001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017
018package org.apache.commons.math3.ode.events;
019
020
021/** This interface represents a handler for discrete events triggered
022 * during ODE integration.
023 *
024 * <p>Some events can be triggered at discrete times as an ODE problem
025 * is solved. This occurs for example when the integration process
026 * should be stopped as some state is reached (G-stop facility) when the
027 * precise date is unknown a priori, or when the derivatives have
028 * discontinuities, or simply when the user wants to monitor some
029 * states boundaries crossings.
030 * </p>
031 *
032 * <p>These events are defined as occurring when a <code>g</code>
033 * switching function sign changes.</p>
034 *
035 * <p>Since events are only problem-dependent and are triggered by the
036 * independent <i>time</i> variable and the state vector, they can
037 * occur at virtually any time, unknown in advance. The integrators will
038 * take care to avoid sign changes inside the steps, they will reduce
039 * the step size when such an event is detected in order to put this
040 * event exactly at the end of the current step. This guarantees that
041 * step interpolation (which always has a one step scope) is relevant
042 * even in presence of discontinuities. This is independent from the
043 * stepsize control provided by integrators that monitor the local
044 * error (this event handling feature is available for all integrators,
045 * including fixed step ones).</p>
046 *
047 * @version $Id: EventHandler.java 1451658 2013-03-01 17:36:46Z luc $
048 * @since 1.2
049 */
050
051public interface EventHandler  {
052
053    /** Enumerate for actions to be performed when an event occurs. */
054    public enum Action {
055
056        /** Stop indicator.
057         * <p>This value should be used as the return value of the {@link
058         * #eventOccurred eventOccurred} method when the integration should be
059         * stopped after the event ending the current step.</p>
060         */
061        STOP,
062
063        /** Reset state indicator.
064         * <p>This value should be used as the return value of the {@link
065         * #eventOccurred eventOccurred} method when the integration should
066         * go on after the event ending the current step, with a new state
067         * vector (which will be retrieved thanks to the {@link #resetState
068         * resetState} method).</p>
069         */
070        RESET_STATE,
071
072        /** Reset derivatives indicator.
073         * <p>This value should be used as the return value of the {@link
074         * #eventOccurred eventOccurred} method when the integration should
075         * go on after the event ending the current step, with a new derivatives
076         * vector (which will be retrieved thanks to the {@link
077         * org.apache.commons.math3.ode.FirstOrderDifferentialEquations#computeDerivatives}
078         * method).</p>
079         */
080        RESET_DERIVATIVES,
081
082        /** Continue indicator.
083         * <p>This value should be used as the return value of the {@link
084         * #eventOccurred eventOccurred} method when the integration should go
085         * on after the event ending the current step.</p>
086         */
087        CONTINUE;
088
089    }
090
091    /** Initialize event handler at the start of an ODE integration.
092     * <p>
093     * This method is called once at the start of the integration. It
094     * may be used by the event handler to initialize some internal data
095     * if needed.
096     * </p>
097     * @param t0 start value of the independent <i>time</i> variable
098     * @param y0 array containing the start value of the state vector
099     * @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}