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diff --git a/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp b/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp new file mode 100644 index 0000000000..a055c7fa5f --- /dev/null +++ b/boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_base.hpp @@ -0,0 +1,659 @@ +/* + [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 ); + } + + + /* + * 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 |