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boost::numeric::odeint::runge_kutta_dopri5 — The Runge-Kutta Dormand-Prince 5 method.
// In header: <boost/numeric/odeint/stepper/runge_kutta_dopri5.hpp> template<typename State, typename Value = double, typename Deriv = State, typename Time = Value, typename Algebra = range_algebra, typename Operations = default_operations, typename Resizer = initially_resizer> class runge_kutta_dopri5 : public boost::numeric::odeint::explicit_error_stepper_fsal_base< Stepper, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer > { public: // types typedef explicit_error_stepper_fsal_base< runge_kutta_dopri5< ... >,... > stepper_base_type; typedef stepper_base_type::state_type state_type; typedef stepper_base_type::value_type value_type; typedef stepper_base_type::deriv_type deriv_type; typedef stepper_base_type::time_type time_type; typedef stepper_base_type::algebra_type algebra_type; typedef stepper_base_type::operations_type operations_type; typedef stepper_base_type::resizer_type resizer_type; // construct/copy/destruct runge_kutta_dopri5(const algebra_type & = algebra_type()); // public member functions template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step_impl(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type); template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename Err> void do_step_impl(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type, Err &); template<typename StateOut, typename StateIn1, typename DerivIn1, typename StateIn2, typename DerivIn2> void calc_state(time_type, StateOut &, const StateIn1 &, const DerivIn1 &, time_type, const StateIn2 &, const DerivIn2 &, time_type) const; template<typename StateIn> void adjust_size(const StateIn &); m_first_call(true); order_type order(void) const; order_type stepper_order(void) const; order_type error_order(void) const; template<typename System, typename StateInOut> void do_step(System, StateInOut &, time_type, time_type); template<typename System, typename StateInOut> void do_step(System, const StateInOut &, time_type, time_type); template<typename System, typename StateInOut, typename DerivInOut> boost::disable_if< boost::is_same< StateInOut, time_type >, void >::type do_step(System, StateInOut &, DerivInOut &, time_type, time_type); template<typename System, typename StateIn, typename StateOut> boost::disable_if< boost::is_same< StateIn, time_type >, void >::type do_step(System, const StateIn &, time_type, StateOut &, time_type); template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type); template<typename System, typename StateInOut, typename Err> void do_step(System, StateInOut &, time_type, time_type, Err &); template<typename System, typename StateInOut, typename Err> void do_step(System, const StateInOut &, time_type, time_type, Err &); template<typename System, typename StateInOut, typename DerivInOut, typename Err> boost::disable_if< boost::is_same< StateInOut, time_type >, void >::type do_step(System, StateInOut &, DerivInOut &, time_type, time_type, Err &); template<typename System, typename StateIn, typename StateOut, typename Err> void do_step(System, const StateIn &, time_type, StateOut &, time_type, Err &); template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename Err> void do_step(System, const StateIn &, const DerivIn &, time_type, StateOut &, DerivOut &, time_type, Err &); void reset(void); template<typename DerivIn> void initialize(const DerivIn &); template<typename System, typename StateIn> void initialize(System, const StateIn &, time_type); bool is_initialized(void) const; const algebra_type & algebra() const; // private member functions template<typename StateIn> bool resize_k_x_tmp_impl(const StateIn &); template<typename StateIn> bool resize_dxdt_tmp_impl(const StateIn &); };
The Runge-Kutta Dormand-Prince 5 method is a very popular method for solving ODEs, see . The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is available which make this method favourable for many applications.
This class derives from explicit_error_stepper_fsal_base and inherits its interface via CRTP (current recurring template pattern). The method possesses the FSAL (first-same-as-last) property. See explicit_error_stepper_fsal_base for more details.
typename State
The state type.
typename Value = double
The value type.
typename Deriv = State
The type representing the time derivative of the state.
typename Time = Value
The time representing the independent variable - the time.
typename Algebra = range_algebra
The algebra type.
typename Operations = default_operations
The operations type.
typename Resizer = initially_resizer
The resizer policy type.
runge_kutta_dopri5
public
construct/copy/destructrunge_kutta_dopri5(const algebra_type & algebra = algebra_type());Constructs the
runge_kutta_dopri5
class. This constructor can be used as a default constructor if the algebra has a default constructor.
Parameters: |
|
runge_kutta_dopri5
public member functionstemplate<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt_in, time_type t, StateOut & out, DerivOut & dxdt_out, time_type dt);This method performs one step. The derivative
dxdt_in
of in
at the time t
is passed to the method. The result is updated out-of-place, hence the input is in in
and the output in out
. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in dxdt_in
and the output in dxdt_out
. Access to this step functionality is provided by explicit_error_stepper_fsal_base
and do_step_impl
should not be called directly.
Parameters: |
|
template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename Err> void do_step_impl(System system, const StateIn & in, const DerivIn & dxdt_in, time_type t, StateOut & out, DerivOut & dxdt_out, time_type dt, Err & xerr);This method performs one step. The derivative
dxdt_in
of in
at the time t
is passed to the method. The result is updated out-of-place, hence the input is in in
and the output in out
. Furthermore, the derivative is update out-of-place, hence the input is assumed to be in dxdt_in
and the output in dxdt_out
. Access to this step functionality is provided by explicit_error_stepper_fsal_base
and do_step_impl
should not be called directly. An estimation of the error is calculated.
Parameters: |
|
template<typename StateOut, typename StateIn1, typename DerivIn1, typename StateIn2, typename DerivIn2> void calc_state(time_type t, StateOut & x, const StateIn1 & x_old, const DerivIn1 & deriv_old, time_type t_old, const StateIn2 &, const DerivIn2 & deriv_new, time_type t_new) const;This method is used for continuous output and it calculates the state
x
at a time t
from the knowledge of two states old_state
and current_state
at time points t_old
and t_new
. It also uses internal variables to calculate the result. Hence this method must be called after two successful do_step
calls. template<typename StateIn> void adjust_size(const StateIn & x);Adjust the size of all temporaries in the stepper manually.
Parameters: |
|
m_first_call(true);
order_type order(void) const;
Returns: |
Returns the order of the stepper if it used without error estimation. |
order_type stepper_order(void) const;
Returns: |
Returns the order of a step if the stepper is used without error estimation. |
order_type error_order(void) const;
Returns: |
Returns the order of an error step if the stepper is used without error estimation. |
template<typename System, typename StateInOut> void do_step(System system, StateInOut & x, time_type t, time_type dt);This method performs one step. It transforms the result in-place.
Note | |
---|---|
This method uses the internal state of the stepper. |
Parameters: |
|
template<typename System, typename StateInOut> void do_step(System system, const StateInOut & x, time_type t, time_type dt);Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
template<typename System, typename StateInOut, typename DerivInOut> 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);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:
* ode( x , dxdt , t ); * for( ... ) * { * stepper.do_step( ode , x , dxdt , t , dt ); * t += dt; * } *
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. |
Parameters: |
|
template<typename System, typename StateIn, typename StateOut> 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);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. This method does not solve the forwarding problem. |
Parameters: |
|
template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut> void do_step(System system, const StateIn & in, const DerivIn & dxdt_in, time_type t, StateOut & out, DerivOut & dxdt_out, time_type dt);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. This method does NOT use the internal state of the stepper. |
Parameters: |
|
template<typename System, typename StateInOut, typename Err> void do_step(System system, StateInOut & x, time_type t, time_type dt, Err & xerr);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. |
Parameters: |
|
template<typename System, typename StateInOut, typename Err> void do_step(System system, const StateInOut & x, time_type t, time_type dt, Err & xerr);Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
template<typename System, typename StateInOut, typename DerivInOut, typename Err> 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);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. This method does not solve the forwarding problem. |
Parameters: |
|
template<typename System, typename StateIn, typename StateOut, typename Err> void do_step(System system, const StateIn & in, time_type t, StateOut & out, time_type dt, Err & xerr);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. This method does not solve the forwarding problem. |
Parameters: |
|
template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename DerivOut, typename 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);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. This method does not solve the forwarding problem. |
Parameters: |
|
void reset(void);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. template<typename DerivIn> void initialize(const DerivIn & deriv);Initializes the internal state of the stepper.
Parameters: |
|
template<typename System, typename StateIn> void initialize(System system, const StateIn & x, time_type t);Initializes the internal state of the stepper.
This method is equivalent to
* Deriv dxdt; * system( x , dxdt , t ); * stepper.initialize( dxdt ); *
Parameters: |
|
bool is_initialized(void) const;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. const algebra_type & algebra() const;
Returns: |
A reference to the algebra which is held by this class. A const reference to the algebra which is held by this class. |