## The FieldEventHandler.java Java example source code

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*
* http://www.apache.org/licenses/LICENSE-2.0
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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.
*
* <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 `g`

* switching function sign changes.</p>
*
* <p>Since events are only problem-dependent and are triggered by the
* independent <i>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).</p>
*
* @param <T> the type of the field elements
* @since 3.6
*/
public interface FieldEventHandler<T extends RealFieldElement {
/** 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.
* <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 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
* {@code h(t)} at bounce points, and {@code sign} is used to <em>unfold 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 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.
* <p>This method is called when the integrator has accepted a step
* ending exactly on a sign change of the function, just <em>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 {@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 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 afterwards. This scheduling allows the integrator to
* pass <code>true as the `isLast`

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 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 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.
* <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 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 state);
}

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