| /* |
| [auto_generated] |
| boost/numeric/odeint/stepper/base/symplectic_rkn_stepper_base.hpp |
| |
| [begin_description] |
| Base class for symplectic Runge-Kutta-Nystrom steppers. |
| [end_description] |
| |
| Copyright 2011-2013 Karsten Ahnert |
| Copyright 2011-2013 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_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED |
| #define BOOST_NUMERIC_ODEINT_STEPPER_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED |
| |
| #include <boost/array.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/is_pair.hpp> |
| |
| #include <boost/numeric/odeint/util/state_wrapper.hpp> |
| #include <boost/numeric/odeint/util/resizer.hpp> |
| |
| #include <boost/numeric/odeint/stepper/stepper_categories.hpp> |
| |
| #include <boost/numeric/odeint/stepper/base/algebra_stepper_base.hpp> |
| |
| |
| |
| |
| namespace boost { |
| namespace numeric { |
| namespace odeint { |
| |
| |
| template< |
| size_t NumOfStages , |
| unsigned short Order , |
| class Coor , |
| class Momentum , |
| class Value , |
| class CoorDeriv , |
| class MomentumDeriv , |
| class Time , |
| class Algebra , |
| class Operations , |
| class Resizer |
| > |
| class symplectic_nystroem_stepper_base : public algebra_stepper_base< Algebra , Operations > |
| { |
| |
| public: |
| |
| typedef algebra_stepper_base< Algebra , Operations > algebra_stepper_base_type; |
| typedef typename algebra_stepper_base_type::algebra_type algebra_type; |
| typedef typename algebra_stepper_base_type::operations_type operations_type; |
| |
| const static size_t num_of_stages = NumOfStages; |
| typedef Coor coor_type; |
| typedef Momentum momentum_type; |
| typedef std::pair< coor_type , momentum_type > state_type; |
| typedef CoorDeriv coor_deriv_type; |
| typedef state_wrapper< coor_deriv_type> wrapped_coor_deriv_type; |
| typedef MomentumDeriv momentum_deriv_type; |
| typedef state_wrapper< momentum_deriv_type > wrapped_momentum_deriv_type; |
| typedef std::pair< coor_deriv_type , momentum_deriv_type > deriv_type; |
| typedef Value value_type; |
| typedef Time time_type; |
| typedef Resizer resizer_type; |
| typedef stepper_tag stepper_category; |
| |
| #ifndef DOXYGEN_SKIP |
| typedef symplectic_nystroem_stepper_base< NumOfStages , Order , Coor , Momentum , Value , |
| CoorDeriv , MomentumDeriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type; |
| #endif |
| typedef unsigned short order_type; |
| |
| static const order_type order_value = Order; |
| |
| typedef boost::array< value_type , num_of_stages > coef_type; |
| |
| symplectic_nystroem_stepper_base( const coef_type &coef_a , const coef_type &coef_b , const algebra_type &algebra = algebra_type() ) |
| : algebra_stepper_base_type( algebra ) , m_coef_a( coef_a ) , m_coef_b( coef_b ) , |
| m_dqdt_resizer() , m_dpdt_resizer() , m_dqdt() , m_dpdt() |
| { } |
| |
| |
| order_type order( void ) const |
| { |
| return order_value; |
| } |
| |
| /* |
| * Version 1 : do_step( system , x , t , dt ) |
| * |
| * This version does not solve the forwarding problem, boost.range can not be used. |
| */ |
| template< class System , class StateInOut > |
| void do_step( System system , const StateInOut &state , time_type t , time_type dt ) |
| { |
| typedef typename odeint::unwrap_reference< System >::type system_type; |
| do_step_impl( system , state , t , state , dt , typename is_pair< system_type >::type() ); |
| } |
| |
| /** |
| * \brief Same function as above. It differs only in a different const specifier in order |
| * to solve the forwarding problem, can be used with Boost.Range. |
| */ |
| template< class System , class StateInOut > |
| void do_step( System system , StateInOut &state , time_type t , time_type dt ) |
| { |
| typedef typename odeint::unwrap_reference< System >::type system_type; |
| do_step_impl( system , state , t , state , dt , typename is_pair< system_type >::type() ); |
| } |
| |
| |
| |
| |
| /* |
| * Version 2 : do_step( system , q , p , t , dt ); |
| * |
| * For Convenience |
| * |
| * The two overloads are needed in order to solve the forwarding problem. |
| */ |
| template< class System , class CoorInOut , class MomentumInOut > |
| void do_step( System system , CoorInOut &q , MomentumInOut &p , time_type t , time_type dt ) |
| { |
| do_step( system , std::make_pair( detail::ref( q ) , detail::ref( p ) ) , t , dt ); |
| } |
| |
| /** |
| * \brief Same function as do_step( system , q , p , t , dt ). It differs only in a different const specifier in order |
| * to solve the forwarding problem, can be called with Boost.Range. |
| */ |
| template< class System , class CoorInOut , class MomentumInOut > |
| void do_step( System system , const CoorInOut &q , const MomentumInOut &p , time_type t , time_type dt ) |
| { |
| do_step( system , std::make_pair( detail::ref( q ) , detail::ref( p ) ) , t , dt ); |
| } |
| |
| |
| |
| |
| |
| /* |
| * Version 3 : do_step( system , in , t , out , dt ) |
| * |
| * The forwarding problem is not solved in this version |
| */ |
| template< class System , class StateIn , class StateOut > |
| void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt ) |
| { |
| typedef typename odeint::unwrap_reference< System >::type system_type; |
| do_step_impl( system , in , t , out , dt , typename is_pair< system_type >::type() ); |
| } |
| |
| |
| template< class StateType > |
| void adjust_size( const StateType &x ) |
| { |
| resize_dqdt( x ); |
| resize_dpdt( x ); |
| } |
| |
| /** \brief Returns the coefficients a. */ |
| const coef_type& coef_a( void ) const { return m_coef_a; } |
| |
| /** \brief Returns the coefficients b. */ |
| const coef_type& coef_b( void ) const { return m_coef_b; } |
| |
| private: |
| |
| // stepper for systems with function for dq/dt = f(p) and dp/dt = -f(q) |
| template< class System , class StateIn , class StateOut > |
| void do_step_impl( System system , const StateIn &in , time_type /* t */ , StateOut &out , time_type dt , boost::mpl::true_ ) |
| { |
| typedef typename odeint::unwrap_reference< System >::type system_type; |
| typedef typename odeint::unwrap_reference< typename system_type::first_type >::type coor_deriv_func_type; |
| typedef typename odeint::unwrap_reference< typename system_type::second_type >::type momentum_deriv_func_type; |
| system_type &sys = system; |
| coor_deriv_func_type &coor_func = sys.first; |
| momentum_deriv_func_type &momentum_func = sys.second; |
| |
| typedef typename odeint::unwrap_reference< StateIn >::type state_in_type; |
| typedef typename odeint::unwrap_reference< typename state_in_type::first_type >::type coor_in_type; |
| typedef typename odeint::unwrap_reference< typename state_in_type::second_type >::type momentum_in_type; |
| const state_in_type &state_in = in; |
| const coor_in_type &coor_in = state_in.first; |
| const momentum_in_type &momentum_in = state_in.second; |
| |
| typedef typename odeint::unwrap_reference< StateOut >::type state_out_type; |
| typedef typename odeint::unwrap_reference< typename state_out_type::first_type >::type coor_out_type; |
| typedef typename odeint::unwrap_reference< typename state_out_type::second_type >::type momentum_out_type; |
| state_out_type &state_out = out; |
| coor_out_type &coor_out = state_out.first; |
| momentum_out_type &momentum_out = state_out.second; |
| |
| m_dqdt_resizer.adjust_size( coor_in , detail::bind( &internal_stepper_base_type::template resize_dqdt< coor_in_type > , detail::ref( *this ) , detail::_1 ) ); |
| m_dpdt_resizer.adjust_size( momentum_in , detail::bind( &internal_stepper_base_type::template resize_dpdt< momentum_in_type > , detail::ref( *this ) , detail::_1 ) ); |
| |
| // ToDo: check sizes? |
| |
| for( size_t l=0 ; l<num_of_stages ; ++l ) |
| { |
| if( l == 0 ) |
| { |
| coor_func( momentum_in , m_dqdt.m_v ); |
| this->m_algebra.for_each3( coor_out , coor_in , m_dqdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) ); |
| momentum_func( coor_out , m_dpdt.m_v ); |
| this->m_algebra.for_each3( momentum_out , momentum_in , m_dpdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) ); |
| } |
| else |
| { |
| coor_func( momentum_out , m_dqdt.m_v ); |
| this->m_algebra.for_each3( coor_out , coor_out , m_dqdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) ); |
| momentum_func( coor_out , m_dpdt.m_v ); |
| this->m_algebra.for_each3( momentum_out , momentum_out , m_dpdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) ); |
| } |
| } |
| } |
| |
| |
| // stepper for systems with only function dp /dt = -f(q), dq/dt = p, time not required but still expected for compatibility reasons |
| template< class System , class StateIn , class StateOut > |
| void do_step_impl( System system , const StateIn &in , time_type /* t */ , StateOut &out , time_type dt , boost::mpl::false_ ) |
| { |
| typedef typename odeint::unwrap_reference< System >::type momentum_deriv_func_type; |
| momentum_deriv_func_type &momentum_func = system; |
| |
| typedef typename odeint::unwrap_reference< StateIn >::type state_in_type; |
| typedef typename odeint::unwrap_reference< typename state_in_type::first_type >::type coor_in_type; |
| typedef typename odeint::unwrap_reference< typename state_in_type::second_type >::type momentum_in_type; |
| const state_in_type &state_in = in; |
| const coor_in_type &coor_in = state_in.first; |
| const momentum_in_type &momentum_in = state_in.second; |
| |
| typedef typename odeint::unwrap_reference< StateOut >::type state_out_type; |
| typedef typename odeint::unwrap_reference< typename state_out_type::first_type >::type coor_out_type; |
| typedef typename odeint::unwrap_reference< typename state_out_type::second_type >::type momentum_out_type; |
| state_out_type &state_out = out; |
| coor_out_type &coor_out = state_out.first; |
| momentum_out_type &momentum_out = state_out.second; |
| |
| |
| // m_dqdt not required when called with momentum_func only - don't resize |
| // m_dqdt_resizer.adjust_size( coor_in , detail::bind( &internal_stepper_base_type::template resize_dqdt< coor_in_type > , detail::ref( *this ) , detail::_1 ) ); |
| m_dpdt_resizer.adjust_size( momentum_in , detail::bind( &internal_stepper_base_type::template resize_dpdt< momentum_in_type > , detail::ref( *this ) , detail::_1 ) ); |
| |
| |
| // ToDo: check sizes? |
| |
| // step 0 |
| this->m_algebra.for_each3( coor_out , coor_in , momentum_in , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[0] * dt ) ); |
| momentum_func( coor_out , m_dpdt.m_v ); |
| this->m_algebra.for_each3( momentum_out , momentum_in , m_dpdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[0] * dt ) ); |
| |
| for( size_t l=1 ; l<num_of_stages ; ++l ) |
| { |
| this->m_algebra.for_each3( coor_out , coor_out , momentum_out , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_a[l] * dt ) ); |
| momentum_func( coor_out , m_dpdt.m_v ); |
| this->m_algebra.for_each3( momentum_out , momentum_out , m_dpdt.m_v , |
| typename operations_type::template scale_sum2< value_type , time_type >( 1.0 , m_coef_b[l] * dt ) ); |
| } |
| } |
| |
| template< class StateIn > |
| bool resize_dqdt( const StateIn &x ) |
| { |
| return adjust_size_by_resizeability( m_dqdt , x , typename is_resizeable<coor_deriv_type>::type() ); |
| } |
| |
| template< class StateIn > |
| bool resize_dpdt( const StateIn &x ) |
| { |
| return adjust_size_by_resizeability( m_dpdt , x , typename is_resizeable<momentum_deriv_type>::type() ); |
| } |
| |
| |
| const coef_type m_coef_a; |
| const coef_type m_coef_b; |
| |
| resizer_type m_dqdt_resizer; |
| resizer_type m_dpdt_resizer; |
| wrapped_coor_deriv_type m_dqdt; |
| wrapped_momentum_deriv_type m_dpdt; |
| |
| }; |
| |
| /********* DOXYGEN *********/ |
| |
| /** |
| * \class symplectic_nystroem_stepper_base |
| * \brief Base class for all symplectic steppers of Nystroem type. |
| * |
| * This class is the base class for the symplectic Runge-Kutta-Nystroem steppers. Symplectic steppers are usually |
| * used to solve Hamiltonian systems and they conserve the phase space volume, see |
| * <a href="http://en.wikipedia.org/wiki/Symplectic_integrator">en.wikipedia.org/wiki/Symplectic_integrator</a>. |
| * Furthermore, the energy is conserved |
| * in average. In detail this class of steppers can be used to solve separable Hamiltonian systems which can be written |
| * in the form H(q,p) = H1(p) + H2(q). q is usually called the coordinate, while p is the momentum. The equations of motion |
| * are dq/dt = dH1/dp, dp/dt = -dH2/dq. |
| * |
| * ToDo : add formula for solver and explanation of the coefficients |
| * |
| * symplectic_nystroem_stepper_base uses odeints algebra and operation system. Step size and error estimation are not |
| * provided for this class of solvers. It derives from algebra_stepper_base. Several `do_step` variants are provided: |
| * |
| * - `do_step( sys , x , t , dt )` - The classical `do_step` method. The sys can be either a pair of function objects |
| * for the coordinate or the momentum part or one function object for the momentum part. `x` is a pair of coordinate |
| * and momentum. The state is updated in-place. |
| * - `do_step( sys , q , p , t , dt )` - This method is similar to the method above with the difference that the coordinate |
| * and the momentum are passed explicitly and not packed into a pair. |
| * - `do_step( sys , x_in , t , x_out , dt )` - This method transforms the state out-of-place. `x_in` and `x_out` are here pairs |
| * of coordinate and momentum. |
| * |
| * \tparam NumOfStages Number of stages. |
| * \tparam Order The order of the stepper. |
| * \tparam Coor The type representing the coordinates q. |
| * \tparam Momentum The type representing the coordinates p. |
| * \tparam Value The basic value type. Should be something like float, double or a high-precision type. |
| * \tparam CoorDeriv The type representing the time derivative of the coordinate dq/dt. |
| * \tparam MomemtnumDeriv The type representing the time derivative of the momentum dp/dt. |
| * \tparam Time The type representing the time t. |
| * \tparam Algebra The algebra. |
| * \tparam Operations The operations. |
| * \tparam Resizer The resizer policy. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::symplectic_nystroem_stepper_base( const coef_type &coef_a , const coef_type &coef_b , const algebra_type &algebra ) |
| * \brief Constructs a symplectic_nystroem_stepper_base class. The parameters of the specific Nystroem method and the |
| * algebra have to be passed. |
| * \param coef_a The coefficients a. |
| * \param coef_b The coefficients b. |
| * \param algebra A copy of algebra is made and stored inside explicit_stepper_base. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::order( void ) const |
| * \return Returns the order of the stepper. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::do_step( System system , const StateInOut &state , time_type t , time_type dt ) |
| * \brief This method performs one step. The system can be either a pair of two function object |
| * describing the momentum part and the coordinate part or one function object describing only |
| * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state |
| * is updated in-place. |
| * |
| * \note boost::ref or std::ref can be used for the system as well as for the state. So, it is correct |
| * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , make_pair( std::ref( q ) , std::ref( p ) ) , t , dt )`. |
| * |
| * \note This method solves the forwarding problem. |
| * |
| * \param system The system, can be represented as a pair of two function object or one function object. See above. |
| * \param state The state of the ODE. It is a pair of Coor and Momentum. The state is updated in-place, therefore, the |
| * new value of the state will be written into this variable. |
| * \param t The time of the ODE. It is not advanced by this method. |
| * \param dt The time step. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::do_step( System system , CoorInOut &q , MomentumInOut &p , time_type t , time_type dt ) |
| * \brief This method performs one step. The system can be either a pair of two function object |
| * describing the momentum part and the coordinate part or one function object describing only |
| * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state |
| * is updated in-place. |
| * |
| * \note boost::ref or std::ref can be used for the system. So, it is correct |
| * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , q , p , t , dt )`. |
| * |
| * \note This method solves the forwarding problem. |
| * |
| * \param system The system, can be represented as a pair of two function object or one function object. See above. |
| * \param q The coordinate of the ODE. It is updated in-place. Therefore, the new value of the coordinate will be written |
| * into this variable. |
| * \param p The momentum of the ODE. It is updated in-place. Therefore, the new value of the momentum will be written info |
| * this variable. |
| * \param t The time of the ODE. It is not advanced by this method. |
| * \param dt The time step. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt ) |
| * \brief This method performs one step. The system can be either a pair of two function object |
| * describing the momentum part and the coordinate part or one function object describing only |
| * the momentum part. In this case the coordinate is assumed to be trivial dq/dt = p. The state |
| * is updated out-of-place. |
| * |
| * \note boost::ref or std::ref can be used for the system. So, it is correct |
| * to write `stepper.do_step( make_pair( std::ref( fq ) , std::ref( fp ) ) , x_in , t , x_out , dt )`. |
| * |
| * \note This method NOT solve the forwarding problem. |
| * |
| * \param system The system, can be represented as a pair of two function object or one function object. See above. |
| * \param in The state of the ODE, which is a pair of coordinate and momentum. The state is updated out-of-place, therefore the |
| * new value is written into out |
| * \param t The time of the ODE. It is not advanced by this method. |
| * \param out The new state of the ODE. |
| * \param dt The time step. |
| */ |
| |
| /** |
| * \fn symplectic_nystroem_stepper_base::adjust_size( const StateType &x ) |
| * \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. |
| */ |
| |
| } // namespace odeint |
| } // namespace numeric |
| } // namespace boost |
| |
| |
| #endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_SYMPLECTIC_RKN_STEPPER_BASE_HPP_INCLUDED |