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
020import org.apache.commons.math3.analysis.UnivariateFunction;
021import org.apache.commons.math3.analysis.solvers.AllowedSolution;
022import org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver;
023import org.apache.commons.math3.analysis.solvers.PegasusSolver;
024import org.apache.commons.math3.analysis.solvers.UnivariateSolver;
025import org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils;
026import org.apache.commons.math3.exception.MaxCountExceededException;
027import org.apache.commons.math3.exception.NoBracketingException;
028import org.apache.commons.math3.ode.EquationsMapper;
029import org.apache.commons.math3.ode.ExpandableStatefulODE;
030import org.apache.commons.math3.ode.sampling.StepInterpolator;
031import org.apache.commons.math3.util.FastMath;
032
033/** This class handles the state for one {@link EventHandler
034 * event handler} during integration steps.
035 *
036 * <p>Each time the integrator proposes a step, the event handler
037 * switching function should be checked. This class handles the state
038 * of one handler during one integration step, with references to the
039 * state at the end of the preceding step. This information is used to
040 * decide if the handler should trigger an event or not during the
041 * proposed step.</p>
042 *
043 * @since 1.2
044 */
045public class EventState {
046
047    /** Event handler. */
048    private final EventHandler handler;
049
050    /** Maximal time interval between events handler checks. */
051    private final double maxCheckInterval;
052
053    /** Convergence threshold for event localization. */
054    private final double convergence;
055
056    /** Upper limit in the iteration count for event localization. */
057    private final int maxIterationCount;
058
059    /** Equation being integrated. */
060    private ExpandableStatefulODE expandable;
061
062    /** Time at the beginning of the step. */
063    private double t0;
064
065    /** Value of the events handler at the beginning of the step. */
066    private double g0;
067
068    /** Simulated sign of g0 (we cheat when crossing events). */
069    private boolean g0Positive;
070
071    /** Indicator of event expected during the step. */
072    private boolean pendingEvent;
073
074    /** Occurrence time of the pending event. */
075    private double pendingEventTime;
076
077    /** Occurrence time of the previous event. */
078    private double previousEventTime;
079
080    /** Integration direction. */
081    private boolean forward;
082
083    /** Variation direction around pending event.
084     *  (this is considered with respect to the integration direction)
085     */
086    private boolean increasing;
087
088    /** Next action indicator. */
089    private EventHandler.Action nextAction;
090
091    /** Root-finding algorithm to use to detect state events. */
092    private final UnivariateSolver solver;
093
094    /** Simple constructor.
095     * @param handler event handler
096     * @param maxCheckInterval maximal time interval between switching
097     * function checks (this interval prevents missing sign changes in
098     * case the integration steps becomes very large)
099     * @param convergence convergence threshold in the event time search
100     * @param maxIterationCount upper limit of the iteration count in
101     * the event time search
102     * @param solver Root-finding algorithm to use to detect state events
103     */
104    public EventState(final EventHandler handler, final double maxCheckInterval,
105                      final double convergence, final int maxIterationCount,
106                      final UnivariateSolver solver) {
107        this.handler           = handler;
108        this.maxCheckInterval  = maxCheckInterval;
109        this.convergence       = FastMath.abs(convergence);
110        this.maxIterationCount = maxIterationCount;
111        this.solver            = solver;
112
113        // some dummy values ...
114        expandable        = null;
115        t0                = Double.NaN;
116        g0                = Double.NaN;
117        g0Positive        = true;
118        pendingEvent      = false;
119        pendingEventTime  = Double.NaN;
120        previousEventTime = Double.NaN;
121        increasing        = true;
122        nextAction        = EventHandler.Action.CONTINUE;
123
124    }
125
126    /** Get the underlying event handler.
127     * @return underlying event handler
128     */
129    public EventHandler getEventHandler() {
130        return handler;
131    }
132
133    /** Set the equation.
134     * @param expandable equation being integrated
135     */
136    public void setExpandable(final ExpandableStatefulODE expandable) {
137        this.expandable = expandable;
138    }
139
140    /** Get the maximal time interval between events handler checks.
141     * @return maximal time interval between events handler checks
142     */
143    public double getMaxCheckInterval() {
144        return maxCheckInterval;
145    }
146
147    /** Get the convergence threshold for event localization.
148     * @return convergence threshold for event localization
149     */
150    public double getConvergence() {
151        return convergence;
152    }
153
154    /** Get the upper limit in the iteration count for event localization.
155     * @return upper limit in the iteration count for event localization
156     */
157    public int getMaxIterationCount() {
158        return maxIterationCount;
159    }
160
161    /** Reinitialize the beginning of the step.
162     * @param interpolator valid for the current step
163     * @exception MaxCountExceededException if the interpolator throws one because
164     * the number of functions evaluations is exceeded
165     */
166    public void reinitializeBegin(final StepInterpolator interpolator)
167        throws MaxCountExceededException {
168
169        t0 = interpolator.getPreviousTime();
170        interpolator.setInterpolatedTime(t0);
171        g0 = handler.g(t0, getCompleteState(interpolator));
172        if (g0 == 0) {
173            // excerpt from MATH-421 issue:
174            // If an ODE solver is setup with an EventHandler that return STOP
175            // when the even is triggered, the integrator stops (which is exactly
176            // the expected behavior). If however the user wants to restart the
177            // solver from the final state reached at the event with the same
178            // configuration (expecting the event to be triggered again at a
179            // later time), then the integrator may fail to start. It can get stuck
180            // at the previous event. The use case for the bug MATH-421 is fairly
181            // general, so events occurring exactly at start in the first step should
182            // be ignored.
183
184            // extremely rare case: there is a zero EXACTLY at interval start
185            // we will use the sign slightly after step beginning to force ignoring this zero
186            final double epsilon = FastMath.max(solver.getAbsoluteAccuracy(),
187                                                FastMath.abs(solver.getRelativeAccuracy() * t0));
188            final double tStart = t0 + 0.5 * epsilon;
189            interpolator.setInterpolatedTime(tStart);
190            g0 = handler.g(tStart, getCompleteState(interpolator));
191        }
192        g0Positive = g0 >= 0;
193
194    }
195
196    /** Get the complete state (primary and secondary).
197     * @param interpolator interpolator to use
198     * @return complete state
199     */
200    private double[] getCompleteState(final StepInterpolator interpolator) {
201
202        final double[] complete = new double[expandable.getTotalDimension()];
203
204        expandable.getPrimaryMapper().insertEquationData(interpolator.getInterpolatedState(),
205                                                         complete);
206        int index = 0;
207        for (EquationsMapper secondary : expandable.getSecondaryMappers()) {
208            secondary.insertEquationData(interpolator.getInterpolatedSecondaryState(index++),
209                                         complete);
210        }
211
212        return complete;
213
214    }
215
216    /** Evaluate the impact of the proposed step on the event handler.
217     * @param interpolator step interpolator for the proposed step
218     * @return true if the event handler triggers an event before
219     * the end of the proposed step
220     * @exception MaxCountExceededException if the interpolator throws one because
221     * the number of functions evaluations is exceeded
222     * @exception NoBracketingException if the event cannot be bracketed
223     */
224    public boolean evaluateStep(final StepInterpolator interpolator)
225        throws MaxCountExceededException, NoBracketingException {
226
227        try {
228            forward = interpolator.isForward();
229            final double t1 = interpolator.getCurrentTime();
230            final double dt = t1 - t0;
231            if (FastMath.abs(dt) < convergence) {
232                // we cannot do anything on such a small step, don't trigger any events
233                return false;
234            }
235            final int    n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
236            final double h = dt / n;
237
238            final UnivariateFunction f = new UnivariateFunction() {
239                public double value(final double t) throws LocalMaxCountExceededException {
240                    try {
241                        interpolator.setInterpolatedTime(t);
242                        return handler.g(t, getCompleteState(interpolator));
243                    } catch (MaxCountExceededException mcee) {
244                        throw new LocalMaxCountExceededException(mcee);
245                    }
246                }
247            };
248
249            double ta = t0;
250            double ga = g0;
251            for (int i = 0; i < n; ++i) {
252
253                // evaluate handler value at the end of the substep
254                final double tb = t0 + (i + 1) * h;
255                interpolator.setInterpolatedTime(tb);
256                final double gb = handler.g(tb, getCompleteState(interpolator));
257
258                // check events occurrence
259                if (g0Positive ^ (gb >= 0)) {
260                    // there is a sign change: an event is expected during this step
261
262                    // variation direction, with respect to the integration direction
263                    increasing = gb >= ga;
264
265                    // find the event time making sure we select a solution just at or past the exact root
266                    final double root;
267                    if (solver instanceof BracketedUnivariateSolver<?>) {
268                        @SuppressWarnings("unchecked")
269                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
270                                (BracketedUnivariateSolver<UnivariateFunction>) solver;
271                        root = forward ?
272                               bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolution.RIGHT_SIDE) :
273                               bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolution.LEFT_SIDE);
274                    } else {
275                        final double baseRoot = forward ?
276                                                solver.solve(maxIterationCount, f, ta, tb) :
277                                                solver.solve(maxIterationCount, f, tb, ta);
278                        final int remainingEval = maxIterationCount - solver.getEvaluations();
279                        BracketedUnivariateSolver<UnivariateFunction> bracketing =
280                                new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
281                        root = forward ?
282                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
283                                                                   baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
284                               UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
285                                                                   baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
286                    }
287
288                    if ((!Double.isNaN(previousEventTime)) &&
289                        (FastMath.abs(root - ta) <= convergence) &&
290                        (FastMath.abs(root - previousEventTime) <= convergence)) {
291                        // we have either found nothing or found (again ?) a past event,
292                        // retry the substep excluding this value, and taking care to have the
293                        // required sign in case the g function is noisy around its zero and
294                        // crosses the axis several times
295                        do {
296                            ta = forward ? ta + convergence : ta - convergence;
297                            ga = f.value(ta);
298                        } while ((g0Positive ^ (ga >= 0)) && (forward ^ (ta >= tb)));
299                        --i;
300                    } else if (Double.isNaN(previousEventTime) ||
301                               (FastMath.abs(previousEventTime - root) > convergence)) {
302                        pendingEventTime = root;
303                        pendingEvent = true;
304                        return true;
305                    } else {
306                        // no sign change: there is no event for now
307                        ta = tb;
308                        ga = gb;
309                    }
310
311                } else {
312                    // no sign change: there is no event for now
313                    ta = tb;
314                    ga = gb;
315                }
316
317            }
318
319            // no event during the whole step
320            pendingEvent     = false;
321            pendingEventTime = Double.NaN;
322            return false;
323
324        } catch (LocalMaxCountExceededException lmcee) {
325            throw lmcee.getException();
326        }
327
328    }
329
330    /** Get the occurrence time of the event triggered in the current step.
331     * @return occurrence time of the event triggered in the current
332     * step or infinity if no events are triggered
333     */
334    public double getEventTime() {
335        return pendingEvent ?
336               pendingEventTime :
337               (forward ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY);
338    }
339
340    /** Acknowledge the fact the step has been accepted by the integrator.
341     * @param t value of the independent <i>time</i> variable at the
342     * end of the step
343     * @param y array containing the current value of the state vector
344     * at the end of the step
345     */
346    public void stepAccepted(final double t, final double[] y) {
347
348        t0 = t;
349        g0 = handler.g(t, y);
350
351        if (pendingEvent && (FastMath.abs(pendingEventTime - t) <= convergence)) {
352            // force the sign to its value "just after the event"
353            previousEventTime = t;
354            g0Positive        = increasing;
355            nextAction        = handler.eventOccurred(t, y, !(increasing ^ forward));
356        } else {
357            g0Positive = g0 >= 0;
358            nextAction = EventHandler.Action.CONTINUE;
359        }
360    }
361
362    /** Check if the integration should be stopped at the end of the
363     * current step.
364     * @return true if the integration should be stopped
365     */
366    public boolean stop() {
367        return nextAction == EventHandler.Action.STOP;
368    }
369
370    /** Let the event handler reset the state if it wants.
371     * @param t value of the independent <i>time</i> variable at the
372     * beginning of the next step
373     * @param y array were to put the desired state vector at the beginning
374     * of the next step
375     * @return true if the integrator should reset the derivatives too
376     */
377    public boolean reset(final double t, final double[] y) {
378
379        if (!(pendingEvent && (FastMath.abs(pendingEventTime - t) <= convergence))) {
380            return false;
381        }
382
383        if (nextAction == EventHandler.Action.RESET_STATE) {
384            handler.resetState(t, y);
385        }
386        pendingEvent      = false;
387        pendingEventTime  = Double.NaN;
388
389        return (nextAction == EventHandler.Action.RESET_STATE) ||
390               (nextAction == EventHandler.Action.RESET_DERIVATIVES);
391
392    }
393
394    /** Local wrapper to propagate exceptions. */
395    private static class LocalMaxCountExceededException extends RuntimeException {
396
397        /** Serializable UID. */
398        private static final long serialVersionUID = 20120901L;
399
400        /** Wrapped exception. */
401        private final MaxCountExceededException wrapped;
402
403        /** Simple constructor.
404         * @param exception exception to wrap
405         */
406        public LocalMaxCountExceededException(final MaxCountExceededException exception) {
407            wrapped = exception;
408        }
409
410        /** Get the wrapped exception.
411         * @return wrapped exception
412         */
413        public MaxCountExceededException getException() {
414            return wrapped;
415        }
416
417    }
418
419}