/*
    * Licensed to the Hipparchus project 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
    *
    *      https://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.hipparchus.ode.events;
  
  import org.hipparchus.analysis.UnivariateFunction;
  import org.hipparchus.analysis.solvers.BracketedUnivariateSolver;
  import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
  import org.hipparchus.ode.ODEIntegrator;
  import org.hipparchus.ode.ODEState;
  import org.hipparchus.ode.ODEStateAndDerivative;
  import org.hipparchus.ode.OrdinaryDifferentialEquation;
  import org.hipparchus.ode.nonstiff.DormandPrince853Integrator;
  import org.hipparchus.ode.nonstiff.LutherIntegrator;
  import org.hipparchus.ode.sampling.ODEStateInterpolator;
  import org.hipparchus.ode.sampling.ODEStepHandler;
  import org.hipparchus.util.FastMath;
  import org.junit.jupiter.api.Test;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.List;
  
  import static org.junit.jupiter.api.Assertions.assertEquals;
  import static org.junit.jupiter.api.Assertions.assertFalse;
  import static org.junit.jupiter.api.Assertions.assertSame;
  import static org.junit.jupiter.api.Assertions.assertTrue;
  import static org.junit.jupiter.api.Assertions.fail;
  
  /**
   * Check events are detected correctly when the event times are close.
   *
   * @author Evan Ward
   */
  class CloseEventsTest {
  
      @Test
      void testEventAtFinalTime() {
          final DormandPrince853Integrator integrator = new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
          final IntervalDetector detector = new IntervalDetector(720, 1e-10, 100, Action.RESET_DERIVATIVES, 16296.238, 17016.238);
          integrator.addEventDetector(detector);
          integrator.integrate(new Equation(), new ODEState(0.0, new double[2]), 17016.238);
          assertEquals(2, detector.getEvents().size());
      }
  
      @Test
      void testCloseEventsFirstOneIsReset() {
          // setup
          // a fairly rare state to reproduce this bug. Two dates, d1 < d2, that
          // are very close. Event triggers on d1 will reset state to break out of
          // event handling loop in AbstractIntegrator.acceptStep(). At this point
          // detector2 has g0Positive == true but the event time is set to just
          // before the event so g(t0) is negative. Now on processing the
          // next step the root solver checks the sign of the start, midpoint,
          // and end of the interval so we need another event less than half a max
          // check interval after d2 so that the g function will be negative at
          // all three times. Then we get a non bracketing exception.
          ODEIntegrator integrator =
                  new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
  
          TimeDetector detector1 = new TimeDetector(10, 1e-9, 100, Action.RESET_DERIVATIVES, 9);
          integrator.addEventDetector(detector1);
          TimeDetector detector2 = new TimeDetector(11, 1e-9, 100, 9 + 1e-15, 9 + 4.9);
          integrator.addEventDetector(detector2);
  
          // action
          integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20);
  
          // verify
          List<Event> events1 = detector1.getEvents();
          assertEquals(1, events1.size());
          assertEquals(9, events1.get(0).getT(), 0.0);
          List<Event> events2 = detector2.getEvents();
          assertEquals(0, events2.size());
      }
  
      @Test
      void testCloseEvents() {
          // setup
          double e = 1e-15;
          ODEIntegrator integrator =
                  new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
  
          TimeDetector detector1 = new TimeDetector(10, 1, 100, 5);
          integrator.addEventDetector(detector1);
          TimeDetector detector2 = new TimeDetector(10, 1, 100, 5.5);
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20);
 
         // verify
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(5, events1.get(0).getT(), 0.0);
         List<Event> events2 = detector2.getEvents();
         assertEquals(1, events2.size());
         assertEquals(5.5, events2.get(0).getT(), 0.0);
     }
 
     @Test
     void testSimultaneousEvents() {
         // setup
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
 
         TimeDetector detector1 = new TimeDetector(10, 1, 100, 5);
         integrator.addEventDetector(detector1);
         TimeDetector detector2 = new TimeDetector(10, 1, 100, 5);
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20);
 
         // verify
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(5, events1.get(0).getT(), 0.0);
         List<Event> events2 = detector2.getEvents();
         assertEquals(1, events2.size());
         assertEquals(5, events2.get(0).getT(), 0.0);
     }
 
     /**
      * Previously there were some branches when tryAdvance() returned false but did not
      * set {@code t0 = t}. This allowed the order of events to not be chronological and to
      * detect events that should not have occurred, both of which are problems.
      */
     @Test
     void testSimultaneousEventsReset() {
         // setup
         double tol = 1e-10;
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
         boolean[] firstEventOccurred = {false};
         List<Event> events = new ArrayList<>();
 
         TimeDetector detector1 = new TimeDetector(10, tol, 100, events, 5) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     firstEventOccurred[0] = true;
                     super.getHandler().eventOccurred(state, detector, increasing);
                     return Action.RESET_STATE;
                 };
             }
         };
         integrator.addEventDetector(detector1);
         // this detector changes it's g function definition when detector1 fires
         TimeDetector detector2 = new TimeDetector(1, tol, 100, events, 1, 3, 5) {
             @Override
             public double g(final ODEStateAndDerivative state) {
                 if (firstEventOccurred[0]) {
                     return super.g(state);
                 }
                 return new TimeDetector(1, tol, 100, 5).g(state);
             }
         };
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20);
 
         // verify
         // order is important to make sure the test checks what it is supposed to
         assertEquals(5, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detector1, events.get(0).getDetector());
         assertEquals(5, events.get(1).getT(), 0.0);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(detector2, events.get(1).getDetector());
         assertEquals(2, events.size());
     }
 
     /**
      * When two event detectors have a discontinuous event caused by a {@link
      * Action#RESET_STATE} or {@link Action#RESET_DERIVATIVES}. The two event detectors
      * would each say they had an event that had to be handled before the other one, but
      * neither would actually back up at all. For Hipparchus GitHub #91.
      */
     @Test
     void testSimultaneousDiscontinuousEventsAfterReset() {
         // setup
         double t = FastMath.PI;
         double tol = 1e-10;
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         List<Event> events = new ArrayList<>();
 
         TimeDetector resetDetector =
                 new ResetDetector(10, tol, 100, events, new ODEState(t, new double[]{1e100, 0}), t);
         integrator.addEventDetector(resetDetector);
         List<BaseDetector> detectors = new ArrayList<>();
         for (int i = 0; i < 2; i++) {
             BaseDetector detector1 = new StateDetector(10, tol, 100, events, 0.0);
             integrator.addEventDetector(detector1);
             detectors.add(detector1);
         }
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[]{-1e100, 0}), 10);
 
         // verify
         assertEquals(t, events.get(0).getT(),  tol);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(resetDetector, events.get(0).getDetector());
         // next two events can occur in either order
         assertEquals(t, events.get(1).getT(),  tol);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(detectors.get(0), events.get(1).getDetector());
         assertEquals(t, events.get(2).getT(),  tol);
         assertTrue(events.get(2).isIncreasing());
         assertEquals(detectors.get(1), events.get(2).getDetector());
         assertEquals(3, events.size());
     }
 
     /**
      * test the g function switching with a period shorter than the tolerance. We don't
      * need to find any of the events, but we do need to not crash. And we need to
      * preserve the alternating increasing / decreasing sequence.
      */
     @Test
     void testFastSwitching() {
         // setup
         // step size of 10 to land in between two events we would otherwise miss
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
 
         TimeDetector detector1 = new TimeDetector(10, 0.2, 100, 9.9, 10.1, 12);
         integrator.addEventDetector(detector1);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20);
 
         //verify
         // finds one or three events. Not 2.
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(9.9, events1.get(0).getT(), 0.1);
         assertTrue(events1.get(0).isIncreasing());
     }
 
     /** "A Tricky Problem" from bug #239. */
     @Test
     void testTrickyCaseLower() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 1.0, t2 = 15, t3 = 16, t4 = 17, t5 = 18;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events, t3);
         TimeDetector detectorB = new TimeDetector(maxCheck, tolerance, 100, events, -10, t1, t2, t5);
         TimeDetector detectorC = new TimeDetector(maxCheck, tolerance, 100, Action.RESET_DERIVATIVES, events, t4);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         // but I only know one way to do that in this case.
         assertEquals(5, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertFalse(events.get(0).isIncreasing());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(t3, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertEquals(t4, events.get(3).getT(), tolerance);
         assertTrue(events.get(3).isIncreasing());
         assertEquals(t5, events.get(4).getT(), tolerance);
         assertFalse(events.get(4).isIncreasing());
     }
 
     /**
      * Test case for two event detectors. DetectorA has event at t2, DetectorB at t3, but
      * due to the root finding tolerance DetectorB's event occurs at t1. With t1 < t2 <
      * t3.
      */
     @Test
     void testRootFindingTolerance() {
         //setup
         double maxCheck = 10;
         double t2 = 11, t3 = t2 + 1e-5;
         List<Event>   events     = new ArrayList<>();
         TimeDetector  detectorA  = new TimeDetector(maxCheck, 1e-6, 100, events, t2);
         TimeDetector  detectorB  = new FlatDetector(maxCheck, 0.5, 100, events, t3);
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         // if these fail the event finding did its job,
         // but this test isn't testing what it is supposed to be
         assertSame(detectorB, events.get(0).getDetector());
         assertSame(detectorA, events.get(1).getDetector());
         assertTrue(events.get(0).getT() < events.get(1).getT());
 
         // check event detection worked
         assertEquals(2, events.size());
         assertEquals(t3, events.get(0).getT(), 0.5);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(t2, events.get(1).getT(), 1e-6);
         assertTrue(events.get(1).isIncreasing());
     }
 
     /** check when g(t < root) < 0,  g(root + convergence) < 0. */
     @Test
     void testRootPlusToleranceHasWrongSign() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         final double toleranceB = 0.3;
         double t1 = 11, t2 = 11.1, t3 = 11.2;
         // shared event list so we know the order in which they occurred
         List<Event>   events     = new ArrayList<>();
         TimeDetector  detectorA  = new TimeDetector(maxCheck, 1e-6, 100, events, t2);
         TimeDetector  detectorB  = new TimeDetector(maxCheck, toleranceB, 100, events, t1, t3);
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         // we only care that the rules are satisfied, there are other solutions
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), toleranceB);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorB, events.get(0).getDetector());
         assertEquals(t3, events.get(1).getT(), toleranceB);
         assertFalse(events.get(1).isIncreasing());
         assertSame(detectorB, events.get(1).getDetector());
         assertEquals(t2, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertSame(detectorA, events.get(2).getDetector());
         // chronological
         for (int i = 1; i < events.size(); i++) {
             assertTrue(events.get(i).getT() >= events.get(i - 1).getT());
         }
     }
 
     /** check when g(t < root) < 0,  g(root + convergence) < 0. */
     @Test
     void testRootPlusToleranceHasWrongSignAndLessThanTb() {
         // setup
         // test is fragile w.r.t. implementation and these parameters
         double maxCheck = 10;
         double tolerance = 0.5;
         double t1 = 11, t2 = 11.4, t3 = 12.0;
         // shared event list so we know the order in which they occurred
         List<Event>   events     = new ArrayList<>();
         TimeDetector  detectorB  = new FlatDetector(maxCheck, tolerance, 100, events, t1, t2, t3);
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         // allowed to find t1 or t3.
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorB, events.get(0).getDetector());
     }
 
     /**
      * Check when g(t) has a multiple root. e.g. g(t < root) < 0, g(root) = 0, g(t > root)
      * < 0.
      */
     @Test
     void testDoubleRoot() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 11;
         // shared event list so we know the order in which they occurred
         List<Event>   events     = new ArrayList<>();
         TimeDetector  detectorA  = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         TimeDetector  detectorB  = new TimeDetector(maxCheck, tolerance, 100, events, t1, t1);
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         // detector worked correctly
         assertEquals(0.0, detectorB.g(state(t1)));
         assertTrue(detectorB.g(state(t1 - 1e-6)) < 0);
         assertTrue(detectorB.g(state(t1 + 1e-6)) < 0);
     }
 
     /**
      * Check when g(t) has a multiple root. e.g. g(t < root) > 0, g(root) = 0, g(t > root)
      * > 0.
      */
     @Test
     void testDoubleRootOppositeSign() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 11;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, -20, t1, t1);
         detectorB.g(state(t1));
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         // detector worked correctly
         assertEquals(0.0, detectorB.g(state(t1)), 0.0);
         assertTrue(detectorB.g(state(t1 - 1e-6)) > 0);
         assertTrue(detectorB.g(state(t1 + 1e-6)) > 0);
     }
 
     /** check root finding when zero at both ends. */
     @Test
     void testZeroAtBeginningAndEndOfInterval() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 10, t2 = 20;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1, t2);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), 0.0);
         assertFalse(events.get(1).isIncreasing());
         assertSame(detectorA, events.get(1).getDetector());
     }
 
     /** check root finding when zero at both ends. */
     @Test
     void testZeroAtBeginningAndEndOfIntervalOppositeSign() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 10, t2 = 20;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, -10, t1, t2);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertFalse(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), 0.0);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorA, events.get(1).getDetector());
     }
 
     /** Test where an event detector has to back up multiple times. */
     @Test
     void testMultipleBackups() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 11.0, t2 = 12, t3 = 13, t4 = 14, t5 = 15, t6 = 16, t7 = 17;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t6);
         TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t1, t3, t4, t7);
         TimeDetector detectorC = new ContinuousDetector(maxCheck, tolerance, 100, events, t2, t5);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         assertEquals(5, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detectorB, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(detectorC, events.get(1).getDetector());
         // reporting t3 and t4 is optional, seeing them is not.
         // we know a root was found at t3 because events are reported at t2 and t5.
         /*
         Assertions.assertEquals(t3, events.get(2).getT(), tolerance);
         Assertions.assertEquals(false, events.get(2).isIncreasing());
         Assertions.assertEquals(detectorB, events.get(2).getDetector());
         Assertions.assertEquals(t4, events.get(3).getT(), tolerance);
         Assertions.assertEquals(true, events.get(3).isIncreasing());
         Assertions.assertEquals(detectorB, events.get(3).getDetector());
         */
         assertEquals(t5, events.get(2).getT(), tolerance);
         assertFalse(events.get(2).isIncreasing());
         assertEquals(detectorC, events.get(2).getDetector());
         assertEquals(t6, events.get(3).getT(), tolerance);
         assertTrue(events.get(3).isIncreasing());
         assertEquals(detectorA, events.get(3).getDetector());
         assertEquals(t7, events.get(4).getT(), tolerance);
         assertFalse(events.get(4).isIncreasing());
         assertEquals(detectorB, events.get(4).getDetector());
     }
 
     /** Test a reset event triggering another event at the same time. */
     @Test
     void testEventCausedByStateReset() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = 15.0;
         final ODEState newState = new ODEState(t1, new double[]{-20, 0});
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ResetDetector(maxCheck, tolerance, 100, events, newState, t1);
         BaseDetector detectorB = new StateDetector(maxCheck, tolerance, 100, events, -1);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 40.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detectorA, events.get(0).getDetector());
         assertEquals(t1, events.get(1).getT(), tolerance);
         assertFalse(events.get(1).isIncreasing());
         assertEquals(detectorB, events.get(1).getDetector());
         assertEquals(t1 + 19, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertEquals(detectorB, events.get(2).getDetector());
     }
 
     /** check when t + tolerance == t. */
     @Test
     void testConvergenceTooTight() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18;
         double t1 = 15;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
     /** check when root finding tolerance > event finding tolerance. */
     @Test
     void testToleranceMismatch() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18;
         double t1 = 15.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new FlatDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         // use root finder tolerance instead of event finder tolerance.
         assertEquals(t1, events.get(0).getT(), 1e-3);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of a continue action. In this case the change
      * creates a new event for a detector that previously had no events occurring. Not
      * sure if this should be officially supported, but it is used in Orekit's
      * DateDetector, it's useful, and not too hard to implement.
      */
     @Test
     void testEventChangesGFunctionDefinition() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = 11, t2 = 19;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return -1;
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * cancels the occurrence of the event.
      */
     @Test
     void testEventChangesGFunctionDefinitionCancel() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = 11, t2 = 11.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (!swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return -1;
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * delays the occurrence of the event.
      */
     @Test
     void testEventChangesGFunctionDefinitionDelay() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = 11, t2 = 11.1, t3 = 11.2;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         final TimeDetector detectorD = new ContinuousDetector(maxCheck, tolerance, 100, events, t3);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (!swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return detectorD.g(state);
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t3, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * causes the event to happen sooner than originally expected.
      */
     @Test
     void testEventChangesGFunctionDefinitionAccelerate() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = 11, t2 = 11.1, t3 = 11.2;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         final TimeDetector detectorD = new ContinuousDetector(maxCheck, tolerance, 100, events, t3);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return detectorD.g(state);
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /** check when root finding tolerance > event finding tolerance. */
     @Test
     void testToleranceStop() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18; // less than 1 ulp
         double t1 = 15.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new FlatDetector(maxCheck, tolerance, 100, Action.STOP, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         ODEStateAndDerivative finalState =
                 integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(1, events.size());
         // use root finder tolerance instead of event finder tolerance.
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t1, finalState.getTime(), tolerance);
 
         // try to resume propagation
         finalState = integrator.integrate(new Equation(), finalState, 30.0);
 
         // verify it got to the end
         assertEquals(30.0, finalState.getTime(), 0.0);
     }
 
     /**
      * Test when g function is initially zero for longer than the tolerance. Can occur
      * when restarting after a stop and cancellation occurs in the g function.
      */
     @Test
     void testLongInitialZero() {
         // setup
         double maxCheck = 10;
         double tolerance = 1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, Action.STOP, events, -50) {
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (state.getTime() < 2) {
                     return 0;
                 } else {
                     return super.g(state);
                 }
             }
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(0, events.size());
     }
 
     /**
      * The root finder requires the start point to be in the interval (a, b) which is hard
      * when there aren't many numbers between a and b. This test uses a second event
      * detector to force a very small window for the first event detector.
      */
     @Test
     void testShortBracketingInterval() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         final double t1 = FastMath.nextUp(10.0), t2 = 10.5;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // never zero so there is no easy way out
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events) {
             @Override
             public double g(ODEStateAndDerivative state) {
                 final double t = state.getTime();
                 if (t < t1) {
                     return -1;
                 } else if (t < t2) {
                     return 1;
                 } else {
                     return -1;
                 }
             }
         };
         TimeDetector detectorB = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), 30.0);
 
         // verify
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t1, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorB, events.get(1).getDetector());
         assertEquals(t2, events.get(2).getT(), tolerance);
         assertFalse(events.get(2).isIncreasing());
         assertSame(detectorA, events.get(2).getDetector());
     }
 
     /** Check that steps are restricted correctly with a continue event. */
     @Test
     void testEventStepHandler() {
         // setup
         double tolerance = 1e-18;
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(new TimeDetector(100, tolerance, 100, 5));
         StepHandler stepHandler = new StepHandler();
         integrator.addStepHandler(stepHandler);
 
         // action
         ODEStateAndDerivative finalState = integrator
                 .integrate(new Equation(), new ODEState(0, new double[2]), 10);
 
         // verify
         assertEquals(10.0, finalState.getTime(), tolerance);
         assertEquals(0.0,
                 stepHandler.initialState.getTime(), tolerance);
         assertEquals(10.0, stepHandler.finalTime, tolerance);
         assertEquals(10.0,
                 stepHandler.finalState.getTime(), tolerance);
         ODEStateInterpolator interpolator = stepHandler.interpolators.get(0);
         assertEquals(0.0,
                 interpolator.getPreviousState().getTime(), tolerance);
         assertEquals(5.0,
                 interpolator.getCurrentState().getTime(), tolerance);
         interpolator = stepHandler.interpolators.get(1);
         assertEquals(5.0,
                 interpolator.getPreviousState().getTime(), tolerance);
         assertEquals(10.0,
                 interpolator.getCurrentState().getTime(), tolerance);
         assertEquals(2, stepHandler.interpolators.size());
     }
 
     /** Test resetState(...) returns {@code null}. */
     @Test
     void testEventCausedByDerivativesReset() {
         // setup
         TimeDetector detectorA = new TimeDetector(10, 1e-6, 100, Action.RESET_STATE, 15.0) {
             @Override
             public ODEEventHandler getHandler() {
                 return new ODEEventHandler() {
                     @Override
                     public Action eventOccurred(ODEStateAndDerivative state, ODEEventDetector detector, boolean increasing) {
                         return Action.RESET_STATE;
                     }
                     @Override
                     public ODEState resetState(ODEEventDetector detector, ODEStateAndDerivative state) {
                         return null;
                     }
                 };
             }
         };
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         try {
             // action
             integrator.integrate(new Equation(), new ODEState(0, new double[2]), 20.0);
             fail("Expected Exception");
         } catch (NullPointerException e) {
             // expected
         }
     }
 
     @Test
     void testResetChangesSign() {
         OrdinaryDifferentialEquation equation = new OrdinaryDifferentialEquation() {
             public int getDimension() { return 1; }
             public double[] computeDerivatives(double t, double[] y) { return new double[] { 1.0 }; }
         };
 
         LutherIntegrator integrator = new LutherIntegrator(20.0);
         final double small = 1.0e-10;
         ResetChangesSignGenerator eventsGenerator = new ResetChangesSignGenerator(6.0, 9.0, -0.5 * small, 8.0, small, 1000);
         integrator.addEventDetector(eventsGenerator);
         final ODEStateAndDerivative end = integrator.integrate(equation, new ODEState(0.0, new double[1]), 100.0);
         assertEquals(2,                 eventsGenerator.getCount());
         assertEquals(9.0,               end.getCompleteState()[0], 1.0e-12);
         assertEquals(9.0 + 0.5 * small, end.getTime(),             1.0e-12);
     }
 
     /* The following tests are copies of the above tests, except that they propagate in
      * the reverse direction and all the signs on the time values are negated.
      */
 
 
     @Test
     void testCloseEventsFirstOneIsResetReverse() {
         // setup
         // a fairly rare state to reproduce this bug. Two dates, d1 < d2, that
         // are very close. Event triggers on d1 will reset state to break out of
         // event handling loop in AbstractIntegrator.acceptStep(). At this point
         // detector2 has g0Positive == true but the event time is set to just
         // before the event so g(t0) is negative. Now on processing the
         // next step the root solver checks the sign of the start, midpoint,
         // and end of the interval so we need another event less than half a max
         // check interval after d2 so that the g function will be negative at
         // all three times. Then we get a non bracketing exception.
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
 
         // switched for 9 to 1 to be close to the start of the step
         double t1 = -1;
         TimeDetector detector1 = new TimeDetector(10, 1e-9, 100, Action.RESET_DERIVATIVES, t1);
         integrator.addEventDetector(detector1);
         TimeDetector detector2 = new TimeDetector(11, 1e-9, 100, t1 - 1e-15, t1 - 4.9);
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20);
 
         // verify
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(t1, events1.get(0).getT(), 0.0);
         List<Event> events2 = detector2.getEvents();
         assertEquals(0, events2.size());
     }
 
     @Test
     void testCloseEventsReverse() {
         // setup
         double e = 1e-15;
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(e, 100.0, 1e-7, 1e-7);
 
         TimeDetector detector1 = new TimeDetector(10, 1, 100, -5);
         integrator.addEventDetector(detector1);
         TimeDetector detector2 = new TimeDetector(10, 1, 100, -5.5);
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20);
 
         // verify
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(-5, events1.get(0).getT(), 0.0);
         List<Event> events2 = detector2.getEvents();
         assertEquals(1, events2.size());
         assertEquals(-5.5, events2.get(0).getT(), 0.0);
     }
 
     @Test
     void testSimultaneousEventsReverse() {
         // setup
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
 
         TimeDetector detector1 = new TimeDetector(10, 1, 100, -5);
         integrator.addEventDetector(detector1);
         TimeDetector detector2 = new TimeDetector(10, 1, 100, -5);
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20);
 
         // verify
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(-5, events1.get(0).getT(), 0.0);
         List<Event> events2 = detector2.getEvents();
         assertEquals(1, events2.size());
         assertEquals(-5, events2.get(0).getT(), 0.0);
     }
 
     /**
      * Previously there were some branches when tryAdvance() returned false but did not
      * set {@code t0 = t}. This allowed the order of events to not be chronological and to
      * detect events that should not have occurred, both of which are problems.
      */
     @Test
     void testSimultaneousEventsResetReverse() {
         // setup
         double tol = 1e-10;
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 100.0, 1e-7, 1e-7);
         boolean[] firstEventOccurred = {false};
         List<Event> events = new ArrayList<>();
 
         TimeDetector detector1 = new TimeDetector(10, tol, 100, events, -5) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     firstEventOccurred[0] = true;
                     super.getHandler().eventOccurred(state, detector, increasing);
                     return Action.RESET_STATE;
                 };
             }
         };
         integrator.addEventDetector(detector1);
         // this detector changes it's g function definition when detector1 fires
         TimeDetector detector2 = new TimeDetector(1, tol, 100, events, -1, -3, -5) {
             @Override
             public double g(final ODEStateAndDerivative state) {
                 if (firstEventOccurred[0]) {
                     return super.g(state);
                 }
                 return new TimeDetector(1, tol, 100, -5).g(state);
             }
         };
         integrator.addEventDetector(detector2);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20);
 
         // verify
         // order is important to make sure the test checks what it is supposed to
         assertEquals(-5, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detector1, events.get(0).getDetector());
         assertEquals(-5, events.get(1).getT(), 0.0);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(detector2, events.get(1).getDetector());
         assertEquals(2, events.size());
     }
 
     /**
      * When two event detectors have a discontinuous event caused by a {@link
      * Action#RESET_STATE} or {@link Action#RESET_DERIVATIVES}. The two event detectors
      * would each say they had an event that had to be handled before the other one, but
      * neither would actually back up at all. For Hipparchus GitHub #91.
      */
     @Test
     void testSimultaneousDiscontinuousEventsAfterResetReverse() {
         // setup
         double t = -FastMath.PI;
         double tol = 1e-10;
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         List<Event> events = new ArrayList<>();
 
         TimeDetector resetDetector =
                 new ResetDetector(10, tol, 100, events, new ODEState(t, new double[]{1e100, 0}), t);
         integrator.addEventDetector(resetDetector);
         List<BaseDetector> detectors = new ArrayList<>();
         for (int i = 0; i < 2; i++) {
             BaseDetector detector1 = new StateDetector(10, tol, 100, events, 0.0);
             integrator.addEventDetector(detector1);
             detectors.add(detector1);
         }
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[]{-1e100, 0}), -10);
 
         // verify
         assertEquals(t, events.get(0).getT(),  tol);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(resetDetector, events.get(0).getDetector());
         // next two events can occur in either order
         assertEquals(t, events.get(1).getT(),  tol);
         assertFalse(events.get(1).isIncreasing());
         assertEquals(detectors.get(0), events.get(1).getDetector());
         assertEquals(t, events.get(2).getT(),  tol);
         assertFalse(events.get(2).isIncreasing());
         assertEquals(detectors.get(1), events.get(2).getDetector());
         assertEquals(3, events.size());
     }
 
     /**
      * test the g function switching with a period shorter than the tolerance. We don't
      * need to find any of the events, but we do need to not crash. And we need to
      * preserve the alternating increasing / decreasing sequence.
      */
     @Test
     void testFastSwitchingReverse() {
         // setup
         // step size of 10 to land in between two events we would otherwise miss
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
 
         TimeDetector detector1 = new TimeDetector(10, 0.2, 100, -9.9, -10.1, -12);
         integrator.addEventDetector(detector1);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20);
 
         //verify
         // finds one or three events. Not 2.
         List<Event> events1 = detector1.getEvents();
         assertEquals(1, events1.size());
         assertEquals(-9.9, events1.get(0).getT(), 0.2);
         assertTrue(events1.get(0).isIncreasing());
     }
 
     /** "A Tricky Problem" from bug #239. */
     @Test
     void testTrickyCaseLowerReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -1.0, t2 = -15, t3 = -16, t4 = -17, t5 = -18;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events, t3);
         TimeDetector detectorB = new TimeDetector(maxCheck, tolerance, 100, events, -50, t1, t2, t5);
         TimeDetector detectorC = new TimeDetector(maxCheck, tolerance, 100, Action.RESET_DERIVATIVES, events, t4);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         // but I only know one way to do that in this case.
         assertEquals(5, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertFalse(events.get(0).isIncreasing());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(t3, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertEquals(t4, events.get(3).getT(), tolerance);
         assertTrue(events.get(3).isIncreasing());
         assertEquals(t5, events.get(4).getT(), tolerance);
         assertFalse(events.get(4).isIncreasing());
     }
 
     /**
      * Test case for two event detectors. DetectorA has event at t2, DetectorB at t3, but
      * due to the root finding tolerance DetectorB's event occurs at t1. With t1 < t2 <
      * t3.
      */
     @Test
     void testRootFindingToleranceReverse() {
         //setup
         double maxCheck = 10;
         double t2 = -11, t3 = t2 - 1e-5;
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, 1e-6, 100, events, t2);
         FlatDetector detectorB = new FlatDetector(maxCheck, 0.5, 100, events, t3);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         // if these fail the event finding did its job,
         // but this test isn't testing what it is supposed to be
         assertSame(detectorB, events.get(0).getDetector());
         assertSame(detectorA, events.get(1).getDetector());
         assertTrue(events.get(0).getT() > events.get(1).getT());
 
         // check event detection worked
         assertEquals(2, events.size());
         assertEquals(t3, events.get(0).getT(), 0.5);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(t2, events.get(1).getT(), 1e-6);
         assertTrue(events.get(1).isIncreasing());
     }
 
     /** check when g(t < root) < 0,  g(root + convergence) < 0. */
     @Test
     void testRootPlusToleranceHasWrongSignReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         final double toleranceB = 0.3;
         double t1 = -11, t2 = -11.1, t3 = -11.2;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance,  100, events, t2);
         TimeDetector detectorB = new TimeDetector(maxCheck, toleranceB, 100, events, -50, t1, t3);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         // we only care that the rules are satisfied. There are multiple solutions.
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), toleranceB);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorB, events.get(0).getDetector());
         assertEquals(t3, events.get(1).getT(), toleranceB);
         assertFalse(events.get(1).isIncreasing());
         assertSame(detectorB, events.get(1).getDetector());
         assertEquals(t2, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertSame(detectorA, events.get(2).getDetector());
         // ascending order
         assertTrue(events.get(0).getT() >= events.get(1).getT());
         assertTrue(events.get(1).getT() >= events.get(2).getT());
     }
 
     /** check when g(t < root) < 0,  g(root + convergence) < 0. */
     @Test
     void testRootPlusToleranceHasWrongSignAndLessThanTbReverse() {
         // setup
         // test is fragile w.r.t. implementation and these parameters
         double maxCheck = 10;
         double tolerance = 0.5;
         double t1 = -11, t2 = -11.4, t3 = -12.0;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorB = new FlatDetector(maxCheck, tolerance, 100, events, t1, t2, t3);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         // allowed to report t1 or t3.
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorB, events.get(0).getDetector());
     }
 
     /**
      * Check when g(t) has a multiple root. e.g. g(t < root) < 0, g(root) = 0, g(t > root)
      * < 0.
      */
     @Test
     void testDoubleRootReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -11;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         TimeDetector detectorB = new TimeDetector(maxCheck, tolerance, 100, events, t1, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         // detector worked correctly
         assertEquals(0.0, detectorB.g(state(t1)));
         assertTrue(detectorB.g(state(t1 + 1e-6)) < 0);
         assertTrue(detectorB.g(state(t1 - 1e-6)) < 0);
     }
 
     /**
      * Check when g(t) has a multiple root. e.g. g(t < root) > 0, g(root) = 0, g(t > root)
      * > 0.
      */
     @Test
     void testDoubleRootOppositeSignReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -11;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, -50, t1, t1);
         detectorB.g(state(t1));
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         // detector worked correctly
         assertEquals(0.0, detectorB.g(state(t1)), 0.0);
         assertTrue(detectorB.g(state(t1 + 1e-6)) > 0);
         assertTrue(detectorB.g(state(t1 - 1e-6)) > 0);
     }
 
     /** check root finding when zero at both ends. */
     @Test
     void testZeroAtBeginningAndEndOfIntervalReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -10, t2 = -20;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, -50, t1, t2);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), 0.0);
         assertFalse(events.get(1).isIncreasing());
         assertSame(detectorA, events.get(1).getDetector());
     }
 
     /** check root finding when zero at both ends. */
     @Test
     void testZeroAtBeginningAndEndOfIntervalOppositeSignReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -10, t2 = -20;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1, t2);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertFalse(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), 0.0);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorA, events.get(1).getDetector());
     }
 
     /** Test where an event detector has to back up multiple times. */
     @Test
     void testMultipleBackupsReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -11.0, t2 = -12, t3 = -13, t4 = -14, t5 = -15, t6 = -16, t7 = -17;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t6);
         TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, -50, t1, t3, t4, t7);
         TimeDetector detectorC = new ContinuousDetector(maxCheck, tolerance, 100, events, -50, t2, t5);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         assertEquals(5, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detectorB, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertEquals(detectorC, events.get(1).getDetector());
         // reporting t3 and t4 is optional, seeing them is not.
         // we know a root was found at t3 because events are reported at t2 and t5.
         /*
         Assertions.assertEquals(t3, events.get(2).getT(), tolerance);
         Assertions.assertEquals(false, events.get(2).isIncreasing());
         Assertions.assertEquals(detectorB, events.get(2).getHandler());
         Assertions.assertEquals(t4, events.get(3).getT(), tolerance);
         Assertions.assertEquals(true, events.get(3).isIncreasing());
         Assertions.assertEquals(detectorB, events.get(3).getHandler());
         */
         assertEquals(t5, events.get(2).getT(), tolerance);
         assertFalse(events.get(2).isIncreasing());
         assertEquals(detectorC, events.get(2).getDetector());
         assertEquals(t6, events.get(3).getT(), tolerance);
         assertTrue(events.get(3).isIncreasing());
         assertEquals(detectorA, events.get(3).getDetector());
         assertEquals(t7, events.get(4).getT(), tolerance);
         assertFalse(events.get(4).isIncreasing());
         assertEquals(detectorB, events.get(4).getDetector());
     }
 
     /** Test a reset event triggering another event at the same time. */
     @Test
     void testEventCausedByStateResetReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         double t1 = -15.0;
         final ODEState newState = new ODEState(t1, new double[]{20, 0});
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ResetDetector(maxCheck, tolerance, 100, events, newState, t1);
         BaseDetector detectorB = new StateDetector(maxCheck, tolerance, 100, events, 1);
 
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -40.0);
 
         //verify
         // really we only care that the Rules of Event Handling are not violated,
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertEquals(detectorA, events.get(0).getDetector());
         assertEquals(t1, events.get(1).getT(), tolerance);
         assertFalse(events.get(1).isIncreasing());
         assertEquals(detectorB, events.get(1).getDetector());
         assertEquals(t1 - 19, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertEquals(detectorB, events.get(2).getDetector());
     }
 
     /** check when t + tolerance == t. */
     @Test
     void testConvergenceTooTightReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18;
         double t1 = -15;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), 0.0);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
     /** check when root finding tolerance > event finding tolerance. */
     @Test
     void testToleranceMismatchReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18;
         double t1 = -15.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new FlatDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         // use root finding tolerance since it is larger
         assertEquals(t1, events.get(0).getT(), 1e-3);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of a continue action. Not sure if this should be
      * officially supported, but it is used in Orekit's DateDetector, it's useful, and not
      * too hard to implement.
      */
     @Test
     void testEventChangesGFunctionDefinitionReverse() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = -11, t2 = -19;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA = new ContinuousDetector(maxCheck, tolerance, 100, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return 1;
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * cancels the occurrence of the event.
      */
     @Test
     void testEventChangesGFunctionDefinitionCancelReverse() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = -11, t2 = -11.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (!swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return 1;
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
     }
 
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * delays the occurrence of the event.
      */
     @Test
     void testEventChangesGFunctionDefinitionDelayReverse() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = -11, t2 = -11.1, t3 = -11.2;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         final TimeDetector detectorD = new ContinuousDetector(maxCheck, tolerance, 100, events, t3);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (!swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return detectorD.g(state);
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t3, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /**
      * test when one event detector changes the definition of another's g function before
      * the end of the step as a result of an event occurring. In this case the change
      * causes the event to happen sooner than originally expected.
      */
     @Test
     void testEventChangesGFunctionDefinitionAccelerateReverse() {
         // setup
         double maxCheck = 5;
         double tolerance = 1e-6;
         double t1 = -11, t2 = -11.1, t3 = -11.2;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // mutable boolean
         boolean[] swap = new boolean[1];
         final TimeDetector detectorA =
                         new ContinuousDetector(maxCheck, tolerance, 100, Action.RESET_EVENTS, events, t1) {
             @Override
             public ODEEventHandler getHandler() {
                 return (state, detector, increasing) -> {
                     swap[0] = true;
                     return super.getHandler().eventOccurred(state, detector, increasing);
                 };
             }
         };
         final TimeDetector detectorB = new ContinuousDetector(maxCheck, tolerance, 100, events, t2);
         final TimeDetector detectorD = new ContinuousDetector(maxCheck, tolerance, 100, events, t3);
         BaseDetector detectorC = new BaseDetector(maxCheck, tolerance, 100, Action.CONTINUE, events) {
 
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (swap[0]) {
                     return detectorB.g(state);
                 } else {
                     return detectorD.g(state);
                 }
             }
 
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorC);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(2, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t2, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorC, events.get(1).getDetector());
     }
 
     /** check when root finding tolerance > event finding tolerance. */
     @Test
     void testToleranceStopReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-18; // less than 1 ulp
         double t1 = -15.1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new FlatDetector(maxCheck, tolerance, 100, Action.STOP, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         ODEStateAndDerivative finalState =
                 integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(1, events.size());
         // use root finder tolerance instead of event finder tolerance.
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertTrue(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t1, finalState.getTime(), tolerance);
 
         // try to resume propagation
         finalState = integrator.integrate(new Equation(), finalState, -30.0);
 
         // verify it got to the end
         assertEquals(-30.0, finalState.getTime(), 0.0);
     }
 
     /**
      * Test when g function is initially zero for longer than the tolerance. Can occur
      * when restarting after a stop and cancellation occurs in the g function.
      */
     @Test
     void testLongInitialZeroReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, Action.STOP, events, 50) {
             @Override
             public double g(ODEStateAndDerivative state) {
                 if (state.getTime() > -2) {
                     return 0;
                 } else {
                     return super.g(state);
                 }
             }
         };
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(0, events.size());
     }
 
     /**
      * The root finder requires the start point to be in the interval (a, b) which is hard
      * when there aren't many numbers between a and b. This test uses a second event
      * detector to force a very small window for the first event detector.
      */
     @Test
     void testShortBracketingIntervalReverse() {
         // setup
         double maxCheck = 10;
         double tolerance = 1e-6;
         final double t1 = FastMath.nextDown(-10.0), t2 = -10.5;
         // shared event list so we know the order in which they occurred
         List<Event> events = new ArrayList<>();
         // never zero so there is no easy way out
         TimeDetector detectorA = new TimeDetector(maxCheck, tolerance, 100, events) {
             @Override
             public double g(ODEStateAndDerivative state) {
                 final double t = state.getTime();
                 if (t > t1) {
                     return -1;
                 } else if (t > t2) {
                     return 1;
                 } else {
                     return -1;
                 }
             }
         };
         TimeDetector detectorB = new TimeDetector(maxCheck, tolerance, 100, events, t1);
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
         integrator.addEventDetector(detectorB);
 
         // action
         integrator.integrate(new Equation(), new ODEState(0, new double[2]), -30.0);
 
         // verify
         assertEquals(3, events.size());
         assertEquals(t1, events.get(0).getT(), tolerance);
         assertFalse(events.get(0).isIncreasing());
         assertSame(detectorA, events.get(0).getDetector());
         assertEquals(t1, events.get(1).getT(), tolerance);
         assertTrue(events.get(1).isIncreasing());
         assertSame(detectorB, events.get(1).getDetector());
         assertEquals(t2, events.get(2).getT(), tolerance);
         assertTrue(events.get(2).isIncreasing());
         assertSame(detectorA, events.get(2).getDetector());
     }
 
     /** Check that steps are restricted correctly with a continue event. */
     @Test
     void testEventStepHandlerReverse() {
         // setup
         double tolerance = 1e-18;
         ODEIntegrator integrator =
                 new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(new TimeDetector(100, tolerance, 100, -5));
         StepHandler stepHandler = new StepHandler();
         integrator.addStepHandler(stepHandler);
 
         // action
         ODEStateAndDerivative finalState = integrator
                 .integrate(new Equation(), new ODEState(0, new double[2]), -10);
 
         // verify
         assertEquals(-10.0, finalState.getTime(), tolerance);
         assertEquals(0.0,
                 stepHandler.initialState.getTime(), tolerance);
         assertEquals(-10.0, stepHandler.finalTime, tolerance);
         assertEquals(-10.0,
                 stepHandler.finalState.getTime(), tolerance);
         ODEStateInterpolator interpolator = stepHandler.interpolators.get(0);
         assertEquals(0.0,
                 interpolator.getPreviousState().getTime(), tolerance);
         assertEquals(-5.0,
                 interpolator.getCurrentState().getTime(), tolerance);
         interpolator = stepHandler.interpolators.get(1);
         assertEquals(-5.0,
                 interpolator.getPreviousState().getTime(), tolerance);
         assertEquals(-10.0,
                 interpolator.getCurrentState().getTime(), tolerance);
         assertEquals(2, stepHandler.interpolators.size());
     }
 
     /** Test resetState(...) returns {@code null}. */
     @Test
     void testEventCausedByDerivativesResetReverse() {
         // setup
         TimeDetector detectorA = new TimeDetector(10, 1e-6, 100, Action.RESET_STATE, -15.0) {
             @Override
             public ODEEventHandler getHandler() {
                 return new ODEEventHandler() {
                     @Override
                     public Action eventOccurred(ODEStateAndDerivative state,
                                                 ODEEventDetector detector, boolean increasing) {
                         return Action.RESET_STATE;
                     }
                     @Override
                     public ODEState resetState(ODEEventDetector detector, ODEStateAndDerivative state) {
                         return null;
                     }
                 };
             }
         };
         ODEIntegrator integrator = new DormandPrince853Integrator(10, 10, 1e-7, 1e-7);
         integrator.addEventDetector(detectorA);
 
         try {
             // action
             integrator.integrate(new Equation(), new ODEState(0, new double[2]), -20.0);
             fail("Expected Exception");
         } catch (NullPointerException e) {
             // expected
         }
     }
 
     @Test
     void testResetChangesSignReverse() {
         OrdinaryDifferentialEquation equation = new OrdinaryDifferentialEquation() {
             public int getDimension() { return 1; }
             public double[] computeDerivatives(double t, double[] y) { return new double[] { 1.0 }; }
         };
 
         LutherIntegrator integrator = new LutherIntegrator(20.0);
         final double small = 1.0e-10;
         ResetChangesSignGenerator eventsGenerator = new ResetChangesSignGenerator(-6.0, -9.0, +0.5 * small, 8.0, small, 1000);
         integrator.addEventDetector(eventsGenerator);
         final ODEStateAndDerivative end = integrator.integrate(equation, new ODEState(0.0, new double[1]), -100.0);
         assertEquals(2,                  eventsGenerator.getCount());
         assertEquals(-9.0,               end.getCompleteState()[0], 1.0e-12);
         assertEquals(-9.0 - 0.5 * small, end.getTime(),             1.0e-12);
     }
 
     /* utility classes and methods */
 
     /**
      * Create a state at a time.
      *
      * @param t time of state.
      * @return new state.
      */
     private ODEStateAndDerivative state(double t) {
         return new ODEStateAndDerivative(t, new double[0], new double[0]);
     }
 
     /** Base class to record events that occurred. */
     private static abstract class BaseDetector implements ODEEventDetector {
 
         private final AdaptableInterval             maxCheck;
         private final int                           maxIter;
         private final BracketingNthOrderBrentSolver solver;
         protected final Action                      action;
 
         /** times the event was actually triggered. */
         private final List<Event> events;
 
         public BaseDetector(final double maxCheck, final double threshold, final int maxIter,
                             Action action, List<Event> events) {
             this.maxCheck  = (s, isForward) -> maxCheck;
             this.maxIter   = maxIter;
             this.solver    = new BracketingNthOrderBrentSolver(0, threshold, 0, 5);
             this.action    = action;
             this.events    = events;
         }
 
         public AdaptableInterval getMaxCheckInterval() {
             return maxCheck;
         }
 
         public int getMaxIterationCount() {
             return maxIter;
         }
 
         public BracketedUnivariateSolver<UnivariateFunction> getSolver() {
             return solver;
         }
 
         /**
          * Get all events that occurred.
          *
          * @return list of events in the order they occurred.
          */
         public List<Event> getEvents() {
             return events;
         }
 
         @Override
         public ODEEventHandler getHandler() {
             return new ODEEventHandler() {
                 @Override
                 public Action eventOccurred(ODEStateAndDerivative state,
                                             ODEEventDetector detector, boolean increasing) {
                     events.add(new Event(state, detector, increasing));
                     return action;
                 }
             };
         }
 
     }
 
     /** Trigger an event at a given time interval. */
     private static class IntervalDetector extends BaseDetector implements ODEEventDetector {
 
         /** Interval start. */
         protected final double start;
 
         /** Interval end. */
         protected final double end;
 
         public IntervalDetector(final double maxCheck, final double threshold, final int maxIter,
                                 final Action action, final double startTime, final double endTime) {
             super(maxCheck, threshold, maxIter, action, new ArrayList<>());
             this.start = startTime;
             this.end = endTime;
         }
 
         @Override
         public double g(final ODEStateAndDerivative state) {
             final double t = state.getTime();
             return (t - start) * (end - t);
         }
 
     }
 
     /** Trigger an event at a particular time. */
     private static class TimeDetector extends BaseDetector implements ODEEventDetector {
 
         /** time of the event to trigger. */
         protected final double[] eventTs;
 
         /**
          * Create a new detector.
          *
          * @param eventTs the time to trigger an event.
          */
         public TimeDetector(final double maxCheck, final double threshold, final int maxIter,
                             double... eventTs) {
             this(maxCheck, threshold, maxIter, Action.CONTINUE, eventTs);
         }
 
         public TimeDetector(final double maxCheck, final double threshold, final int maxIter,
                             List<Event> events, double... eventTs) {
             this(maxCheck, threshold, maxIter, Action.CONTINUE, events, eventTs);
         }
 
         public TimeDetector(final double maxCheck, final double threshold, final int maxIter,
                             Action action, double... eventTs) {
             this(maxCheck, threshold, maxIter, action, new ArrayList<Event>(), eventTs);
         }
 
         public TimeDetector(final double maxCheck, final double threshold, final int maxIter,
                             Action action, List<Event> events, double... eventTs) {
             super(maxCheck, threshold, maxIter, action, events);
             this.eventTs = eventTs.clone();
             Arrays.sort(this.eventTs);
         }
 
         @Override
         public double g(final ODEStateAndDerivative state) {
             final double t = state.getTime();
             int i = 0;
             while (i < eventTs.length && t > eventTs[i]) {
                 i++;
             }
             i--;
             if (i < 0) {
                 return t - eventTs[0];
             } else {
                 int sign = (i % 2) * 2 - 1;
                 return -sign * (t - eventTs[i]);
             }
         }
 
     }
 
     private static class Event {
 
         private final ODEStateAndDerivative state;
         private final boolean increasing;
         private final ODEEventDetector detector;
 
         public Event(ODEStateAndDerivative state, ODEEventDetector detector, boolean increasing) {
             this.increasing = increasing;
             this.state      = state;
             this.detector   = detector;
         }
 
         public boolean isIncreasing() {
             return increasing;
         }
 
         public double getT() {
             return state.getTime();
         }
 
         public ODEEventDetector getDetector() {
             return detector;
         }
 
         @Override
         public String toString() {
             return "Event{" +
                     "increasing=" + increasing +
                     ", time=" + state.getTime() +
                     ", state=" + Arrays.toString(state.getCompleteState()) +
                     '}';
         }
     }
 
     /**
      * Same as {@link TimeDetector} except that it has a very flat g function which makes
      * root finding hard.
      */
     private static class FlatDetector extends TimeDetector {
 
         public FlatDetector(double maxCheck, double threshold, int maxIter,
                             double... eventTs) {
             super(maxCheck, threshold, maxIter, eventTs);
         }
 
         public FlatDetector(double maxCheck, double threshold, int maxIter,
                             List<Event> events, double... eventTs) {
             super(maxCheck, threshold, maxIter, events, eventTs);
         }
 
         public FlatDetector(double maxCheck, double threshold, int maxIter,
                             Action action, List<Event> events, double... eventTs) {
             super(maxCheck, threshold, maxIter, action, events, eventTs);
         }
 
         @Override
         public double g(ODEStateAndDerivative state) {
             final double g = super.g(state);
             return FastMath.signum(g);
         }
 
     }
 
     /** Linear on both ends, parabolic in the middle. */
     private static class ContinuousDetector extends TimeDetector {
 
         public ContinuousDetector(double maxCheck, double threshold, int maxIter,
                                   List<Event> events, double... eventTs) {
             super(maxCheck, threshold, maxIter, events, eventTs);
         }
 
         public ContinuousDetector(double maxCheck, double threshold, int maxIter,
                                   Action action, List<Event> events, double... eventTs) {
             super(maxCheck, threshold, maxIter, action, events, eventTs);
         }
 
         @Override
         public double g(ODEStateAndDerivative state) {
             final double t = state.getTime();
             int i = 0;
             while (i < eventTs.length && t > eventTs[i]) {
                 i++;
             }
             i--;
             if (i < 0) {
                 return t - eventTs[0];
             } else if (i < eventTs.length - 1) {
                 int sign = (i % 2) * 2 - 1;
                 return -sign * (t - eventTs[i]) * (eventTs[i + 1] - t);
             } else {
                 int sign = (i % 2) * 2 - 1;
                 return -sign * (t - eventTs[i]);
             }
         }
     }
 
     /** Reset the state at a particular time. */
     private static class ResetDetector extends TimeDetector {
 
         private final ODEState resetState;
 
         public ResetDetector(double maxCheck, double threshold, int maxIter,
                              List<Event> events, ODEState state, double eventT) {
             super(maxCheck, threshold, maxIter, Action.RESET_STATE, events, eventT);
             this.resetState = state;
         }
 
         @Override
         public ODEEventHandler getHandler() {
             return new ODEEventHandler() {
                 @Override
                 public Action eventOccurred(ODEStateAndDerivative state,
                                             ODEEventDetector detector, boolean increasing) {
                     return ResetDetector.super.getHandler().eventOccurred(state, detector, increasing);
                 }
                 @Override
                 public ODEState resetState(ODEEventDetector detector, ODEStateAndDerivative state) {
                     assertEquals(eventTs[0], state.getTime(), 0);
                     return resetState;
                 }
             };
         }
 
     }
 
     /** Switching function based on the first primary state. */
     private static class StateDetector extends BaseDetector {
 
         private final double triggerState;
 
         public StateDetector(double maxCheck, double threshold, int maxIter,
                              List<Event> events, double triggerState) {
             super(maxCheck, threshold, maxIter, Action.CONTINUE, events);
             this.triggerState = triggerState;
         }
 
         @Override
         public double g(ODEStateAndDerivative state) {
             return state.getPrimaryState()[0] - this.triggerState;
         }
     }
 
     /** Some basic equations to integrate. */
     public static class Equation implements OrdinaryDifferentialEquation {
 
         public int getDimension() {
             return 2;
         }
 
         public double[] computeDerivatives(double t, double[] y) {
             return new double[]{1.0, 2.0};
         }
 
     }
 
     private static class StepHandler implements ODEStepHandler {
 
         private ODEStateAndDerivative initialState;
         private double finalTime;
         private List<ODEStateInterpolator> interpolators = new ArrayList<>();
         private ODEStateAndDerivative finalState;
 
         @Override
         public void init(ODEStateAndDerivative initialState, double finalTime) {
             this.initialState = initialState;
             this.finalTime = finalTime;
         }
 
         @Override
         public void handleStep(ODEStateInterpolator interpolator) {
             this.interpolators.add(interpolator);
         }
 
         @Override
         public void finish(ODEStateAndDerivative finalState) {
             this.finalState = finalState;
         }
     }
 
     private class ResetChangesSignGenerator implements ODEEventDetector {
 
         private final AdaptableInterval             maxCheck;
         private final int                           maxIter;
         private final BracketingNthOrderBrentSolver solver;
         final double                                y1;
         final double                                y2;
         final double                                change;
         int                                         count;
 
         public ResetChangesSignGenerator(final double y1, final double y2, final double change,
                                          final double maxCheck, final double threshold, final int maxIter) {
             this.maxCheck  = (s, isForward) -> maxCheck;
             this.maxIter   = maxIter;
             this.solver    = new BracketingNthOrderBrentSolver(0, threshold, 0, 5);
             this.y1        = y1;
             this.y2        = y2;
             this.change    = change;
             this.count     = 0;
         }
 
         public AdaptableInterval getMaxCheckInterval() {
             return maxCheck;
         }
 
         public int getMaxIterationCount() {
             return maxIter;
         }
 
         public BracketedUnivariateSolver<UnivariateFunction> getSolver() {
             return solver;
         }
 
         public ODEEventHandler getHandler() {
             return new ODEEventHandler() {
                 public Action eventOccurred(ODEStateAndDerivative s, ODEEventDetector detector, boolean increasing) {
                     return ++count < 2 ? Action.RESET_STATE : Action.STOP;
                 }
 
                 public ODEState resetState(ODEEventDetector detector, ODEStateAndDerivative s) {
                     return new ODEState(s.getTime(), new double[] { s.getCompleteState()[0] + change });
                 }
             };
         }
 
         public double g(ODEStateAndDerivative s) {
             return (s.getCompleteState()[0] - y1) * (s.getCompleteState()[0] - y2);
         }
 
         public int getCount() {
             return count;
         }
 
     }
 
 }