boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp
/* [auto_generated] boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp [begin_description] Base class for all explicit first-same-as-last Runge Kutta steppers. [end_description] Copyright 2010-2013 Karsten Ahnert Copyright 2010-2012 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_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED #define BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED #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/state_wrapper.hpp> #include <boost/numeric/odeint/util/is_resizeable.hpp> #include <boost/numeric/odeint/util/resizer.hpp> #include <boost/numeric/odeint/util/copy.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 { /* * base class for explicit stepper and error steppers with the fsal property * models the stepper AND the error stepper fsal concept * * this class provides the following do_step overloads * do_step( sys , x , t , dt ) * do_step( sys , x , dxdt , t , dt ) * do_step( sys , in , t , out , dt ) * do_step( sys , in , dxdt_in , t , out , dxdt_out , dt ) * do_step( sys , x , t , dt , xerr ) * do_step( sys , x , dxdt , t , dt , xerr ) * do_step( sys , in , t , out , dt , xerr ) * do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr ) */ template< class Stepper , unsigned short Order , unsigned short StepperOrder , unsigned short ErrorOrder , class State , class Value , class Deriv , class Time , class Algebra , class Operations , class Resizer > class explicit_error_stepper_fsal_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 State state_type; typedef Value value_type; typedef Deriv deriv_type; typedef Time time_type; typedef Resizer resizer_type; typedef Stepper stepper_type; typedef explicit_error_stepper_fsal_tag stepper_category; #ifndef DOXYGEN_SKIP typedef state_wrapper< state_type > wrapped_state_type; typedef state_wrapper< deriv_type > wrapped_deriv_type; typedef explicit_error_stepper_fsal_base< Stepper , Order , StepperOrder , ErrorOrder , State , Value , Deriv , Time , Algebra , Operations , Resizer > internal_stepper_base_type; #endif typedef unsigned short order_type; static const order_type order_value = Order; static const order_type stepper_order_value = StepperOrder; static const order_type error_order_value = ErrorOrder; explicit_error_stepper_fsal_base( const algebra_type &algebra = algebra_type() ) : algebra_stepper_base_type( algebra ) , m_first_call( true ) { } order_type order( void ) const { return order_value; } order_type stepper_order( void ) const { return stepper_order_value; } order_type error_order( void ) const { return error_order_value; } /* * version 1 : do_step( sys , x , t , dt ) * * the two overloads are needed in order to solve the forwarding problem */ template< class System , class StateInOut > void do_step( System system , StateInOut &x , time_type t , time_type dt ) { do_step_v1( system , x , t , dt ); } /** * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. */ template< class System , class StateInOut > void do_step( System system , const StateInOut &x , time_type t , time_type dt ) { do_step_v1( system , x , t , dt ); } /* * version 2 : do_step( sys , x , dxdt , t , 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 */ template< class System , class StateInOut , class DerivInOut > typename boost::disable_if< boost::is_same< StateInOut , time_type > , void >::type do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt ) { m_first_call = true; this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt ); } /* * named Version 2: do_step_dxdt_impl( sys , in , dxdt , t , dt ) * * this version is needed when this stepper is used for initializing * multistep stepper like adams-bashforth. Hence we provide an explicitely * named version that is not disabled. Meant for internal use only. */ template< class System , class StateInOut , class DerivInOut > void do_step_dxdt_impl( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt ) { m_first_call = true; this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt ); } /* * version 3 : do_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 */ template< class System , class StateIn , class StateOut > typename boost::disable_if< boost::is_same< StateIn , time_type > , void >::type do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt ) { if( m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call ) { initialize( system , in , t ); } this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , m_dxdt.m_v , dt ); } /* * version 4 : do_step( sys , in , dxdt_in , t , out , dxdt_out , dt ) * * this version does not solve the forwarding problem, boost.range can not be used */ template< class System, class StateIn, class DerivIn, class StateOut, class DerivOut > void do_step( System system, const StateIn &in, const DerivIn &dxdt_in, time_type t, StateOut &out, DerivOut &dxdt_out, time_type dt ) { m_first_call = true; this->stepper().do_step_impl( system, in, dxdt_in, t, out, dxdt_out, dt ); } /* * version 5 : do_step( sys , x , t , dt , xerr ) * * the two overloads are needed in order to solve the forwarding problem */ template< class System , class StateInOut , class Err > void do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr ) { do_step_v5( system , x , t , dt , xerr ); } /** * \brief Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut. */ template< class System , class StateInOut , class Err > void do_step( System system , const StateInOut &x , time_type t , time_type dt , Err &xerr ) { do_step_v5( system , x , t , dt , xerr ); } /* * version 6 : do_step( sys , x , dxdt , t , dt , xerr ) * * 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 */ template< class System , class StateInOut , class DerivInOut , class Err > typename boost::disable_if< boost::is_same< StateInOut , time_type > , void >::type do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt , Err &xerr ) { m_first_call = true; this->stepper().do_step_impl( system , x , dxdt , t , x , dxdt , dt , xerr ); } /* * version 7 : do_step( sys , in , t , out , dt , xerr ) * * this version does not solve the forwarding problem, boost.range can not be used */ template< class System , class StateIn , class StateOut , class Err > void do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr ) { if( m_resizer.adjust_size( in , detail::bind( &internal_stepper_base_type::template resize_impl< StateIn > , detail::ref( *this ) , detail::_1 ) ) || m_first_call ) { initialize( system , in , t ); } this->stepper().do_step_impl( system , in , m_dxdt.m_v , t , out , m_dxdt.m_v , dt , xerr ); } /* * version 8 : do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr ) * * this version does not solve the forwarding problem, boost.range can not be used */ template< class System , class StateIn , class DerivIn , class StateOut , class DerivOut , class Err > void do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr ) { m_first_call = true; this->stepper().do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt , xerr ); } template< class StateIn > void adjust_size( const StateIn &x ) { resize_impl( x ); } void reset( void ) { m_first_call = true; } template< class DerivIn > void initialize( const DerivIn &deriv ) { boost::numeric::odeint::copy( deriv , m_dxdt.m_v ); m_first_call = false; } 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; } bool is_initialized( void ) const { return ! m_first_call; } private: template< class System , class StateInOut > void do_step_v1( System system , StateInOut &x , time_type t , time_type dt ) { if( m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call ) { initialize( system , x , t ); } this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , m_dxdt.m_v , dt ); } template< class System , class StateInOut , class Err > void do_step_v5( System system , StateInOut &x , time_type t , time_type dt , Err &xerr ) { if( m_resizer.adjust_size( x , detail::bind( &internal_stepper_base_type::template resize_impl< StateInOut > , detail::ref( *this ) , detail::_1 ) ) || m_first_call ) { initialize( system , x , t ); } this->stepper().do_step_impl( system , x , m_dxdt.m_v , t , x , m_dxdt.m_v , dt , xerr ); } template< class StateIn > bool resize_impl( const StateIn &x ) { return adjust_size_by_resizeability( m_dxdt , x , typename is_resizeable<deriv_type>::type() ); } stepper_type& stepper( void ) { return *static_cast< stepper_type* >( this ); } const stepper_type& stepper( void ) const { return *static_cast< const stepper_type* >( this ); } resizer_type m_resizer; bool m_first_call; protected: wrapped_deriv_type m_dxdt; }; /******* DOXYGEN *******/ /** * \class explicit_error_stepper_fsal_base * \brief Base class for explicit steppers with error estimation and stepper fulfilling the FSAL (first-same-as-last) * property. This class can be used with controlled steppers for step size control. * * This class serves as the base class for all explicit steppers with algebra and operations and which fulfill the FSAL * property. In contrast to explicit_stepper_base it also estimates the error and can be used in a controlled stepper * to provide step size control. * * The FSAL property means that the derivative of the system at t+dt is already used in the current step going from * t to t +dt. Therefore, some more do_steps method can be introduced and the controlled steppers can explicitly make use * of this property. * * \note This stepper provides `do_step` methods with and without error estimation. It has therefore three orders, * one for the order of a step if the error is not estimated. The other two orders are the orders of the step and * the error step if the error estimation is performed. * * explicit_error_stepper_fsal_base is used as the interface in a CRTP (currently recurring template * pattern). In order to work correctly the parent class needs to have a method * `do_step_impl( system , in , dxdt_in , t , out , dxdt_out , dt , xerr )`. * explicit_error_stepper_fsal_base derives from algebra_stepper_base. * * This class can have an intrinsic state depending on the explicit usage of the `do_step` method. This means that some * `do_step` methods are expected to be called in order. For example the `do_step( sys , x , t , dt , xerr )` will keep track * of the derivative of `x` which is the internal state. The first call of this method is recognized such that one * does not explicitly initialize the internal state, so it is safe to use this method like * * \code * stepper_type stepper; * stepper.do_step( sys , x , t , dt , xerr ); * stepper.do_step( sys , x , t , dt , xerr ); * stepper.do_step( sys , x , t , dt , xerr ); * \endcode * * But it is unsafe to call this method with different system functions after each other. Do do so, one must initialize the * internal state with the `initialize` method or reset the internal state with the `reset` method. * * explicit_error_stepper_fsal_base provides several overloaded `do_step` methods, see the list below. Only two of them are needed * to fulfill the Error Stepper concept. The other ones are for convenience and for better performance. Some of them * simply update the state out-of-place, while other expect that the first derivative at `t` is passed to the stepper. * * - `do_step( sys , x , t , dt )` - The classical `do_step` method needed to fulfill the Error Stepper concept. The * state is updated in-place. A type modelling a Boost.Range can be used for x. * - `do_step( sys , x , dxdt , t , dt )` - This method updates the state x and the derivative dxdt in-place. It is expected * that dxdt has the value of the derivative of x at time t. * - `do_step( sys , in , t , out , dt )` - This method updates the state out-of-place, hence the result of the step * is stored in `out`. * - `do_step( sys , in , dxdt_in , t , out , dxdt_out , dt )` - This method updates the state and the derivative * out-of-place. It expects that the derivative at the point `t` is explicitly passed in `dxdt_in`. * - `do_step( sys , x , t , dt , xerr )` - This `do_step` method is needed to fulfill the Error Stepper concept. The * state is updated in-place and an error estimate is calculated. A type modelling a Boost.Range can be used for x. * - `do_step( sys , x , dxdt , t , dt , xerr )` - This method updates the state and the derivative in-place. It is assumed * that the dxdt has the value of the derivative of x at time t. An error estimate is calculated. * - `do_step( sys , in , t , out , dt , xerr )` - This method updates the state out-of-place and estimates the error * during the step. * - `do_step( sys , in , dxdt_in , t , out , dxdt_out , dt , xerr )` - This methods updates the state and the derivative * out-of-place and estimates the error during the step. It is assumed the dxdt_in is derivative of in at time t. * * \note The system is always passed as value, which might result in poor performance if it contains data. In this * case it can be used with `boost::ref` or `std::ref`, for example `stepper.do_step( boost::ref( sys ) , x , t , dt );` * * \note The time `t` is not advanced by the stepper. This has to done manually, or by the appropriate `integrate` * routines or `iterator`s. * * \tparam Stepper The stepper on which this class should work. It is used via CRTP, hence explicit_stepper_base * provides the interface for the Stepper. * \tparam Order The order of a stepper if the stepper is used without error estimation. * \tparam StepperOrder The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have * the same value. * \tparam ErrorOrder The order of the error step if the stepper is used with error estimation. * \tparam State The state type for the stepper. * \tparam Value The value type for the stepper. This should be a floating point type, like float, * double, or a multiprecision type. It must not necessary be the value_type of the State. For example * the State can be a `vector< complex< double > >` in this case the Value must be double. * The default value is double. * \tparam Deriv The type representing time derivatives of the state type. It is usually the same type as the * state type, only if used with Boost.Units both types differ. * \tparam Time The type representing the time. Usually the same type as the value type. When Boost.Units is * used, this type has usually a unit. * \tparam Algebra The algebra type which must fulfill the Algebra Concept. * \tparam Operations The type for the operations which must fulfill the Operations Concept. * \tparam Resizer The resizer policy class. */ /** * \fn explicit_error_stepper_fsal_base::explicit_error_stepper_fsal_base( const algebra_type &algebra ) * \brief Constructs a explicit_stepper_fsal_base 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. */ /** * \fn explicit_error_stepper_fsal_base::order( void ) const * \return Returns the order of the stepper if it used without error estimation. */ /** * \fn explicit_error_stepper_fsal_base::stepper_order( void ) const * \return Returns the order of a step if the stepper is used without error estimation. */ /** * \fn explicit_error_stepper_fsal_base::error_order( void ) const * \return Returns the order of an error step if the stepper is used without error estimation. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , time_type t , time_type dt ) * \brief This method performs one step. It transforms the result in-place. * * \note This method uses the internal state of the stepper. * * \param system The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the * Simple System concept. * \param x The state of the ODE which should be solved. After calling do_step the result is updated in x. * \param t The value of the time, at which the step should be performed. * \param dt The step size. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt ) * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other methods * the derivative of x is also passed to this method. Therefore, dxdt must be evaluated initially: * * \code * ode( x , dxdt , t ); * for( ... ) * { * stepper.do_step( ode , x , dxdt , t , dt ); * t += dt; * } * \endcode * * \note This method does NOT use the initial state, since the first derivative is explicitly passed to this method. * * The result is updated in place in x as well as the derivative dxdt. This method is disabled if * Time and StateInOut are of the same type. In this case the method could not be distinguished from other `do_step` * versions. * * \note This method does not solve the forwarding problem. * * \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. After calling do_step the result is updated in x. * \param dxdt The derivative of x at t. After calling `do_step` dxdt is updated to the new value. * \param t The value of the time, at which the step should be performed. * \param dt The step size. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt ) * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. * This method is disabled if StateIn and Time are the same type. In this case the method can not be distinguished from * other `do_step` variants. * * \note This method uses the internal state of the stepper. * * \note This method does not solve the forwarding problem. * * \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. in is not modified in this method * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dt The step size. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt ) * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. * Furthermore, the derivative of x at t is passed to the stepper and updated by the stepper to its new value at * t+dt. * * \note This method does not solve the forwarding problem. * * \note This method does NOT use the internal state of the stepper. * * \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. in is not modified in this method * \param dxdt_in The derivative of x at t. * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dxdt_out The updated derivative of `out` at `t+dt`. * \param dt The step size. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , time_type t , time_type dt , Err &xerr ) * \brief The method performs one step with the stepper passed by Stepper and estimates the error. The state of the ODE * is updated in-place. * * * \note This method uses the internal state of the stepper. * * \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. x is updated by this method. * \param t The value of the time, at which the step should be performed. * \param dt The step size. * \param xerr The estimation of the error is stored in xerr. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , StateInOut &x , DerivInOut &dxdt , time_type t , time_type dt , Err &xerr ) * \brief The method performs one step with the stepper passed by Stepper. Additionally to the other method * the derivative of x is also passed to this method and updated by this method. * * \note This method does NOT use the internal state of the stepper. * * The result is updated in place in x. This method is disabled if Time and Deriv are of the same type. In this * case the method could not be distinguished from other `do_step` versions. This method is disabled if StateInOut and * Time are of the same type. * * \note This method does NOT use the internal state of the stepper. * * \note This method does not solve the forwarding problem. * * \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. After calling do_step the result is updated in x. * \param dxdt The derivative of x at t. After calling `do_step` this value is updated to the new value at `t+dt`. * \param t The value of the time, at which the step should be performed. * \param dt The step size. * \param xerr The error estimate is stored in xerr. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , time_type t , StateOut &out , time_type dt , Err &xerr ) * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. * Furthermore, the error is estimated. * * \note This method uses the internal state of the stepper. * * \note This method does not solve the forwarding problem. * * \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. in is not modified in this method * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dt The step size. * \param xerr The error estimate. */ /** * \fn explicit_error_stepper_fsal_base::do_step( System system , const StateIn &in , const DerivIn &dxdt_in , time_type t , StateOut &out , DerivOut &dxdt_out , time_type dt , Err &xerr ) * \brief The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place. * Furthermore, the derivative of x at t is passed to the stepper and the error is estimated. * * \note This method does NOT use the internal state of the stepper. * * \note This method does not solve the forwarding problem. * * \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. in is not modified in this method * \param dxdt_in The derivative of x at t. * \param t The value of the time, at which the step should be performed. * \param out The result of the step is written in out. * \param dxdt_out The new derivative at `t+dt` is written into this variable. * \param dt The step size. * \param xerr The error estimate. */ /** * \fn explicit_error_stepper_fsal_base::adjust_size( const StateIn &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. */ /** * \fn explicit_error_stepper_fsal_base::reset( void ) * \brief Resets the internal state of this stepper. After calling this method it is safe to use all * `do_step` method without explicitly initializing the stepper. */ /** * \fn explicit_error_stepper_fsal_base::initialize( const DerivIn &deriv ) * \brief Initializes the internal state of the stepper. * \param deriv The derivative of x. The next call of `do_step` expects that the derivative of `x` passed to `do_step` * has the value of `deriv`. */ /** * \fn explicit_error_stepper_fsal_base::initialize( System system , const StateIn &x , time_type t ) * \brief Initializes the internal state of the stepper. * * This method is equivalent to * \code * Deriv dxdt; * system( x , dxdt , t ); * stepper.initialize( dxdt ); * \endcode * * \param system The system function for the next calls of `do_step`. * \param x The current state of the ODE. * \param t The current time of the ODE. */ /** * \fn explicit_error_stepper_fsal_base::is_initialized( void ) const * \brief Returns if the stepper is already initialized. If the stepper is not initialized, the first * call of `do_step` will initialize the state of the stepper. If the stepper is already initialized * the system function can not be safely exchanged between consecutive `do_step` calls. */ } // odeint } // numeric } // boost #endif // BOOST_NUMERIC_ODEINT_STEPPER_BASE_EXPLICIT_ERROR_STEPPER_FSAL_BASE_HPP_INCLUDED