error_stepper_tag > controlled_stepper_type;
#endif //DOXYGEN_SKIP
/**
* \brief Constructs the controlled Runge-Kutta stepper.
* \param error_checker An instance of the error checker.
* \param stepper An instance of the underlying stepper.
*/
controlled_runge_kutta(
const error_checker_type &error_checker = error_checker_type( ) ,
const step_adjuster_type &step_adjuster = step_adjuster_type() ,
const stepper_type &stepper = stepper_type( )
)
: m_stepper(stepper), m_error_checker(error_checker) , m_step_adjuster(step_adjuster)
{ }
/*
* Version 1 : try_step( sys , x , t , dt )
*
* The overloads are needed to solve the forwarding problem
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut >
controlled_step_result try_step( System system , StateInOut &x , time_type &t , time_type &dt )
{
return try_step_v1( system , x , t, dt );
}
/**
* \brief Tries to perform one step. Solves the forwarding problem and
* allows for using boost range as state_type.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful. Can be a boost range.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut >
controlled_step_result try_step( System system , const StateInOut &x , time_type &t , time_type &dt )
{
return try_step_v1( system , x , t, dt );
}
/*
* Version 2 : try_step( sys , x , dxdt , t , dt )
*
* this version does not solve the forwarding problem, boost.range can not be used
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful.
* \param dxdt The derivative of state.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut , class DerivIn >
controlled_step_result try_step( System system , StateInOut &x , const DerivIn &dxdt , time_type &t , time_type &dt )
{
m_xnew_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_xnew_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , dt );
if( res == success )
{
boost::numeric::odeint::copy( m_xnew.m_v , x );
}
return res;
}
/*
* Version 3 : try_step( sys , in , t , out , dt )
*
* this version does not solve the forwarding problem, boost.range can not be used
*
* the disable is needed to avoid ambiguous overloads if state_type = time_type
*/
/**
* \brief Tries to perform one step.
*
* \note This method is disabled if state_type=time_type to avoid ambiguity.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param in The state of the ODE which should be solved.
* \param t The value of the time. Updated if the step is successful.
* \param out Used to store the result of the step.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateIn , class StateOut >
typename boost::disable_if< boost::is_same< StateIn , time_type > , controlled_step_result >::type
try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
{
typename odeint::unwrap_reference< System >::type &sys = system;
m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
sys( in , m_dxdt.m_v , t );
return try_step( system , in , m_dxdt.m_v , t , out , dt );
}
/*
* Version 4 : try_step( sys , in , dxdt , t , out , dt )
*
* this version does not solve the forwarding problem, boost.range can not be used
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param in The state of the ODE which should be solved.
* \param dxdt The derivative of state.
* \param t The value of the time. Updated if the step is successful.
* \param out Used to store the result of the step.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateIn , class DerivIn , class StateOut >
controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt , time_type &t , StateOut &out , time_type &dt )
{
if( !m_step_adjuster.check_step_size_limit(dt) )
{
// given dt was above step size limit - adjust and return fail;
dt = m_step_adjuster.get_max_dt();
return fail;
}
m_xerr_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_xerr_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
// do one step with error calculation
m_stepper.do_step( system , in , dxdt , t , out , dt , m_xerr.m_v );
value_type max_rel_err = m_error_checker.error( m_stepper.algebra() , in , dxdt , m_xerr.m_v , dt );
if( max_rel_err > 1.0 )
{
// error too big, decrease step size and reject this step
dt = m_step_adjuster.decrease_step(dt, max_rel_err, m_stepper.error_order());
return fail;
} else
{
// otherwise, increase step size and accept
t += dt;
dt = m_step_adjuster.increase_step(dt, max_rel_err, m_stepper.stepper_order());
return success;
}
}
/**
* \brief Adjust the size of all temporaries in the stepper manually.
* \param x A state from which the size of the temporaries to be resized is deduced.
*/
template< class StateType >
void adjust_size( const StateType &x )
{
resize_m_xerr_impl( x );
resize_m_dxdt_impl( x );
resize_m_xnew_impl( x );
m_stepper.adjust_size( x );
}
/**
* \brief Returns the instance of the underlying stepper.
* \returns The instance of the underlying stepper.
*/
stepper_type& stepper( void )
{
return m_stepper;
}
/**
* \brief Returns the instance of the underlying stepper.
* \returns The instance of the underlying stepper.
*/
const stepper_type& stepper( void ) const
{
return m_stepper;
}
private:
template< class System , class StateInOut >
controlled_step_result try_step_v1( System system , StateInOut &x , time_type &t , time_type &dt )
{
typename odeint::unwrap_reference< System >::type &sys = system;
m_dxdt_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
sys( x , m_dxdt.m_v ,t );
return try_step( system , x , m_dxdt.m_v , t , dt );
}
template< class StateIn >
bool resize_m_xerr_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_xerr , x , typename is_resizeable<state_type>::type() );
}
template< class StateIn >
bool resize_m_dxdt_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
}
template< class StateIn >
bool resize_m_xnew_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
}
stepper_type m_stepper;
error_checker_type m_error_checker;
step_adjuster_type m_step_adjuster;
resizer_type m_dxdt_resizer;
resizer_type m_xerr_resizer;
resizer_type m_xnew_resizer;
wrapped_deriv_type m_dxdt;
wrapped_state_type m_xerr;
wrapped_state_type m_xnew;
};
/*
* explicit stepper fsal version
*
* the class introduces the following try_step overloads
* try_step( sys , x , t , dt )
* try_step( sys , in , t , out , dt )
* try_step( sys , x , dxdt , t , dt )
* try_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
*/
/**
* \brief Implements step size control for Runge-Kutta FSAL steppers with
* error estimation.
*
* This class implements the step size control for FSAL Runge-Kutta
* steppers with error estimation.
*
* \tparam ErrorStepper The stepper type with error estimation, has to fulfill the ErrorStepper concept.
* \tparam ErrorChecker The error checker
* \tparam Resizer The resizer policy type.
*/
template<
class ErrorStepper ,
class ErrorChecker ,
class StepAdjuster ,
class Resizer
>
class controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster , Resizer , explicit_error_stepper_fsal_tag >
{
public:
typedef ErrorStepper stepper_type;
typedef typename stepper_type::state_type state_type;
typedef typename stepper_type::value_type value_type;
typedef typename stepper_type::deriv_type deriv_type;
typedef typename stepper_type::time_type time_type;
typedef typename stepper_type::algebra_type algebra_type;
typedef typename stepper_type::operations_type operations_type;
typedef Resizer resizer_type;
typedef ErrorChecker error_checker_type;
typedef StepAdjuster step_adjuster_type;
typedef explicit_controlled_stepper_fsal_tag stepper_category;
#ifndef DOXYGEN_SKIP
typedef typename stepper_type::wrapped_state_type wrapped_state_type;
typedef typename stepper_type::wrapped_deriv_type wrapped_deriv_type;
typedef controlled_runge_kutta< ErrorStepper , ErrorChecker , StepAdjuster , Resizer , explicit_error_stepper_tag > controlled_stepper_type;
#endif // DOXYGEN_SKIP
/**
* \brief Constructs the controlled Runge-Kutta stepper.
* \param error_checker An instance of the error checker.
* \param stepper An instance of the underlying stepper.
*/
controlled_runge_kutta(
const error_checker_type &error_checker = error_checker_type() ,
const step_adjuster_type &step_adjuster = step_adjuster_type() ,
const stepper_type &stepper = stepper_type()
)
: m_stepper( stepper ) , m_error_checker( error_checker ) , m_step_adjuster(step_adjuster) ,
m_first_call( true )
{ }
/*
* Version 1 : try_step( sys , x , t , dt )
*
* The two overloads are needed in order to solve the forwarding problem
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut >
controlled_step_result try_step( System system , StateInOut &x , time_type &t , time_type &dt )
{
return try_step_v1( system , x , t , dt );
}
/**
* \brief Tries to perform one step. Solves the forwarding problem and
* allows for using boost range as state_type.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful. Can be a boost range.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut >
controlled_step_result try_step( System system , const StateInOut &x , time_type &t , time_type &dt )
{
return try_step_v1( system , x , t , dt );
}
/*
* Version 2 : try_step( sys , in , t , out , dt );
*
* This version does not solve the forwarding problem, boost::range can not be used.
*
* The disabler is needed to solve ambiguous overloads
*/
/**
* \brief Tries to perform one step.
*
* \note This method is disabled if state_type=time_type to avoid ambiguity.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param in The state of the ODE which should be solved.
* \param t The value of the time. Updated if the step is successful.
* \param out Used to store the result of the step.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateIn , class StateOut >
typename boost::disable_if< boost::is_same< StateIn , time_type > , controlled_step_result >::type
try_step( System system , const StateIn &in , time_type &t , StateOut &out , time_type &dt )
{
if( m_dxdt_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
{
initialize( system , in , t );
}
return try_step( system , in , m_dxdt.m_v , t , out , dt );
}
/*
* Version 3 : try_step( sys , x , dxdt , t , dt )
*
* This version does not solve the forwarding problem, boost::range can not be used.
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The state of the ODE which should be solved. Overwritten if
* the step is successful.
* \param dxdt The derivative of state.
* \param t The value of the time. Updated if the step is successful.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateInOut , class DerivInOut >
controlled_step_result try_step( System system , StateInOut &x , DerivInOut &dxdt , time_type &t , time_type &dt )
{
m_xnew_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_xnew_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
m_dxdt_new_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_new_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) );
controlled_step_result res = try_step( system , x , dxdt , t , m_xnew.m_v , m_dxdtnew.m_v , dt );
if( res == success )
{
boost::numeric::odeint::copy( m_xnew.m_v , x );
boost::numeric::odeint::copy( m_dxdtnew.m_v , dxdt );
}
return res;
}
/*
* Version 4 : try_step( sys , in , dxdt_in , t , out , dxdt_out , dt )
*
* This version does not solve the forwarding problem, boost::range can not be used.
*/
/**
* \brief Tries to perform one step.
*
* This method tries to do one step with step size dt. If the error estimate
* is to large, the step is rejected and the method returns fail and the
* step size dt is reduced. If the error estimate is acceptably small, the
* step is performed, success is returned and dt might be increased to make
* the steps as large as possible. This method also updates t if a step is
* performed.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param in The state of the ODE which should be solved.
* \param dxdt The derivative of state.
* \param t The value of the time. Updated if the step is successful.
* \param out Used to store the result of the step.
* \param dt The step size. Updated.
* \return success if the step was accepted, fail otherwise.
*/
template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut >
controlled_step_result try_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type &t ,
StateOut &out , DerivOut &dxdt_out , time_type &dt )
{
if( !m_step_adjuster.check_step_size_limit(dt) )
{
// given dt was above step size limit - adjust and return fail;
dt = m_step_adjuster.get_max_dt();
return fail;
}
m_xerr_resizer.adjust_size( in , detail::bind( &controlled_runge_kutta::template resize_m_xerr_impl< StateIn > , detail::ref( *this ) , detail::_1 ) );
//fsal: m_stepper.get_dxdt( dxdt );
//fsal: m_stepper.do_step( sys , x , dxdt , t , dt , m_x_err );
m_stepper.do_step( system , in , dxdt_in , t , out , dxdt_out , dt , m_xerr.m_v );
// this potentially overwrites m_x_err! (standard_error_checker does, at least)
value_type max_rel_err = m_error_checker.error( m_stepper.algebra() , in , dxdt_in , m_xerr.m_v , dt );
if( max_rel_err > 1.0 )
{
// error too big, decrease step size and reject this step
dt = m_step_adjuster.decrease_step(dt, max_rel_err, m_stepper.error_order());
return fail;
}
// otherwise, increase step size and accept
t += dt;
dt = m_step_adjuster.increase_step(dt, max_rel_err, m_stepper.stepper_order());
return success;
}
/**
* \brief Resets the internal state of the underlying FSAL stepper.
*/
void reset( void )
{
m_first_call = true;
}
/**
* \brief Initializes the internal state storing an internal copy of the derivative.
*
* \param deriv The initial derivative of the ODE.
*/
template< class DerivIn >
void initialize( const DerivIn &deriv )
{
boost::numeric::odeint::copy( deriv , m_dxdt.m_v );
m_first_call = false;
}
/**
* \brief Initializes the internal state storing an internal copy of the derivative.
*
* \param system The system function to solve, hence the r.h.s. of the ODE. It must fulfill the
* Simple System concept.
* \param x The initial state of the ODE which should be solved.
* \param t The initial time.
*/
template< class System , class StateIn >
void initialize( System system , const StateIn &x , time_type t )
{
typename odeint::unwrap_reference< System >::type &sys = system;
sys( x , m_dxdt.m_v , t );
m_first_call = false;
}
/**
* \brief Returns true if the stepper has been initialized, false otherwise.
*
* \return true, if the stepper has been initialized, false otherwise.
*/
bool is_initialized( void ) const
{
return ! m_first_call;
}
/**
* \brief Adjust the size of all temporaries in the stepper manually.
* \param x A state from which the size of the temporaries to be resized is deduced.
*/
template< class StateType >
void adjust_size( const StateType &x )
{
resize_m_xerr_impl( x );
resize_m_dxdt_impl( x );
resize_m_dxdt_new_impl( x );
resize_m_xnew_impl( x );
}
/**
* \brief Returns the instance of the underlying stepper.
* \returns The instance of the underlying stepper.
*/
stepper_type& stepper( void )
{
return m_stepper;
}
/**
* \brief Returns the instance of the underlying stepper.
* \returns The instance of the underlying stepper.
*/
const stepper_type& stepper( void ) const
{
return m_stepper;
}
private:
template< class StateIn >
bool resize_m_xerr_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_xerr , x , typename is_resizeable<state_type>::type() );
}
template< class StateIn >
bool resize_m_dxdt_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() );
}
template< class StateIn >
bool resize_m_dxdt_new_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_dxdtnew , x , typename is_resizeable<deriv_type>::type() );
}
template< class StateIn >
bool resize_m_xnew_impl( const StateIn &x )
{
return adjust_size_by_resizeability( m_xnew , x , typename is_resizeable<state_type>::type() );
}
template< class System , class StateInOut >
controlled_step_result try_step_v1( System system , StateInOut &x , time_type &t , time_type &dt )
{
if( m_dxdt_resizer.adjust_size( x , detail::bind( &controlled_runge_kutta::template resize_m_dxdt_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call )
{
initialize( system , x , t );
}
return try_step( system , x , m_dxdt.m_v , t , dt );
}
stepper_type m_stepper;
error_checker_type m_error_checker;
step_adjuster_type m_step_adjuster;
resizer_type m_dxdt_resizer;
resizer_type m_xerr_resizer;
resizer_type m_xnew_resizer;
resizer_type m_dxdt_new_resizer;
wrapped_deriv_type m_dxdt;
wrapped_state_type m_xerr;
wrapped_state_type m_xnew;
wrapped_deriv_type m_dxdtnew;
bool m_first_call;
};
/********** DOXYGEN **********/
/**** DEFAULT ERROR CHECKER ****/
/**
* \class default_error_checker
* \brief The default error checker to be used with Runge-Kutta error steppers
*
* This class provides the default mechanism to compare the error estimates
* reported by Runge-Kutta error steppers with user defined error bounds.
* It is used by the controlled_runge_kutta steppers.
*
* \tparam Value The value type.
* \tparam Time The time type.
* \tparam Algebra The algebra type.
* \tparam Operations The operations type.
*/
/**
* \fn default_error_checker( value_type eps_abs , value_type eps_rel , value_type a_x , value_type a_dxdt ,
* time_type max_dt)
* \brief Constructs the error checker.
*
* The error is calculated as follows: ????
*
* \param eps_abs Absolute tolerance level.
* \param eps_rel Relative tolerance level.
* \param a_x Factor for the weight of the state.
* \param a_dxdt Factor for the weight of the derivative.
* \param max_dt Maximum allowed step size.
*/
/**
* \fn error( const State &x_old , const Deriv &dxdt_old , Err &x_err , time_type dt ) const
* \brief Calculates the error level.
*
* If the returned error level is greater than 1, the estimated error was
* larger than the permitted error bounds and the step should be repeated
* with a smaller step size.
*
* \param x_old State at the beginning of the step.
* \param dxdt_old Derivative at the beginning of the step.
* \param x_err Error estimate.
* \param dt Time step.
* \return error
*/
/**
* \fn error( algebra_type &algebra , const State &x_old , const Deriv &dxdt_old , Err &x_err , time_type dt ) const
* \brief Calculates the error level using a given algebra.
*
* If the returned error level is greater than 1, the estimated error was
* larger than the permitted error bounds and the step should be repeated
* with a smaller step size.
*
* \param algebra The algebra used for calculation of the error.
* \param x_old State at the beginning of the step.
* \param dxdt_old Derivative at the beginning of the step.
* \param x_err Error estimate.
* \param dt Time step.
* \return error
*/
/**
* \fn time_type decrease_step(const time_type dt, const value_type error, const int error_order)
* \brief Returns a decreased step size based on the given error and order
*
* Calculates a new smaller step size based on the given error and its order.
*
* \param dt The old step size.
* \param error The computed error estimate.
* \param error_order The error order of the stepper.
* \return dt_new The new, reduced step size.
*/
/**
* \fn time_type increase_step(const time_type dt, const value_type error, const int error_order)
* \brief Returns an increased step size based on the given error and order.
*
* Calculates a new bigger step size based on the given error and its order. If max_dt != 0, the
* new step size is limited to max_dt.
*
* \param dt The old step size.
* \param error The computed error estimate.
* \param error_order The order of the stepper.
* \return dt_new The new, increased step size.
*/
} // odeint
} // numeric
} // boost
#endif // BOOST_NUMERIC_ODEINT_STEPPER_CONTROLLED_RUNGE_KUTTA_HPP_INCLUDED
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