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    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
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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.gnss.attitude;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.analysis.UnivariateFunction;
  import org.hipparchus.analysis.differentiation.FDSFactory;
  import org.hipparchus.analysis.differentiation.FieldDerivativeStructure;
  import org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver;
  import org.hipparchus.analysis.solvers.UnivariateSolverUtils;
  import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  import org.hipparchus.geometry.euclidean.threed.Vector3D;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.FieldSinCos;
  import org.hipparchus.util.SinCos;
  import org.orekit.frames.FieldTransform;
  import org.orekit.frames.Frame;
  import org.orekit.frames.LOFType;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.time.FieldTimeStamped;
  import org.orekit.utils.ExtendedPVCoordinatesProvider;
  import org.orekit.utils.FieldPVCoordinates;
  import org.orekit.utils.FieldPVCoordinatesProvider;
  import org.orekit.utils.PVCoordinates;
  import org.orekit.utils.TimeStampedFieldAngularCoordinates;
  import org.orekit.utils.TimeStampedFieldPVCoordinates;
  
  /**
   * Boilerplate computations for GNSS attitude.
   *
   * <p>
   * This class is intended to hold throw-away data pertaining to <em>one</em> call
   * to {@link GNSSAttitudeProvider#getAttitude(org.orekit.utils.FieldPVCoordinatesProvider,
   * org.orekit.time.FieldAbsoluteDate, org.orekit.frames.Frame)) getAttitude}. It allows
   * the various {@link GNSSAttitudeProvider} implementations to be immutable as they
   * do not store any state, and hence to be thread-safe and reentrant.
   * </p>
   *
   * @author Luc Maisonobe
   * @since 9.2
   */
  class GNSSFieldAttitudeContext<T extends CalculusFieldElement<T>> implements FieldTimeStamped<T> {
  
      /** Derivation order. */
      private static final int ORDER = 2;
  
      /** Constant Y axis. */
      private static final PVCoordinates PLUS_Y_PV =
              new PVCoordinates(Vector3D.PLUS_J, Vector3D.ZERO, Vector3D.ZERO);
  
      /** Constant Z axis. */
      private static final PVCoordinates MINUS_Z_PV =
              new PVCoordinates(Vector3D.MINUS_K, Vector3D.ZERO, Vector3D.ZERO);
  
      /** Limit value below which we shoud use replace beta by betaIni. */
      private static final double BETA_SIGN_CHANGE_PROTECTION = FastMath.toRadians(0.07);
  
      /** Time derivation factory. */
      private final FDSFactory<T> factory;
  
      /** Constant Y axis. */
      private final FieldPVCoordinates<T> plusY;
  
      /** Constant Z axis. */
      private final FieldPVCoordinates<T> minusZ;
  
      /** Context date. */
      private final AbsoluteDate dateDouble;
  
      /** Current date. */
      private final FieldAbsoluteDate<T> date;
  
      /** Current date. */
      private final FieldAbsoluteDate<FieldDerivativeStructure<T>> dateDS;
  
      /** Provider for Sun position. */
      private final ExtendedPVCoordinatesProvider sun;
  
      /** Provider for spacecraft position. */
      private final FieldPVCoordinatesProvider<T> pvProv;
  
      /** Inertial frame where velocity are computed. */
      private final Frame inertialFrame;
 
     /** Cosine of the angle between spacecraft and Sun direction. */
     private final FieldDerivativeStructure<T> svbCos;
 
     /** Morning/Evening half orbit indicator. */
     private final boolean morning;
 
     /** Relative orbit angle to turn center. */
     private final FieldDerivativeStructure<T> delta;
 
     /** Spacecraft angular velocity. */
     private T muRate;
 
     /** Limit cosine for the midnight turn. */
     private double cNight;
 
     /** Limit cosine for the noon turn. */
     private double cNoon;
 
     /** Turn time data. */
     private FieldTurnSpan<T> turnSpan;
 
     /** Simple constructor.
      * @param date current date
      * @param sun provider for Sun position
      * @param pvProv provider for spacecraft position
      * @param inertialFrame inertial frame where velocity are computed
      * @param turnSpan turn time data, if a turn has already been identified in the date neighborhood,
      * null otherwise
      */
     GNSSFieldAttitudeContext(final FieldAbsoluteDate<T> date,
                              final ExtendedPVCoordinatesProvider sun, final FieldPVCoordinatesProvider<T> pvProv,
                              final Frame inertialFrame,  final FieldTurnSpan<T> turnSpan) {
 
         final Field<T> field = date.getField();
         factory  = new FDSFactory<>(field, 1, ORDER);
         plusY    = new FieldPVCoordinates<>(field, PLUS_Y_PV);
         minusZ   = new FieldPVCoordinates<>(field, MINUS_Z_PV);
 
         this.dateDouble    = date.toAbsoluteDate();
         this.date          = date;
         this.dateDS        = addDerivatives(date);
         this.sun           = sun;
         this.pvProv        = pvProv;
         this.inertialFrame = inertialFrame;
         final FieldPVCoordinates<FieldDerivativeStructure<T>> sunPVDS = sun.getPVCoordinates(dateDS, inertialFrame);
 
         final TimeStampedFieldPVCoordinates<T> svPV = pvProv.getPVCoordinates(date, inertialFrame);
         final FieldPVCoordinates<FieldDerivativeStructure<T>> svPVDS  =
                         svPV.toDerivativeStructurePV(factory.getCompiler().getOrder());
         this.svbCos  = FieldVector3D.dotProduct(sunPVDS.getPosition(), svPVDS.getPosition()).
                        divide(sunPVDS.getPosition().getNorm().multiply(svPVDS.getPosition().getNorm()));
         this.morning = Vector3D.dotProduct(svPV.getVelocity().toVector3D(), sunPVDS.getPosition().toVector3D()) >= 0.0;
 
         this.muRate = svPV.getAngularVelocity().getNorm();
 
         this.turnSpan = turnSpan;
 
         final FieldDerivativeStructure<T> absDelta;
         if (svbCos.getValue().getReal() <= 0) {
             // in eclipse turn mode
             absDelta = inOrbitPlaneAbsoluteAngle(svbCos.acos().negate().add(svbCos.getPi()));
         } else {
             // in noon turn mode
             absDelta = inOrbitPlaneAbsoluteAngle(svbCos.acos());
         }
         delta = absDelta.copySign(absDelta.getPartialDerivative(1).negate());
 
     }
 
     /** Convert a date, removing derivatives.
      * @param d date to convert
      * @return date without derivatives
      */
     private FieldAbsoluteDate<T> removeDerivatives(final FieldAbsoluteDate<FieldDerivativeStructure<T>> d) {
         final AbsoluteDate                dd     = d.toAbsoluteDate();
         final FieldDerivativeStructure<T> offset = d.durationFrom(dd);
         return new FieldAbsoluteDate<>(date.getField(), dd).shiftedBy(offset.getValue());
     }
 
     /** Convert a date, adding derivatives.
      * @param d date to convert
      * @return date without derivatives
      */
     private FieldAbsoluteDate<FieldDerivativeStructure<T>> addDerivatives(final FieldAbsoluteDate<T> d) {
         final AbsoluteDate dd     = d.toAbsoluteDate();
         final T            offset = d.durationFrom(dd);
         return new FieldAbsoluteDate<>(factory.getDerivativeField(), dd).shiftedBy(factory.variable(0, offset));
     }
 
     /** Compute nominal yaw steering.
      * @param d computation date
      * @return nominal yaw steering
      */
     public TimeStampedFieldAngularCoordinates<T> nominalYaw(final FieldAbsoluteDate<T> d) {
         final TimeStampedFieldPVCoordinates<T> svPV = pvProv.getPVCoordinates(d, inertialFrame);
         return new TimeStampedFieldAngularCoordinates<>(d,
                                                         svPV.normalize(),
                                                         sun.getPVCoordinates(d, inertialFrame).crossProduct(svPV).normalize(),
                                                         minusZ,
                                                         plusY,
                                                         1.0e-9);
     }
 
     /** Compute Sun elevation.
      * @param d computation date
      * @return Sun elevation
      */
     public T beta(final FieldAbsoluteDate<T> d) {
         final TimeStampedFieldPVCoordinates<T> svPV = pvProv.getPVCoordinates(d, inertialFrame);
         return FieldVector3D.angle(sun.getPVCoordinates(d, inertialFrame).getPosition(), svPV.getMomentum()).
                negate().
                add(svPV.getPosition().getX().getPi().multiply(0.5));
     }
 
     /** Compute Sun elevation.
      * @param d computation date
      * @return Sun elevation
      */
     private FieldDerivativeStructure<T> betaDS(final FieldAbsoluteDate<FieldDerivativeStructure<T>> d) {
         final FieldPVCoordinates<FieldDerivativeStructure<T>> svPV =
                         pvProv.getPVCoordinates(removeDerivatives(d), inertialFrame).
                         toDerivativeStructurePV(d.getField().getZero().getOrder());
         return FieldVector3D.angle(sun.getPVCoordinates(d, inertialFrame).getPosition(), svPV.getMomentum()).
                negate().
                add(svPV.getPosition().getX().getPi().multiply(0.5));
     }
 
     /** Compute Sun elevation.
      * @return Sun elevation
      */
     public FieldDerivativeStructure<T> betaDS() {
         return betaDS(dateDS);
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldAbsoluteDate<T> getDate() {
         return date;
     }
 
     /** Get the turn span.
      * @return turn span, may be null if context is outside of turn
      */
     public FieldTurnSpan<T> getTurnSpan() {
         return turnSpan;
     }
 
     /** Get the cosine of the angle between spacecraft and Sun direction.
      * @return cosine of the angle between spacecraft and Sun direction.
      */
     public T getSVBcos() {
         return svbCos.getValue();
     }
 
     /** Get a Sun elevation angle that does not change sign within the turn.
      * <p>
      * This method either returns the current beta or replaces it with the
      * value at turn start, so the sign remains constant throughout the
      * turn. As of 9.2, it is used for GPS, Glonass and Galileo.
      * </p>
      * @return secured Sun elevation angle
      * @see #beta(FieldAbsoluteDate)
      * @see #betaDS(FieldAbsoluteDate)
      */
     public T getSecuredBeta() {
         final T beta = beta(getDate());
         return FastMath.abs(beta.getReal()) < BETA_SIGN_CHANGE_PROTECTION ?
                beta(turnSpan.getTurnStartDate()) :
                beta;
     }
 
     /** Check if a linear yaw model is still active or if we already reached target yaw.
      * @param linearPhi value of the linear yaw model
      * @param phiDot slope of the linear yaw model
      * @return true if linear model is still active
      */
     public boolean linearModelStillActive(final T linearPhi, final T phiDot) {
         final AbsoluteDate absDate = date.toAbsoluteDate();
         final double dt0 = turnSpan.getTurnEndDate().durationFrom(date).getReal();
         final UnivariateFunction yawReached = dt -> {
             final AbsoluteDate  t       = absDate.shiftedBy(dt);
             final Vector3D      pSun    = sun.getPVCoordinates(t, inertialFrame).getPosition();
             final PVCoordinates pv      = pvProv.getPVCoordinates(date.shiftedBy(dt), inertialFrame).toPVCoordinates();
             final Vector3D      pSat    = pv.getPosition();
             final Vector3D      targetX = Vector3D.crossProduct(pSat, Vector3D.crossProduct(pSun, pSat)).normalize();
 
             final double        phi         = linearPhi.getReal() + dt * phiDot.getReal();
             final SinCos        sc          = FastMath.sinCos(phi);
             final Vector3D      pU          = pv.getPosition().normalize();
             final Vector3D      mU          = pv.getMomentum().normalize();
             final Vector3D      omega       = new Vector3D(-phiDot.getReal(), pU);
             final Vector3D      currentX    = new Vector3D(-sc.sin(), mU, -sc.cos(), Vector3D.crossProduct(pU, mU));
             final Vector3D      currentXDot = Vector3D.crossProduct(omega, currentX);
 
             return Vector3D.dotProduct(targetX, currentXDot);
         };
         final double fullTurn = 2 * FastMath.PI / FastMath.abs(phiDot.getReal());
         final double dtMin    = FastMath.min(turnSpan.getTurnStartDate().durationFrom(date).getReal(), dt0 - 60.0);
         final double dtMax    = FastMath.max(dtMin + fullTurn, dt0 + 60.0);
         double[] bracket = UnivariateSolverUtils.bracket(yawReached, dt0,
                                                          dtMin, dtMax, fullTurn / 100, 1.0, 100);
         if (yawReached.value(bracket[0]) <= 0.0) {
             // we have bracketed the wrong crossing
             bracket = UnivariateSolverUtils.bracket(yawReached, 0.5 * (bracket[0] + bracket[1] + fullTurn),
                                                     bracket[1], bracket[1] + fullTurn, fullTurn / 100, 1.0, 100);
         }
         final double dt = new BracketingNthOrderBrentSolver(1.0e-3, 5).
                           solve(100, yawReached, bracket[0], bracket[1]);
         turnSpan.updateEnd(date.shiftedBy(dt), absDate);
 
         return dt > 0.0;
 
     }
 
     /** Set up the midnight/noon turn region.
      * @param cosNight limit cosine for the midnight turn
      * @param cosNoon limit cosine for the noon turn
      * @return true if spacecraft is in the midnight/noon turn region
      */
     public boolean setUpTurnRegion(final double cosNight, final double cosNoon) {
         this.cNight = cosNight;
         this.cNoon  = cosNoon;
 
         if (svbCos.getValue().getReal() < cNight || svbCos.getValue().getReal() > cNoon) {
             // we are within turn triggering zone
             return true;
         } else {
             // we are outside of turn triggering zone,
             // but we may still be trying to recover nominal attitude at the end of a turn
             return inTurnTimeRange();
         }
 
     }
 
     /** Get the relative orbit angle to turn center.
      * @return relative orbit angle to turn center
      */
     public FieldDerivativeStructure<T> getDeltaDS() {
         return delta;
     }
 
     /** Get the orbit angle since solar midnight.
      * @return orbit angle since solar midnight
      */
     public T getOrbitAngleSinceMidnight() {
         final T absAngle = inOrbitPlaneAbsoluteAngle(FastMath.acos(svbCos.getValue()).negate().add(svbCos.getValue().getPi()));
         return morning ? absAngle : absAngle.negate();
     }
 
     /** Check if spacecraft is in the half orbit closest to Sun.
      * @return true if spacecraft is in the half orbit closest to Sun
      */
     public boolean inSunSide() {
         return svbCos.getValue().getReal() > 0;
     }
 
     /** Get yaw at turn start.
      * @param sunBeta Sun elevation above orbital plane
      * (it <em>may</em> be different from {@link #getBeta()} in
      * some special cases)
      * @return yaw at turn start
      */
     public T getYawStart(final T sunBeta) {
         final T halfSpan = turnSpan.getTurnDuration().multiply(muRate).multiply(0.5);
         return computePhi(sunBeta, FastMath.copySign(halfSpan, svbCos.getValue()));
     }
 
     /** Get yaw at turn end.
      * @param sunBeta Sun elevation above orbital plane
      * (it <em>may</em> be different from {@link #getBeta()} in
      * some special cases)
      * @return yaw at turn end
      */
     public T getYawEnd(final T sunBeta) {
         final T halfSpan = turnSpan.getTurnDuration().multiply(muRate).multiply(0.5);
         return computePhi(sunBeta, FastMath.copySign(halfSpan, svbCos.getValue().negate()));
     }
 
     /** Compute yaw rate.
      * @param sunBeta Sun elevation above orbital plane
      * (it <em>may</em> be different from {@link #getBeta()} in
      * some special cases)
      * @return yaw rate
      */
     public T yawRate(final T sunBeta) {
         return getYawEnd(sunBeta).subtract(getYawStart(sunBeta)).divide(turnSpan.getTurnDuration());
     }
 
     /** Get the spacecraft angular velocity.
      * @return spacecraft angular velocity
      */
     public T getMuRate() {
         return muRate;
     }
 
     /** Project a spacecraft/Sun angle into orbital plane.
      * <p>
      * This method is intended to find the limits of the noon and midnight
      * turns in orbital plane. The return angle is signed, depending on the
      * spacecraft being before or after turn middle point.
      * </p>
      * @param angle spacecraft/Sun angle (or spacecraft/opposite-of-Sun)
      * @return angle projected into orbital plane, always positive
      */
     private FieldDerivativeStructure<T> inOrbitPlaneAbsoluteAngle(final FieldDerivativeStructure<T> angle) {
         return FastMath.acos(FastMath.cos(angle).divide(FastMath.cos(beta(getDate()))));
     }
 
     /** Project a spacecraft/Sun angle into orbital plane.
      * <p>
      * This method is intended to find the limits of the noon and midnight
      * turns in orbital plane. The return angle is always positive. The
      * correct sign to apply depends on the spacecraft being before or
      * after turn middle point.
      * </p>
      * @param angle spacecraft/Sun angle (or spacecraft/opposite-of-Sun)
      * @return angle projected into orbital plane, always positive
      */
     public T inOrbitPlaneAbsoluteAngle(final T angle) {
         return FastMath.acos(FastMath.cos(angle).divide(FastMath.cos(beta(getDate()))));
     }
 
     /** Compute yaw.
      * @param sunBeta Sun elevation above orbital plane
      * (it <em>may</em> be different from {@link #getBeta()} in
      * some special cases)
      * @param inOrbitPlaneAngle in orbit angle between spacecraft
      * and Sun (or opposite of Sun) projection
      * @return yaw angle
      */
     public T computePhi(final T sunBeta, final T inOrbitPlaneAngle) {
         return FastMath.atan2(FastMath.tan(sunBeta).negate(), FastMath.sin(inOrbitPlaneAngle));
     }
 
     /** Set turn half span and compute corresponding turn time range.
      * @param halfSpan half span of the turn region, as an angle in orbit plane
      * @param endMargin margin in seconds after turn end
      */
     public void setHalfSpan(final T halfSpan, final double endMargin) {
         final FieldAbsoluteDate<T> start = date.shiftedBy(delta.getValue().subtract(halfSpan).divide(muRate));
         final FieldAbsoluteDate<T> end   = date.shiftedBy(delta.getValue().add(halfSpan).divide(muRate));
         final AbsoluteDate estimationDate = getDate().toAbsoluteDate();
         if (turnSpan == null) {
             turnSpan = new FieldTurnSpan<>(start, end, estimationDate, endMargin);
         } else {
             turnSpan.updateStart(start, estimationDate);
             turnSpan.updateEnd(end, estimationDate);
         }
     }
 
     /** Check if context is within turn range.
      * @return true if context is within range extended by end margin
      */
     public boolean inTurnTimeRange() {
         return turnSpan != null && turnSpan.inTurnTimeRange(dateDouble);
     }
 
     /** Get elapsed time since turn start.
      * @return elapsed time from turn start to current date
      */
     public T timeSinceTurnStart() {
         return getDate().durationFrom(turnSpan.getTurnStartDate());
     }
 
     /** Generate an attitude with turn-corrected yaw.
      * @param yaw yaw value to apply
      * @param yawDot yaw first time derivative
      * @return attitude with specified yaw
      */
     public TimeStampedFieldAngularCoordinates<T> turnCorrectedAttitude(final T yaw, final T yawDot) {
         return turnCorrectedAttitude(factory.build(yaw, yawDot, yaw.getField().getZero()));
     }
 
     /** Generate an attitude with turn-corrected yaw.
      * @param yaw yaw value to apply
      * @return attitude with specified yaw
      */
     public TimeStampedFieldAngularCoordinates<T> turnCorrectedAttitude(final FieldDerivativeStructure<T> yaw) {
 
         // Earth pointing (Z aligned with position) with linear yaw (momentum with known cos/sin in the X/Y plane)
         final FieldPVCoordinates<T> svPV          = pvProv.getPVCoordinates(date, inertialFrame);
         final FieldVector3D<T>      p             = svPV.getPosition();
         final FieldVector3D<T>      v             = svPV.getVelocity();
         final FieldVector3D<T>      a             = svPV.getAcceleration();
         final T                     r2            = p.getNormSq();
         final T                     r             = FastMath.sqrt(r2);
         final FieldVector3D<T>      keplerianJerk = new FieldVector3D<>(FieldVector3D.dotProduct(p, v).multiply(-3).divide(r2), a,
                                                                         a.getNorm().negate().divide(r), v);
         final FieldPVCoordinates<T> velocity      = new FieldPVCoordinates<>(v, a, keplerianJerk);
         final FieldPVCoordinates<T> momentum      = svPV.crossProduct(velocity);
 
         final FieldSinCos<FieldDerivativeStructure<T>> sc = FastMath.sinCos(yaw);
         final FieldDerivativeStructure<T> c = sc.cos().negate();
         final FieldDerivativeStructure<T> s = sc.sin().negate();
         final T                           z = yaw.getFactory().getValueField().getZero();
         final FieldVector3D<T> m0 = new FieldVector3D<>(s.getValue(),              c.getValue(),              z);
         final FieldVector3D<T> m1 = new FieldVector3D<>(s.getPartialDerivative(1), c.getPartialDerivative(1), z);
         final FieldVector3D<T> m2 = new FieldVector3D<>(s.getPartialDerivative(2), c.getPartialDerivative(2), z);
         return new TimeStampedFieldAngularCoordinates<>(date,
                                                         svPV.normalize(), momentum.normalize(),
                                                         minusZ, new FieldPVCoordinates<>(m0, m1, m2),
                                                         1.0e-9);
 
     }
 
     /** Compute Orbit Normal (ON) yaw.
      * @return Orbit Normal yaw, using inertial frame as reference
      */
     public TimeStampedFieldAngularCoordinates<T> orbitNormalYaw() {
         final FieldTransform<T> t = LOFType.LVLH_CCSDS.transformFromInertial(date, pvProv.getPVCoordinates(date, inertialFrame));
         return new TimeStampedFieldAngularCoordinates<>(date,
                                                         t.getRotation(),
                                                         t.getRotationRate(),
                                                         t.getRotationAcceleration());
     }
 
 }