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boost::numeric::odeint::explicit_error_stepper_base — Base class for explicit steppers with error estimation. This class can used with controlled steppers for step size control.
// In header: <boost/numeric/odeint/stepper/base/explicit_error_stepper_base.hpp> template<typename Stepper, unsigned short Order, unsigned short StepperOrder, unsigned short ErrorOrder, typename State, typename Value, typename Deriv, typename Time, typename Algebra, typename Operations, typename Resizer> class explicit_error_stepper_base : public boost::numeric::odeint::algebra_stepper_base< Algebra, Operations > { public: // types typedef algebra_stepper_base< Algebra, Operations > algebra_stepper_base_type; typedef 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_tag stepper_category; typedef unsigned short order_type; // construct/copy/destruct explicit_error_stepper_base(const algebra_type & = algebra_type()); // public member functions 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 DerivIn> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System, StateInOut &, const DerivIn &, 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> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System, const StateIn &, const DerivIn &, time_type, StateOut &, 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 DerivIn, typename Err> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System, StateInOut &, const DerivIn &, 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 Err> void do_step(System, const StateIn &, const DerivIn &, time_type, StateOut &, time_type, Err &); template<typename StateIn> void adjust_size(const StateIn &); algebra_type & algebra(); const algebra_type & algebra() const; // private member functions template<typename System, typename StateInOut> void do_step_v1(System, StateInOut &, time_type, time_type); template<typename System, typename StateInOut, typename Err> void do_step_v5(System, StateInOut &, time_type, time_type, Err &); template<typename StateIn> bool resize_impl(const StateIn &); stepper_type & stepper(void); const stepper_type & stepper(void) const; // public data members static const order_type order_value; static const order_type stepper_order_value; static const order_type error_order_value; };
This class serves as the base class for all explicit steppers with algebra and operations. In contrast to explicit_stepper_base it also estimates the error and can be used in a controlled stepper to provide step size control.
Note | |
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This stepper provides |
explicit_error_stepper_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 , dt , xerr )
. explicit_error_stepper_base derives from algebra_stepper_base.
explicit_error_stepper_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 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 in-place, but the derivative at the point t
must be explicitly passed in dxdt
.
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 , t , out , dt )
- This method update the state out-of-place and expects that the derivative at the point t
is explicitly passed in dxdt
. It is a combination of the two do_step
methods above.
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 in-place, but the derivative at the point t
must be passed in dxdt
. 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 , t , out , dt , xerr )
- This methods updates the state out-of-place and estimates the error during the step. Furthermore, the derivative at t
must be passed in dxdt
.
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 The time |
typename Stepper
The stepper on which this class should work. It is used via CRTP, hence explicit_stepper_base
provides the interface for the Stepper.
unsigned short Order
The order of a stepper if the stepper is used without error estimation.
unsigned short StepperOrder
The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have the same value.
unsigned short ErrorOrder
The order of the error step if the stepper is used with error estimation.
typename State
The state type for the stepper.
typename 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.
typename 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.
typename 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.
typename Algebra
The algebra type which must fulfill the Algebra Concept.
typename Operations
The type for the operations which must fulfill the Operations Concept.
typename Resizer
The resizer policy class.
explicit_error_stepper_base
public
construct/copy/destructexplicit_error_stepper_base(const algebra_type & algebra = algebra_type());Constructs a
explicit_error_stepper_base
class. This constructor can be used as a default constructor if the algebra has a default constructor.
Parameters: |
|
explicit_error_stepper_base
public member functionsorder_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.
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 DerivIn> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System system, StateInOut & x, const DerivIn & dxdt, time_type t, time_type dt);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. It is supposed to be used in the following way:
sys( x , dxdt , t ); stepper.do_step( sys , x , dxdt , t , dt );
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.
Note | |
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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 does not solve the forwarding problem. |
Parameters: |
|
template<typename System, typename StateIn, typename DerivIn, typename StateOut> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System system, const StateIn & in, const DerivIn & dxdt, 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. Furthermore, the derivative of x at t is passed to the stepper. It is supposed to be used in the following way:
sys( in , dxdt , t ); stepper.do_step( sys , in , dxdt , t , out , dt );
This method is disabled if DerivIn and Time are of same type.
Note | |
---|---|
This method does not solve the forwarding problem. |
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.
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 DerivIn, typename Err> boost::disable_if< boost::is_same< DerivIn, time_type >, void >::type do_step(System system, StateInOut & x, const DerivIn & 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. It is supposed to be used in the following way:
sys( x , dxdt , t ); stepper.do_step( sys , x , dxdt , t , dt , xerr );
The result is updated in place in x. This method is disabled if Time and DerivIn 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, 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 does not solve the forwarding problem. |
Parameters: |
|
template<typename System, typename StateIn, typename DerivIn, typename StateOut, typename Err> void do_step(System system, const StateIn & in, const DerivIn & dxdt, 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 derivative of x at t is passed to the stepper and the error is estimated. It is supposed to be used in the following way:
sys( in , dxdt , t ); stepper.do_step( sys , in , dxdt , t , out , dt );
This method is disabled if DerivIn and Time are of same type.
Note | |
---|---|
This method does not solve the forwarding problem. |
Parameters: |
|
template<typename StateIn> void adjust_size(const StateIn & x);Adjust the size of all temporaries in the stepper manually.
Parameters: |
|
algebra_type & algebra();
Returns: |
A reference to the algebra which is held by this class. |
const algebra_type & algebra() const;
Returns: |
A const reference to the algebra which is held by this class. |
explicit_error_stepper_base
private member functionstemplate<typename System, typename StateInOut> void do_step_v1(System system, StateInOut & x, time_type t, time_type dt);
template<typename System, typename StateInOut, typename Err> void do_step_v5(System system, StateInOut & x, time_type t, time_type dt, Err & xerr);
template<typename StateIn> bool resize_impl(const StateIn & x);
stepper_type & stepper(void);
const stepper_type & stepper(void) const;