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.math4.legacy.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 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.math4.legacy.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 /** Initialize event handler at the start of an ODE integration. 090 * <p> 091 * This method is called once at the start of the integration. It 092 * may be used by the event handler to initialize some internal data 093 * if needed. 094 * </p> 095 * @param t0 start value of the independent <i>time</i> variable 096 * @param y0 array containing the start value of the state vector 097 * @param t target time for the integration 098 */ 099 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}