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use root bracketing to find events on the appropriate side according to integration direction 

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1144889 13f79535-47bb-0310-9956-ffa450edef68
This commit is contained in:
Luc Maisonobe 2011-07-10 16:05:39 +00:00
parent f31af98c0d
commit c65e8fdd4e
1 changed files with 96 additions and 76 deletions
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172
src/main/java/org/apache/commons/math/ode/events/EventState.java
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@ -19,8 +19,11 @@ package org.apache.commons.math.ode.events;
import org.apache.commons.math.ConvergenceException; import org.apache.commons.math.ConvergenceException;
import org.apache.commons.math.analysis.UnivariateRealFunction; import org.apache.commons.math.analysis.UnivariateRealFunction;
import org.apache.commons.math.analysis.solvers.AllowedSolutions;
import org.apache.commons.math.analysis.solvers.BracketedUnivariateRealSolver;
import org.apache.commons.math.analysis.solvers.PegasusSolver;
import org.apache.commons.math.analysis.solvers.UnivariateRealSolver; import org.apache.commons.math.analysis.solvers.UnivariateRealSolver;
import org.apache.commons.math.exception.MathInternalError; import org.apache.commons.math.analysis.solvers.UnivariateRealSolverUtils;
import org.apache.commons.math.exception.MathUserException; import org.apache.commons.math.exception.MathUserException;
import org.apache.commons.math.ode.sampling.StepInterpolator; import org.apache.commons.math.ode.sampling.StepInterpolator;
import org.apache.commons.math.util.FastMath; import org.apache.commons.math.util.FastMath;
@ -151,38 +154,31 @@ public class EventState {
public void reinitializeBegin(final StepInterpolator interpolator) public void reinitializeBegin(final StepInterpolator interpolator)
throws EventException { throws EventException {
try { try {
// 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 want 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 t0 = interpolator.getPreviousTime();
// less than epsilon after the solver start in the first step should be ignored,
// where epsilon is the convergence threshold of the event. The sign of the g
// function should be evaluated after this initial ignore zone, not exactly at
// beginning (if there are no event at the very beginning g(t0) and g(t0+epsilon)
// have the same sign, so this does not hurt ; if there is an event at the very
// beginning, g(t0) and g(t0+epsilon) have opposite signs and we want to start
// with the second one. Of course, the sign of epsilon depend on the integration
// direction (forward or backward). This explains what is done below.
final double ignoreZone = interpolator.isForward() ? getConvergence() : -getConvergence();
t0 = interpolator.getPreviousTime() + ignoreZone;
interpolator.setInterpolatedTime(t0); interpolator.setInterpolatedTime(t0);
g0 = handler.g(t0, interpolator.getInterpolatedState()); g0 = handler.g(t0, interpolator.getInterpolatedState());
if (g0 == 0) { if (g0 == 0) {
// extremely rare case: there is a zero EXACTLY at end of ignore zone // excerpt from MATH-421 issue:
// we will use the opposite of sign at step beginning to force ignoring this zero // If an ODE solver is setup with an EventHandler that return STOP
final double tStart = interpolator.getPreviousTime(); // 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); interpolator.setInterpolatedTime(tStart);
g0Positive = handler.g(tStart, interpolator.getInterpolatedState()) <= 0; g0 = handler.g(tStart, interpolator.getInterpolatedState());
} else {
g0Positive = g0 >= 0;
} }
g0Positive = g0 >= 0;
} catch (MathUserException mue) { } catch (MathUserException mue) {
throw new EventException(mue); throw new EventException(mue);
@ -206,21 +202,31 @@ public class EventState {
forward = interpolator.isForward(); forward = interpolator.isForward();
final double t1 = interpolator.getCurrentTime(); final double t1 = interpolator.getCurrentTime();
if (FastMath.abs(t1 - t0) < convergence) { final double dt = t1 - t0;
if (FastMath.abs(dt) < convergence) {
// we cannot do anything on such a small step, don't trigger any events // we cannot do anything on such a small step, don't trigger any events
return false; return false;
} }
final double start = forward ? (t0 + convergence) : t0 - convergence; final int n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
final double dt = t1 - start; final double h = dt / n;
final int n = FastMath.max(1, (int) FastMath.ceil(FastMath.abs(dt) / maxCheckInterval));
final double h = dt / n; final UnivariateRealFunction f = new UnivariateRealFunction() {
public double value(final double t) {
try {
interpolator.setInterpolatedTime(t);
return handler.g(t, interpolator.getInterpolatedState());
} catch (EventException e) {
throw new ConveyedException(e);
}
}
};
double ta = t0; double ta = t0;
double ga = g0; double ga = g0;
for (int i = 0; i < n; ++i) { for (int i = 0; i < n; ++i) {
// evaluate handler value at the end of the substep // evaluate handler value at the end of the substep
final double tb = start + (i + 1) * h; final double tb = t0 + (i + 1) * h;
interpolator.setInterpolatedTime(tb); interpolator.setInterpolatedTime(tb);
final double gb = handler.g(tb, interpolator.getInterpolatedState()); final double gb = handler.g(tb, interpolator.getInterpolatedState());
@ -231,46 +237,37 @@ public class EventState {
// variation direction, with respect to the integration direction // variation direction, with respect to the integration direction
increasing = gb >= ga; increasing = gb >= ga;
final UnivariateRealFunction f = new UnivariateRealFunction() { // find the event time making sure we select a solution just at or past the exact root
public double value(final double t) throws MathUserException { final double root;
try { if (solver instanceof BracketedUnivariateRealSolver<?>) {
interpolator.setInterpolatedTime(t); @SuppressWarnings("unchecked")
return handler.g(t, interpolator.getInterpolatedState()); BracketedUnivariateRealSolver<UnivariateRealFunction> bracketing =
} catch (EventException e) { (BracketedUnivariateRealSolver<UnivariateRealFunction>) solver;
throw new MathUserException(e); root = forward ?
} bracketing.solve(maxIterationCount, f, ta, tb, AllowedSolutions.RIGHT_SIDE) :
} bracketing.solve(maxIterationCount, f, tb, ta, AllowedSolutions.LEFT_SIDE);
}; } else {
final double baseRoot = forward ?
if (ga * gb >= 0) { solver.solve(maxIterationCount, f, ta, tb) :
// this is a corner case: solver.solve(maxIterationCount, f, tb, ta);
// - there was an event near ta, final int remainingEval = maxIterationCount - solver.getEvaluations();
// - there is another event between ta and tb BracketedUnivariateRealSolver<UnivariateRealFunction> bracketing =
// - when ta was computed, convergence was reached on the "wrong side" of the interval new PegasusSolver(solver.getRelativeAccuracy(), solver.getAbsoluteAccuracy());
// this implies that the real sign of ga is the same as gb, so we need to slightly root = forward ?
// shift ta to make sure ga and gb get opposite signs and the solver won't complain UnivariateRealSolverUtils.forceSide(remainingEval, f, bracketing,
// about bracketing baseRoot, ta, tb, AllowedSolutions.RIGHT_SIDE) :
final double epsilon = (forward ? 0.25 : -0.25) * convergence; UnivariateRealSolverUtils.forceSide(remainingEval, f, bracketing,
for (int k = 0; (k < 4) && (ga * gb > 0); ++k) { baseRoot, tb, ta, AllowedSolutions.LEFT_SIDE);
ta += epsilon;
ga = f.value(ta);
}
if (ga * gb > 0) {
// this should never happen
throw new MathInternalError();
}
} }
final double root = (ta <= tb) ?
solver.solve(maxIterationCount, f, ta, tb) :
solver.solve(maxIterationCount, f, tb, ta);
if ((!Double.isNaN(previousEventTime)) && if ((!Double.isNaN(previousEventTime)) &&
(FastMath.abs(root - ta) <= convergence) && (FastMath.abs(root - ta) <= convergence) &&
(FastMath.abs(root - previousEventTime) <= convergence)) { (FastMath.abs(root - previousEventTime) <= convergence)) {
// we have either found nothing or found (again ?) a past event, we simply ignore it // we have either found nothing or found (again ?) a past event,
ta = tb; // retry the substep excluding this value
ga = gb; ta = forward ? ta + convergence : ta - convergence;
ga = f.value(ta);
--i;
} else if (Double.isNaN(previousEventTime) || } else if (Double.isNaN(previousEventTime) ||
(FastMath.abs(previousEventTime - root) > convergence)) { (FastMath.abs(previousEventTime - root) > convergence)) {
pendingEventTime = root; pendingEventTime = root;
@ -295,22 +292,20 @@ public class EventState {
pendingEventTime = Double.NaN; pendingEventTime = Double.NaN;
return false; return false;
} catch (MathUserException mue) { } catch (ConveyedException ce) {
final Throwable cause = mue.getCause(); throw ce.getConveyedException();
if ((cause != null) && (cause instanceof EventException)) {
throw (EventException) cause;
}
throw mue;
} }
} }
/** Get the occurrence time of the event triggered in the current step. /** Get the occurrence time of the event triggered in the current step.
* @return occurrence time of the event triggered in the current * @return occurrence time of the event triggered in the current
* step or positive infinity if no events are triggered * step or infinity if no events are triggered
*/ */
public double getEventTime() { public double getEventTime() {
return pendingEvent ? pendingEventTime : Double.POSITIVE_INFINITY; return pendingEvent ?
pendingEventTime :
(forward ? Double.POSITIVE_INFINITY : Double.NEGATIVE_INFINITY);
} }
/** Acknowledge the fact the step has been accepted by the integrator. /** Acknowledge the fact the step has been accepted by the integrator.
@ -373,4 +368,29 @@ public class EventState {
} }
/** Local exception to convey EventException instances through root finding algorithms. */
private static class ConveyedException extends RuntimeException {
/** Serializable uid. */
private static final long serialVersionUID = 2668348550531980574L;
/** Conveyed exception. */
private final EventException conveyedException;
/** Simple constructor.
* @param conveyedException conveyed exception
*/
public ConveyedException(final EventException conveyedException) {
this.conveyedException = conveyedException;
}
/** Get the conveyed exception.
* @return conveyed exception
*/
public EventException getConveyedException() {
return conveyedException;
}
}
} }