From 04050f35522f2a6d35a2e11bdfe4cd2997346fa8 Mon Sep 17 00:00:00 2001
From: Luc Maisonobe <luc@apache.org>
Date: Fri, 1 Mar 2013 17:36:46 +0000
Subject: [PATCH] Improved javadoc to explain how switching functions should
 behave across events in ODE events detection.

JIRA: MATH-937

git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1451658 13f79535-47bb-0310-9956-ffa450edef68
---
 src/changes/changes.xml                       |  4 ++++
 .../math3/ode/events/EventHandler.java        | 23 +++++++++++++++++++
 2 files changed, 27 insertions(+)

diff --git a/src/changes/changes.xml b/src/changes/changes.xml
index fa7e28f03..343940724 100644
--- a/src/changes/changes.xml
+++ b/src/changes/changes.xml
@@ -55,6 +55,10 @@ This is a minor release: It combines bug fixes and new features.
   Changes to existing features were made in a backwards-compatible
   way such as to allow drop-in replacement of the v3.1[.1] JAR file.
 ">
+      <action dev="luc" type="fix" issue="MATH-937" >
+        Improved javadoc to explain how switching functions should
+        behave across events in ODE events detection.
+      </action>
       <action dev="luc" type="add" >
         Added Hermite interpolator for ExtendFieldElement instances.
       </action>
diff --git a/src/main/java/org/apache/commons/math3/ode/events/EventHandler.java b/src/main/java/org/apache/commons/math3/ode/events/EventHandler.java
index 53cd38455..561be8f39 100644
--- a/src/main/java/org/apache/commons/math3/ode/events/EventHandler.java
+++ b/src/main/java/org/apache/commons/math3/ode/events/EventHandler.java
@@ -17,6 +17,7 @@
 
 package org.apache.commons.math3.ode.events;
 
+
 /** This interface represents a handler for discrete events triggered
  * during ODE integration.
  *
@@ -107,6 +108,28 @@ public interface EventHandler  {
    * The switching function must be continuous in its roots neighborhood
    * (but not necessarily smooth), as the integrator will need to find its
    * roots to locate precisely the events.</p>
+   * <p>Also note that the integrator expect that once an event has occurred,
+   * the sign of the switching function at the start of the next step (i.e.
+   * just after the event) is the opposite of the sign just before the event.
+   * This consistency between the steps <string>must</strong> be preserved,
+   * otherwise {@link org.apache.commons.math3.exception.NoBracketingException
+   * exceptions} related to root not being bracketed will occur.</p>
+   * <p>This need for consistency is sometimes tricky to achieve. A typical
+   * example is using an event to model a ball bouncing on the floor. The first
+   * idea to represent this would be to have {@code g(t) = h(t)} where h is the
+   * height above the floor at time {@code t}. When {@code g(t)} reaches 0, the
+   * ball is on the floor, so it should bounce and the typical way to do this is
+   * to reverse its vertical velocity. However, this would mean that before the
+   * event {@code g(t)} was decreasing from positive values to 0, and after the
+   * event {@code g(t)} would be increasing from 0 to positive values again.
+   * Consistency is broken here! The solution here is to have {@code g(t) = sign
+   * * h(t)}, where sign is a variable with initial value set to {@code +1}. Each
+   * time {@link #eventOccurred(double, double[], boolean) eventOccurred} is called,
+   * {@code sign} is reset to {@code -sign}. This allows the {@code g(t)}
+   * function to remain continuous (and even smooth) even across events, despite
+   * {@code h(t)} is not. Basically, the event is used to <em>fold</em> {@code h(t)}
+   * at bounce points, and {@code sign} is used to <em>unfold</em> it back, so the
+   * solvers sees a {@code g(t)} function which behaves smoothly even across events.</p>
 
    * @param t current value of the independent <i>time</i> variable
    * @param y array containing the current value of the state vector