| /* |
| [auto_generated] |
| boost/numeric/odeint/stepper/runge_kutta_cash_karp54.hpp |
| |
| [begin_description] |
| Implementation of the Runge Kutta Cash Karp 5(4) method. It uses the generic error stepper. |
| [end_description] |
| |
| Copyright 2011-2013 Mario Mulansky |
| Copyright 2011-2013 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_CASH_KARP54_HPP_INCLUDED |
| #define BOOST_NUMERIC_ODEINT_STEPPER_RUNGE_KUTTA_CASH_KARP54_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/numeric/odeint/util/state_wrapper.hpp> |
| #include <boost/numeric/odeint/util/is_resizeable.hpp> |
| #include <boost/numeric/odeint/util/resizer.hpp> |
| |
| #include <boost/array.hpp> |
| |
| |
| |
| |
| namespace boost { |
| namespace numeric { |
| namespace odeint { |
| |
| |
| #ifndef DOXYGEN_SKIP |
| template< class Value = double > |
| struct rk54_ck_coefficients_a1 : boost::array< Value , 1 > |
| { |
| rk54_ck_coefficients_a1( void ) |
| { |
| (*this)[0] = static_cast< Value >( 1 )/static_cast< Value >( 5 ); |
| } |
| }; |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_a2 : boost::array< Value , 2 > |
| { |
| rk54_ck_coefficients_a2( void ) |
| { |
| (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 40 ); |
| (*this)[1] = static_cast<Value>( 9 )/static_cast<Value>( 40 ); |
| } |
| }; |
| |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_a3 : boost::array< Value , 3 > |
| { |
| rk54_ck_coefficients_a3( void ) |
| { |
| (*this)[0] = static_cast<Value>( 3 )/static_cast<Value>( 10 ); |
| (*this)[1] = static_cast<Value>( -9 )/static_cast<Value>( 10 ); |
| (*this)[2] = static_cast<Value>( 6 )/static_cast<Value>( 5 ); |
| } |
| }; |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_a4 : boost::array< Value , 4 > |
| { |
| rk54_ck_coefficients_a4( void ) |
| { |
| (*this)[0] = static_cast<Value>( -11 )/static_cast<Value>( 54 ); |
| (*this)[1] = static_cast<Value>( 5 )/static_cast<Value>( 2 ); |
| (*this)[2] = static_cast<Value>( -70 )/static_cast<Value>( 27 ); |
| (*this)[3] = static_cast<Value>( 35 )/static_cast<Value>( 27 ); |
| } |
| }; |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_a5 : boost::array< Value , 5 > |
| { |
| rk54_ck_coefficients_a5( void ) |
| { |
| (*this)[0] = static_cast<Value>( 1631 )/static_cast<Value>( 55296 ); |
| (*this)[1] = static_cast<Value>( 175 )/static_cast<Value>( 512 ); |
| (*this)[2] = static_cast<Value>( 575 )/static_cast<Value>( 13824 ); |
| (*this)[3] = static_cast<Value>( 44275 )/static_cast<Value>( 110592 ); |
| (*this)[4] = static_cast<Value>( 253 )/static_cast<Value>( 4096 ); |
| } |
| }; |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_b : boost::array< Value , 6 > |
| { |
| rk54_ck_coefficients_b( void ) |
| { |
| (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 ); |
| (*this)[1] = static_cast<Value>( 0 ); |
| (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 ); |
| (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 ); |
| (*this)[4] = static_cast<Value>( 0 ); |
| (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 ); |
| } |
| }; |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_db : boost::array< Value , 6 > |
| { |
| rk54_ck_coefficients_db( void ) |
| { |
| (*this)[0] = static_cast<Value>( 37 )/static_cast<Value>( 378 ) - static_cast<Value>( 2825 )/static_cast<Value>( 27648 ); |
| (*this)[1] = static_cast<Value>( 0 ); |
| (*this)[2] = static_cast<Value>( 250 )/static_cast<Value>( 621 ) - static_cast<Value>( 18575 )/static_cast<Value>( 48384 ); |
| (*this)[3] = static_cast<Value>( 125 )/static_cast<Value>( 594 ) - static_cast<Value>( 13525 )/static_cast<Value>( 55296 ); |
| (*this)[4] = static_cast<Value>( -277 )/static_cast<Value>( 14336 ); |
| (*this)[5] = static_cast<Value>( 512 )/static_cast<Value>( 1771 ) - static_cast<Value>( 1 )/static_cast<Value>( 4 ); |
| } |
| }; |
| |
| |
| template< class Value = double > |
| struct rk54_ck_coefficients_c : boost::array< Value , 6 > |
| { |
| rk54_ck_coefficients_c( void ) |
| { |
| (*this)[0] = static_cast<Value>(0); |
| (*this)[1] = static_cast<Value>( 1 )/static_cast<Value>( 5 ); |
| (*this)[2] = static_cast<Value>( 3 )/static_cast<Value>( 10 ); |
| (*this)[3] = static_cast<Value>( 3 )/static_cast<Value>( 5 ); |
| (*this)[4] = static_cast<Value>( 1 ); |
| (*this)[5] = static_cast<Value>( 7 )/static_cast<Value>( 8 ); |
| } |
| }; |
| #endif |
| |
| |
| 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_cash_karp54 : public explicit_error_generic_rk< 6 , 5 , 5 , 4 , |
| State , Value , Deriv , Time , Algebra , Operations , Resizer > |
| #else |
| class runge_kutta_cash_karp54 : public explicit_error_generic_rk |
| #endif |
| { |
| |
| public: |
| #ifndef DOXYGEN_SKIP |
| typedef explicit_error_generic_rk< 6 , 5 , 5 , 4 , 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_typ; |
| |
| #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 |
| |
| |
| runge_kutta_cash_karp54( const algebra_type &algebra = algebra_type() ) : stepper_base_type( |
| boost::fusion::make_vector( rk54_ck_coefficients_a1<Value>() , |
| rk54_ck_coefficients_a2<Value>() , |
| rk54_ck_coefficients_a3<Value>() , |
| rk54_ck_coefficients_a4<Value>() , |
| rk54_ck_coefficients_a5<Value>() ) , |
| rk54_ck_coefficients_b<Value>() , rk54_ck_coefficients_db<Value>() , rk54_ck_coefficients_c<Value>() , |
| algebra ) |
| { } |
| }; |
| |
| |
| /********** DOXYGEN **********/ |
| |
| /** |
| * \class runge_kutta_cash_karp54 |
| * \brief The Runge-Kutta Cash-Karp method. |
| * |
| * The Runge-Kutta Cash-Karp method is one of the standard methods for |
| * solving ordinary differential equations, see |
| * <a href="http://en.wikipedia.org/wiki/Cash%E2%80%93Karp_methods">en.wikipedia.org/wiki/Cash-Karp_methods</a>. |
| * 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_cash_karp54::runge_kutta_cash_karp54( const algebra_type &algebra ) |
| * \brief Constructs the runge_kutta_cash_karp54 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_CASH_KARP54_HPP_INCLUDED |