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 import org.apache.commons.math4.legacy.core.RealFieldElement;
21 import org.apache.commons.math4.legacy.ode.FieldODEState;
22 import org.apache.commons.math4.legacy.ode.FieldODEStateAndDerivative;
23
24 /** This interface represents a handler for discrete events triggered
25 * during ODE integration.
26 *
27 * <p>Some events can be triggered at discrete times as an ODE problem
28 * is solved. This occurs for example when the integration process
29 * should be stopped as some state is reached (G-stop facility) when the
30 * precise date is unknown a priori, or when the derivatives have
31 * discontinuities, or simply when the user wants to monitor some
32 * states boundaries crossings.
33 * </p>
34 *
35 * <p>These events are defined as occurring when a <code>g</code>
36 * switching function sign changes.</p>
37 *
38 * <p>Since events are only problem-dependent and are triggered by the
39 * independent <i>time</i> variable and the state vector, they can
40 * occur at virtually any time, unknown in advance. The integrators will
41 * take care to avoid sign changes inside the steps, they will reduce
42 * the step size when such an event is detected in order to put this
43 * event exactly at the end of the current step. This guarantees that
44 * step interpolation (which always has a one step scope) is relevant
45 * even in presence of discontinuities. This is independent from the
46 * stepsize control provided by integrators that monitor the local
47 * error (this event handling feature is available for all integrators,
48 * including fixed step ones).</p>
49 *
50 * @param <T> the type of the field elements
51 * @since 3.6
52 */
53 public interface FieldEventHandler<T extends RealFieldElement<T>> {
54
55 /** Initialize event handler at the start of an ODE integration.
56 * <p>
57 * This method is called once at the start of the integration. It
58 * may be used by the event handler to initialize some internal data
59 * if needed.
60 * </p>
61 * @param initialState initial time, state vector and derivative
62 * @param finalTime target time for the integration
63 */
64 void init(FieldODEStateAndDerivative<T> initialState, T finalTime);
65
66 /** Compute the value of the switching function.
67
68 * <p>The discrete events are generated when the sign of this
69 * switching function changes. The integrator will take care to change
70 * the stepsize in such a way these events occur exactly at step boundaries.
71 * The switching function must be continuous in its roots neighborhood
72 * (but not necessarily smooth), as the integrator will need to find its
73 * roots to locate precisely the events.</p>
74 * <p>Also note that the integrator expect that once an event has occurred,
75 * the sign of the switching function at the start of the next step (i.e.
76 * just after the event) is the opposite of the sign just before the event.
77 * This consistency between the steps <strong>must</strong> be preserved,
78 * otherwise {@link org.apache.commons.math4.legacy.exception.NoBracketingException
79 * exceptions} related to root not being bracketed will occur.</p>
80 * <p>This need for consistency is sometimes tricky to achieve. A typical
81 * example is using an event to model a ball bouncing on the floor. The first
82 * idea to represent this would be to have {@code g(t) = h(t)} where h is the
83 * height above the floor at time {@code t}. When {@code g(t)} reaches 0, the
84 * ball is on the floor, so it should bounce and the typical way to do this is
85 * to reverse its vertical velocity. However, this would mean that before the
86 * event {@code g(t)} was decreasing from positive values to 0, and after the
87 * event {@code g(t)} would be increasing from 0 to positive values again.
88 * Consistency is broken here! The solution here is to have {@code g(t) = sign
89 * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
90 * time {@link #eventOccurred(FieldODEStateAndDerivative, boolean) eventOccurred}
91 * method is called, {@code sign} is reset to {@code -sign}. This allows the
92 * {@code g(t)} function to remain continuous (and even smooth) even across events,
93 * despite {@code h(t)} is not. Basically, the event is used to <em>fold</em>
94 * {@code h(t)} at bounce points, and {@code sign} is used to <em>unfold</em> it
95 * back, so the solvers sees a {@code g(t)} function which behaves smoothly even
96 * across events.</p>
97
98 * @param state current value of the independent <i>time</i> variable, state vector
99 * and derivative
100 * @return value of the g switching function
101 */
102 T g(FieldODEStateAndDerivative<T> state);
103
104 /** Handle an event and choose what to do next.
105
106 * <p>This method is called when the integrator has accepted a step
107 * ending exactly on a sign change of the function, just <em>before</em>
108 * the step handler itself is called (see below for scheduling). It
109 * allows the user to update his internal data to acknowledge the fact
110 * the event has been handled (for example setting a flag in the {@link
111 * org.apache.commons.math4.legacy.ode.FirstOrderDifferentialEquations
112 * differential equations} to switch the derivatives computation in
113 * case of discontinuity), or to direct the integrator to either stop
114 * or continue integration, possibly with a reset state or derivatives.</p>
115
116 * <ul>
117 * <li>if {@link Action#STOP} is returned, the step handler will be called
118 * with the <code>isLast</code> flag of the {@link
119 * org.apache.commons.math4.legacy.ode.sampling.StepHandler#handleStep handleStep}
120 * method set to true and the integration will be stopped,</li>
121 * <li>if {@link Action#RESET_STATE} is returned, the {@link #resetState
122 * resetState} method will be called once the step handler has
123 * finished its task, and the integrator will also recompute the
124 * derivatives,</li>
125 * <li>if {@link Action#RESET_DERIVATIVES} is returned, the integrator
126 * will recompute the derivatives,
127 * <li>if {@link Action#CONTINUE} is returned, no specific action will
128 * be taken (apart from having called this method) and integration
129 * will continue.</li>
130 * </ul>
131
132 * <p>The scheduling between this method and the {@link
133 * org.apache.commons.math4.legacy.ode.sampling.FieldStepHandler FieldStepHandler} method {@link
134 * org.apache.commons.math4.legacy.ode.sampling.FieldStepHandler#handleStep(
135 * org.apache.commons.math4.legacy.ode.sampling.FieldStepInterpolator, boolean)
136 * handleStep(interpolator, isLast)} is to call this method first and
137 * <code>handleStep</code> afterwards. This scheduling allows the integrator to
138 * pass <code>true</code> as the <code>isLast</code> parameter to the step
139 * handler to make it aware the step will be the last one if this method
140 * returns {@link Action#STOP}. As the interpolator may be used to navigate back
141 * throughout the last step, user code called by this method and user
142 * code called by step handlers may experience apparently out of order values
143 * of the independent time variable. As an example, if the same user object
144 * implements both this {@link FieldEventHandler FieldEventHandler} interface and the
145 * {@link org.apache.commons.math4.legacy.ode.sampling.FieldStepHandler FieldStepHandler}
146 * interface, a <em>forward</em> integration may call its
147 * {code eventOccurred} method with t = 10 first and call its
148 * {code handleStep} method with t = 9 afterwards. Such out of order
149 * calls are limited to the size of the integration step for {@link
150 * org.apache.commons.math4.legacy.ode.sampling.FieldStepHandler variable step handlers}.</p>
151
152 * @param state current value of the independent <i>time</i> variable, state vector
153 * and derivative
154 * @param increasing if true, the value of the switching function increases
155 * when times increases around event (note that increase is measured with respect
156 * to physical time, not with respect to integration which may go backward in time)
157 * @return indication of what the integrator should do next, this
158 * value must be one of {@link Action#STOP}, {@link Action#RESET_STATE},
159 * {@link Action#RESET_DERIVATIVES} or {@link Action#CONTINUE}
160 */
161 Action eventOccurred(FieldODEStateAndDerivative<T> state, boolean increasing);
162
163 /** Reset the state prior to continue the integration.
164
165 * <p>This method is called after the step handler has returned and
166 * before the next step is started, but only when {@link
167 * #eventOccurred(FieldODEStateAndDerivative, boolean) eventOccurred} has itself
168 * returned the {@link Action#RESET_STATE} indicator. It allows the user to reset
169 * the state vector for the next step, without perturbing the step handler of the
170 * finishing step. If the {@link #eventOccurred(FieldODEStateAndDerivative, boolean)
171 * eventOccurred} never returns the {@link Action#RESET_STATE} indicator, this
172 * function will never be called, and it is safe to leave its body empty.</p>
173 * @param state current value of the independent <i>time</i> variable, state vector
174 * and derivative
175 * @return reset state (note that it does not include the derivatives, they will
176 * be added automatically by the integrator afterwards)
177 */
178 FieldODEState<T> resetState(FieldODEStateAndDerivative<T> state);
179 }