boost/numeric/odeint/stepper/controlled_runge_kutta.hpp
/* [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