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boost::numeric::odeint::explicit_error_stepper_fsal_base — 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.
// In header: <boost/numeric/odeint/stepper/base/explicit_error_stepper_fsal_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_fsal_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_fsal_tag stepper_category; typedef unsigned short order_type; // construct/copy/destruct explicit_error_stepper_fsal_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 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 &); template<typename StateIn> void adjust_size(const StateIn &); 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; 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 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.
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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
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 );
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.
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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 );` The time `t` is not advanced by the stepper. This has to done manually, or by the appropriate `integrate` routines or `iterator`s. |
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_fsal_base
public
construct/copy/destructexplicit_error_stepper_fsal_base(const algebra_type & algebra = algebra_type());Constructs a explicit_stepper_fsal_base class. This constructor can be used as a default constructor if the algebra has a default constructor.
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explicit_error_stepper_fsal_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.
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This method uses the internal state of the stepper. |
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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; }
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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.
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This method does not solve the forwarding problem. |
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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.
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This method uses the internal state of the stepper. This method does not solve the forwarding problem. |
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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.
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This method does not solve the forwarding problem. This method does NOT use the internal state of the stepper. |
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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.
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This method uses the internal state of the stepper. |
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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.
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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.
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This method does NOT use the internal state of the stepper. This method does not solve the forwarding problem. |
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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.
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This method uses the internal state of the stepper. This method does not solve the forwarding problem. |
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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.
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This method does NOT use the internal state of the stepper. This method does not solve the forwarding problem. |
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template<typename StateIn> void adjust_size(const StateIn & x);Adjust the size of all temporaries in the stepper manually.
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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.
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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 );
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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.
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_fsal_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;