EventHandler (Apache Commons Math 3.3 API)

org.apache.commons.math3.ode.events

## Interface EventHandler

- All Known Implementing Classes:
    EventFilter

      public interface EventHandler

  This interface represents a handler for discrete events triggered during ODE integration.

  Some events can be triggered at discrete times as an ODE problem is solved. This occurs for example when the integration process should be stopped as some state is reached (G-stop facility) when the precise date is unknown a priori, or when the derivatives have discontinuities, or simply when the user wants to monitor some states boundaries crossings.

  These events are defined as occurring when a `g` switching function sign changes.

  Since events are only problem-dependent and are triggered by the independent time variable and the state vector, they can occur at virtually any time, unknown in advance. The integrators will take care to avoid sign changes inside the steps, they will reduce the step size when such an event is detected in order to put this event exactly at the end of the current step. This guarantees that step interpolation (which always has a one step scope) is relevant even in presence of discontinuities. This is independent from the stepsize control provided by integrators that monitor the local error (this event handling feature is available for all integrators, including fixed step ones).

  Since:
    1.2
  Version:
    $Id: EventHandler.java 1451658 2013-03-01 17:36:46Z luc $

- - ### Nested Class Summary

    Nested Classes
    Modifier and Type | Interface and Description
    --- | ---
    `static class` | `EventHandler.Action` Enumerate for actions to be performed when an event occurs.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `EventHandler.Action` | `eventOccurred(double t, double[] y, boolean increasing)` Handle an event and choose what to do next.
    `double` | `g(double t, double[] y)` Compute the value of the switching function.
    `void` | `init(double t0, double[] y0, double t)` Initialize event handler at the start of an ODE integration.
    `void` | `resetState(double t, double[] y)` Reset the state prior to continue the integration.

- - ### Method Detail

    - #### init

          void init(double t0,
                  double[] y0,
                  double t)

      Initialize event handler at the start of an ODE integration.

      This method is called once at the start of the integration. It may be used by the event handler to initialize some internal data if needed.

      Parameters:
        `t0` - start value of the independent time variable
        `y0` - array containing the start value of the state vector
        `t` - target time for the integration

    - #### g

          double g(double t,
                 double[] y)

      Compute the value of the switching function.

      The discrete events are generated when the sign of this switching function changes. The integrator will take care to change the stepsize in such a way these events occur exactly at step boundaries. The switching function must be continuous in its roots neighborhood (but not necessarily smooth), as the integrator will need to find its roots to locate precisely the events.

      Also note that the integrator expect that once an event has occurred, the sign of the switching function at the start of the next step (i.e. just after the event) is the opposite of the sign just before the event. This consistency between the steps must be preserved, otherwise `exceptions` related to root not being bracketed will occur.

      This need for consistency is sometimes tricky to achieve. A typical example is using an event to model a ball bouncing on the floor. The first idea to represent this would be to have `g(t) = h(t)` where h is the height above the floor at time `t`. When `g(t)` reaches 0, the ball is on the floor, so it should bounce and the typical way to do this is to reverse its vertical velocity. However, this would mean that before the event `g(t)` was decreasing from positive values to 0, and after the event `g(t)` would be increasing from 0 to positive values again. Consistency is broken here! The solution here is to have `g(t) = sign * h(t)`, where sign is a variable with initial value set to `+1`. Each time `eventOccurred` is called, `sign` is reset to `-sign`. This allows the `g(t)` function to remain continuous (and even smooth) even across events, despite `h(t)` is not. Basically, the event is used to fold `h(t)` at bounce points, and `sign` is used to unfold it back, so the solvers sees a `g(t)` function which behaves smoothly even across events.

      Parameters:
        `t` - current value of the independent time variable
        `y` - array containing the current value of the state vector
      Returns:
        value of the g switching function

    - #### eventOccurred

          EventHandler.Action eventOccurred(double t,
                                          double[] y,
                                          boolean increasing)

      Handle an event and choose what to do next.

      This method is called when the integrator has accepted a step ending exactly on a sign change of the function, just before the step handler itself is called (see below for scheduling). It allows the user to update his internal data to acknowledge the fact the event has been handled (for example setting a flag in the `differential equations` to switch the derivatives computation in case of discontinuity), or to direct the integrator to either stop or continue integration, possibly with a reset state or derivatives.

      - if `EventHandler.Action.STOP` is returned, the step handler will be called with the `isLast` flag of the `handleStep` method set to true and the integration will be stopped,
      - if `EventHandler.Action.RESET_STATE` is returned, the `resetState` method will be called once the step handler has finished its task, and the integrator will also recompute the derivatives,
      - if `EventHandler.Action.RESET_DERIVATIVES` is returned, the integrator will recompute the derivatives,
      - if `EventHandler.Action.CONTINUE` is returned, no specific action will be taken (apart from having called this method) and integration will continue.

      The scheduling between this method and the `StepHandler` method `handleStep(interpolator, isLast)` is to call this method first and `handleStep` afterwards. This scheduling allows the integrator to pass `true` as the `isLast` parameter to the step handler to make it aware the step will be the last one if this method returns `EventHandler.Action.STOP`. As the interpolator may be used to navigate back throughout the last step (as `StepNormalizer` does for example), user code called by this method and user code called by step handlers may experience apparently out of order values of the independent time variable. As an example, if the same user object implements both this `EventHandler` interface and the `FixedStepHandler` interface, a forward integration may call its `eventOccurred` method with t = 10 first and call its `handleStep` method with t = 9 afterwards. Such out of order calls are limited to the size of the integration step for `variable step handlers` and to the size of the fixed step for `fixed step handlers`.

      Parameters:
        `t` - current value of the independent time variable
        `y` - array containing the current value of the state vector
        `increasing` - if true, the value of the switching function increases when times increases around event (note that increase is measured with respect to physical time, not with respect to integration which may go backward in time)
      Returns:
        indication of what the integrator should do next, this value must be one of `EventHandler.Action.STOP`, `EventHandler.Action.RESET_STATE`, `EventHandler.Action.RESET_DERIVATIVES` or `EventHandler.Action.CONTINUE`

    - #### resetState

          void resetState(double t,
                        double[] y)

      Reset the state prior to continue the integration.

      This method is called after the step handler has returned and before the next step is started, but only when `eventOccurred(double, double[], boolean)` has itself returned the `EventHandler.Action.RESET_STATE` indicator. It allows the user to reset the state vector for the next step, without perturbing the step handler of the finishing step. If the `eventOccurred(double, double[], boolean)` never returns the `EventHandler.Action.RESET_STATE` indicator, this function will never be called, and it is safe to leave its body empty.

      Parameters:
        `t` - current value of the independent time variable
        `y` - array containing the current value of the state vector the new state should be put in the same array

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