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package org.apache.commons.math3.ode.events;

import org.apache.commons.math3.RealFieldElement;
import org.apache.commons.math3.ode.FieldODEState;
import org.apache.commons.math3.ode.FieldODEStateAndDerivative;

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).
Type parameters:
<T> – the type of the field elements
Since:
3.6/** This interface represents a handler for discrete events triggered
 * during ODE integration.
 *
 * <p>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.
 * </p>
 *
 * <p>These events are defined as occurring when a <code>g</code>
 * switching function sign changes.</p>
 *
 * <p>Since events are only problem-dependent and are triggered by the
 * independent <i>time</i> 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).</p>
 *
 * @param <T> the type of the field elements
 * @since 3.6
 */
public interface FieldEventHandler<T extends RealFieldElement<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.

Params:
initialState – initial time, state vector and derivative
finalTime – target time for the integration/** Initialize event handler at the start of an ODE integration.
     * <p>
     * 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.
     * </p>
     * @param initialState initial time, state vector and derivative
     * @param finalTime target time for the integration
     */
    void init(FieldODEStateAndDerivative<T> initialState, T finalTime);

    
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 method 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.
Params:
state – current value of the independent time variable, state vector
and derivative
Returns:
value of the g switching function/** Compute the value of the switching function.

     * <p>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.</p>
     * <p>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 <string>must</strong> be preserved,
     * otherwise {@link org.apache.commons.math3.exception.NoBracketingException
     * exceptions} related to root not being bracketed will occur.</p>
     * <p>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 {@code g(t) = h(t)} where h is the
     * height above the floor at time {@code t}. When {@code 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 {@code g(t)} was decreasing from positive values to 0, and after the
     * event {@code g(t)} would be increasing from 0 to positive values again.
     * Consistency is broken here! The solution here is to have {@code g(t) = sign
     * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
     * time {@link #eventOccurred(FieldODEStateAndDerivative, boolean) eventOccurred}
     * method is called, {@code sign} is reset to {@code -sign}. This allows the
     * {@code g(t)} function to remain continuous (and even smooth) even across events,
     * despite {@code h(t)} is not. Basically, the event is used to <em>fold</em>
     * {@code h(t)} at bounce points, and {@code sign} is used to <em>unfold</em> it
     * back, so the solvers sees a {@code g(t)} function which behaves smoothly even
     * across events.</p>

     * @param state current value of the independent <i>time</i> variable, state vector
     * and derivative
     * @return value of the g switching function
     */
    T g(FieldODEStateAndDerivative<T> state);

    
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 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 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 Action.RESET_DERIVATIVES is returned, the integrator will recompute the derivatives, 
if 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 FieldStepHandler 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 Action.STOP. As the interpolator may be used to navigate back throughout the last step, 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 FieldEventHandler interface and the FieldStepHandler interface, a forward integration may call its {code eventOccurred} method with t = 10 first and call its {code handleStep} method with t = 9 afterwards. Such out of order calls are limited to the size of the integration step for variable step handlers.
Params:
state – current value of the independent time variable, state vector
and derivative
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 Action.STOP, Action.RESET_STATE, Action.RESET_DERIVATIVES or Action.CONTINUE/** Handle an event and choose what to do next.

     * <p>This method is called when the integrator has accepted a step
     * ending exactly on a sign change of the function, just <em>before</em>
     * 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 {@link
     * org.apache.commons.math3.ode.FirstOrderDifferentialEquations
     * 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.</p>

     * <ul>
     *   <li>if {@link Action#STOP} is returned, the step handler will be called
     *   with the <code>isLast</code> flag of the {@link
     *   org.apache.commons.math3.ode.sampling.StepHandler#handleStep handleStep}
     *   method set to true and the integration will be stopped,</li>
     *   <li>if {@link Action#RESET_STATE} is returned, the {@link #resetState
     *   resetState} method will be called once the step handler has
     *   finished its task, and the integrator will also recompute the
     *   derivatives,</li>
     *   <li>if {@link Action#RESET_DERIVATIVES} is returned, the integrator
     *   will recompute the derivatives,
     *   <li>if {@link Action#CONTINUE} is returned, no specific action will
     *   be taken (apart from having called this method) and integration
     *   will continue.</li>
     * </ul>

     * <p>The scheduling between this method and the {@link
     * org.apache.commons.math3.ode.sampling.FieldStepHandler FieldStepHandler} method {@link
     * org.apache.commons.math3.ode.sampling.FieldStepHandler#handleStep(
     * org.apache.commons.math3.ode.sampling.FieldStepInterpolator, boolean)
     * handleStep(interpolator, isLast)} is to call this method first and
     * <code>handleStep</code> afterwards. This scheduling allows the integrator to
     * pass <code>true</code> as the <code>isLast</code> parameter to the step
     * handler to make it aware the step will be the last one if this method
     * returns {@link Action#STOP}. As the interpolator may be used to navigate back
     * throughout the last step, 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 {@link FieldEventHandler FieldEventHandler} interface and the
     * {@link org.apache.commons.math3.ode.sampling.FieldStepHandler FieldStepHandler}
     * interface, a <em>forward</em> integration may call its
     * {code eventOccurred} method with t = 10 first and call its
     * {code handleStep} method with t = 9 afterwards. Such out of order
     * calls are limited to the size of the integration step for {@link
     * org.apache.commons.math3.ode.sampling.FieldStepHandler variable step handlers}.</p>

     * @param state current value of the independent <i>time</i> variable, state vector
     * and derivative
     * @param 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)
     * @return indication of what the integrator should do next, this
     * value must be one of {@link Action#STOP}, {@link Action#RESET_STATE},
     * {@link Action#RESET_DERIVATIVES} or {@link Action#CONTINUE}
     */
    Action eventOccurred(FieldODEStateAndDerivative<T> state, boolean increasing);

    
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 has itself returned the 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 never returns the Action.RESET_STATE indicator, this function will never be called, and it is safe to leave its body empty.
Params:
state – current value of the independent time variable, state vector
and derivative
Returns:
reset state (note that it does not include the derivatives, they will
be added automatically by the integrator afterwards)/** Reset the state prior to continue the integration.

     * <p>This method is called after the step handler has returned and
     * before the next step is started, but only when {@link
     * #eventOccurred(FieldODEStateAndDerivative, boolean) eventOccurred} has itself
     * returned the {@link 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 {@link #eventOccurred(FieldODEStateAndDerivative, boolean)
     * eventOccurred} never returns the {@link Action#RESET_STATE} indicator, this
     * function will never be called, and it is safe to leave its body empty.</p>
     * @param state current value of the independent <i>time</i> variable, state vector
     * and derivative
     * @return reset state (note that it does not include the derivatives, they will
     * be added automatically by the integrator afterwards)
     */
    FieldODEState<T> resetState(FieldODEStateAndDerivative<T> state);

}