/* Copyright 2002-2022 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * 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
    * the License.  You may obtain a copy of the License at
    *
    *   http://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.orekit.propagation.integration;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collection;
  import java.util.Collections;
  import java.util.HashMap;
  import java.util.LinkedList;
  import java.util.List;
  import java.util.Map;
  import java.util.Queue;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.Field;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathIllegalStateException;
  import org.hipparchus.ode.FieldDenseOutputModel;
  import org.hipparchus.ode.FieldExpandableODE;
  import org.hipparchus.ode.FieldODEIntegrator;
  import org.hipparchus.ode.FieldODEState;
  import org.hipparchus.ode.FieldODEStateAndDerivative;
  import org.hipparchus.ode.FieldOrdinaryDifferentialEquation;
  import org.hipparchus.ode.FieldSecondaryODE;
  import org.hipparchus.ode.events.Action;
  import org.hipparchus.ode.events.FieldEventHandlerConfiguration;
  import org.hipparchus.ode.events.FieldODEEventHandler;
  import org.hipparchus.ode.sampling.AbstractFieldODEStateInterpolator;
  import org.hipparchus.ode.sampling.FieldODEStateInterpolator;
  import org.hipparchus.ode.sampling.FieldODEStepHandler;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.Precision;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.errors.OrekitException;
  import org.orekit.errors.OrekitInternalError;
  import org.orekit.errors.OrekitMessages;
  import org.orekit.frames.Frame;
  import org.orekit.orbits.OrbitType;
  import org.orekit.orbits.PositionAngle;
  import org.orekit.propagation.FieldAbstractPropagator;
  import org.orekit.propagation.FieldBoundedPropagator;
  import org.orekit.propagation.FieldEphemerisGenerator;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.PropagationType;
  import org.orekit.propagation.events.FieldEventDetector;
  import org.orekit.propagation.sampling.FieldOrekitStepHandler;
  import org.orekit.propagation.sampling.FieldOrekitStepInterpolator;
  import org.orekit.time.FieldAbsoluteDate;
  import org.orekit.utils.FieldArrayDictionary;
  
  
  /** Common handling of {@link org.orekit.propagation.FieldPropagator FieldPropagator}
   *  methods for both numerical and semi-analytical propagators.
   *  @param <T> the type of the field elements
   *  @author Luc Maisonobe
   */
  public abstract class FieldAbstractIntegratedPropagator<T extends CalculusFieldElement<T>> extends FieldAbstractPropagator<T> {
  
      /** Internal name used for complete secondary state dimension.
       * @since 11.1
       */
      private static final String SECONDARY_DIMENSION = "Orekit-secondary-dimension";
  
      /** Event detectors not related to force models. */
      private final List<FieldEventDetector<T>> detectors;
  
      /** Step handlers dedicated to ephemeris generation. */
      private final List<FieldStoringStepHandler> ephemerisGenerators;
  
      /** Integrator selected by the user for the orbital extrapolation process. */
      private final FieldODEIntegrator<T> integrator;
  
      /** Offsets of secondary states managed by {@link AdditionalEquations}.
       * @since 11.1
       */
      private final Map<String, Integer> secondaryOffsets;
  
      /** Additional derivatives providers.
       * @since 11.1
       */
      private List<FieldAdditionalDerivativesProvider<T>> additionalDerivativesProviders;
  
      /** Counter for differential equations calls. */
      private int calls;
 
     /** Mapper between raw double components and space flight dynamics objects. */
     private FieldStateMapper<T> stateMapper;
 
     /** Flag for resetting the state at end of propagation. */
     private boolean resetAtEnd;
 
     /** Type of orbit to output (mean or osculating) <br/>
      * <p>
      * This is used only in the case of semianalitical propagators where there is a clear separation between
      * mean and short periodic elements. It is ignored by the Numerical propagator.
      * </p>
      */
     private PropagationType propagationType;
 
     /** Build a new instance.
      * @param integrator numerical integrator to use for propagation.
      * @param propagationType type of orbit to output (mean or osculating).
      * @param field Field used by default
      */
     protected FieldAbstractIntegratedPropagator(final Field<T> field, final FieldODEIntegrator<T> integrator, final PropagationType propagationType) {
         super(field);
         detectors                      = new ArrayList<>();
         ephemerisGenerators            = new ArrayList<>();
         additionalDerivativesProviders = new ArrayList<>();
         this.secondaryOffsets          = new HashMap<>();
         this.integrator                = integrator;
         this.propagationType           = propagationType;
         this.resetAtEnd                = true;
     }
 
     /** Allow/disallow resetting the initial state at end of propagation.
      * <p>
      * By default, at the end of the propagation, the propagator resets the initial state
      * to the final state, thus allowing a new propagation to be started from there without
      * recomputing the part already performed. Calling this method with {@code resetAtEnd} set
      * to false changes prevents such reset.
      * </p>
      * @param resetAtEnd if true, at end of each propagation, the {@link
      * #getInitialState() initial state} will be reset to the final state of
      * the propagation, otherwise the initial state will be preserved
      * @since 9.0
      */
     public void setResetAtEnd(final boolean resetAtEnd) {
         this.resetAtEnd = resetAtEnd;
     }
 
     /** Initialize the mapper.
      * @param field Field used by default
      */
     protected void initMapper(final Field<T> field) {
         final T zero = field.getZero();
         stateMapper = createMapper(null, zero.add(Double.NaN), null, null, null, null);
     }
 
     /**  {@inheritDoc} */
     public void setAttitudeProvider(final AttitudeProvider attitudeProvider) {
         super.setAttitudeProvider(attitudeProvider);
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                    attitudeProvider, stateMapper.getFrame());
     }
 
     /** Set propagation orbit type.
      * @param orbitType orbit type to use for propagation
      */
     protected void setOrbitType(final OrbitType orbitType) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    orbitType, stateMapper.getPositionAngleType(),
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get propagation parameter type.
      * @return orbit type used for propagation
      */
     protected OrbitType getOrbitType() {
         return stateMapper.getOrbitType();
     }
 
     /** Check if only the mean elements should be used in a semianalitical propagation.
      * @return {@link PropagationType MEAN} if only mean elements have to be used or
      *         {@link PropagationType OSCULATING} if osculating elements have to be also used.
      */
     protected PropagationType isMeanOrbit() {
         return propagationType;
     }
 
     /** Set position angle type.
      * <p>
      * The position parameter type is meaningful only if {@link
      * #getOrbitType() propagation orbit type}
      * support it. As an example, it is not meaningful for propagation
      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
      * </p>
      * @param positionAngleType angle type to use for propagation
      */
     protected void setPositionAngleType(final PositionAngle positionAngleType) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), stateMapper.getMu(),
                                    stateMapper.getOrbitType(), positionAngleType,
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get propagation parameter type.
      * @return angle type to use for propagation
      */
     protected PositionAngle getPositionAngleType() {
         return stateMapper.getPositionAngleType();
     }
 
     /** Set the central attraction coefficient μ.
      * @param mu central attraction coefficient (m³/s²)
      */
     public void setMu(final T mu) {
         stateMapper = createMapper(stateMapper.getReferenceDate(), mu,
                                    stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                    stateMapper.getAttitudeProvider(), stateMapper.getFrame());
     }
 
     /** Get the central attraction coefficient μ.
      * @return mu central attraction coefficient (m³/s²)
      * @see #setMu(CalculusFieldElement)
      */
     public T getMu() {
         return stateMapper.getMu();
     }
 
     /** Get the number of calls to the differential equations computation method.
      * <p>The number of calls is reset each time the {@link #propagate(FieldAbsoluteDate)}
      * method is called.</p>
      * @return number of calls to the differential equations computation method
      */
     public int getCalls() {
         return calls;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isAdditionalStateManaged(final String name) {
 
         // first look at already integrated states
         if (super.isAdditionalStateManaged(name)) {
             return true;
         }
 
         // then look at states we integrate ourselves
         for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
             if (provider.getName().equals(name)) {
                 return true;
             }
         }
 
         return false;
     }
 
     /** {@inheritDoc} */
     @Override
     public String[] getManagedAdditionalStates() {
         final String[] alreadyIntegrated = super.getManagedAdditionalStates();
         final String[] managed = new String[alreadyIntegrated.length + additionalDerivativesProviders.size()];
         System.arraycopy(alreadyIntegrated, 0, managed, 0, alreadyIntegrated.length);
         for (int i = 0; i < additionalDerivativesProviders.size(); ++i) {
             managed[i + alreadyIntegrated.length] = additionalDerivativesProviders.get(i).getName();
         }
         return managed;
     }
 
     /** Add a set of user-specified equations to be integrated along with the orbit propagation.
      * @param additional additional equations
      * @deprecated as of 11.1, replaced by {@link #addAdditionalDerivativesProvider(FieldAdditionalDerivativesProvider)}
      */
     @Deprecated
     public void addAdditionalEquations(final FieldAdditionalEquations<T> additional) {
         addAdditionalDerivativesProvider(new FieldAdditionalEquationsAdapter<>(additional, this::getInitialState));
     }
 
     /** Add a provider for user-specified state derivatives to be integrated along with the orbit propagation.
      * @param provider provider for additional derivatives
      * @see #addAdditionalStateProvider(org.orekit.propagation.FieldAdditionalStateProvider)
      * @since 11.1
      */
     public void addAdditionalDerivativesProvider(final FieldAdditionalDerivativesProvider<T> provider) {
         // check if the name is already used
         if (isAdditionalStateManaged(provider.getName())) {
             // these derivatives are already registered, complain
             throw new OrekitException(OrekitMessages.ADDITIONAL_STATE_NAME_ALREADY_IN_USE,
                                       provider.getName());
         }
 
         // this is really a new set of derivatives, add it
         additionalDerivativesProviders.add(provider);
 
         secondaryOffsets.clear();
 
     }
 
     /** Get an unmodifiable list of providers for additional derivatives.
      * @return providers for additional derivatives
      * @since 11.1
      */
     public List<FieldAdditionalDerivativesProvider<T>> getAdditionalDerivativesProviders() {
         return Collections.unmodifiableList(additionalDerivativesProviders);
     }
 
     /** {@inheritDoc} */
     public <D extends FieldEventDetector<T>> void addEventDetector(final D detector) {
         detectors.add(detector);
     }
 
     /** {@inheritDoc} */
     public Collection<FieldEventDetector<T>> getEventsDetectors() {
         return Collections.unmodifiableCollection(detectors);
     }
 
     /** {@inheritDoc} */
     public void clearEventsDetectors() {
         detectors.clear();
     }
 
     /** Set up all user defined event detectors.
      */
     protected void setUpUserEventDetectors() {
         for (final FieldEventDetector<T> detector : detectors) {
             setUpEventDetector(integrator, detector);
         }
     }
 
     /** Wrap an Orekit event detector and register it to the integrator.
      * @param integ integrator into which event detector should be registered
      * @param detector event detector to wrap
      */
     protected void setUpEventDetector(final FieldODEIntegrator<T> integ, final FieldEventDetector<T> detector) {
         integ.addEventHandler(new FieldAdaptedEventDetector(detector),
                               detector.getMaxCheckInterval().getReal(),
                               detector.getThreshold().getReal(),
                               detector.getMaxIterationCount());
     }
 
     /** {@inheritDoc} */
     @Override
     public FieldEphemerisGenerator<T> getEphemerisGenerator() {
         final FieldStoringStepHandler storingHandler = new FieldStoringStepHandler();
         ephemerisGenerators.add(storingHandler);
         return storingHandler;
     }
 
     /** Create a mapper between raw double components and spacecraft state.
     /** Simple constructor.
      * <p>
      * The position parameter type is meaningful only if {@link
      * #getOrbitType() propagation orbit type}
      * support it. As an example, it is not meaningful for propagation
      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
      * </p>
      * @param referenceDate reference date
      * @param mu central attraction coefficient (m³/s²)
      * @param orbitType orbit type to use for mapping
      * @param positionAngleType angle type to use for propagation
      * @param attitudeProvider attitude provider
      * @param frame inertial frame
      * @return new mapper
      */
     protected abstract FieldStateMapper<T> createMapper(FieldAbsoluteDate<T> referenceDate, T mu,
                                                         OrbitType orbitType, PositionAngle positionAngleType,
                                                         AttitudeProvider attitudeProvider, Frame frame);
 
     /** Get the differential equations to integrate (for main state only).
      * @param integ numerical integrator to use for propagation.
      * @return differential equations for main state
      */
     protected abstract MainStateEquations<T> getMainStateEquations(FieldODEIntegrator<T> integ);
 
     /** {@inheritDoc} */
     public FieldSpacecraftState<T> propagate(final FieldAbsoluteDate<T> target) {
         if (getStartDate() == null) {
             if (getInitialState() == null) {
                 throw new OrekitException(OrekitMessages.INITIAL_STATE_NOT_SPECIFIED_FOR_ORBIT_PROPAGATION);
             }
             setStartDate(getInitialState().getDate());
         }
         return propagate(getStartDate(), target);
     }
 
     /** {@inheritDoc} */
     public FieldSpacecraftState<T> propagate(final FieldAbsoluteDate<T> tStart, final FieldAbsoluteDate<T> tEnd) {
 
         if (getInitialState() == null) {
             throw new OrekitException(OrekitMessages.INITIAL_STATE_NOT_SPECIFIED_FOR_ORBIT_PROPAGATION);
         }
 
         // make sure the integrator will be reset properly even if we change its events handlers and step handlers
         try (IntegratorResetter<T> resetter = new IntegratorResetter<>(integrator)) {
 
             if (!tStart.equals(getInitialState().getDate())) {
                 // if propagation start date is not initial date,
                 // propagate from initial to start date without event detection
                 try (IntegratorResetter<T> startResetter = new IntegratorResetter<>(integrator)) {
                     integrateDynamics(tStart);
                 }
             }
 
             // set up events added by user
             setUpUserEventDetectors();
 
             // set up step handlers
             for (final FieldOrekitStepHandler<T> handler : getMultiplexer().getHandlers()) {
                 integrator.addStepHandler(new FieldAdaptedStepHandler(handler));
             }
             for (final FieldStoringStepHandler generator : ephemerisGenerators) {
                 generator.setEndDate(tEnd);
                 integrator.addStepHandler(generator);
             }
 
             // propagate from start date to end date with event detection
             return integrateDynamics(tEnd);
 
         }
 
     }
 
     /** Propagation with or without event detection.
      * @param tEnd target date to which orbit should be propagated
      * @return state at end of propagation
      */
     private FieldSpacecraftState<T> integrateDynamics(final FieldAbsoluteDate<T> tEnd) {
         try {
 
             initializePropagation();
 
             if (getInitialState().getDate().equals(tEnd)) {
                 // don't extrapolate
                 return getInitialState();
             }
             // space dynamics view
             stateMapper = createMapper(getInitialState().getDate(), stateMapper.getMu(),
                                        stateMapper.getOrbitType(), stateMapper.getPositionAngleType(),
                                        stateMapper.getAttitudeProvider(), getInitialState().getFrame());
 
 
             // set propagation orbit type
             //final FieldOrbit<T> initialOrbit = stateMapper.getOrbitType().convertType(getInitialState().getOrbit());
             if (Double.isNaN(getMu().getReal())) {
                 setMu(getInitialState().getMu());
             }
             if (getInitialState().getMass().getReal() <= 0.0) {
                 throw new OrekitException(OrekitMessages.SPACECRAFT_MASS_BECOMES_NEGATIVE,
                                                getInitialState().getMass());
             }
 
             // convert space flight dynamics API to math API
             final FieldSpacecraftState<T> initialIntegrationState = getInitialIntegrationState();
             final FieldODEState<T> mathInitialState = createInitialState(initialIntegrationState);
             final FieldExpandableODE<T> mathODE = createODE(integrator, mathInitialState);
 
             // mathematical integration
             final FieldODEStateAndDerivative<T> mathFinalState;
             beforeIntegration(initialIntegrationState, tEnd);
             mathFinalState = integrator.integrate(mathODE, mathInitialState,
                                                   tEnd.durationFrom(getInitialState().getDate()));
 
             afterIntegration();
 
             // get final state
             FieldSpacecraftState<T> finalState =
                             stateMapper.mapArrayToState(stateMapper.mapDoubleToDate(mathFinalState.getTime(), tEnd),
                                                         mathFinalState.getPrimaryState(),
                                                         mathFinalState.getPrimaryDerivative(),
                                                         propagationType);
             if (!additionalDerivativesProviders.isEmpty()) {
                 final T[] secondary            = mathFinalState.getSecondaryState(1);
                 final T[] secondaryDerivatives = mathFinalState.getSecondaryDerivative(1);
                 for (FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
                     final String   name        = provider.getName();
                     final int      offset      = secondaryOffsets.get(name);
                     final int      dimension   = provider.getDimension();
                     finalState = finalState.
                                  addAdditionalState(name, Arrays.copyOfRange(secondary, offset, offset + dimension)).
                                  addAdditionalStateDerivative(name, Arrays.copyOfRange(secondaryDerivatives, offset, offset + dimension));
                 }
             }
             finalState = updateAdditionalStates(finalState);
 
             if (resetAtEnd) {
                 resetInitialState(finalState);
                 setStartDate(finalState.getDate());
             }
 
             return finalState;
 
         } catch (OrekitException pe) {
             throw pe;
         } catch (MathIllegalArgumentException | MathIllegalStateException me) {
             throw OrekitException.unwrap(me);
         }
     }
 
     /** Get the initial state for integration.
      * @return initial state for integration
      */
     protected FieldSpacecraftState<T> getInitialIntegrationState() {
         return getInitialState();
     }
 
     /** Create an initial state.
      * @param initialState initial state in flight dynamics world
      * @return initial state in mathematics world
      */
     private FieldODEState<T> createInitialState(final FieldSpacecraftState<T> initialState) {
 
         // retrieve initial state
         final T[] primary  = MathArrays.buildArray(initialState.getA().getField(), getBasicDimension());
         stateMapper.mapStateToArray(initialState, primary, null);
 
         if (secondaryOffsets.isEmpty()) {
             // compute dimension of the secondary state
             int offset = 0;
             for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
                 secondaryOffsets.put(provider.getName(), offset);
                 offset += provider.getDimension();
             }
             secondaryOffsets.put(SECONDARY_DIMENSION, offset);
         }
 
         return new FieldODEState<>(initialState.getA().getField().getZero(), primary, secondary(initialState));
 
     }
 
     /** Create secondary state.
      * @param state spacecraft state
      * @return secondary state
      * @since 11.1
      */
     private T[][] secondary(final FieldSpacecraftState<T> state) {
 
         if (secondaryOffsets.isEmpty()) {
             return null;
         }
 
         final T[][] secondary = MathArrays.buildArray(state.getDate().getField(), 1, secondaryOffsets.get(SECONDARY_DIMENSION));
         for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
             final String name       = provider.getName();
             final int    offset     = secondaryOffsets.get(name);
             final T[]    additional = state.getAdditionalState(name);
             System.arraycopy(additional, 0, secondary[0], offset, additional.length);
         }
 
         return secondary;
 
     }
 
     /** Create secondary state derivative.
      * @param state spacecraft state
      * @return secondary state derivative
      * @since 11.1
      */
     private T[][] secondaryDerivative(final FieldSpacecraftState<T> state) {
 
         if (secondaryOffsets.isEmpty()) {
             return null;
         }
 
         final T[][] secondaryDerivative = MathArrays.buildArray(state.getDate().getField(), 1, secondaryOffsets.get(SECONDARY_DIMENSION));
         for (final FieldAdditionalDerivativesProvider<T> providcer : additionalDerivativesProviders) {
             final String name       = providcer.getName();
             final int    offset     = secondaryOffsets.get(name);
             final T[]    additionalDerivative = state.getAdditionalStateDerivative(name);
             System.arraycopy(additionalDerivative, 0, secondaryDerivative[0], offset, additionalDerivative.length);
         }
 
         return secondaryDerivative;
 
     }
 
     /** Create an ODE with all equations.
      * @param integ numerical integrator to use for propagation.
      * @param mathInitialState initial state
      * @return a new ode
      */
     private FieldExpandableODE<T> createODE(final FieldODEIntegrator<T> integ,
                                     final FieldODEState<T> mathInitialState) {
 
         final FieldExpandableODE<T> ode =
                 new FieldExpandableODE<>(new ConvertedMainStateEquations(getMainStateEquations(integ)));
 
         // secondary part of the ODE
         if (!additionalDerivativesProviders.isEmpty()) {
             ode.addSecondaryEquations(new ConvertedSecondaryStateEquations());
         }
 
         return ode;
 
     }
 
     /** Method called just before integration.
      * <p>
      * The default implementation does nothing, it may be specialized in subclasses.
      * </p>
      * @param initialState initial state
      * @param tEnd target date at which state should be propagated
      */
     protected void beforeIntegration(final FieldSpacecraftState<T> initialState,
                                      final FieldAbsoluteDate<T> tEnd) {
         // do nothing by default
     }
 
     /** Method called just after integration.
      * <p>
      * The default implementation does nothing, it may be specialized in subclasses.
      * </p>
      */
     protected void afterIntegration() {
         // do nothing by default
     }
 
     /** Get state vector dimension without additional parameters.
      * @return state vector dimension without additional parameters.
      */
     public int getBasicDimension() {
         return 7;
 
     }
 
     /** Get the integrator used by the propagator.
      * @return the integrator.
      */
     protected FieldODEIntegrator<T> getIntegrator() {
         return integrator;
     }
 
     /** Convert a state from mathematical world to space flight dynamics world.
      * @param os mathematical state
      * @return space flight dynamics state
      */
     private FieldSpacecraftState<T> convert(final FieldODEStateAndDerivative<T> os) {
 
         FieldSpacecraftState<T> s =
                         stateMapper.mapArrayToState(os.getTime(),
                                                     os.getPrimaryState(),
                                                     os.getPrimaryDerivative(),
                                                     propagationType);
         if (os.getNumberOfSecondaryStates() > 0) {
             final T[] secondary           = os.getSecondaryState(1);
             final T[] secondaryDerivative = os.getSecondaryDerivative(1);
             for (final FieldAdditionalDerivativesProvider<T> equations : additionalDerivativesProviders) {
                 final String name      = equations.getName();
                 final int    offset    = secondaryOffsets.get(name);
                 final int    dimension = equations.getDimension();
                 s = s.addAdditionalState(name, Arrays.copyOfRange(secondary, offset, offset + dimension));
                 s = s.addAdditionalStateDerivative(name, Arrays.copyOfRange(secondaryDerivative, offset, offset + dimension));
             }
         }
         s = updateAdditionalStates(s);
 
         return s;
 
     }
 
     /** Convert a state from space flight dynamics world to mathematical world.
      * @param state space flight dynamics state
      * @return mathematical state
      */
     private FieldODEStateAndDerivative<T> convert(final FieldSpacecraftState<T> state) {
 
         // retrieve initial state
         final T[] primary    = MathArrays.buildArray(getField(), getBasicDimension());
         final T[] primaryDot = MathArrays.buildArray(getField(), getBasicDimension());
         stateMapper.mapStateToArray(state, primary, primaryDot);
 
         // secondary part of the ODE
         final T[][] secondary           = secondary(state);
         final T[][] secondaryDerivative = secondaryDerivative(state);
 
         return new FieldODEStateAndDerivative<>(stateMapper.mapDateToDouble(state.getDate()),
                                                 primary, primaryDot,
                                                 secondary, secondaryDerivative);
 
     }
 
     /** Differential equations for the main state (orbit, attitude and mass). */
     public interface MainStateEquations<T extends CalculusFieldElement<T>> {
 
         /**
          * Initialize the equations at the start of propagation. This method will be
          * called before any calls to {@link #computeDerivatives(FieldSpacecraftState)}.
          *
          * <p> The default implementation of this method does nothing.
          *
          * @param initialState initial state information at the start of propagation.
          * @param target       date of propagation. Not equal to {@code
          *                     initialState.getDate()}.
          */
         void init(FieldSpacecraftState<T> initialState, FieldAbsoluteDate<T> target);
 
         /** Compute differential equations for main state.
          * @param state current state
          * @return derivatives of main state
          */
         T[] computeDerivatives(FieldSpacecraftState<T> state);
 
     }
 
     /** Differential equations for the main state (orbit, attitude and mass), with converted API. */
     private class ConvertedMainStateEquations implements FieldOrdinaryDifferentialEquation<T> {
 
         /** Main state equations. */
         private final MainStateEquations<T> main;
 
         /** Simple constructor.
          * @param main main state equations
          */
         ConvertedMainStateEquations(final MainStateEquations<T> main) {
             this.main = main;
             calls = 0;
         }
 
         /** {@inheritDoc} */
         public int getDimension() {
             return getBasicDimension();
         }
 
         @Override
         public void init(final T t0, final T[] y0, final T finalTime) {
             // update space dynamics view
             FieldSpacecraftState<T> initialState = stateMapper.mapArrayToState(t0, y0, null, PropagationType.MEAN);
             initialState = updateAdditionalStates(initialState);
             final FieldAbsoluteDate<T> target = stateMapper.mapDoubleToDate(finalTime);
             main.init(initialState, target);
         }
         /** {@inheritDoc} */
         public T[] computeDerivatives(final T t, final T[] y) {
 
             // increment calls counter
             ++calls;
 
             // update space dynamics view
             FieldSpacecraftState<T> currentState = stateMapper.mapArrayToState(t, y, null, PropagationType.MEAN);
             currentState = updateAdditionalStates(currentState);
 
             // compute main state differentials
             return main.computeDerivatives(currentState);
 
         }
 
     }
 
     /** Differential equations for the secondary state (Jacobians, user variables ...), with converted API. */
     private class ConvertedSecondaryStateEquations implements FieldSecondaryODE<T> {
 
         /** Dimension of the combined additional states. */
         private final int combinedDimension;
 
         /** Simple constructor.
          */
         ConvertedSecondaryStateEquations() {
             this.combinedDimension = secondaryOffsets.get(SECONDARY_DIMENSION);
         }
 
         /** {@inheritDoc} */
         @Override
         public int getDimension() {
             return combinedDimension;
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final T t0, final T[] primary0,
                          final T[] secondary0, final T finalTime) {
             // update space dynamics view
             final FieldSpacecraftState<T> initialState = convert(t0, primary0, null, secondary0);
 
             final FieldAbsoluteDate<T> target = stateMapper.mapDoubleToDate(finalTime);
             for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
                 provider.init(initialState, target);
             }
 
         }
 
         /** {@inheritDoc} */
         @Override
         public T[] computeDerivatives(final T t, final T[] primary,
                                       final T[] primaryDot, final T[] secondary) {
 
             // update space dynamics view
             // the integrable generators generate method will be called here,
             // according to the generators yield order
             FieldSpacecraftState<T> updated = convert(t, primary, primaryDot, secondary);
 
             // set up queue for equations
             final Queue<FieldAdditionalDerivativesProvider<T>> pending = new LinkedList<>(additionalDerivativesProviders);
 
             // gather the derivatives from all additional equations, taking care of dependencies
             final T[] secondaryDot = MathArrays.buildArray(t.getField(), combinedDimension);
             int yieldCount = 0;
             while (!pending.isEmpty()) {
                 final FieldAdditionalDerivativesProvider<T> equations = pending.remove();
                 if (equations.yield(updated)) {
                     // these equations have to wait for another set,
                     // we put them again in the pending queue
                     pending.add(equations);
                     if (++yieldCount >= pending.size()) {
                         // all pending equations yielded!, they probably need data not yet initialized
                         // we let the propagation proceed, if these data are really needed right now
                         // an appropriate exception will be triggered when caller tries to access them
                         break;
                     }
                 } else {
                     // we can use these equations right now
                     final String name        = equations.getName();
                     final int    offset      = secondaryOffsets.get(name);
                     final int    dimension   = equations.getDimension();
                     final T[]    derivatives = equations.derivatives(updated);
                     System.arraycopy(derivatives, 0, secondaryDot, offset, dimension);
                     updated = updated.addAdditionalStateDerivative(name, derivatives);
                     yieldCount = 0;
                 }
             }
 
             return secondaryDot;
 
         }
 
         /** Convert mathematical view to space view.
          * @param t current value of the independent <I>time</I> variable
          * @param primary array containing the current value of the primary state vector
          * @param primaryDot array containing the derivative of the primary state vector
          * @param secondary array containing the current value of the secondary state vector
          * @return space view of the state
          */
         private FieldSpacecraftState<T> convert(final T t, final T[] primary,
                                                 final T[] primaryDot, final T[] secondary) {
 
             FieldSpacecraftState<T> initialState = stateMapper.mapArrayToState(t, primary, primaryDot, PropagationType.MEAN);
 
             for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
                 final String name      = provider.getName();
                 final int    offset    = secondaryOffsets.get(name);
                 final int    dimension = provider.getDimension();
                 initialState = initialState.addAdditionalState(name, Arrays.copyOfRange(secondary, offset, offset + dimension));
             }
 
             return updateAdditionalStates(initialState);
 
         }
 
     }
 
     /** Adapt an {@link org.orekit.propagation.events.FieldEventDetector<T>}
      * to Hipparchus {@link org.hipparchus.ode.events.FieldODEEventHandler<T>} interface.
      * @param <T> class type for the generic version
      * @author Fabien Maussion
      */
     private class FieldAdaptedEventDetector implements FieldODEEventHandler<T> {
 
         /** Underlying event detector. */
         private final FieldEventDetector<T> detector;
 
         /** Time of the previous call to g. */
         private T lastT;
 
         /** Value from the previous call to g. */
         private T lastG;
 
         /** Build a wrapped event detector.
          * @param detector event detector to wrap
         */
         FieldAdaptedEventDetector(final FieldEventDetector<T> detector) {
             this.detector = detector;
             this.lastT    = getField().getZero().add(Double.NaN);
             this.lastG    = getField().getZero().add(Double.NaN);
         }
 
         /** {@inheritDoc} */
         public void init(final FieldODEStateAndDerivative<T> s0, final T t) {
             detector.init(convert(s0), stateMapper.mapDoubleToDate(t));
             this.lastT = getField().getZero().add(Double.NaN);
             this.lastG = getField().getZero().add(Double.NaN);
         }
 
         /** {@inheritDoc} */
         public T g(final FieldODEStateAndDerivative<T> s) {
             if (!Precision.equals(lastT.getReal(), s.getTime().getReal(), 0)) {
                 lastT = s.getTime();
                 lastG = detector.g(convert(s));
             }
             return lastG;
         }
 
         /** {@inheritDoc} */
         public Action eventOccurred(final FieldODEStateAndDerivative<T> s, final boolean increasing) {
             return detector.eventOccurred(convert(s), increasing);
         }
 
         /** {@inheritDoc} */
         public FieldODEState<T> resetState(final FieldODEStateAndDerivative<T> s) {
 
             final FieldSpacecraftState<T> oldState = convert(s);
             final FieldSpacecraftState<T> newState = detector.resetState(oldState);
             stateChanged(newState);
 
             // main part
             final T[] primary    = MathArrays.buildArray(getField(), s.getPrimaryStateDimension());
             stateMapper.mapStateToArray(newState, primary, null);
 
             // secondary part
             final T[][] secondary = MathArrays.buildArray(getField(), 1, additionalDerivativesProviders.size());
             for (final FieldAdditionalDerivativesProvider<T> provider : additionalDerivativesProviders) {
                 final String name      = provider.getName();
                 final int    offset    = secondaryOffsets.get(name);
                 final int    dimension = provider.getDimension();
                 System.arraycopy(newState.getAdditionalState(name), 0, secondary[0], offset, dimension);
             }
 
             return new FieldODEState<>(newState.getDate().durationFrom(getStartDate()),
                                        primary, secondary);
         }
 
     }
 
     /** Adapt an {@link org.orekit.propagation.sampling.FieldOrekitStepHandler<T>}
      * to Hipparchus {@link FieldODEStepHandler<T>} interface.
      * @author Luc Maisonobe
      */
     private class FieldAdaptedStepHandler implements FieldODEStepHandler<T> {
 
         /** Underlying handler. */
         private final FieldOrekitStepHandler<T> handler;
 
         /** Build an instance.
          * @param handler underlying handler to wrap
          */
         FieldAdaptedStepHandler(final FieldOrekitStepHandler<T> handler) {
             this.handler = handler;
         }
 
         /** {@inheritDoc} */
         public void init(final FieldODEStateAndDerivative<T> s0, final T t) {
             handler.init(convert(s0), stateMapper.mapDoubleToDate(t));
         }
 
         /** {@inheritDoc} */
         public void handleStep(final FieldODEStateInterpolator<T> interpolator) {
             handler.handleStep(new FieldAdaptedStepInterpolator(interpolator));
         }
 
         /** {@inheritDoc} */
         @Override
         public void finish(final FieldODEStateAndDerivative<T> finalState) {
             handler.finish(convert(finalState));
         }
 
     }
 
     /** Adapt an {@link org.orekit.propagation.sampling.FieldOrekitStepInterpolator<T>}
      * to Hipparchus {@link FieldODEStepInterpolator<T>} interface.
      * @author Luc Maisonobe
      */
     private class FieldAdaptedStepInterpolator implements FieldOrekitStepInterpolator<T> {
 
         /** Underlying raw rawInterpolator. */
         private final FieldODEStateInterpolator<T> mathInterpolator;
 
         /** Build an instance.
          * @param mathInterpolator underlying raw interpolator
          */
         FieldAdaptedStepInterpolator(final FieldODEStateInterpolator<T> mathInterpolator) {
             this.mathInterpolator = mathInterpolator;
         }
 
         /** {@inheritDoc}} */
         @Override
         public FieldSpacecraftState<T> getPreviousState() {
             return convert(mathInterpolator.getPreviousState());
         }
 
         /** {@inheritDoc}} */
         @Override
         public FieldSpacecraftState<T> getCurrentState() {
             return convert(mathInterpolator.getCurrentState());
         }
 
         /** {@inheritDoc}} */
         @Override
         public FieldSpacecraftState<T> getInterpolatedState(final FieldAbsoluteDate<T> date) {
             return convert(mathInterpolator.getInterpolatedState(date.durationFrom(getStartDate())));
         }
 
         /** Check is integration direction is forward in date.
          * @return true if integration is forward in date
          */
         public boolean isForward() {
             return mathInterpolator.isForward();
         }
 
         /** {@inheritDoc}} */
         @Override
         public FieldAdaptedStepInterpolator restrictStep(final FieldSpacecraftState<T> newPreviousState,
                                                          final FieldSpacecraftState<T> newCurrentState) {
             try {
                 final AbstractFieldODEStateInterpolator<T> aosi = (AbstractFieldODEStateInterpolator<T>) mathInterpolator;
                 return new FieldAdaptedStepInterpolator(aosi.restrictStep(convert(newPreviousState),
                                                                           convert(newCurrentState)));
             } catch (ClassCastException cce) {
                 // this should never happen
                 throw new OrekitInternalError(cce);
             }
         }
 
     }
 
     /** Specialized step handler storing interpolators for ephemeris generation.
      * @since 11.0
      */
     private class FieldStoringStepHandler implements FieldODEStepHandler<T>, FieldEphemerisGenerator<T> {
 
         /** Underlying raw mathematical model. */
         private FieldDenseOutputModel<T> model;
 
         /** the user supplied end date. Propagation may not end on this date. */
         private FieldAbsoluteDate<T> endDate;
 
         /** Generated ephemeris. */
         private FieldBoundedPropagator<T> ephemeris;
 
         /** Set the end date.
          * @param endDate end date
          */
         public void setEndDate(final FieldAbsoluteDate<T> endDate) {
             this.endDate = endDate;
         }
 
         /** {@inheritDoc} */
         @Override
         public void init(final FieldODEStateAndDerivative<T> s0, final T t) {
             this.model = new FieldDenseOutputModel<>();
             model.init(s0, t);
 
             // ephemeris will be generated when last step is processed
             this.ephemeris = null;
 
         }
 
         /** {@inheritDoc} */
         @Override
         public FieldBoundedPropagator<T> getGeneratedEphemeris() {
             return ephemeris;
         }
 
         /** {@inheritDoc} */
         @Override
         public void handleStep(final FieldODEStateInterpolator<T> interpolator) {
             model.handleStep(interpolator);
         }
 
         /** {@inheritDoc} */
         @Override
         public void finish(final FieldODEStateAndDerivative<T> finalState) {
 
             // set up the boundary dates
             final T tI = model.getInitialTime();
             final T tF = model.getFinalTime();
             // tI is almost? always zero
             final FieldAbsoluteDate<T> startDate =
                             stateMapper.mapDoubleToDate(tI);
             final FieldAbsoluteDate<T> finalDate =
                             stateMapper.mapDoubleToDate(tF, this.endDate);
             final FieldAbsoluteDate<T> minDate;
             final FieldAbsoluteDate<T> maxDate;
             if (tF.getReal() < tI.getReal()) {
                 minDate = finalDate;
                 maxDate = startDate;
             } else {
                 minDate = startDate;
                 maxDate = finalDate;
             }
 
             // get the initial additional states that are not managed
             final FieldArrayDictionary<T> unmanaged = new FieldArrayDictionary<>(startDate.getField());
             for (final FieldArrayDictionary<T>.Entry initial : getInitialState().getAdditionalStatesValues().getData()) {
                 if (!isAdditionalStateManaged(initial.getKey())) {
                     // this additional state was in the initial state, but is unknown to the propagator
                     // we simply copy its initial value as is
                     unmanaged.put(initial.getKey(), initial.getValue());
                 }
             }
 
             // get the names of additional states managed by differential equations
             final String[] names = new String[additionalDerivativesProviders.size()];
             for (int i = 0; i < names.length; ++i) {
                 names[i] = additionalDerivativesProviders.get(i).getName();
             }
 
             // create the ephemeris
             ephemeris = new FieldIntegratedEphemeris<>(startDate, minDate, maxDate,
                                                        stateMapper, propagationType, model,
                                                        unmanaged, getAdditionalStateProviders(), names);
 
         }
 
     }
 
     /** Wrapper for resetting an integrator handlers.
      * <p>
      * This class is intended to be used in a try-with-resource statement.
      * If propagator-specific event handlers and step handlers are added to
      * the integrator in the try block, they will be removed automatically
      * when leaving the block, so the integrator only keep its own handlers
      * between calls to {@link AbstractIntegratedPropagator#propagate(AbsoluteDate, AbsoluteDate).
      * </p>
      * @param <T> the type of the field elements
      * @since 11.0
      */
     private static class IntegratorResetter<T extends CalculusFieldElement<T>> implements AutoCloseable {
 
         /** Wrapped integrator. */
         private final FieldODEIntegrator<T> integrator;
 
         /** Initial event handlers list. */
         private final List<FieldEventHandlerConfiguration<T>> eventHandlersConfigurations;
 
         /** Initial step handlers list. */
         private final List<FieldODEStepHandler<T>> stepHandlers;
 
         /** Simple constructor.
          * @param integrator wrapped integrator
          */
         IntegratorResetter(final FieldODEIntegrator<T> integrator) {
             this.integrator                  = integrator;
             this.eventHandlersConfigurations = new ArrayList<>(integrator.getEventHandlersConfigurations());
             this.stepHandlers                = new ArrayList<>(integrator.getStepHandlers());
         }
 
         /** {@inheritDoc}
          * <p>
          * Reset event handlers and step handlers back to the initial list
          * </p>
          */
         @Override
         public void close() {
 
             // reset event handlers
             integrator.clearEventHandlers();
             eventHandlersConfigurations.forEach(c -> integrator.addEventHandler(c.getEventHandler(),
                                                                                 c.getMaxCheckInterval(),
                                                                                 c.getConvergence().getReal(),
                                                                                 c.getMaxIterationCount(),
                                                                                 c.getSolver()));
 
             // reset step handlers
             integrator.clearStepHandlers();
             stepHandlers.forEach(stepHandler -> integrator.addStepHandler(stepHandler));
 
         }
 
     }
 
 }