# odeint Reference

Adapter to combine observer and checker.
Observer
Checker
observer_type &
checker_type &
void `const State &` `Time`
typename base_tag<typename Stepper::stepper_category>::type
ControlledStepper
Checker
controlled_stepper_tag
Adapter to combine controlled stepper and checker.
ControlledStepper
Checker
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type &
checker_type &
Construct the checked_stepper.
controlled_step_result `System` `StateInOut &` `time_type &` `time_type &` forward of the do_step method
DenseOutStepper
Checker
dense_output_stepper_tag
Adapter to combine dense out stepper and checker.
DenseOutStepper
Checker
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type &
checker_type &
Construct the checked_stepper.
std::pair< time_type, time_type > `System`
void `const StateType &` `time_type` `time_type`
void `time_type` `StateOut &`
void `time_type` `const StateOut &`
const state_type & `void`
time_type `void`
const state_type & `void`
time_type `void`
time_type `void`
Stepper
Checker
stepper_tag
Adapter to combine basic stepper and checker.
Stepper
Checker
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type &
checker_type &
Construct the checked_stepper.
void `System` `StateInOut &` `const time_type` `const time_type` forward of the do_step method
boost::enable_if< typenamehas_value_type< State >::type, size_t >::type `System

The system function to solve, hence the r.h.s. of the ordinary differential equation.

` `State &

The initial state.

` `Time

Start time of the integration.

` `Time

End time of the integration.

` `Time

Initial step size, will be adjusted during the integration.

` `Observer

Observer that will be called after each time step.

` Integrates the ODE.

Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. After each step, the observer is called.

A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt , obs );

The number of steps performed.

size_t `System` `State &` `Time` `Time` `Time` `Observer`
size_t `System

The system function to solve, hence the r.h.s. of the ordinary differential equation.

` `State &

The initial state.

` `Time

Start time of the integration.

` `Time

End time of the integration.

` `Time

Initial step size, will be adjusted during the integration.

` Integrates the ODE without observer calls.

Integrates the ODE given by system from start_time to end_time starting with start_state as initial condition and dt as initial time step. This function uses a dense output dopri5 stepper and performs an adaptive integration with step size control, thus dt changes during the integration. This method uses standard error bounds of 1E-6. No observer is called.

A second version of this function template exists which explicitly expects the value type as template parameter, i.e. integrate< double >( sys , x , t0 , t1 , dt );

The number of steps performed.

size_t `System` `State &` `Time` `Time` `Time`
size_t `Stepper

The stepper to be used for numerical integration.

` `System

Function/Functor defining the rhs of the ODE.

` `State &

The initial condition x0.

` `Time

The initial time t0.

` `Time

The final integration time tend.

` `Time

The time step between observer calls, not necessarily the time step of the integration.

` `Observer

Function/Functor called at equidistant time intervals.

` Integrates the ODE with adaptive step size.

This function integrates the ODE given by system with the given stepper. The observer is called after each step. If the stepper has no error control, the step size remains constant and the observer is called at equidistant time points t0+n*dt. If the stepper is a ControlledStepper, the step size is adjusted and the observer is called in non-equidistant intervals.

The number of steps performed.

size_t `Stepper` `System` `const State &` `Time` `Time` `Time` `Observer` Second version to solve the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `Time` `Time` `Time` integrate_adaptive without an observer.
size_t `Stepper` `System` `const State &` `Time` `Time` `Time` Second version to solve the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper

The stepper to be used for numerical integration.

` `System

Function/Functor defining the rhs of the ODE.

` `State &

The initial condition x0.

` `Time

The initial time t0.

` `Time

The final integration time tend.

` `Time

The time step between observer calls, not necessarily the time step of the integration.

` `Observer

[optional] Function/Functor called at equidistant time intervals.

` `StepOverflowChecker

[optional] Functor to check for step count overflows, if no checker is provided, no exception is thrown.

` Integrates the ODE with constant step size.

Integrates the ODE defined by system using the given stepper. This method ensures that the observer is called at constant intervals dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. If a max_step_checker is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.

The number of steps performed.

size_t `Stepper` `System` `const State &` `Time` `Time` `Time` `Observer` `StepOverflowChecker` Second version to solve the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `Time` `Time` `Time` `Observer` integrate_const without step overflow checker
size_t `Stepper` `System` `const State &` `Time` `Time` `Time` `Observer` Second version to solve the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `Time` `Time` `Time` integrate_const without observer calls
size_t `Stepper` `System` `const State &` `Time` `Time` `Time` Second version to solve the forwarding problem, can be called with Boost.Range as start_state.
Time `Stepper` `System` `State &` `Time` `Time` `size_t` `Observer` `StepOverflowChecker`
Time `Stepper` `System` `const State &` `Time` `Time` `size_t` `Observer` `StepOverflowChecker` Solves the forwarding problem, can be called with Boost.Range as start_state.
Time `Stepper

The stepper to be used for numerical integration.

` `System

Function/Functor defining the rhs of the ODE.

` `State &

The initial condition x0.

` `Time

The initial time t0.

` `Time

The time step between observer calls, not necessarily the time step of the integration.

` `size_t

Number of steps to be performed

` `Observer

Function/Functor called at equidistant time intervals.

` The same function as above, but without checker.

Integrates the ODE with constant step size.

This function is similar to integrate_const. The observer is called at equidistant time intervals t0 + n*dt. If the Stepper is a normal stepper without step size control, dt is also used for the numerical scheme. If a ControlledStepper is provided, the algorithm might reduce the step size to meet the error bounds, but it is ensured that the observer is always called at equidistant time points t0 + n*dt. If a DenseOutputStepper is used, the step size also may vary and the dense output is used to call the observer at equidistant time points. The final integration time is always t0 + num_of_steps*dt. If a max_step_checker is provided as StepOverflowChecker, a no_progress_errror is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.

The number of steps performed.

Time `Stepper` `System` `const State &` `Time` `Time` `size_t` `Observer` Solves the forwarding problem, can be called with Boost.Range as start_state.
Time `Stepper` `System` `State &` `Time` `Time` `size_t` The same function as above, but without observer calls.
Time `Stepper` `System` `const State &` `Time` `Time` `size_t` Solves the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `TimeIterator` `TimeIterator` `Time` `Observer` `StepOverflowChecker`
size_t `Stepper` `System` `const State &` `TimeIterator` `TimeIterator` `Time` `Observer` `StepOverflowChecker` Solves the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `const TimeRange &` `Time` `Observer` `StepOverflowChecker` The same function as above, but with the observation times given as range.
size_t `Stepper` `System` `const State &` `const TimeRange &` `Time` `Observer` `StepOverflowChecker` Solves the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper

The stepper to be used for numerical integration.

` `System

Function/Functor defining the rhs of the ODE.

` `State &

The initial condition x0.

` `TimeIterator

Iterator to the start time

` `TimeIterator

Iterator to the end time

` `Time

The time step between observer calls, not necessarily the time step of the integration.

` `Observer

Function/Functor called at equidistant time intervals.

` Integrates the ODE with observer calls at given time points.

Integrates the ODE given by system using the given stepper. This function does observer calls at the subsequent time points given by the range times_start, times_end. If the stepper has not step size control, the step size might be reduced occasionally to ensure observer calls exactly at the time points from the given sequence. If the stepper is a ControlledStepper, the step size is adjusted to meet the error bounds, but also might be reduced occasionally to ensure correct observer calls. If a DenseOutputStepper is provided, the dense output functionality is used to call the observer at the given times. The end time of the integration is always *(end_time-1). If a max_step_checker is provided as StepOverflowChecker, a no_progress_error is thrown if too many steps (default: 500) are performed without progress, i.e. in between observer calls. If no checker is provided, no such overflow check is performed.

The number of steps performed.

size_t `Stepper` `System` `const State &` `TimeIterator` `TimeIterator` `Time` `Observer` Solves the forwarding problem, can be called with Boost.Range as start_state.
size_t `Stepper` `System` `State &` `const TimeRange &` `Time` `Observer` The same function as above, but with the observation times given as range.
size_t `Stepper` `System` `const State &` `const TimeRange &` `Time` `Observer` Solves the forwarding problem, can be called with Boost.Range as start_state.
boost::numeric::odeint::max_step_checker
A class for performing overflow checks on the failed step count in step size adjustments.

Used internally within the dense output stepper and integrate routines.

const int
500
Construct the failed_step_checker. max_steps is the maximal number of iterations allowed before runtime_error is thrown.
void `void` Increases the counter and performs the iteration check.
void Resets the max_step_checker by setting the internal counter to 0.
A class for performing overflow checks on the step count in integrate functions.

Provide an instance of this class to integrate functions if you want to throw a runtime error if too many steps are performed without progress during the integrate routine.

const int
500
Construct the max_step_checker. max_steps is the maximal number of iterations allowed before runtime_error is thrown.
void Resets the max_step_checker by setting the internal counter to 0.
void `void` Increases the counter and performs the iteration check.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with adaptive step size. The value type of this iterator is the state type of the stepper.

Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.

adaptive_iterator is a model of single-pass iterator.

The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.

Stepper
System
State &
time_type
time_type
time_type
Stepper
System
State &
`adaptive_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for adaptive_iterator. Constructs a begin iterator.

The adaptive iterator.

`adaptive_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state.

` Factory function for adaptive_iterator. Constructs a end iterator.

The adaptive iterator.

std::pair< `adaptive_iterator`< Stepper, System, State >, `adaptive_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of adaptive iterators. A range is here a pair of adaptive_iterator.

The adaptive range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with adaptive step size. The value type of this iterator is a std::pair containing state and time.

Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with an adaptive step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt where dt is controlled by the stepper. This iterator can be used with ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_adaptive routine.

adaptive_iterator is a model of single-pass iterator.

The value type of this iterator is a std::pair of state and time of the stepper.

Stepper
System
State &
time_type
time_type
time_type
Stepper
System
State &
`adaptive_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for adaptive_time_iterator. Constructs a begin iterator.

The adaptive time iterator.

`adaptive_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.

` Factory function for adaptive_time_iterator. Constructs a end iterator.

The adaptive time iterator.

std::pair< `adaptive_time_iterator`< Stepper, System, State >, `adaptive_time_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. adaptive_time_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of adaptive time iterators. A range is here a pair of adaptive_time_iterators.

The adaptive time range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.

Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.

const_step_iterator is a model of single-pass iterator.

The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.

Stepper
System
State &
time_type
time_type
time_type
Stepper
System
State &
`const_step_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for const_step_iterator. Constructs a begin iterator.

The const step iterator.

`const_step_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` Factory function for const_step_iterator. Constructs a end iterator.

The const_step_iterator.

std::pair< `const_step_iterator`< Stepper, System, State >, `const_step_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator store a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of const step iterators. A range is here a pair of const_step_iterator.

The const step range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time.

Implements an iterator representing the solution of an ODE from t_start to t_end evaluated at steps with constant step size dt. After each iteration the iterator dereferences to a pair containing state and time at the next time point t+dt.. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_const routine.

const_step_time_iterator is a model of single-pass iterator.

The value type of this iterator is a pair with the state type and time type of the stepper.

Stepper
System
State &
time_type
time_type
time_type
Stepper
System
State &
`const_step_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for const_step_time_iterator. Constructs a begin iterator.

The const step time iterator.

`const_step_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_time_iterator store a reference of s and changes its value during the iteration.

` Factory function for const_step_time_iterator. Constructs a end iterator.

The const step time iterator.

std::pair< `const_step_time_iterator`< Stepper, System, State >, `const_step_time_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_time_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type` `typename traits::time_type< Stepper >::type

The end time, at which the iteration should stop.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of const_step_time_iterator. A range is here a pair of const_step_time_iterator.

The const step time range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with constant step size. The value type of this iterator is the state type of the stepper.

Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to the state x at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.

n_step_iterator is a model of single-pass iterator.

The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.

Stepper
System
State &
time_type
time_type
size_t
Stepper
System
State &
`n_step_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The initial time step.

` `size_t

The number of steps to be executed.

` Factory function for n_step_iterator. Constructs a begin iterator.

The n-step iterator.

`n_step_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` Factory function for n_step_iterator. Constructs an end iterator.

The const_step_iterator.

std::pair< `n_step_iterator`< Stepper, System, State >, `n_step_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator store a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The initial time step.

` `size_t

The number of steps to be executed.

` Factory function to construct a single pass range of n-step iterators. A range is here a pair of n_step_iterator.

The n-step range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

ODE Iterator with constant step size. The value type of this iterator is a std::pair containing state and time.

Implements an iterator representing the solution of an ODE starting from t with n steps and a constant step size dt. After each iteration the iterator dereferences to a pair of state and time at the next time t+dt. This iterator can be used with Steppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_n_steps routine.

n_step_time_iterator is a model of single-pass iterator.

The value type of this iterator is pair of state and time.

Stepper
System
State &
time_type
time_type
size_t
Stepper
System
State &
`n_step_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The initial time step.

` `size_t

The number of steps to be executed.

` Factory function for n_step_time_iterator. Constructs a begin iterator.

The n-step iterator.

`n_step_time_iterator`< Stepper, System, State > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` Factory function for n_step_time_iterator. Constructs an end iterator.

The const_step_iterator.

std::pair< `n_step_time_iterator`< Stepper, System, State >, `n_step_time_iterator`< Stepper, System, State > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator store a reference of s and changes its value during the iteration.

` `typename traits::time_type< Stepper >::type

The initial time.

` `typename traits::time_type< Stepper >::type

The initial time step.

` `size_t

The number of steps to be executed.

` Factory function to construct a single pass range of n-step iterators. A range is here a pair of n_step_time_iterator.

The n-step range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

The iterator type for the sequence of time points.

ODE Iterator with given evaluation points. The value type of this iterator is the state type of the stepper.

Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to the state x at the next time *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.

times_iterator is a model of single-pass iterator.

The value type of this iterator is the state type of the stepper. Hence one can only access the state and not the current time.

Stepper
System
State &
TimeIterator
TimeIterator
time_type
Stepper
System
State &
`times_iterator`< Stepper, System, State, TimeIterator > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` `TimeIterator

Begin iterator of the sequence of evaluation time points.

` `TimeIterator

End iterator of the sequence of evaluation time points.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for times_iterator. Constructs a begin iterator.

The times iterator.

`times_iterator`< Stepper, System, State, TimeIterator > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` Factory function for times_iterator. Constructs an end iterator.

This function needs the TimeIterator type specifically defined as a template parameter.

The times iterator.

std::pair< `times_iterator`< Stepper, System, State, TimeIterator >, `times_iterator`< Stepper, System, State, TimeIterator > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator store a reference of s and changes its value during the iteration.

` `TimeIterator

Begin iterator of the sequence of evaluation time points.

` `TimeIterator

End iterator of the sequence of evaluation time points.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of times iterators. A range is here a pair of times_iterator.

The times iterator range.

The stepper type which should be used during the iteration.

The type of the system function (ODE) which should be solved.

The state type of the ODE.

The iterator type for the sequence of time points.

ODE Iterator with given evaluation points. The value type of this iterator is a std::pair containing state and time.

Implements an iterator representing the solution of an ODE from *t_start to *t_end evaluated at time points given by the sequence t_start to t_end. t_start and t_end are iterators representing a sequence of time points where the solution of the ODE should be evaluated. After each iteration the iterator dereferences to a pair with the state and the time at the next evaluation point *t_start++ until t_end is reached. This iterator can be used with Steppers, ControlledSteppers and DenseOutputSteppers and it always makes use of the all the given steppers capabilities. A for_each over such an iterator range behaves similar to the integrate_times routine.

times_time_iterator is a model of single-pass iterator.

The value type of this iterator is a pair of state and time type.

Stepper
System
State &
TimeIterator
TimeIterator
time_type
Stepper
System
State &
`times_time_iterator`< Stepper, System, State, TimeIterator > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` `TimeIterator

Begin iterator of the sequence of evaluation time points.

` `TimeIterator

End iterator of the sequence of evaluation time points.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function for times_time_iterator. Constructs a begin iterator.

The times_time iterator.

`times_time_iterator`< Stepper, System, State, TimeIterator > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator stores a reference of s and changes its value during the iteration.

` Factory function for times_time_iterator. Constructs an end iterator.

This function needs the TimeIterator type specifically defined as a template parameter.

The times_time iterator.

std::pair< `times_time_iterator`< Stepper, System, State, TimeIterator >, `times_time_iterator`< Stepper, System, State, TimeIterator > > `Stepper

The stepper to use during the iteration.

` `System

The system function (ODE) to solve.

` `State &

The initial state. const_step_iterator store a reference of s and changes its value during the iteration.

` `TimeIterator

Begin iterator of the sequence of evaluation time points.

` `TimeIterator

End iterator of the sequence of evaluation time points.

` `typename traits::time_type< Stepper >::type

The initial time step.

` Factory function to construct a single pass range of times_time iterators. A range is here a pair of times_iterator.

The times_time iterator range.

size_t

The number of steps (maximal 8).

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

extrapolation_stepper< order_helper<Steps>::value, State, Value, Deriv, Time, Algebra, Operations, Resizer >

The stepper for the first two steps.

algebra_stepper_base< typename algebra_dispatcher< State >::algebra_type, typename operations_dispatcher< State >::operations_type >
The Adams-Bashforth multistep algorithm.

The Adams-Bashforth method is a multi-step algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also en.wikipedia.org/wiki/Linear_multistep_method. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.

This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base.

State
state_wrapper< state_type >
Value
Deriv
state_wrapper< deriv_type >
Time
Resizer
stepper_tag
InitializingStepper
algebra_stepper_base< Algebra, Operations >
algebra_stepper_base_type::algebra_type
algebra_stepper_base_type::operations_type
unsigned short
unspecified
const size_t
const order_type
order_type `void` Returns the order of the algorithm, which is equal to the number of steps.

order of the method.

const algebra_type &
algebra_type()

A copy of algebra is made and stored.

Constructs the adams_bashforth class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. After calling do_step the result is updated in x.

` `time_type

The value of the time, at which the step should be performed.

` `time_type

The step size.

` This method performs one step. It transforms the result in-place.

void `System` `const StateInOut &` `time_type` `time_type` Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.

void `System` `const StateIn &` `time_type` `const StateOut &` `time_type` Second version to solve the forwarding problem, can be called with Boost.Range as StateOut.
void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

const step_storage_type & `void` Returns the storage of intermediate results.

The storage of intermediate results.

step_storage_type & `void` Returns the storage of intermediate results.

The storage of intermediate results.

void `ExplicitStepper

the stepper used to fill the buffer of previous step results

` `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateIn &

The state of the ODE which should be solved. After calling do_step the result is updated in x.

` `time_type &

The value of the time, at which the step should be performed.

` `time_type

The step size.

` Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer.

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateIn &

The initial state of the ODE which should be solved, updated in this method.

` `time_type &

The initial value of the time, updated in this method.

` `time_type

The step size.

` Initialized the stepper. Does Steps-1 steps with an internal instance of InitializingStepper to fill the buffer.

The state x and time t are updated to the values after Steps-1 initial steps.

void `void` Resets the internal buffer of the stepper.
bool `void` Returns true if the stepper has been initialized.

bool true if stepper is initialized, false otherwise

const initializing_stepper_type & `void` Returns the internal initializing stepper instance.

initializing_stepper

initializing_stepper_type & `void` Returns the internal initializing stepper instance.

initializing_stepper

void `System` `const StateIn &` `time_type` `StateOut &` `time_type`
bool `const StateIn &`
int
mpl::max::type
size_t

The number of steps (maximal 8).

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

runge_kutta4< State , Value , Deriv , Time , Algebra , Operations, Resizer >

The stepper for the first two steps.

The Adams-Bashforth-Moulton multistep algorithm.

The Adams-Bashforth method is a multi-step predictor-corrector algorithm with configurable step number. The step number is specified as template parameter Steps and it then uses the result from the previous Steps steps. See also en.wikipedia.org/wiki/Linear_multistep_method. Currently, a maximum of Steps=8 is supported. The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.

This class derives from algebra_base and inherits its interface via CRTP (current recurring template pattern). For more details see algebra_stepper_base.

State
state_wrapper< state_type >
Value
Deriv
state_wrapper< deriv_type >
Time
Algebra
Operations
Resizer
stepper_tag
InitializingStepper
unsigned short
const size_t
const order_type
void
Constructs the adams_bashforth class.
const algebra_type &

A copy of algebra is made and stored.

Constructs the adams_bashforth class. This constructor can be used as a default constructor if the algebra has a default constructor.

order_type `void` Returns the order of the algorithm, which is equal to the number of steps+1.

order of the method.

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. After calling do_step the result is updated in x.

` `time_type

The value of the time, at which the step should be performed.

` `time_type

The step size.

` This method performs one step. It transforms the result in-place.

void `System` `const StateInOut &` `time_type` `time_type` Second version to solve the forwarding problem, can be called with Boost.Range as StateInOut.
void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `time_type

The value of the time, at which the step should be performed.

` `const StateOut &

The result of the step is written in out.

` `time_type

The step size.

` The method performs one step with the stepper passed by Stepper. The state of the ODE is updated out-of-place.

void `System` `const StateIn &` `time_type` `StateOut &` `time_type` Second version to solve the forwarding problem, can be called with Boost.Range as StateOut.
void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

void `ExplicitStepper

the stepper used to fill the buffer of previous step results

` `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateIn &

The initial state of the ODE which should be solved, updated after in this method.

` `time_type &

The initial time, updated in this method.

` `time_type

The step size.

` Initialized the stepper. Does Steps-1 steps with the explicit_stepper to fill the buffer.

The state x and time t are updated to the values after Steps-1 initial steps.

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` `StateIn &

The state of the ODE which should be solved. After calling do_step the result is updated in x.

` `time_type &

The value of the time, at which the step should be performed.

` `time_type

The step size.

` Initialized the stepper. Does Steps-1 steps using the standard initializing stepper of the underlying adams_bashforth stepper.

void `void` Resets the internal buffers of the stepper.
void `System` `StateInOut &` `time_type` `time_type`
void `System` `StateIn const &` `time_type` `StateInOut &` `time_type`
bool `const StateIn &`
size_t
double
State
Value
typename algebra_dispatcher< State >::algebra_type
typename operations_dispatcher< State >::operations_type
initially_resizer
State
state_wrapper< state_type >
Value
Deriv
state_wrapper< deriv_type >
Time
Algebra
Operations
Resizer
stepper_tag
adams_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer >
unsigned short
unspecified
const size_t
const order_type
algebra_type &
adams_moulton & `const adams_moulton &`
order_type `void`
void `System` `StateInOut &` `StateIn const &` `time_type` `time_type` `const ABBuf &`
void `System` `const StateInOut &` `StateIn const &` `time_type` `time_type` `const ABBuf &`
void `System` `const StateIn &` `const PredIn &` `time_type` `StateOut &` `time_type` `const ABBuf &`
void `System` `const StateIn &` `const PredIn &` `time_type` `const StateOut &` `time_type` `const ABBuf &`
void `const StateType &`
algebra_type &
const algebra_type &
void `System` `const StateIn &` `const PredIn &` `time_type` `StateOut &` `time_type` `const ABBuf &`
bool `const StateIn &`
size_t
double
State
Value
typename algebra_dispatcher< State >::algebra_type
typename operations_dispatcher< State >::operations_type
initially_resizer
algebra_stepper_base< typename algebra_dispatcher< State >::algebra_type, typename operations_dispatcher< State >::operations_type >
unsigned short
State
Value
Deriv
Time
state_wrapper< state_type >
state_wrapper< deriv_type >
algebra_stepper_base< Algebra, Operations >
algebra_stepper_base_type::algebra_type
algebra_stepper_base_type::operations_type
Resizer
error_stepper_tag
unspecified
adaptive_adams_bashforth_moulton< Steps, State, Value, Deriv, Time, Algebra, Operations, Resizer >
const size_t
const order_type
order_type
order_type
order_type
const algebra_type &
algebra_type()
void `System` `state_type &` `time_type` `time_type`
void `System` `const state_type &` `time_type` `state_type &` `time_type`
void `System` `state_type &` `time_type` `time_type` `state_type &`
void `System` `const state_type &` `time_type` `state_type &` `time_type` `state_type &`
void `ExplicitStepper` `System` `state_type &` `time_type &` `time_type`
void `System` `state_type &` `time_type &` `time_type`
void `System` `const state_type &` `time_type` `state_type &` `time_type &` `state_type &`
const coeff_type &
coeff_type &
void
const deriv_type &
bool `const StateType &`
bool `const StateType &`
bool `const StateType &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

The Bulirsch-Stoer algorithm.

The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution.

State
Value
Deriv
Time
Algebra
Operations
Resizer
const size_t
value_type
1E-6

Absolute tolerance level.

value_type
1E-6

Relative tolerance level.

value_type
1.0

Factor for the weight of the state.

value_type
1.0

Factor for the weight of the derivative.

time_type
static_cast< time_type >(0)
Constructs the bulirsch_stoer class, including initialization of the error bounds.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

success if the step was accepted, fail otherwise.

controlled_step_result `System` `const StateInOut &` `time_type &` `time_type &` Second version to solve the forwarding problem, can be used with Boost.Range as StateInOut.
controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `const DerivIn &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

success if the step was accepted, fail otherwise.

boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method is disabled if state_type=time_type to avoid ambiguity.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `const DerivIn &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

success if the step was accepted, fail otherwise.

void Resets the internal state of the stepper.
void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`
bool `const StateIn &`
bool `const StateIn &`
controlled_step_result `System` `StateInOut &` `time_type &` `time_type &`
void `size_t` `state_table_type &` `const value_matrix &` `StateInOut &`
time_type `time_type` `value_type` `size_t`
controlled_step_result `size_t` `const inv_time_vector &` `const time_vector &` `time_type &`
bool `size_t`
bool `value_type` `size_t`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

The Bulirsch-Stoer algorithm.

The Bulirsch-Stoer is a controlled stepper that adjusts both step size and order of the method. The algorithm uses the modified midpoint and a polynomial extrapolation compute the solution. This class also provides dense output facility.

State
Value
Deriv
Time
Algebra
Operations
Resizer
dense_output_stepper_tag
const size_t
value_type
1E-6

Absolute tolerance level.

value_type
1E-6

Relative tolerance level.

value_type
1.0

Factor for the weight of the state.

value_type
1.0

Factor for the weight of the derivative.

time_type
static_cast< time_type >(0)
bool
false

Set true to additionally control the error of the interpolation.

Constructs the bulirsch_stoer class, including initialization of the error bounds.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `const DerivIn &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `DerivOut &` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed. Also, the internal order of the stepper is adjusted if required.

success if the step was accepted, fail otherwise.

void `const StateType &

The initial state.

` `const time_type &

The initial time.

` `const time_type &

The initial time step.

` Initializes the dense output stepper.

std::pair< time_type, time_type > `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` Does one time step. This is the main method that should be used to integrate an ODE with this stepper.

initialize has to be called before using this method to set the initial conditions x,t and the stepsize.

Pair with start and end time of the integration step.

void `time_type

The time at which the solution should be calculated, has to be in the current time interval.

` `StateOut &

The output variable where the result is written into.

` Calculates the solution at an intermediate point within the last step.

const state_type & `void` Returns the current state of the solution.

The current state of the solution x(t).

time_type `void` Returns the current time of the solution.

The current time of the solution t.

const state_type & `void` Returns the last state of the solution.

The last state of the solution x(t-dt).

time_type `void` Returns the last time of the solution.

The last time of the solution t-dt.

time_type `void` Returns the current step size.

The current step size.

void Resets the internal state of the stepper.
void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

void `size_t` `StateVector &` `const value_matrix &` `StateInOut &` `size_t0`
void `size_t` `StateVector &` `const value_matrix &` `size_t0`
time_type `time_type` `value_type` `size_t`
bool `size_t`
bool `value_type` `size_t`
value_type `int` `const StateIn1 &` `const DerivIn1 &` `const StateIn2 &` `const DerivIn2 &` `time_type`
void `size_t` `size_t` `value_type` `const DerivIn &`
void `time_type` `StateOut &`
bool `const StateIn &`
state_type & `void`
const state_type & `void`
state_type & `void`
const state_type & `void`
deriv_type & `void`
const deriv_type & `void`
deriv_type & `void`
const deriv_type & `void`
void `void`
unspecified
default_order_adjuster< ErrorStepper::order_value, typename ErrorStepper::state_type, typename ErrorStepper::value_type, typename ErrorStepper::algebra_type >
initially_resizer
ErrorStepper
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type::algebra_type
stepper_type::operations_type
Resizer
StepAdjuster
OrderAdjuster
controlled_stepper_tag
stepper_type::wrapped_state_type
stepper_type::wrapped_deriv_type
std::array< wrapped_state_type, 4 >
stepper_type::coeff_type
controlled_adams_bashforth_moulton< ErrorStepper, StepAdjuster, OrderAdjuster, Resizer >
const stepper_type::order_type
step_adjuster_type
step_adjuster_type()
void `ExplicitStepper` `System` `state_type &` `time_type &` `time_type`
void `System` `state_type &` `time_type &` `time_type`
void `ExplicitStepper` `System` `state_type &` `time_type &` `time_type &`
controlled_step_result `System` `state_type &` `time_type &` `time_type &`
controlled_step_result `System` `const state_type &` `time_type &` `state_type &` `time_type &`
void
bool `const StateType &`
bool `const StateType &`
bool `const StateType &`
size_t
double
typename algebra_dispatcher< State >::algebra_type
State
Value
state_wrapper< state_type >
Algebra
const algebra_type &
algebra_type()
size_t `size_t` `size_t` `std::array< wrapped_state_type, 4 > &`
default_error_checker< typename ErrorStepper::value_type , typename ErrorStepper::algebra_type , typename ErrorStepper::operations_type >
default_step_adjuster< typename ErrorStepper::value_type , typename ErrorStepper::time_type >
typename ErrorStepper::resizer_type
typename ErrorStepper::stepper_category

The stepper type with error estimation, has to fulfill the ErrorStepper concept.

The error checker

The resizer policy type.

ErrorStepper
ErrorChecker
StepAdjuster
Resizer
explicit_error_stepper_fsal_tag
Implements step size control for Runge-Kutta FSAL steppers with error estimation.

This class implements the step size control for FSAL Runge-Kutta steppers with error estimation.

ErrorStepper
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type::algebra_type
stepper_type::operations_type
Resizer
ErrorChecker
StepAdjuster
explicit_controlled_stepper_fsal_tag
const error_checker_type &
error_checker_type()

An instance of the error checker.

const step_adjuster_type &
step_adjuster_type()
const stepper_type &
stepper_type()

An instance of the underlying stepper.

Constructs the controlled Runge-Kutta stepper.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method is disabled if state_type=time_type to avoid ambiguity.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `DerivInOut &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `const DerivIn &` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `DerivOut &` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

void `void` Resets the internal state of the underlying FSAL stepper.
void `const DerivIn &

The initial derivative of the ODE.

` Initializes the internal state storing an internal copy of the derivative.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The initial state of the ODE which should be solved.

` `time_type

The initial time.

` Initializes the internal state storing an internal copy of the derivative.

bool `void` Returns true if the stepper has been initialized, false otherwise.

true, if the stepper has been initialized, false otherwise.

void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

stepper_type & `void` Returns the instance of the underlying stepper.

The instance of the underlying stepper.

const stepper_type & `void` Returns the instance of the underlying stepper.

The instance of the underlying stepper.

bool `const StateIn &`
bool `const StateIn &`
bool `const StateIn &`
bool `const StateIn &`
controlled_step_result `System` `StateInOut &` `time_type &` `time_type &`

The stepper type with error estimation, has to fulfill the ErrorStepper concept.

The error checker

The resizer policy type.

ErrorStepper
ErrorChecker
StepAdjuster
Resizer
explicit_error_stepper_tag
Implements step size control for Runge-Kutta steppers with error estimation.

This class implements the step size control for standard Runge-Kutta steppers with error estimation.

ErrorStepper
stepper_type::state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::time_type
stepper_type::algebra_type
stepper_type::operations_type
Resizer
ErrorChecker
StepAdjuster
explicit_controlled_stepper_tag
const error_checker_type &
error_checker_type()

An instance of the error checker.

const step_adjuster_type &
step_adjuster_type()
const stepper_type &
stepper_type()

An instance of the underlying stepper.

Constructs the controlled Runge-Kutta stepper.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is too large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful. Can be a boost range.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step. Solves the forwarding problem and allows for using boost range as state_type.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `StateInOut &

The state of the ODE which should be solved. Overwritten if the step is successful.

` `const DerivIn &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

boost::disable_if< boost::is_same< StateIn, time_type >, controlled_step_result >::type `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method is disabled if state_type=time_type to avoid ambiguity.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

controlled_step_result `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved.

` `const DerivIn &

The derivative of state.

` `time_type &

The value of the time. Updated if the step is successful.

` `StateOut &

Used to store the result of the step.

` `time_type &

The step size. Updated.

` Tries to perform one step.

This method tries to do one step with step size dt. If the error estimate is to large, the step is rejected and the method returns fail and the step size dt is reduced. If the error estimate is acceptably small, the step is performed, success is returned and dt might be increased to make the steps as large as possible. This method also updates t if a step is performed.

success if the step was accepted, fail otherwise.

void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

stepper_type & `void` Returns the instance of the underlying stepper.

The instance of the underlying stepper.

const stepper_type & `void` Returns the instance of the underlying stepper.

The instance of the underlying stepper.

controlled_step_result `System` `StateInOut &` `time_type &` `time_type &`
bool `const StateIn &`
bool `const StateIn &`
bool `const StateIn &`

The value type.

The algebra type.

The operations type.

The default error checker to be used with Runge-Kutta error steppers.

This class provides the default mechanism to compare the error estimates reported by Runge-Kutta error steppers with user defined error bounds. It is used by the controlled_runge_kutta steppers.

Value
Algebra
Operations
value_type
static_cast< value_type >(1.0e-6)
value_type
static_cast< value_type >(1.0e-6)
value_type
static_cast< value_type >(1)
value_type
static_cast< value_type >(1)
value_type `const State &` `const Deriv &` `Err &` `Time`
value_type `algebra_type &` `const State &` `const Deriv &` `Err &` `Time`
Time
Value
const time_type
static_cast< time_type >(0)
time_type `time_type` `const value_type` `const int`
time_type `time_type` `value_type` `const int`
bool `const time_type`
time_type

The trial step was successful, hence the state and the time have been advanced.

The step was not successful and might possibly be repeated with a small step size.

Enum representing the return values of the controlled steppers.
typename Stepper::stepper_category

The stepper type of the underlying algorithm.

Stepper
explicit_controlled_stepper_fsal_tag
The class representing dense-output Runge-Kutta steppers with FSAL property.

The interface is the same as for dense_output_runge_kutta< Stepper , stepper_tag >. This class provides dense output functionality based on methods with step size controlled

Stepper
controlled_stepper_type::stepper_type
stepper_type::state_type
stepper_type::wrapped_state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::wrapped_deriv_type
stepper_type::time_type
stepper_type::algebra_type
stepper_type::operations_type
stepper_type::resizer_type
dense_output_stepper_tag
dense_output_runge_kutta< Stepper >
const controlled_stepper_type &
controlled_stepper_type()
void `const StateType &` `time_type` `time_type`
std::pair< time_type, time_type > `System`
void `time_type` `StateOut &`
void `time_type` `const StateOut &`
bool `const StateIn &`
void `const StateType &`
const state_type & `void`
time_type `void`
const state_type & `void`
time_type `void`
time_type `void`
state_type & `void`
const state_type & `void`
state_type & `void`
const state_type & `void`
deriv_type & `void`
const deriv_type & `void`
deriv_type & `void`
const deriv_type & `void`
void `void`

The stepper type of the underlying algorithm.

Stepper
stepper_tag
The class representing dense-output Runge-Kutta steppers.

In this stepper, the initialize method has to be called before using the do_step method.

The dense-output functionality allows to interpolate the solution between subsequent integration points using intermediate results obtained during the computation. This version works based on a normal stepper without step-size control.

Stepper
stepper_type::state_type
stepper_type::wrapped_state_type
stepper_type::value_type
stepper_type::deriv_type
stepper_type::wrapped_deriv_type
stepper_type::time_type
stepper_type::algebra_type
stepper_type::operations_type
stepper_type::resizer_type
dense_output_stepper_tag
dense_output_runge_kutta< Stepper >
const stepper_type &
stepper_type()

An instance of the underlying stepper.

Constructs the dense_output_runge_kutta class. An instance of the underlying stepper can be provided.

void `const StateType &

The initial state of the ODE which should be solved.

` `time_type

The initial time, at which the step should be performed.

` `time_type

The step size.

` Initializes the stepper. Has to be called before do_step can be used to set the initial conditions and the step size.

std::pair< time_type, time_type > `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Simple System concept.

` Does one time step.

initialize has to be called before using this method to set the initial conditions x,t and the stepsize.

Pair with start and end time of the integration step.

void `time_type

The time at which the solution should be calculated, has to be in the current time interval.

` `StateOut &

The output variable where the result is written into.

` Calculates the solution at an intermediate point.

void `time_type

The time at which the solution should be calculated, has to be in the current time interval.

` `const StateOut &

The output variable where the result is written into, can be a boost range.

` Calculates the solution at an intermediate point. Solves the forwarding problem.

void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

const state_type & `void` Returns the current state of the solution.

The current state of the solution x(t).

time_type `void` Returns the current time of the solution.

The current time of the solution t.

const state_type & `void` Returns the last state of the solution.

The last state of the solution x(t-dt).

time_type `void` Returns the last time of the solution.

The last time of the solution t-dt.

time_type `void` Returns the current time step.

dt.

state_type & `void`
const state_type & `void`
state_type & `void`
const state_type & `void`
void `void`
bool `const StateIn &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

explicit_stepper_base
An implementation of the Euler method.

The Euler method is a very simply solver for ordinary differential equations. This method should not be used for real applications. It is only useful for demonstration purposes. Step size control is not provided but trivial continuous output is available.

This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern), see explicit_stepper_base

explicit_stepper_base< `euler`< ... >,... >
stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the euler class. This constructor can be used as a default constructor of the algebra has a default constructor.

void `System` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `StateOut &` `time_type` `const StateIn1 &` `time_type` `const StateIn2 &` `time_type` 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`.
void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

size_t

The number of stages of the Runge-Kutta algorithm.

size_t

The order of a stepper if the stepper is used without error estimation.

size_t

The order of a step if the stepper is used with error estimation. Usually Order and StepperOrder have the same value.

size_t

The order of the error step if the stepper is used with error estimation.

The type representing the state of the ODE.

double

The floating point type which is used in the computations.

State
Value

The type representing the independent variable - the time - of the ODE.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

explicit_error_stepper_base
A generic implementation of explicit Runge-Kutta algorithms with error estimation. This class is as a base class for all explicit Runge-Kutta steppers with error estimation.

This class implements the explicit Runge-Kutta algorithms with error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!

This class derives explicit_error_stepper_base which provides the stepper interface.

explicit_stepper_base< ... >
stepper_base_type::state_type
stepper_base_type::wrapped_state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::wrapped_deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
unspecified
rk_algorithm_type::coef_a_type
rk_algorithm_type::coef_b_type
rk_algorithm_type::coef_c_type
const size_t
const coef_a_type &

Triangular matrix of parameters b in the Butcher tableau.

const coef_b_type &

Last row of the butcher tableau.

const coef_b_type &

Parameters for lower-order evaluation to estimate the error.

const coef_c_type &

Parameters to calculate the time points in the Butcher tableau.

const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the explicit_error_generik_rk class with the given parameters a, b, b2 and c. See examples section for details on the coefficients.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` `Err &

The result of the error estimation is written in xerr.

` This method performs one step. The derivative `dxdt` 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`. Futhermore, an estimation of the error is stored in `xerr`. `do_step_impl` is used by explicit_error_stepper_base.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`
size_t

The number of stages of the Runge-Kutta algorithm.

size_t

The order of the stepper.

The type representing the state of the ODE.

The floating point type which is used in the computations.

The type representing the independent variable - the time - of the ODE.

The algebra type.

The operations type.

The resizer policy type.

explicit_stepper_base
A generic implementation of explicit Runge-Kutta algorithms. This class is as a base class for all explicit Runge-Kutta steppers.

This class implements the explicit Runge-Kutta algorithms without error estimation in a generic way. The Butcher tableau is passed to the stepper which constructs the stepper scheme with the help of a template-metaprogramming algorithm. ToDo : Add example!

This class derives explicit_stepper_base which provides the stepper interface.

explicit_stepper_base< ... >
stepper_base_type::state_type
stepper_base_type::wrapped_state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::wrapped_deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
unspecified
rk_algorithm_type::coef_a_type
rk_algorithm_type::coef_b_type
rk_algorithm_type::coef_c_type
const coef_a_type &

Triangular matrix of parameters b in the Butcher tableau.

const coef_b_type &

Last row of the butcher tableau.

const coef_c_type &

Parameters to calculate the time points in the Butcher tableau.

const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the explicit_generic_rk class. See examples section for details on the coefficients.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`
unsigned short
double
State
Value
typename algebra_dispatcher< State >::algebra_type
typename operations_dispatcher< State >::operations_type
initially_resizer
explicit_error_stepper_base
Extrapolation stepper with configurable order, and error estimation.

The extrapolation stepper is a stepper with error estimation and configurable order. The order is given as template parameter and needs to be an odd number. The stepper is based on several executions of the modified midpoint method and a Richardson extrapolation. This is essentially the same technique as for bulirsch_stoer, but without the variable order.

The Order parameter has to be an even number greater 2.

explicit_error_stepper_base< `extrapolation_stepper`< ... >,... >
stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
unsigned short
const order_type
const order_type
const order_type
const size_t
const algebra_type &
algebra_type()
void `System` `const StateIn &` `const DerivIn &` `time_type` `StateOut &` `time_type` `Err &`
void `System` `StateInOut &` `const DerivIn &` `time_type` `time_type` `Err &`
void `System` `const StateIn &` `const DerivIn &` `time_type` `StateOut &` `time_type`
void `System` `StateInOut &` `const DerivIn &` `time_type` `time_type`
void `System` `StateInOut &` `const DerivIn &` `time_type` `time_type`
void `System` `const StateIn &` `const DerivIn &` `time_type` `StateOut &` `time_type`
void `const StateIn &`
bool `const StateIn &`
bool `const StateIn &`
void `size_t` `state_table_type &` `const value_matrix &` `StateInOut &`
initially_resizer
ValueType
value_type
boost::numeric::ublas::vector< value_type >
state_wrapper< state_type >
state_type
state_wrapper< deriv_type >
boost::numeric::ublas::matrix< value_type >
state_wrapper< matrix_type >
boost::numeric::ublas::permutation_matrix< size_t >
state_wrapper< pmatrix_type >
Resizer
stepper_tag
implicit_euler< ValueType, Resizer >
value_type
1E-6
void `System` `state_type &` `time_type` `time_type`
void `const StateType &`
bool `const StateIn &`
void `state_type &` `matrix_type &`
double
State
Value
typename algebra_dispatcher< State >::algebra_type
typename operations_dispatcher< State >::operations_type
initially_resizer
explicit_stepper_base

Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the Bulirsch-Stoer algorithm and is not meant for direct usage.

explicit_stepper_base< `modified_midpoint`< State, Value, Deriv, Time, Algebra, Operations, Resizer >, 2, State, Value, Deriv, Time, Algebra, Operations, Resizer >
stepper_base_type::state_type
stepper_base_type::wrapped_state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::wrapped_deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
stepper_base_type::stepper_type
unsigned short
2
const algebra_type &
algebra_type()
void `System` `const StateIn &` `const DerivIn &` `time_type` `StateOut &` `time_type`
void `unsigned short`
unsigned short `void`
void `const StateIn &`
bool `const StateIn &`
double
State
Value
typename algebra_dispatcher< State >::algebra_type
typename operations_dispatcher< State >::operations_type
initially_resizer

Implementation of the modified midpoint method with a configurable number of intermediate steps. This class is used by the dense output Bulirsch-Stoer algorithm and is not meant for direct usage.

This stepper is for internal use only and does not meet any stepper concept.

State
Value
Deriv
Time
Algebra
Operations
Resizer
state_wrapper< state_type >
state_wrapper< deriv_type >
`modified_midpoint_dense_out`< State, Value, Deriv, Time, Algebra, Operations, Resizer >
std::vector< wrapped_deriv_type >
unsigned short
2
const algebra_type &
algebra_type()
void `System` `const StateIn &` `const DerivIn &` `time_type` `StateOut &` `time_type` `state_type &` `deriv_table_type &`
void `unsigned short`
unsigned short `void`
bool `const StateIn &`
void `const StateIn &`
Value
unsigned short
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const value_type
const order_type
const order_type
void
default_rosenbrock_coefficients< Value >
initially_resizer
Value
boost::numeric::ublas::vector< value_type >
state_type
value_type
boost::numeric::ublas::matrix< value_type >
boost::numeric::ublas::permutation_matrix< size_t >
Resizer
Coefficients
stepper_tag
unsigned short
state_wrapper< state_type >
state_wrapper< deriv_type >
state_wrapper< matrix_type >
state_wrapper< pmatrix_type >
rosenbrock4< Value, Coefficients, Resizer >
const order_type
const order_type
void
order_type
void `System` `const state_type &` `time_type` `state_type &` `time_type` `state_type &`
void `System` `state_type &` `time_type` `time_type` `state_type &`
void `System` `const state_type &` `time_type` `state_type &` `time_type`
void `System` `state_type &` `time_type` `time_type`
void
void `time_type` `state_type &` `const state_type &` `time_type` `const state_type &` `time_type`
void `const StateType &`
bool `const StateIn &`
bool `const StateIn &`
Stepper
stepper_type::value_type
stepper_type::state_type
stepper_type::wrapped_state_type
stepper_type::time_type
stepper_type::deriv_type
stepper_type::wrapped_deriv_type
stepper_type::resizer_type
controlled_stepper_tag
rosenbrock4_controller< Stepper >
value_type
1.0e-6
value_type
1.0e-6
const stepper_type &
stepper_type()
value_type
value_type
time_type
const stepper_type &
stepper_type()
value_type `const state_type &` `const state_type &` `const state_type &`
value_type `void`
boost::numeric::odeint::controlled_step_result `System` `state_type &` `time_type &` `time_type &`
boost::numeric::odeint::controlled_step_result `System` `const state_type &` `time_type &` `state_type &` `time_type &`
void `const StateType &`
stepper_type & `void`
const stepper_type & `void`
bool `const StateIn &`
bool `const StateIn &`
ControlledStepper
unwrap_reference< controlled_stepper_type >::type
unwrapped_controlled_stepper_type::stepper_type
stepper_type::value_type
stepper_type::state_type
stepper_type::wrapped_state_type
stepper_type::time_type
stepper_type::deriv_type
stepper_type::wrapped_deriv_type
stepper_type::resizer_type
dense_output_stepper_tag
rosenbrock4_dense_output< ControlledStepper >
const controlled_stepper_type &
controlled_stepper_type()
void `const StateType &` `time_type` `time_type`
std::pair< time_type, time_type > `System`
void `time_type` `StateOut &`
void `time_type` `const StateOut &`
void `const StateType &`
const state_type & `void`
time_type `void`
const state_type & `void`
time_type `void`
time_type `void`
state_type & `void`
const state_type & `void`
state_type & `void`
const state_type & `void`
void `void`
bool `const StateIn &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

boost::numeric::odeint::explicit_generic_rk< StageCount, Order, State, Value, Deriv, Time, Algebra, Operations, Resizer >
The classical Runge-Kutta stepper of fourth order.

The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also en.wikipedia.org/wiki/Runge-Kutta_methods The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided.

This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_generic_rk which is a generic Runge-Kutta algorithm. For more details see explicit_stepper_base and explicit_generic_rk.

stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta4 class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

explicit_stepper_base
The classical Runge-Kutta stepper of fourth order.

The Runge-Kutta method of fourth order is one standard method for solving ordinary differential equations and is widely used, see also en.wikipedia.org/wiki/Runge-Kutta_methods The method is explicit and fulfills the Stepper concept. Step size control or continuous output are not provided. This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.

This class derives from explicit_stepper_base and inherits its interface via CRTP (current recurring template pattern). For more details see explicit_stepper_base.

explicit_stepper_base< `runge_kutta4_classic`< ... >,... >
stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta4_classic class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateType &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer >
The Runge-Kutta Cash-Karp method.

The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see en.wikipedia.org/wiki/Cash-Karp_methods. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.

This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and explicit_error_generic_rk.

stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta_cash_karp54 class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` `Err &

The result of the error estimation is written in xerr.

` This method performs one step. The derivative `dxdt` 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`. Futhermore, an estimation of the error is stored in `xerr`. `do_step_impl` is used by explicit_error_stepper_base.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

explicit_error_stepper_base
The Runge-Kutta Cash-Karp method implemented without the generic Runge-Kutta algorithm.

The Runge-Kutta Cash-Karp method is one of the standard methods for solving ordinary differential equations, see en.wikipedia.org/wiki/Cash-Karp_method. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.

This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). This class implements the method directly, hence the generic Runge-Kutta algorithm is not used.

explicit_error_stepper_base< `runge_kutta_cash_karp54_classic`< ... >,... >
stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta_cash_karp54_classic class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` `Err &

The result of the error estimation is written in xerr.

` This method performs one step. The derivative `dxdt` 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`. Futhermore, an estimation of the error is stored in `xerr`. Access to this step functionality is provided by explicit_error_stepper_base and `do_step_impl` should not be called directly.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_error_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

explicit_error_stepper_fsal_base
The Runge-Kutta Dormand-Prince 5 method.

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.

explicit_error_stepper_fsal_base< `runge_kutta_dopri5`< ... >,... >
stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta_dopri5 class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t. dxdt_in is not modified by this method

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `DerivOut &

The result of the new derivative at time t+dt.

` `time_type

The step size.

` 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.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t. dxdt_in is not modified by this method

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `DerivOut &

The result of the new derivative at time t+dt.

` `time_type

The step size.

` `Err &

An estimation of the error.

` 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.

void `time_type` `StateOut &` `const StateIn1 &` `const DerivIn1 &` `time_type` `const StateIn2 &` `const DerivIn2 &` `time_type` 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.
void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

bool `const StateIn &`
bool `const StateIn &`

The state type.

double

The value type.

State

The type representing the time derivative of the state.

Value

The time representing the independent variable - the time.

typename algebra_dispatcher< State >::algebra_type

The algebra type.

typename operations_dispatcher< State >::operations_type

The operations type.

initially_resizer

The resizer policy type.

boost::numeric::odeint::explicit_error_generic_rk< StageCount, Order, StepperOrder, ErrorOrder, State, Value, Deriv, Time, Algebra, Operations, Resizer >
The Runge-Kutta Fehlberg 78 method.

The Runge-Kutta Fehlberg 78 method is a standard method for high-precision applications. The method is explicit and fulfills the Error Stepper concept. Step size control is provided but continuous output is not available for this method.

This class derives from explicit_error_stepper_base and inherits its interface via CRTP (current recurring template pattern). Furthermore, it derivs from explicit_error_generic_rk which is a generic Runge-Kutta algorithm with error estimation. For more details see explicit_error_stepper_base and explicit_error_generic_rk.

stepper_base_type::state_type
stepper_base_type::value_type
stepper_base_type::deriv_type
stepper_base_type::time_type
stepper_base_type::algebra_type
stepper_base_type::operations_type
stepper_base_type::resizer_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the runge_kutta_cash_fehlberg78 class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` `Err &

The result of the error estimation is written in xerr.

` This method performs one step. The derivative `dxdt` 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`. Futhermore, an estimation of the error is stored in `xerr`. `do_step_impl` is used by explicit_error_stepper_base.

void `System

The system function to solve, hence the r.h.s. of the ODE. It must fulfill the Simple System concept.

` `const StateIn &

The state of the ODE which should be solved. in is not modified in this method

` `const DerivIn &

The derivative of x at t.

` `time_type

The value of the time, at which the step should be performed.

` `StateOut &

The result of the step is written in out.

` `time_type

The step size.

` This method performs one step. The derivative `dxdt` 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`. Access to this step functionality is provided by explicit_stepper_base and `do_step_impl` should not be called directly.

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

controlled_stepper_tag
controlled_stepper_tag
dense_output_stepper_tag
dense_output_stepper_tag
error_stepper_tag
stepper_tag
explicit_controlled_stepper_fsal_tag
controlled_stepper_tag
explicit_controlled_stepper_tag
controlled_stepper_tag
explicit_error_stepper_fsal_tag
stepper_tag
explicit_error_stepper_tag
stepper_tag
stepper_tag
stepper_tag
boost::numeric::odeint::stepper_tag
boost::numeric::odeint::controlled_stepper_tag
boost::numeric::odeint::controlled_stepper_tag
boost::numeric::odeint::error_stepper_tag
boost::numeric::odeint::error_stepper_tag

The type representing the coordinates q.

Coor

The type representing the coordinates p.

double

The basic value type. Should be something like float, double or a high-precision type.

Coor

The type representing the time derivative of the coordinate dq/dt.

Coor
Value

The type representing the time t.

typename algebra_dispatcher< Coor >::algebra_type

The algebra.

typename operations_dispatcher< Coor >::operations_type

The operations.

initially_resizer

The resizer policy.

symplectic_nystroem_stepper_base
Implementation of the symplectic Euler method.

The method is of first order and has one stage. It is described HERE.

stepper_base_type::algebra_type
stepper_base_type::value_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the symplectic_euler. This constructor can be used as a default constructor if the algebra has a default constructor.

The type representing the coordinates q.

Coor

The type representing the coordinates p.

double

The basic value type. Should be something like float, double or a high-precision type.

Coor

The type representing the time derivative of the coordinate dq/dt.

Coor
Value

The type representing the time t.

typename algebra_dispatcher< Coor >::algebra_type

The algebra.

typename operations_dispatcher< Coor >::operations_type

The operations.

initially_resizer

The resizer policy.

symplectic_nystroem_stepper_base
Implementation of the symmetric B3A Runge-Kutta Nystroem method of fifth order.

The method is of fourth order and has five stages. It is described HERE. This method can be used with multiprecision types since the coefficients are defined analytically.

ToDo: add reference to paper.

stepper_base_type::algebra_type
stepper_base_type::value_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the symplectic_rkn_sb3a_m4_mclachlan. This constructor can be used as a default constructor if the algebra has a default constructor.

The type representing the coordinates q.

Coor

The type representing the coordinates p.

double

The basic value type. Should be something like float, double or a high-precision type.

Coor

The type representing the time derivative of the coordinate dq/dt.

Coor
Value

The type representing the time t.

typename algebra_dispatcher< Coor >::algebra_type

The algebra.

typename operations_dispatcher< Coor >::operations_type

The operations.

initially_resizer

The resizer policy.

symplectic_nystroem_stepper_base
Implement of the symmetric B3A method of Runge-Kutta-Nystroem method of sixth order.

The method is of fourth order and has six stages. It is described HERE. This method cannot be used with multiprecision types since the coefficients are not defined analytically.

ToDo Add reference to the paper.

stepper_base_type::algebra_type
stepper_base_type::value_type
const algebra_type &
algebra_type()

A copy of algebra is made and stored inside explicit_stepper_base.

Constructs the symplectic_rkn_sb3a_mclachlan. This constructor can be used as a default constructor if the algebra has a default constructor.

The type representing the coordinates.

Coor

The type representing the velocities.

double

The type value type.

Coor

The type representing the acceleration.

Value

The time representing the independent variable - the time.

Time

The time representing the square of the time.

typename algebra_dispatcher< Coor >::algebra_type

The algebra.

typename operations_dispatcher< Coor >::operations_type

The operations type.

initially_resizer

The resizer policy type.

algebra_stepper_base< typename algebra_dispatcher< Coor >::algebra_type, typename operations_dispatcher< Coor >::operations_type >
The Velocity-Verlet algorithm.

The Velocity-Verlet algorithm is a method for simulation of molecular dynamics systems. It solves the ODE a=f(r,v',t) where r are the coordinates, v are the velocities and a are the accelerations, hence v = dr/dt, a=dv/dt.

algebra_stepper_base< Algebra, Operations >
algebra_stepper_base_type::algebra_type
algebra_stepper_base_type::operations_type
Coor
Velocity
Acceleration
std::pair< coor_type, velocity_type >
std::pair< velocity_type, acceleration_type >
state_wrapper< acceleration_type >
Value
Time
TimeSq
Resizer
stepper_tag
unsigned short
const order_type
order_type `void`

Returns the order of the stepper.

const algebra_type &
algebra_type()

A copy of algebra is made and stored.

Constructs the velocity_verlet class. This constructor can be used as a default constructor if the algebra has a default constructor.

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.

` `StateInOut &

The state of the ODE which should be solved. The state is pair of Coor and Velocity.

` `time_type

The value of the time, at which the step should be performed.

` `time_type

The step size.

` This method performs one step. It transforms the result in-place.

It can be used like

    pair< coordinates , velocities > state;
    stepper.do_step( sys , x , t , dt );

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.

` `const StateInOut &

The state of the ODE which should be solved. The state is pair of Coor and Velocity.

` `time_type

The value of the time, at which the step should be performed.

` `time_type

The step size.

` This method performs one step. It transforms the result in-place.

It can be used like

    pair< coordinates , velocities > state;
    stepper.do_step( sys , x , t , dt );

void `System

The system function to solve, hence the r.h.s. of the ordinary differential equation. It must fulfill the Second Order System concept.

` `CoorIn const &` `VelocityIn const &` `AccelerationIn const &` `CoorOut &` `VelocityOut &` `AccelerationOut &` `time_type

The value of the time, at which the step should be performed.

` `time_type

The step size.

` This method performs one step. It transforms the result in-place. Additionally to the other methods the coordinates, velocities and accelerations are passed directly to do_step and they are transformed out-of-place.

It can be used like

    coordinates qin , qout;
    velocities pin , pout;
    accelerations ain, aout;
    stepper.do_step( sys , qin , pin , ain , qout , pout , aout , t , dt );

void `const StateIn &

A state from which the size of the temporaries to be resized is deduced.

` Adjust the size of all temporaries in the stepper manually.

void `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.
void `const AccelerationIn &` Initializes the internal state of the stepper.

void `System

The system function for the next calls of `do_step`.

` `const CoorIn &

The current coordinates of the ODE.

` `const VelocityIn &

The current velocities of the ODE.

` `time_type

The current time of the ODE.

` Initializes the internal state of the stepper.

This method is equivalent to

    Acceleration a;
    system( qin , pin , a , t );
    stepper.initialize( a );

bool `void`

Returns if the stepper is initialized.

void `System` `const CoorIn &` `const VelocityIn &` `time_type`
void `System` `StateInOut &` `time_type` `time_type`
bool `const StateIn &`
acceleration_type & `void`
const acceleration_type & `void`
acceleration_type & `void`
const acceleration_type & `void`
void `void`