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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  
18  package org.apache.commons.math3.ode.events;
19  
20  
21  /** This interface represents a handler for discrete events triggered
22   * during ODE integration.
23   *
24   * <p>Some events can be triggered at discrete times as an ODE problem
25   * is solved. This occurs for example when the integration process
26   * should be stopped as some state is reached (G-stop facility) when the
27   * precise date is unknown a priori, or when the derivatives have
28   * discontinuities, or simply when the user wants to monitor some
29   * states boundaries crossings.
30   * </p>
31   *
32   * <p>These events are defined as occurring when a <code>g</code>
33   * switching function sign changes.</p>
34   *
35   * <p>Since events are only problem-dependent and are triggered by the
36   * independent <i>time</i> variable and the state vector, they can
37   * occur at virtually any time, unknown in advance. The integrators will
38   * take care to avoid sign changes inside the steps, they will reduce
39   * the step size when such an event is detected in order to put this
40   * event exactly at the end of the current step. This guarantees that
41   * step interpolation (which always has a one step scope) is relevant
42   * even in presence of discontinuities. This is independent from the
43   * stepsize control provided by integrators that monitor the local
44   * error (this event handling feature is available for all integrators,
45   * including fixed step ones).</p>
46   *
47   * @version $Id: EventHandler.java 1451658 2013-03-01 17:36:46Z luc $
48   * @since 1.2
49   */
50  
51  public interface EventHandler  {
52  
53      /** Enumerate for actions to be performed when an event occurs. */
54      public enum Action {
55  
56          /** Stop indicator.
57           * <p>This value should be used as the return value of the {@link
58           * #eventOccurred eventOccurred} method when the integration should be
59           * stopped after the event ending the current step.</p>
60           */
61          STOP,
62  
63          /** Reset state indicator.
64           * <p>This value should be used as the return value of the {@link
65           * #eventOccurred eventOccurred} method when the integration should
66           * go on after the event ending the current step, with a new state
67           * vector (which will be retrieved thanks to the {@link #resetState
68           * resetState} method).</p>
69           */
70          RESET_STATE,
71  
72          /** Reset derivatives indicator.
73           * <p>This value should be used as the return value of the {@link
74           * #eventOccurred eventOccurred} method when the integration should
75           * go on after the event ending the current step, with a new derivatives
76           * vector (which will be retrieved thanks to the {@link
77           * org.apache.commons.math3.ode.FirstOrderDifferentialEquations#computeDerivatives}
78           * method).</p>
79           */
80          RESET_DERIVATIVES,
81  
82          /** Continue indicator.
83           * <p>This value should be used as the return value of the {@link
84           * #eventOccurred eventOccurred} method when the integration should go
85           * on after the event ending the current step.</p>
86           */
87          CONTINUE;
88  
89      }
90  
91      /** Initialize event handler at the start of an ODE integration.
92       * <p>
93       * This method is called once at the start of the integration. It
94       * may be used by the event handler to initialize some internal data
95       * if needed.
96       * </p>
97       * @param t0 start value of the independent <i>time</i> variable
98       * @param y0 array containing the start value of the state vector
99       * @param t target time for the integration
100      */
101     void init(double t0, double[] y0, double t);
102 
103   /** Compute the value of the switching function.
104 
105    * <p>The discrete events are generated when the sign of this
106    * switching function changes. The integrator will take care to change
107    * the stepsize in such a way these events occur exactly at step boundaries.
108    * The switching function must be continuous in its roots neighborhood
109    * (but not necessarily smooth), as the integrator will need to find its
110    * roots to locate precisely the events.</p>
111    * <p>Also note that the integrator expect that once an event has occurred,
112    * the sign of the switching function at the start of the next step (i.e.
113    * just after the event) is the opposite of the sign just before the event.
114    * This consistency between the steps <string>must</strong> be preserved,
115    * otherwise {@link org.apache.commons.math3.exception.NoBracketingException
116    * exceptions} related to root not being bracketed will occur.</p>
117    * <p>This need for consistency is sometimes tricky to achieve. A typical
118    * example is using an event to model a ball bouncing on the floor. The first
119    * idea to represent this would be to have {@code g(t) = h(t)} where h is the
120    * height above the floor at time {@code t}. When {@code g(t)} reaches 0, the
121    * ball is on the floor, so it should bounce and the typical way to do this is
122    * to reverse its vertical velocity. However, this would mean that before the
123    * event {@code g(t)} was decreasing from positive values to 0, and after the
124    * event {@code g(t)} would be increasing from 0 to positive values again.
125    * Consistency is broken here! The solution here is to have {@code g(t) = sign
126    * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
127    * time {@link #eventOccurred(double, double[], boolean) eventOccurred} is called,
128    * {@code sign} is reset to {@code -sign}. This allows the {@code g(t)}
129    * function to remain continuous (and even smooth) even across events, despite
130    * {@code h(t)} is not. Basically, the event is used to <em>fold</em> {@code h(t)}
131    * at bounce points, and {@code sign} is used to <em>unfold</em> it back, so the
132    * solvers sees a {@code g(t)} function which behaves smoothly even across events.</p>
133 
134    * @param t current value of the independent <i>time</i> variable
135    * @param y array containing the current value of the state vector
136    * @return value of the g switching function
137    */
138   double g(double t, double[] y);
139 
140   /** Handle an event and choose what to do next.
141 
142    * <p>This method is called when the integrator has accepted a step
143    * ending exactly on a sign change of the function, just <em>before</em>
144    * the step handler itself is called (see below for scheduling). It
145    * allows the user to update his internal data to acknowledge the fact
146    * the event has been handled (for example setting a flag in the {@link
147    * org.apache.commons.math3.ode.FirstOrderDifferentialEquations
148    * differential equations} to switch the derivatives computation in
149    * case of discontinuity), or to direct the integrator to either stop
150    * or continue integration, possibly with a reset state or derivatives.</p>
151 
152    * <ul>
153    *   <li>if {@link Action#STOP} is returned, the step handler will be called
154    *   with the <code>isLast</code> flag of the {@link
155    *   org.apache.commons.math3.ode.sampling.StepHandler#handleStep handleStep}
156    *   method set to true and the integration will be stopped,</li>
157    *   <li>if {@link Action#RESET_STATE} is returned, the {@link #resetState
158    *   resetState} method will be called once the step handler has
159    *   finished its task, and the integrator will also recompute the
160    *   derivatives,</li>
161    *   <li>if {@link Action#RESET_DERIVATIVES} is returned, the integrator
162    *   will recompute the derivatives,
163    *   <li>if {@link Action#CONTINUE} is returned, no specific action will
164    *   be taken (apart from having called this method) and integration
165    *   will continue.</li>
166    * </ul>
167 
168    * <p>The scheduling between this method and the {@link
169    * org.apache.commons.math3.ode.sampling.StepHandler StepHandler} method {@link
170    * org.apache.commons.math3.ode.sampling.StepHandler#handleStep(
171    * org.apache.commons.math3.ode.sampling.StepInterpolator, boolean)
172    * handleStep(interpolator, isLast)} is to call this method first and
173    * <code>handleStep</code> afterwards. This scheduling allows the integrator to
174    * pass <code>true</code> as the <code>isLast</code> parameter to the step
175    * handler to make it aware the step will be the last one if this method
176    * returns {@link Action#STOP}. As the interpolator may be used to navigate back
177    * throughout the last step (as {@link
178    * org.apache.commons.math3.ode.sampling.StepNormalizer StepNormalizer}
179    * does for example), user code called by this method and user
180    * code called by step handlers may experience apparently out of order values
181    * of the independent time variable. As an example, if the same user object
182    * implements both this {@link EventHandler EventHandler} interface and the
183    * {@link org.apache.commons.math3.ode.sampling.FixedStepHandler FixedStepHandler}
184    * interface, a <em>forward</em> integration may call its
185    * <code>eventOccurred</code> method with t = 10 first and call its
186    * <code>handleStep</code> method with t = 9 afterwards. Such out of order
187    * calls are limited to the size of the integration step for {@link
188    * org.apache.commons.math3.ode.sampling.StepHandler variable step handlers} and
189    * to the size of the fixed step for {@link
190    * org.apache.commons.math3.ode.sampling.FixedStepHandler fixed step handlers}.</p>
191 
192    * @param t current value of the independent <i>time</i> variable
193    * @param y array containing the current value of the state vector
194    * @param increasing if true, the value of the switching function increases
195    * when times increases around event (note that increase is measured with respect
196    * to physical time, not with respect to integration which may go backward in time)
197    * @return indication of what the integrator should do next, this
198    * value must be one of {@link Action#STOP}, {@link Action#RESET_STATE},
199    * {@link Action#RESET_DERIVATIVES} or {@link Action#CONTINUE}
200    */
201   Action eventOccurred(double t, double[] y, boolean increasing);
202 
203   /** Reset the state prior to continue the integration.
204 
205    * <p>This method is called after the step handler has returned and
206    * before the next step is started, but only when {@link
207    * #eventOccurred} has itself returned the {@link Action#RESET_STATE}
208    * indicator. It allows the user to reset the state vector for the
209    * next step, without perturbing the step handler of the finishing
210    * step. If the {@link #eventOccurred} never returns the {@link
211    * Action#RESET_STATE} indicator, this function will never be called, and it is
212    * safe to leave its body empty.</p>
213 
214    * @param t current value of the independent <i>time</i> variable
215    * @param y array containing the current value of the state vector
216    * the new state should be put in the same array
217    */
218   void resetState(double t, double[] y);
219 
220 }