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 * @since 1.2
048 */
049
050public interface EventHandler  {
051
052    /** Enumerate for actions to be performed when an event occurs. */
053    public enum Action {
054
055        /** Stop indicator.
056         * <p>This value should be used as the return value of the {@link
057         * #eventOccurred eventOccurred} method when the integration should be
058         * stopped after the event ending the current step.</p>
059         */
060        STOP,
061
062        /** Reset state indicator.
063         * <p>This value should be used as the return value of the {@link
064         * #eventOccurred eventOccurred} method when the integration should
065         * go on after the event ending the current step, with a new state
066         * vector (which will be retrieved thanks to the {@link #resetState
067         * resetState} method).</p>
068         */
069        RESET_STATE,
070
071        /** Reset derivatives indicator.
072         * <p>This value should be used as the return value of the {@link
073         * #eventOccurred eventOccurred} method when the integration should
074         * go on after the event ending the current step, with a new derivatives
075         * vector (which will be retrieved thanks to the {@link
076         * org.apache.commons.math3.ode.FirstOrderDifferentialEquations#computeDerivatives}
077         * method).</p>
078         */
079        RESET_DERIVATIVES,
080
081        /** Continue indicator.
082         * <p>This value should be used as the return value of the {@link
083         * #eventOccurred eventOccurred} method when the integration should go
084         * on after the event ending the current step.</p>
085         */
086        CONTINUE;
087
088    }
089
090    /** Initialize event handler at the start of an ODE integration.
091     * <p>
092     * This method is called once at the start of the integration. It
093     * may be used by the event handler to initialize some internal data
094     * if needed.
095     * </p>
096     * @param t0 start value of the independent <i>time</i> variable
097     * @param y0 array containing the start value of the state vector
098     * @param t target time for the integration
099     */
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}