| /* |
| [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 |