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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   * @since 1.2
48   */
49  
50  public interface EventHandler  {
51  
52      /** Enumerate for actions to be performed when an event occurs. */
53      public enum Action {
54  
55          /** Stop indicator.
56           * <p>This value should be used as the return value of the {@link
57           * #eventOccurred eventOccurred} method when the integration should be
58           * stopped after the event ending the current step.</p>
59           */
60          STOP,
61  
62          /** Reset state indicator.
63           * <p>This value should be used as the return value of the {@link
64           * #eventOccurred eventOccurred} method when the integration should
65           * go on after the event ending the current step, with a new state
66           * vector (which will be retrieved thanks to the {@link #resetState
67           * resetState} method).</p>
68           */
69          RESET_STATE,
70  
71          /** Reset derivatives indicator.
72           * <p>This value should be used as the return value of the {@link
73           * #eventOccurred eventOccurred} method when the integration should
74           * go on after the event ending the current step, with a new derivatives
75           * vector (which will be retrieved thanks to the {@link
76           * org.apache.commons.math3.ode.FirstOrderDifferentialEquations#computeDerivatives}
77           * method).</p>
78           */
79          RESET_DERIVATIVES,
80  
81          /** Continue indicator.
82           * <p>This value should be used as the return value of the {@link
83           * #eventOccurred eventOccurred} method when the integration should go
84           * on after the event ending the current step.</p>
85           */
86          CONTINUE;
87  
88      }
89  
90      /** Initialize event handler at the start of an ODE integration.
91       * <p>
92       * This method is called once at the start of the integration. It
93       * may be used by the event handler to initialize some internal data
94       * if needed.
95       * </p>
96       * @param t0 start value of the independent <i>time</i> variable
97       * @param y0 array containing the start value of the state vector
98       * @param t target time for the integration
99       */
100     void init(double t0, double[] y0, double t);
101 
102   /** Compute the value of the switching function.
103 
104    * <p>The discrete events are generated when the sign of this
105    * switching function changes. The integrator will take care to change
106    * the stepsize in such a way these events occur exactly at step boundaries.
107    * The switching function must be continuous in its roots neighborhood
108    * (but not necessarily smooth), as the integrator will need to find its
109    * roots to locate precisely the events.</p>
110    * <p>Also note that the integrator expect that once an event has occurred,
111    * the sign of the switching function at the start of the next step (i.e.
112    * just after the event) is the opposite of the sign just before the event.
113    * This consistency between the steps <string>must</strong> be preserved,
114    * otherwise {@link org.apache.commons.math3.exception.NoBracketingException
115    * exceptions} related to root not being bracketed will occur.</p>
116    * <p>This need for consistency is sometimes tricky to achieve. A typical
117    * example is using an event to model a ball bouncing on the floor. The first
118    * idea to represent this would be to have {@code g(t) = h(t)} where h is the
119    * height above the floor at time {@code t}. When {@code g(t)} reaches 0, the
120    * ball is on the floor, so it should bounce and the typical way to do this is
121    * to reverse its vertical velocity. However, this would mean that before the
122    * event {@code g(t)} was decreasing from positive values to 0, and after the
123    * event {@code g(t)} would be increasing from 0 to positive values again.
124    * Consistency is broken here! The solution here is to have {@code g(t) = sign
125    * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
126    * time {@link #eventOccurred(double, double[], boolean) eventOccurred} is called,
127    * {@code sign} is reset to {@code -sign}. This allows the {@code g(t)}
128    * function to remain continuous (and even smooth) even across events, despite
129    * {@code h(t)} is not. Basically, the event is used to <em>fold</em> {@code h(t)}
130    * at bounce points, and {@code sign} is used to <em>unfold</em> it back, so the
131    * solvers sees a {@code g(t)} function which behaves smoothly even across events.</p>
132 
133    * @param t current value of the independent <i>time</i> variable
134    * @param y array containing the current value of the state vector
135    * @return value of the g switching function
136    */
137   double g(double t, double[] y);
138 
139   /** Handle an event and choose what to do next.
140 
141    * <p>This method is called when the integrator has accepted a step
142    * ending exactly on a sign change of the function, just <em>before</em>
143    * the step handler itself is called (see below for scheduling). It
144    * allows the user to update his internal data to acknowledge the fact
145    * the event has been handled (for example setting a flag in the {@link
146    * org.apache.commons.math3.ode.FirstOrderDifferentialEquations
147    * differential equations} to switch the derivatives computation in
148    * case of discontinuity), or to direct the integrator to either stop
149    * or continue integration, possibly with a reset state or derivatives.</p>
150 
151    * <ul>
152    *   <li>if {@link Action#STOP} is returned, the step handler will be called
153    *   with the <code>isLast</code> flag of the {@link
154    *   org.apache.commons.math3.ode.sampling.StepHandler#handleStep handleStep}
155    *   method set to true and the integration will be stopped,</li>
156    *   <li>if {@link Action#RESET_STATE} is returned, the {@link #resetState
157    *   resetState} method will be called once the step handler has
158    *   finished its task, and the integrator will also recompute the
159    *   derivatives,</li>
160    *   <li>if {@link Action#RESET_DERIVATIVES} is returned, the integrator
161    *   will recompute the derivatives,
162    *   <li>if {@link Action#CONTINUE} is returned, no specific action will
163    *   be taken (apart from having called this method) and integration
164    *   will continue.</li>
165    * </ul>
166 
167    * <p>The scheduling between this method and the {@link
168    * org.apache.commons.math3.ode.sampling.StepHandler StepHandler} method {@link
169    * org.apache.commons.math3.ode.sampling.StepHandler#handleStep(
170    * org.apache.commons.math3.ode.sampling.StepInterpolator, boolean)
171    * handleStep(interpolator, isLast)} is to call this method first and
172    * <code>handleStep</code> afterwards. This scheduling allows the integrator to
173    * pass <code>true</code> as the <code>isLast</code> parameter to the step
174    * handler to make it aware the step will be the last one if this method
175    * returns {@link Action#STOP}. As the interpolator may be used to navigate back
176    * throughout the last step (as {@link
177    * org.apache.commons.math3.ode.sampling.StepNormalizer StepNormalizer}
178    * does for example), user code called by this method and user
179    * code called by step handlers may experience apparently out of order values
180    * of the independent time variable. As an example, if the same user object
181    * implements both this {@link EventHandler EventHandler} interface and the
182    * {@link org.apache.commons.math3.ode.sampling.FixedStepHandler FixedStepHandler}
183    * interface, a <em>forward</em> integration may call its
184    * <code>eventOccurred</code> method with t = 10 first and call its
185    * <code>handleStep</code> method with t = 9 afterwards. Such out of order
186    * calls are limited to the size of the integration step for {@link
187    * org.apache.commons.math3.ode.sampling.StepHandler variable step handlers} and
188    * to the size of the fixed step for {@link
189    * org.apache.commons.math3.ode.sampling.FixedStepHandler fixed step handlers}.</p>
190 
191    * @param t current value of the independent <i>time</i> variable
192    * @param y array containing the current value of the state vector
193    * @param increasing if true, the value of the switching function increases
194    * when times increases around event (note that increase is measured with respect
195    * to physical time, not with respect to integration which may go backward in time)
196    * @return indication of what the integrator should do next, this
197    * value must be one of {@link Action#STOP}, {@link Action#RESET_STATE},
198    * {@link Action#RESET_DERIVATIVES} or {@link Action#CONTINUE}
199    */
200   Action eventOccurred(double t, double[] y, boolean increasing);
201 
202   /** Reset the state prior to continue the integration.
203 
204    * <p>This method is called after the step handler has returned and
205    * before the next step is started, but only when {@link
206    * #eventOccurred} has itself returned the {@link Action#RESET_STATE}
207    * indicator. It allows the user to reset the state vector for the
208    * next step, without perturbing the step handler of the finishing
209    * step. If the {@link #eventOccurred} never returns the {@link
210    * Action#RESET_STATE} indicator, this function will never be called, and it is
211    * safe to leave its body empty.</p>
212 
213    * @param t current value of the independent <i>time</i> variable
214    * @param y array containing the current value of the state vector
215    * the new state should be put in the same array
216    */
217   void resetState(double t, double[] y);
218 
219 }