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.math4.legacy.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 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.math4.legacy.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 /** Initialize event handler at the start of an ODE integration.
90 * <p>
91 * This method is called once at the start of the integration. It
92 * may be used by the event handler to initialize some internal data
93 * if needed.
94 * </p>
95 * @param t0 start value of the independent <i>time</i> variable
96 * @param y0 array containing the start value of the state vector
97 * @param t target time for the integration
98 */
99 void init(double t0, double[] y0, double t);
100
101 /** Compute the value of the switching function.
102
103 * <p>The discrete events are generated when the sign of this
104 * switching function changes. The integrator will take care to change
105 * the stepsize in such a way these events occur exactly at step boundaries.
106 * The switching function must be continuous in its roots neighborhood
107 * (but not necessarily smooth), as the integrator will need to find its
108 * roots to locate precisely the events.</p>
109 * <p>Also note that the integrator expect that once an event has occurred,
110 * the sign of the switching function at the start of the next step (i.e.
111 * just after the event) is the opposite of the sign just before the event.
112 * This consistency between the steps <strong>must</strong> be preserved,
113 * otherwise {@link org.apache.commons.math4.legacy.exception.NoBracketingException
114 * exceptions} related to root not being bracketed will occur.</p>
115 * <p>This need for consistency is sometimes tricky to achieve. A typical
116 * example is using an event to model a ball bouncing on the floor. The first
117 * idea to represent this would be to have {@code g(t) = h(t)} where h is the
118 * height above the floor at time {@code t}. When {@code g(t)} reaches 0, the
119 * ball is on the floor, so it should bounce and the typical way to do this is
120 * to reverse its vertical velocity. However, this would mean that before the
121 * event {@code g(t)} was decreasing from positive values to 0, and after the
122 * event {@code g(t)} would be increasing from 0 to positive values again.
123 * Consistency is broken here! The solution here is to have {@code g(t) = sign
124 * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
125 * time {@link #eventOccurred(double, double[], boolean) eventOccurred} is called,
126 * {@code sign} is reset to {@code -sign}. This allows the {@code g(t)}
127 * function to remain continuous (and even smooth) even across events, despite
128 * {@code h(t)} is not. Basically, the event is used to <em>fold</em> {@code h(t)}
129 * at bounce points, and {@code sign} is used to <em>unfold</em> it back, so the
130 * solvers sees a {@code g(t)} function which behaves smoothly even across events.</p>
131
132 * @param t current value of the independent <i>time</i> variable
133 * @param y array containing the current value of the state vector
134 * @return value of the g switching function
135 */
136 double g(double t, double[] y);
137
138 /** Handle an event and choose what to do next.
139
140 * <p>This method is called when the integrator has accepted a step
141 * ending exactly on a sign change of the function, just <em>before</em>
142 * the step handler itself is called (see below for scheduling). It
143 * allows the user to update his internal data to acknowledge the fact
144 * the event has been handled (for example setting a flag in the {@link
145 * org.apache.commons.math4.legacy.ode.FirstOrderDifferentialEquations
146 * differential equations} to switch the derivatives computation in
147 * case of discontinuity), or to direct the integrator to either stop
148 * or continue integration, possibly with a reset state or derivatives.</p>
149
150 * <ul>
151 * <li>if {@link Action#STOP} is returned, the step handler will be called
152 * with the <code>isLast</code> flag of the {@link
153 * org.apache.commons.math4.legacy.ode.sampling.StepHandler#handleStep handleStep}
154 * method set to true and the integration will be stopped,</li>
155 * <li>if {@link Action#RESET_STATE} is returned, the {@link #resetState
156 * resetState} method will be called once the step handler has
157 * finished its task, and the integrator will also recompute the
158 * derivatives,</li>
159 * <li>if {@link Action#RESET_DERIVATIVES} is returned, the integrator
160 * will recompute the derivatives,
161 * <li>if {@link Action#CONTINUE} is returned, no specific action will
162 * be taken (apart from having called this method) and integration
163 * will continue.</li>
164 * </ul>
165
166 * <p>The scheduling between this method and the {@link
167 * org.apache.commons.math4.legacy.ode.sampling.StepHandler StepHandler} method {@link
168 * org.apache.commons.math4.legacy.ode.sampling.StepHandler#handleStep(
169 * org.apache.commons.math4.legacy.ode.sampling.StepInterpolator, boolean)
170 * handleStep(interpolator, isLast)} is to call this method first and
171 * <code>handleStep</code> afterwards. This scheduling allows the integrator to
172 * pass <code>true</code> as the <code>isLast</code> parameter to the step
173 * handler to make it aware the step will be the last one if this method
174 * returns {@link Action#STOP}. As the interpolator may be used to navigate back
175 * throughout the last step (as {@link
176 * org.apache.commons.math4.legacy.ode.sampling.StepNormalizer StepNormalizer}
177 * does for example), user code called by this method and user
178 * code called by step handlers may experience apparently out of order values
179 * of the independent time variable. As an example, if the same user object
180 * implements both this {@link EventHandler EventHandler} interface and the
181 * {@link org.apache.commons.math4.legacy.ode.sampling.FixedStepHandler FixedStepHandler}
182 * interface, a <em>forward</em> integration may call its
183 * <code>eventOccurred</code> method with t = 10 first and call its
184 * <code>handleStep</code> method with t = 9 afterwards. Such out of order
185 * calls are limited to the size of the integration step for {@link
186 * org.apache.commons.math4.legacy.ode.sampling.StepHandler variable step handlers} and
187 * to the size of the fixed step for {@link
188 * org.apache.commons.math4.legacy.ode.sampling.FixedStepHandler fixed step handlers}.</p>
189
190 * @param t current value of the independent <i>time</i> variable
191 * @param y array containing the current value of the state vector
192 * @param increasing if true, the value of the switching function increases
193 * when times increases around event (note that increase is measured with respect
194 * to physical time, not with respect to integration which may go backward in time)
195 * @return indication of what the integrator should do next, this
196 * value must be one of {@link Action#STOP}, {@link Action#RESET_STATE},
197 * {@link Action#RESET_DERIVATIVES} or {@link Action#CONTINUE}
198 */
199 Action eventOccurred(double t, double[] y, boolean increasing);
200
201 /** Reset the state prior to continue the integration.
202
203 * <p>This method is called after the step handler has returned and
204 * before the next step is started, but only when {@link
205 * #eventOccurred} has itself returned the {@link Action#RESET_STATE}
206 * indicator. It allows the user to reset the state vector for the
207 * next step, without perturbing the step handler of the finishing
208 * step. If the {@link #eventOccurred} never returns the {@link
209 * Action#RESET_STATE} indicator, this function will never be called, and it is
210 * safe to leave its body empty.</p>
211
212 * @param t current value of the independent <i>time</i> variable
213 * @param y array containing the current value of the state vector
214 * the new state should be put in the same array
215 */
216 void resetState(double t, double[] y);
217 }