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    * CS licenses this file to You under the Apache License, Version 2.0
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    *   http://www.apache.org/licenses/LICENSE-2.0
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   * Unless required by applicable law or agreed to in writing, software
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  package org.orekit.orbits;
  
  import org.hipparchus.geometry.euclidean.threed.Rotation;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.ode.events.Action;
  import org.hipparchus.ode.nonstiff.AdaptiveStepsizeIntegrator;
  import org.hipparchus.ode.nonstiff.DormandPrince853Integrator;
  import org.hipparchus.util.FastMath;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.attitudes.InertialProvider;
  import org.orekit.bodies.CR3BPSystem;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.events.HaloXZPlaneCrossingDetector;
  import org.orekit.propagation.numerical.NumericalPropagator;
  import org.orekit.propagation.numerical.cr3bp.CR3BPForceModel;
  import org.orekit.propagation.numerical.cr3bp.STMEquations;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.TimeScale;
  import org.orekit.utils.AbsolutePVCoordinates;
  import org.orekit.utils.PVCoordinates;
  
  
  /**
   * Class implementing the differential correction method for Halo or Lyapunov
   * Orbits. It is not a simple differential correction, it uses higher order
   * terms to be more accurate and meet orbits requirements.
   * @see "Three-dimensional, periodic, Halo Orbits by Kathleen Connor Howell, Stanford University"
   * @author Vincent Mouraux
   * @since 10.2
   */
  public class CR3BPDifferentialCorrection {
  
      /** Maximum number of iterations. */
      private static final int MAX_ITER = 30;
  
      /** Max check interval for crossing plane. */
      private static final double CROSSING_MAX_CHECK = 3600.0;
  
      /** Convergence tolerance for plane crossing time. */
      private static final double CROSSING_TOLERANCE = 1.0e-10;
  
      /** Arbitrary start date. */
      private static final AbsoluteDate START_DATE = AbsoluteDate.ARBITRARY_EPOCH;
  
      /** Boolean return true if the propagated trajectory crosses the plane. */
      private boolean cross;
  
      /** first guess PVCoordinates of the point to start differential correction. */
      private final PVCoordinates firstGuess;
  
      /** CR3BP System considered. */
      private final CR3BPSystem syst;
  
      /** orbitalPeriodApprox Orbital Period of the firstGuess. */
      private final double orbitalPeriodApprox;
  
      /** orbitalPeriod Orbital Period of the required orbit. */
      private double orbitalPeriod;
  
      /** Simple Constructor.
       * <p> Standard constructor using DormandPrince853 integrator for the differential correction </p>
       * @param firstguess first guess PVCoordinates of the point to start differential correction
       * @param syst CR3BP System considered
       * @param orbitalPeriod Orbital Period of the required orbit
       */
      public CR3BPDifferentialCorrection(final PVCoordinates firstguess,
                                         final CR3BPSystem syst, final double orbitalPeriod) {
          this.firstGuess = firstguess;
          this.syst = syst;
          this.orbitalPeriodApprox = orbitalPeriod;
  
      }
  
      /** Simple Constructor.
       * <p> Standard constructor using DormandPrince853 integrator for the differential correction </p>
       * @param firstguess first guess PVCoordinates of the point to start differential correction
       * @param syst CR3BP System considered
       * @param orbitalPeriod Orbital Period of the required orbit
       * @param attitudeProvider the attitude law for the numerical propagator
       * @param utc UTC time scale
      * @deprecated as of 11.1, replaced by {@link #CR3BPDifferentialCorrection(PVCoordinates, CR3BPSystem, double)}
      */
     @Deprecated
     public CR3BPDifferentialCorrection(final PVCoordinates firstguess,
                                        final CR3BPSystem syst,
                                        final double orbitalPeriod,
                                        final AttitudeProvider attitudeProvider,
                                        final TimeScale utc) {
         this(firstguess, syst, orbitalPeriod);
     }
 
     /** Build the propagator.
      * @return propagator
      * @since 11.1
      */
     private NumericalPropagator buildPropagator() {
 
         // Adaptive stepsize boundaries
         final double minStep = 1E-12;
         final double maxstep = 0.001;
 
         // Integrator tolerances
         final double positionTolerance = 1E-5;
         final double velocityTolerance = 1E-5;
         final double massTolerance = 1.0e-6;
         final double[] vecAbsoluteTolerances = {positionTolerance, positionTolerance, positionTolerance, velocityTolerance, velocityTolerance, velocityTolerance, massTolerance};
         final double[] vecRelativeTolerances = new double[vecAbsoluteTolerances.length];
 
         // Integrator definition
         final AdaptiveStepsizeIntegrator integrator = new DormandPrince853Integrator(minStep, maxstep,
                                                                                      vecAbsoluteTolerances,
                                                                                      vecRelativeTolerances);
 
         // Propagator definition
         final NumericalPropagator propagator =
                         new NumericalPropagator(integrator, new InertialProvider(Rotation.IDENTITY, syst.getRotatingFrame()));
 
         // CR3BP has no defined orbit type
         propagator.setOrbitType(null);
 
         // CR3BP has central Attraction
         propagator.setIgnoreCentralAttraction(true);
 
         // Add CR3BP Force Model to the propagator
         propagator.addForceModel(new CR3BPForceModel(syst));
 
         // Add event detector for crossing plane
         propagator.addEventDetector(new HaloXZPlaneCrossingDetector(CROSSING_MAX_CHECK, CROSSING_TOLERANCE).
                                     withHandler((state, detector, increasing) -> {
                                         cross = true;
                                         return Action.STOP;
                                     }));
 
         return propagator;
 
     }
 
     /**
      * Return the real starting PVCoordinates on the Libration orbit type
      * after differential correction from a first guess.
      * @param type libration orbit type
      * @return pv Position-Velocity of the starting point on the Halo Orbit
      */
     public PVCoordinates compute(final LibrationOrbitType type) {
         return type == LibrationOrbitType.HALO ? computeHalo() : computeLyapunov();
     }
 
     /** Return the real starting PVCoordinates on the Halo orbit after differential correction from a first guess.
      * @return pv Position-Velocity of the starting point on the Halo Orbit
      */
     private PVCoordinates computeHalo() {
 
         // Initializing PVCoordinates with first guess
         PVCoordinates pvHalo = firstGuess;
 
         // Start a new differentially corrected propagation until it converges to a Halo Orbit
         // Converge within 1E-8 tolerance and under 5 iterations
         for (int iHalo = 0; iHalo < MAX_ITER; ++iHalo) {
 
             // SpacecraftState initialization
             final AbsolutePVCoordinates initialAbsPVHalo = new AbsolutePVCoordinates(syst.getRotatingFrame(), START_DATE, pvHalo);
             final SpacecraftState       initialStateHalo = new SpacecraftState(initialAbsPVHalo);
 
             // setup propagator
             final NumericalPropagator propagator = buildPropagator();
             final STMEquations        stm        = new STMEquations(syst);
             propagator.addAdditionalDerivativesProvider(stm);
             propagator.setInitialState(stm.setInitialPhi(initialStateHalo));
 
             // boolean changed to true by crossing XZ plane during propagation. Has to be true for the differential correction to converge
             cross = false;
 
             // Propagate until trajectory crosses XZ Plane
             final SpacecraftState finalStateHalo =
                 propagator.propagate(START_DATE.shiftedBy(orbitalPeriodApprox));
 
             // Stops computation if trajectory did not cross XZ Plane after one full orbital period
             if (cross == false) {
                 throw new OrekitException(OrekitMessages.TRAJECTORY_NOT_CROSSING_XZPLANE);
             }
 
             // Get State Transition Matrix phi
             final RealMatrix phiHalo = stm.getStateTransitionMatrix(finalStateHalo);
 
             // Gap from desired X and Z axis velocity value ()
             final double dvxf = -finalStateHalo.getPVCoordinates().getVelocity().getX();
             final double dvzf = -finalStateHalo.getPVCoordinates().getVelocity().getZ();
 
             orbitalPeriod = 2 * finalStateHalo.getDate().durationFrom(START_DATE);
 
             if (FastMath.abs(dvxf) <= 1E-8 && FastMath.abs(dvzf) <= 1E-8) {
                 break;
             }
 
             // Y axis velocity
             final double vy = finalStateHalo.getPVCoordinates().getVelocity().getY();
 
             // Spacecraft acceleration
             final Vector3D acc  = finalStateHalo.getPVCoordinates().getAcceleration();
             final double   accx = acc.getX();
             final double   accz = acc.getZ();
 
             // Compute A coefficients
             final double a11 = phiHalo.getEntry(3, 0) - accx * phiHalo.getEntry(1, 0) / vy;
             final double a12 = phiHalo.getEntry(3, 4) - accx * phiHalo.getEntry(1, 4) / vy;
             final double a21 = phiHalo.getEntry(5, 0) - accz * phiHalo.getEntry(1, 0) / vy;
             final double a22 = phiHalo.getEntry(5, 4) - accz * phiHalo.getEntry(1, 4) / vy;
 
             // A determinant used for matrix inversion
             final double aDet = a11 * a22 - a21 * a12;
 
             // Correction to apply to initial conditions
             final double deltax0  = (a22 * dvxf - a12 * dvzf) / aDet;
             final double deltavy0 = (-a21 * dvxf + a11 * dvzf) / aDet;
 
             // Computation of the corrected initial PVCoordinates
             final double newx  = pvHalo.getPosition().getX() + deltax0;
             final double newvy = pvHalo.getVelocity().getY() + deltavy0;
 
             pvHalo = new PVCoordinates(new Vector3D(newx,
                                                     pvHalo.getPosition().getY(),
                                                     pvHalo.getPosition().getZ()),
                                        new Vector3D(pvHalo.getVelocity().getX(),
                                                     newvy,
                                                     pvHalo.getVelocity().getZ()));
         }
 
         // Return
         return pvHalo;
     }
 
     /** Return the real starting PVCoordinates on the Lyapunov orbit after differential correction from a first guess.
      * @return pv Position-Velocity of the starting point on the Lyapunov Orbit
      */
     public PVCoordinates computeLyapunov() {
 
         // Initializing PVCoordinates with first guess
         PVCoordinates pvLyapunov = firstGuess;
 
         // Start a new differentially corrected propagation until it converges to a Halo Orbit
         // Converge within 1E-8 tolerance and under 5 iterations
         for (int iLyapunov = 0; iLyapunov < MAX_ITER; ++iLyapunov) {
 
             // SpacecraftState initialization
             final AbsolutePVCoordinates initialAbsPVLyapunov = new AbsolutePVCoordinates(syst.getRotatingFrame(), START_DATE, pvLyapunov);
             final SpacecraftState       initialStateLyapunov = new SpacecraftState(initialAbsPVLyapunov);
 
             // setup propagator
             final NumericalPropagator propagator = buildPropagator();
             final STMEquations        stm        = new STMEquations(syst);
             propagator.addAdditionalDerivativesProvider(stm);
             propagator.setInitialState(stm.setInitialPhi(initialStateLyapunov));
 
             // boolean changed to true by crossing XZ plane during propagation. Has to be true for the differential correction to converge
             cross = false;
 
             // Propagate until trajectory crosses XZ Plane
             final SpacecraftState finalStateLyapunov =
                 propagator.propagate(START_DATE.shiftedBy(orbitalPeriodApprox));
 
             // Stops computation if trajectory did not cross XZ Plane after one full orbital period
             if (cross == false) {
                 throw new OrekitException(OrekitMessages.TRAJECTORY_NOT_CROSSING_XZPLANE);
             }
 
             // Get State Transition Matrix phi
             final RealMatrix phi = stm.getStateTransitionMatrix(finalStateLyapunov);
 
             // Gap from desired y position and x velocity value ()
             final double dvxf = -finalStateLyapunov.getPVCoordinates().getVelocity().getX();
 
             orbitalPeriod = 2 * finalStateLyapunov.getDate().durationFrom(START_DATE);
 
             if (FastMath.abs(dvxf) <= 1E-14) {
                 break;
             }
 
             // Y axis velocity
             final double vy = finalStateLyapunov.getPVCoordinates().getVelocity().getY();
 
             // Spacecraft acceleration
             final double accy = finalStateLyapunov.getPVCoordinates().getAcceleration().getY();
 
             // Compute A coefficients
             final double deltavy0 = dvxf / (phi.getEntry(3, 4) - accy * phi.getEntry(1, 4) / vy);
 
             // Computation of the corrected initial PVCoordinates
             final double newvy = pvLyapunov.getVelocity().getY() + deltavy0;
 
             pvLyapunov = new PVCoordinates(new Vector3D(pvLyapunov.getPosition().getX(),
                                                         pvLyapunov.getPosition().getY(),
                                                         0),
                                            new Vector3D(pvLyapunov.getVelocity().getX(),
                                                         newvy,
                                                         0));
 
         }
 
         // Return
         return pvLyapunov;
     }
 
     /** Get the orbital period of the required orbit.
      * @return the orbitalPeriod
      */
     public double getOrbitalPeriod() {
         return orbitalPeriod;
     }
 
 }