boost/numeric/odeint/stepper/runge_kutta_fehlberg78.hpp
/* [auto_generated] boost/numeric/odeint/stepper/runge_kutta_fehlberg87.hpp [begin_description] Implementation of the Runge-Kutta-Fehlberg stepper with the generic stepper. [end_description] Copyright 2011-2013 Mario Mulansky Copyright 2012-2013 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_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED #define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED #include <boost/fusion/container/vector.hpp> #include <boost/fusion/container/generation/make_vector.hpp> #include <boost/numeric/odeint/stepper/explicit_error_generic_rk.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/algebra/operations_dispatcher.hpp> #include <boost/array.hpp> #include <boost/numeric/odeint/util/state_wrapper.hpp> #include <boost/numeric/odeint/util/is_resizeable.hpp> #include <boost/numeric/odeint/util/resizer.hpp> namespace boost { namespace numeric { namespace odeint { #ifndef DOXYGEN_SKIP template< class Value = double > struct rk78_coefficients_a1 : boost::array< Value , 1 > { rk78_coefficients_a1( void ) { (*this)[0] = static_cast< Value >( 2 )/static_cast< Value >( 27 ); } }; template< class Value = double > struct rk78_coefficients_a2 : boost::array< Value , 2 > { rk78_coefficients_a2( void ) { (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 36 ); (*this)[1] = static_cast< Value >( 1 )/static_cast< Value >( 12 ); } }; template< class Value = double > struct rk78_coefficients_a3 : boost::array< Value , 3 > { rk78_coefficients_a3( void ) { (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 24 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 8 ); } }; template< class Value = double > struct rk78_coefficients_a4 : boost::array< Value , 4 > { rk78_coefficients_a4( void ) { (*this)[0] = static_cast< Value >( 5 )/static_cast< Value >( 12 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( -25 )/static_cast< Value >( 16 ); (*this)[3] = static_cast< Value >( 25 )/static_cast< Value >( 16 ); } }; template< class Value = double > struct rk78_coefficients_a5 : boost::array< Value , 5 > { rk78_coefficients_a5( void ) { (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 20 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 1 )/static_cast< Value >( 4 ); (*this)[4] = static_cast< Value >( 1 )/static_cast< Value >( 5 ); } }; template< class Value = double > struct rk78_coefficients_a6 : boost::array< Value , 6 > { rk78_coefficients_a6( void ) { (*this)[0] = static_cast< Value >( -25 )/static_cast< Value >( 108 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 125 )/static_cast< Value >( 108 ); (*this)[4] = static_cast< Value >( -65 )/static_cast< Value >( 27 ); (*this)[5] = static_cast< Value >( 125 )/static_cast< Value >( 54 ); } }; template< class Value = double > struct rk78_coefficients_a7 : boost::array< Value , 7 > { rk78_coefficients_a7( void ) { (*this)[0] = static_cast< Value >( 31 )/static_cast< Value >( 300 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 0 ); (*this)[4] = static_cast< Value >( 61 )/static_cast< Value >( 225 ); (*this)[5] = static_cast< Value >( -2 )/static_cast< Value >( 9 ); (*this)[6] = static_cast< Value >( 13 )/static_cast< Value >( 900 ); } }; template< class Value = double > struct rk78_coefficients_a8 : boost::array< Value , 8 > { rk78_coefficients_a8( void ) { (*this)[0] = static_cast< Value >( 2 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( -53 )/static_cast< Value >( 6 ); (*this)[4] = static_cast< Value >( 704 )/static_cast< Value >( 45 ); (*this)[5] = static_cast< Value >( -107 )/static_cast< Value >( 9 ); (*this)[6] = static_cast< Value >( 67 )/static_cast< Value >( 90 ); (*this)[7] = static_cast< Value >( 3 ); } }; template< class Value = double > struct rk78_coefficients_a9 : boost::array< Value , 9 > { rk78_coefficients_a9( void ) { (*this)[0] = static_cast< Value >( -91 )/static_cast< Value >( 108 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 23 )/static_cast< Value >( 108 ); (*this)[4] = static_cast< Value >( -976 )/static_cast< Value >( 135 ); (*this)[5] = static_cast< Value >( 311 )/static_cast< Value >( 54 ); (*this)[6] = static_cast< Value >( -19 )/static_cast< Value >( 60 ); (*this)[7] = static_cast< Value >( 17 )/static_cast< Value >( 6 ); (*this)[8] = static_cast< Value >( -1 )/static_cast< Value >( 12 ); } }; template< class Value = double > struct rk78_coefficients_a10 : boost::array< Value , 10 > { rk78_coefficients_a10( void ) { (*this)[0] = static_cast< Value >( 2383 )/static_cast< Value >( 4100 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 ); (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 ); (*this)[5] = static_cast< Value >( -301 )/static_cast< Value >( 82 ); (*this)[6] = static_cast< Value >( 2133 )/static_cast< Value >( 4100 ); (*this)[7] = static_cast< Value >( 45 )/static_cast< Value >( 82 ); (*this)[8] = static_cast< Value >( 45 )/static_cast< Value >( 164 ); (*this)[9] = static_cast< Value >( 18 )/static_cast< Value >( 41 ); } }; template< class Value = double > struct rk78_coefficients_a11 : boost::array< Value , 11 > { rk78_coefficients_a11( void ) { (*this)[0] = static_cast< Value >( 3 )/static_cast< Value >( 205 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 0 ); (*this)[4] = static_cast< Value >( 0 ); (*this)[5] = static_cast< Value >( -6 )/static_cast< Value >( 41 ); (*this)[6] = static_cast< Value >( -3 )/static_cast< Value >( 205 ); (*this)[7] = static_cast< Value >( -3 )/static_cast< Value >( 41 ); (*this)[8] = static_cast< Value >( 3 )/static_cast< Value >( 41 ); (*this)[9] = static_cast< Value >( 6 )/static_cast< Value >( 41 ); (*this)[10] = static_cast< Value >( 0 ); } }; template< class Value = double > struct rk78_coefficients_a12 : boost::array< Value , 12 > { rk78_coefficients_a12( void ) { (*this)[0] = static_cast< Value >( -1777 )/static_cast< Value >( 4100 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( -341 )/static_cast< Value >( 164 ); (*this)[4] = static_cast< Value >( 4496 )/static_cast< Value >( 1025 ); (*this)[5] = static_cast< Value >( -289 )/static_cast< Value >( 82 ); (*this)[6] = static_cast< Value >( 2193 )/static_cast< Value >( 4100 ); (*this)[7] = static_cast< Value >( 51 )/static_cast< Value >( 82 ); (*this)[8] = static_cast< Value >( 33 )/static_cast< Value >( 164 ); (*this)[9] = static_cast< Value >( 12 )/static_cast< Value >( 41 ); (*this)[10] = static_cast< Value >( 0 ); (*this)[11] = static_cast< Value >( 1 ); } }; template< class Value = double > struct rk78_coefficients_b : boost::array< Value , 13 > { rk78_coefficients_b( void ) { (*this)[0] = static_cast< Value >( 0 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 0 ); (*this)[4] = static_cast< Value >( 0 ); (*this)[5] = static_cast< Value >( 34 )/static_cast<Value>( 105 ); (*this)[6] = static_cast< Value >( 9 )/static_cast<Value>( 35 ); (*this)[7] = static_cast< Value >( 9 )/static_cast<Value>( 35 ); (*this)[8] = static_cast< Value >( 9 )/static_cast<Value>( 280 ); (*this)[9] = static_cast< Value >( 9 )/static_cast<Value>( 280 ); (*this)[10] = static_cast< Value >( 0 ); (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 ); (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 ); } }; template< class Value = double > struct rk78_coefficients_db : boost::array< Value , 13 > { rk78_coefficients_db( void ) { (*this)[0] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 ); (*this)[1] = static_cast< Value >( 0 ); (*this)[2] = static_cast< Value >( 0 ); (*this)[3] = static_cast< Value >( 0 ); (*this)[4] = static_cast< Value >( 0 ); (*this)[5] = static_cast< Value >( 0 ); (*this)[6] = static_cast< Value >( 0 ); (*this)[7] = static_cast< Value >( 0 ); (*this)[8] = static_cast< Value >( 0 ); (*this)[9] = static_cast< Value >( 0 ); (*this)[10] = static_cast< Value >( 0 ) - static_cast< Value >( 41 )/static_cast<Value>( 840 ); (*this)[11] = static_cast< Value >( 41 )/static_cast<Value>( 840 ); (*this)[12] = static_cast< Value >( 41 )/static_cast<Value>( 840 ); } }; template< class Value = double > struct rk78_coefficients_c : boost::array< Value , 13 > { rk78_coefficients_c( void ) { (*this)[0] = static_cast< Value >( 0 ); (*this)[1] = static_cast< Value >( 2 )/static_cast< Value >( 27 ); (*this)[2] = static_cast< Value >( 1 )/static_cast< Value >( 9 ); (*this)[3] = static_cast< Value >( 1 )/static_cast<Value>( 6 ); (*this)[4] = static_cast< Value >( 5 )/static_cast<Value>( 12 ); (*this)[5] = static_cast< Value >( 1 )/static_cast<Value>( 2 ); (*this)[6] = static_cast< Value >( 5 )/static_cast<Value>( 6 ); (*this)[7] = static_cast< Value >( 1 )/static_cast<Value>( 6 ); (*this)[8] = static_cast< Value >( 2 )/static_cast<Value>( 3 ); (*this)[9] = static_cast< Value >( 1 )/static_cast<Value>( 3 ); (*this)[10] = static_cast< Value >( 1 ); (*this)[11] = static_cast< Value >( 0 ); (*this)[12] = static_cast< Value >( 1 ); } }; #endif // DOXYGEN_SKIP template< class State , class Value = double , class Deriv = State , class Time = Value , class Algebra = typename algebra_dispatcher< State >::algebra_type , class Operations = typename operations_dispatcher< State >::operations_type , class Resizer = initially_resizer > #ifndef DOXYGEN_SKIP class runge_kutta_fehlberg78 : public explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time , Algebra , Operations , Resizer > #else class runge_kutta_fehlberg78 : public explicit_error_generic_rk #endif { public: #ifndef DOXYGEN_SKIP typedef explicit_error_generic_rk< 13 , 8 , 8 , 7 , State , Value , Deriv , Time , Algebra , Operations , Resizer > stepper_base_type; #endif typedef typename stepper_base_type::state_type state_type; typedef typename stepper_base_type::value_type value_type; typedef typename stepper_base_type::deriv_type deriv_type; typedef typename stepper_base_type::time_type time_type; typedef typename stepper_base_type::algebra_type algebra_type; typedef typename stepper_base_type::operations_type operations_type; typedef typename stepper_base_type::resizer_type resizer_type; #ifndef DOXYGEN_SKIP typedef typename stepper_base_type::stepper_type stepper_type; typedef typename stepper_base_type::wrapped_state_type wrapped_state_type; typedef typename stepper_base_type::wrapped_deriv_type wrapped_deriv_type; #endif // DOXYGEN_SKIP runge_kutta_fehlberg78( const algebra_type &algebra = algebra_type() ) : stepper_base_type( boost::fusion::make_vector( rk78_coefficients_a1<Value>() , rk78_coefficients_a2<Value>() , rk78_coefficients_a3<Value>() , rk78_coefficients_a4<Value>() , rk78_coefficients_a5<Value>() , rk78_coefficients_a6<Value>() , rk78_coefficients_a7<Value>() , rk78_coefficients_a8<Value>() , rk78_coefficients_a9<Value>() , rk78_coefficients_a10<Value>() , rk78_coefficients_a11<Value>() , rk78_coefficients_a12<Value>() ) , rk78_coefficients_b<Value>() , rk78_coefficients_db<Value>() , rk78_coefficients_c<Value>() , algebra ) { } }; /************* DOXYGEN *************/ /** * \class runge_kutta_fehlberg78 * \brief The Runge-Kutta Fehlberg 78 method. * * The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications. * The method is explicit and fulfills the Error Stepper concept. Step size control * is provided but continuous output is not available for this method. * * This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). * Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. * For more details see explicit_error_stepper_base and explicit_error_generic_rk. * * \tparam State The state type. * \tparam Value The value type. * \tparam Deriv The type representing the time derivative of the state. * \tparam Time The time representing the independent variable - the time. * \tparam Algebra The algebra type. * \tparam Operations The operations type. * \tparam Resizer The resizer policy type. */ /** * \fn runge_kutta_fehlberg78::runge_kutta_fehlberg78( const algebra_type &algebra ) * \brief Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default * constructor if the algebra has a default constructor. * \param algebra A copy of algebra is made and stored inside explicit_stepper_base. */ } } } #endif //BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_FEHLBERG87_HPP_INCLUDED