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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.ode.events;
import org.apache.commons.math3.analysis.UnivariateFunction;
import org.apache.commons.math3.analysis.solvers.AllowedSolution;
import org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver;
import org.apache.commons.math3.analysis.solvers.PegasusSolver;
import org.apache.commons.math3.analysis.solvers.UnivariateSolver;
import org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils;
import org.apache.commons.math3.exception.MaxCountExceededException;
import org.apache.commons.math3.exception.NoBracketingException;
import org.apache.commons.math3.ode.EquationsMapper;
import org.apache.commons.math3.ode.ExpandableStatefulODE;
import org.apache.commons.math3.ode.sampling.StepInterpolator;
import org.apache.commons.math3.util.FastMath;
/** This class handles the state for one {@link EventHandler
* event handler} during integration steps.
*
* Each time the integrator proposes a step, the event handler
* switching function should be checked. This class handles the state
* of one handler during one integration step, with references to the
* state at the end of the preceding step. This information is used to
* decide if the handler should trigger an event or not during the
* proposed step.
*
* @since 1.2
*/
public class EventState {
/** Event handler. */
private final EventHandler handler;
/** Maximal time interval between events handler checks. */
private final double maxCheckInterval;
/** Convergence threshold for event localization. */
private final double convergence;
/** Upper limit in the iteration count for event localization. */
private final int maxIterationCount;
/** Equation being integrated. */
private ExpandableStatefulODE expandable;
/** Time at the beginning of the step. */
private double t0;
/** Value of the events handler at the beginning of the step. */
private double g0;
/** Simulated sign of g0 (we cheat when crossing events). */
private boolean g0Positive;
/** Indicator of event expected during the step. */
private boolean pendingEvent;
/** Occurrence time of the pending event. */
private double pendingEventTime;
/** Occurrence time of the previous event. */
private double previousEventTime;
/** Integration direction. */
private boolean forward;
/** Variation direction around pending event.
* (this is considered with respect to the integration direction)
*/
private boolean increasing;
/** Next action indicator. */
private EventHandler.Action nextAction;
/** Root-finding algorithm to use to detect state events. */
private final UnivariateSolver solver;
/** Simple constructor.
* @param handler event handler
* @param maxCheckInterval maximal time interval between switching
* function checks (this interval prevents missing sign changes in
* case the integration steps becomes very large)
* @param convergence convergence threshold in the event time search
* @param maxIterationCount upper limit of the iteration count in
* the event time search
* @param solver Root-finding algorithm to use to detect state events
*/
public EventState(final EventHandler handler, final double maxCheckInterval,
final double convergence, final int maxIterationCount,
final UnivariateSolver solver) {
this.handler = handler;
this.maxCheckInterval = maxCheckInterval;
this.convergence = FastMath.abs(convergence);
this.maxIterationCount = maxIterationCount;
this.solver = solver;
// some dummy values ...
expandable = null;
t0 = Double.NaN;
g0 = Double.NaN;
g0Positive = true;
pendingEvent = false;
pendingEventTime = Double.NaN;
previousEventTime = Double.NaN;
increasing = true;
nextAction = EventHandler.Action.CONTINUE;
}
/** Get the underlying event handler.
* @return underlying event handler
*/
public EventHandler getEventHandler() {
return handler;
}
/** Set the equation.
* @param expandable equation being integrated
*/
public void setExpandable(final ExpandableStatefulODE expandable) {
this.expandable = expandable;
}
/** Get the maximal time interval between events handler checks.
* @return maximal time interval between events handler checks
*/
public double getMaxCheckInterval() {
return maxCheckInterval;
}
/** Get the convergence threshold for event localization.
* @return convergence threshold for event localization
*/
public double getConvergence() {
return convergence;
}
/** Get the upper limit in the iteration count for event localization.
* @return upper limit in the iteration count for event localization
*/
public int getMaxIterationCount() {
return maxIterationCount;
}
/** Reinitialize the beginning of the step.
* @param interpolator valid for the current step
* @exception MaxCountExceededException if the interpolator throws one because
* the number of functions evaluations is exceeded
*/
public void reinitializeBegin(final StepInterpolator interpolator)
throws MaxCountExceededException {
t0 = interpolator.getPreviousTime();
interpolator.setInterpolatedTime(t0);
g0 = handler.g(t0, getCompleteState(interpolator));
if (g0 == 0) {
// excerpt from MATH-421 issue:
// If an ODE solver is setup with an EventHandler that return STOP
// when the even is triggered, the integrator stops (which is exactly
// the expected behavior). If however the user wants to restart the
// solver from the final state reached at the event with the same
// configuration (expecting the event to be triggered again at a
// later time), then the integrator may fail to start. It can get stuck
// at the previous event. The use case for the bug MATH-421 is fairly
// general, so events occurring exactly at start in the first step should
// be ignored.
// extremely rare case: there is a zero EXACTLY at interval start
// we will use the sign slightly after step beginning to force ignoring this zero
final double epsilon = FastMath.max(solver.getAbsoluteAccuracy(),
FastMath.abs(solver.getRelativeAccuracy() * t0));
final double tStart = t0 + 0.5 * epsilon;
interpolator.setInterpolatedTime(tStart);
g0 = handler.g(tStart, getCompleteState(interpolator));
}
g0Positive = g0 >= 0;
}
/** Get the complete state (primary and secondary).
* @param interpolator interpolator to use
* @return complete state
*/
private double[] getCompleteState(final StepInterpolator interpolator) {
final double[] complete = new double[expandable.getTotalDimension()];
expandable.getPrimaryMapper().insertEquationData(interpolator.getInterpolatedState(),
complete);
int index = 0;
for (EquationsMapper secondary : expandable.getSecondaryMappers()) {
secondary.insertEquationData(interpolator.getInterpolatedSecondaryState(index++),
complete);
}
return complete;
}
/** Evaluate the impact of the proposed step on the event handler.
* @param interpolator step interpolator for the proposed step
* @return true if the event handler triggers an event before
* the end of the proposed step
* @exception MaxCountExceededException if the interpolator throws one because
* the number of functions evaluations is exceeded
* @exception NoBracketingException if the event cannot be bracketed
*/
public boolean evaluateStep(final StepInterpolator interpolator)
throws MaxCountExceededException, NoBracketingException {
try {
forward = interpolator.isForward();
final double t1 = interpolator.getCurrentTime();
final double dt = t1 - t0;
if (FastMath.abs(dt) < convergence) {
// we cannot do anything on such a small step, don't trigger any events
return false;
}
final int n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
final double h = dt / n;
final UnivariateFunction f = new UnivariateFunction() {
/** {@inheritDoc} */
public double value(final double t) throws LocalMaxCountExceededException {
try {
interpolator.setInterpolatedTime(t);
return handler.g(t, getCompleteState(interpolator));
} catch (MaxCountExceededException mcee) {
throw new LocalMaxCountExceededException(mcee);
}
}
};
double ta = t0;
double ga = g0;
for (int i = 0; i < n; ++i) {
// evaluate handler value at the end of the substep
final double tb = (i == n - 1) ? t1 : t0 + (i + 1) * h;
interpolator.setInterpolatedTime(tb);
final double gb = handler.g(tb, getCompleteState(interpolator));
// check events occurrence
if (g0Positive ^ (gb >= 0)) {
// there is a sign change: an event is expected during this step
// variation direction, with respect to the integration direction
increasing = gb >= ga;
// find the event time making sure we select a solution just at or past the exact root
final double root;
if (solver instanceof BracketedUnivariateSolver) {
@SuppressWarnings("unchecked")
BracketedUnivariateSolver bracketing =
(BracketedUnivariateSolver) solver;
root = forward ?
bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolution.RIGHT_SIDE) :
bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolution.LEFT_SIDE);
} else {
final double baseRoot = forward ?
solver.solve(maxIterationCount, f, ta, tb) :
solver.solve(maxIterationCount, f, tb, ta);
final int remainingEval = maxIterationCount - solver.getEvaluations();
BracketedUnivariateSolver bracketing =
new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
root = forward ?
UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
baseRoot, ta, tb, AllowedSolution.RIGHT_SIDE) :
UnivariateSolverUtils.forceSide(remainingEval, f, bracketing,
baseRoot, tb, ta, AllowedSolution.LEFT_SIDE);
}
if ((!Double.isNaN(previousEventTime)) &&
(FastMath.abs(root - ta) <= convergence) &&
(FastMath.abs(root - previousEventTime) <= convergence)) {
// we have either found nothing or found (again ?) a past event,
// retry the substep excluding this value, and taking care to have the
// required sign in case the g function is noisy around its zero and
// crosses the axis several times
do {
ta = forward ? ta + convergence : ta - convergence;
ga = f.value(ta);
} while ((g0Positive ^ (ga >= 0)) && (forward ^ (ta >= tb)));
if (forward ^ (ta >= tb)) {
// we were able to skip this spurious root
--i;
} else {
// we can't avoid this root before the end of the step,
// we have to handle it despite it is close to the former one
// maybe we have two very close roots
pendingEventTime = root;
pendingEvent = true;
return true;
}
} else if (Double.isNaN(previousEventTime) ||
(FastMath.abs(previousEventTime - root) > convergence)) {
pendingEventTime = root;
pendingEvent = true;
return true;
} else {
// no sign change: there is no event for now
ta = tb;
ga = gb;
}
} else {
// no sign change: there is no event for now
ta = tb;
ga = gb;
}
}
// no event during the whole step
pendingEvent = false;
pendingEventTime = Double.NaN;
return false;
} catch (LocalMaxCountExceededException lmcee) {
throw lmcee.getException();
}
}
/** Get the occurrence time of the event triggered in the current step.
* @return occurrence time of the event triggered in the current
* step or infinity if no events are triggered
*/
public double getEventTime() {
return pendingEvent ?
pendingEventTime :
(forward ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY);
}
/** Acknowledge the fact the step has been accepted by the integrator.
* @param t value of the independent time variable at the
* end of the step
* @param y array containing the current value of the state vector
* at the end of the step
*/
public void stepAccepted(final double t, final double[] y) {
t0 = t;
g0 = handler.g(t, y);
if (pendingEvent && (FastMath.abs(pendingEventTime - t) <= convergence)) {
// force the sign to its value "just after the event"
previousEventTime = t;
g0Positive = increasing;
nextAction = handler.eventOccurred(t, y, !(increasing ^ forward));
} else {
g0Positive = g0 >= 0;
nextAction = EventHandler.Action.CONTINUE;
}
}
/** Check if the integration should be stopped at the end of the
* current step.
* @return true if the integration should be stopped
*/
public boolean stop() {
return nextAction == EventHandler.Action.STOP;
}
/** Let the event handler reset the state if it wants.
* @param t value of the independent time variable at the
* beginning of the next step
* @param y array were to put the desired state vector at the beginning
* of the next step
* @return true if the integrator should reset the derivatives too
*/
public boolean reset(final double t, final double[] y) {
if (!(pendingEvent && (FastMath.abs(pendingEventTime - t) <= convergence))) {
return false;
}
if (nextAction == EventHandler.Action.RESET_STATE) {
handler.resetState(t, y);
}
pendingEvent = false;
pendingEventTime = Double.NaN;
return (nextAction == EventHandler.Action.RESET_STATE) ||
(nextAction == EventHandler.Action.RESET_DERIVATIVES);
}
/** Local wrapper to propagate exceptions. */
private static class LocalMaxCountExceededException extends RuntimeException {
/** Serializable UID. */
private static final long serialVersionUID = 20120901L;
/** Wrapped exception. */
private final MaxCountExceededException wrapped;
/** Simple constructor.
* @param exception exception to wrap
*/
LocalMaxCountExceededException(final MaxCountExceededException exception) {
wrapped = exception;
}
/** Get the wrapped exception.
* @return wrapped exception
*/
public MaxCountExceededException getException() {
return wrapped;
}
}
}