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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.propagation.semianalytical.dsst;
  
  import org.hipparchus.analysis.differentiation.Gradient;
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.linear.MatrixUtils;
  import org.hipparchus.linear.RealMatrix;
  import org.orekit.attitudes.AttitudeProvider;
  import org.orekit.errors.OrekitException;
  import org.orekit.propagation.FieldSpacecraftState;
  import org.orekit.propagation.PropagationType;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.integration.AdditionalDerivativesProvider;
  import org.orekit.propagation.integration.CombinedDerivatives;
  import org.orekit.propagation.semianalytical.dsst.forces.DSSTForceModel;
  import org.orekit.propagation.semianalytical.dsst.utilities.FieldAuxiliaryElements;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.utils.DoubleArrayDictionary;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.TimeSpanMap.Span;
  
  import java.util.HashMap;
  import java.util.List;
  import java.util.Map;
  
  /** Generator for State Transition Matrix.
   * @author Luc Maisonobe
   * @since 11.1
   */
  class DSSTStateTransitionMatrixGenerator implements AdditionalDerivativesProvider {
  
      /** Space dimension. */
      private static final int SPACE_DIMENSION = 3;
  
      /** Retrograde factor I.
       *  <p>
       *  DSST model needs equinoctial orbit as internal representation.
       *  Classical equinoctial elements have discontinuities when inclination
       *  is close to zero. In this representation, I = +1. <br>
       *  To avoid this discontinuity, another representation exists and equinoctial
       *  elements can be expressed in a different way, called "retrograde" orbit.
       *  This implies I = -1. <br>
       *  As Orekit doesn't implement the retrograde orbit, I is always set to +1.
       *  But for the sake of consistency with the theory, the retrograde factor
       *  has been kept in the formulas.
       *  </p>
       */
      private static final int I = 1;
  
      /** State dimension. */
      public static final int STATE_DIMENSION = 2 * SPACE_DIMENSION;
  
      /** Name of the Cartesian STM additional state. */
      private final String stmName;
  
      /** Force models used in propagation. */
      private final List<DSSTForceModel> forceModels;
  
      /** Attitude provider used in propagation. */
      private final AttitudeProvider attitudeProvider;
  
      /** Observers for partial derivatives. */
      private final Map<String, DSSTPartialsObserver> partialsObservers;
  
      /** Mean or osculating. */
      private final PropagationType propagationType;
  
      /** Simple constructor.
       * @param stmName name of the Cartesian STM additional state
       * @param forceModels force models used in propagation
       * @param attitudeProvider attitude provider used in propagation
       * @param propagationType mean or osculating.
       */
      DSSTStateTransitionMatrixGenerator(final String stmName,
                                         final List<DSSTForceModel> forceModels,
                                         final AttitudeProvider attitudeProvider,
                                         final PropagationType propagationType) {
          this.stmName           = stmName;
          this.forceModels       = forceModels;
          this.attitudeProvider  = attitudeProvider;
          this.propagationType   = propagationType;
          this.partialsObservers = new HashMap<>();
      }
  
     /** Register an observer for partial derivatives.
      * <p>
      * The observer {@link DSSTPartialsObserver#partialsComputed(SpacecraftState, RealMatrix, double[])} partialsComputed}
      * method will be called when partial derivatives are computed, as a side effect of
      * calling {@link #computePartials(SpacecraftState)} (SpacecraftState)}
      * </p>
      * @param name name of the parameter driver this observer is interested in (may be null)
      * @param observer observer to register
      */
     void addObserver(final String name, final DSSTPartialsObserver observer) {
         partialsObservers.put(name, observer);
     }
 
     /** {@inheritDoc} */
     @Override
     public String getName() {
         return stmName;
     }
 
     /** {@inheritDoc} */
     @Override
     public int getDimension() {
         return STATE_DIMENSION * STATE_DIMENSION;
     }
 
     @Override
     @SuppressWarnings("unchecked")
     public void init(final SpacecraftState initialState, final AbsoluteDate target) {
         // initialize short period terms.
         // the propagator will have called the non-field method
         // so just call the field method here
         // This should be a Field copy of the code in DSSTPropagator.beforeIntegration(...)
         // but with just the short period initialization calls
         // See also how the field state is set up in computePartials(...)
 
         final DSSTGradientConverter converter =
                 new DSSTGradientConverter(initialState, attitudeProvider);
 
         // check if only mean elements must be used
         final PropagationType type = propagationType;
 
         // initialize all perturbing forces
         for (final DSSTForceModel forceModel : forceModels) {
             final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
             final Gradient[] parameters = converter.getParametersAtStateDate(dsState, forceModel);
             final FieldAuxiliaryElements<Gradient> auxiliaryElements = new FieldAuxiliaryElements<>(dsState.getOrbit(), I);
             forceModel.initializeShortPeriodTerms(auxiliaryElements, type, parameters);
         }
 
         // if required, insert the special short periodics step handler
         if (type == PropagationType.OSCULATING) {
             // Compute short periodic coefficients for this point
             for (DSSTForceModel forceModel : forceModels) {
                 final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
                 final Gradient[] parameters = converter.getParametersAtStateDate(dsState, forceModel);
                 forceModel.updateShortPeriodTerms(parameters, dsState);
             }
         }
 
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean yields(final SpacecraftState state) {
         return !state.hasAdditionalData(getName());
     }
 
     /** Set the initial value of the State Transition Matrix.
      * <p>
      * The returned state must be added to the propagator.
      * </p>
      * @param state initial state
      * @param dYdY0 initial State Transition Matrix ∂Y/∂Y₀,
      * if null (which is the most frequent case), assumed to be 6x6 identity
      * @return state with initial STM (converted to Cartesian ∂C/∂Y₀) added
      */
     SpacecraftState setInitialStateTransitionMatrix(final SpacecraftState state, final RealMatrix dYdY0) {
 
         if (dYdY0 != null) {
             if (dYdY0.getRowDimension() != STATE_DIMENSION ||
                             dYdY0.getColumnDimension() != STATE_DIMENSION) {
                 throw new OrekitException(LocalizedCoreFormats.DIMENSIONS_MISMATCH_2x2,
                                           dYdY0.getRowDimension(), dYdY0.getColumnDimension(),
                                           STATE_DIMENSION, STATE_DIMENSION);
             }
         }
 
         // flatten matrix
         final double[] flat = new double[STATE_DIMENSION * STATE_DIMENSION];
         int k = 0;
         for (int i = 0; i < STATE_DIMENSION; ++i) {
             for (int j = 0; j < STATE_DIMENSION; ++j) {
                 flat[k++] = dYdY0.getEntry(i, j);
             }
         }
 
         // set additional state
         return state.addAdditionalData(stmName, flat);
 
     }
 
     /** {@inheritDoc} */
     public CombinedDerivatives combinedDerivatives(final SpacecraftState state) {
 
         final double[] p = state.getAdditionalState(getName());
         final double[] res = new double[p.length];
 
         // perform matrix multiplication with matrices flatten
         final RealMatrix factor = computePartials(state);
         int index = 0;
         for (int i = 0; i < STATE_DIMENSION; ++i) {
             for (int j = 0; j < STATE_DIMENSION; ++j) {
                 double sum = 0;
                 for (int k = 0; k < STATE_DIMENSION; ++k) {
                     sum += factor.getEntry(i, k) * p[j + k * STATE_DIMENSION];
                 }
                 res[index++] = sum;
             }
         }
 
         return new CombinedDerivatives(res, null);
 
     }
 
     /** Compute the various partial derivatives.
      * @param state current spacecraft state
      * @return factor matrix
      */
     private RealMatrix computePartials(final SpacecraftState state) {
 
         // set up containers for partial derivatives
         final RealMatrix            factor               = MatrixUtils.createRealMatrix(STATE_DIMENSION, STATE_DIMENSION);
         final DoubleArrayDictionary meanElementsPartials = new DoubleArrayDictionary();
         final DSSTGradientConverter converter            = new DSSTGradientConverter(state, attitudeProvider);
 
         // Compute Jacobian
         for (final DSSTForceModel forceModel : forceModels) {
 
             final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
             final Gradient[] parameters = converter.getParametersAtStateDate(dsState, forceModel);
             final FieldAuxiliaryElements<Gradient> auxiliaryElements = new FieldAuxiliaryElements<>(dsState.getOrbit(), I);
 
             final Gradient[] meanElementRate = forceModel.getMeanElementRate(dsState, auxiliaryElements, parameters);
             final double[] derivativesA  = meanElementRate[0].getGradient();
             final double[] derivativesEx = meanElementRate[1].getGradient();
             final double[] derivativesEy = meanElementRate[2].getGradient();
             final double[] derivativesHx = meanElementRate[3].getGradient();
             final double[] derivativesHy = meanElementRate[4].getGradient();
             final double[] derivativesL  = meanElementRate[5].getGradient();
 
             // update Jacobian with respect to state
             addToRow(derivativesA,  0, factor);
             addToRow(derivativesEx, 1, factor);
             addToRow(derivativesEy, 2, factor);
             addToRow(derivativesHx, 3, factor);
             addToRow(derivativesHy, 4, factor);
             addToRow(derivativesL,  5, factor);
 
             // partials derivatives with respect to parameters
             int paramsIndex = converter.getFreeStateParameters();
             for (ParameterDriver driver : forceModel.getParametersDrivers()) {
                 if (driver.isSelected()) {
                     // for each span (for each estimated value) corresponding name is added
                     for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
 
                         // get the partials derivatives for this driver
                         DoubleArrayDictionary.Entry entry = meanElementsPartials.getEntry(span.getData());
                         if (entry == null) {
                             // create an entry filled with zeroes
                             meanElementsPartials.put(span.getData(), new double[STATE_DIMENSION]);
                             entry = meanElementsPartials.getEntry(span.getData());
                         }
                         // add the contribution of the current force model
                         entry.increment(new double[] {
                             derivativesA[paramsIndex], derivativesEx[paramsIndex], derivativesEy[paramsIndex],
                             derivativesHx[paramsIndex], derivativesHy[paramsIndex], derivativesL[paramsIndex]
                         });
                         ++paramsIndex;
                     }
 
                 }
             }
 
         }
 
         // notify observers
         for (Map.Entry<String, DSSTPartialsObserver> observersEntry : partialsObservers.entrySet()) {
             final DoubleArrayDictionary.Entry entry = meanElementsPartials.getEntry(observersEntry.getKey());
             observersEntry.getValue().partialsComputed(state, factor, entry == null ? new double[STATE_DIMENSION] : entry.getValue());
         }
 
         return factor;
 
     }
 
     /** Fill Jacobians rows.
      * @param derivatives derivatives of a component
      * @param index component index (0 for a, 1 for ex, 2 for ey, 3 for hx, 4 for hy, 5 for l)
      * @param factor Jacobian of mean elements rate with respect to mean elements
      */
     private void addToRow(final double[] derivatives, final int index, final RealMatrix factor) {
         for (int i = 0; i < 6; i++) {
             factor.addToEntry(index, i, derivatives[i]);
         }
     }
 
     /** Interface for observing partials derivatives. */
     @FunctionalInterface
     public interface DSSTPartialsObserver {
 
         /** Callback called when partial derivatives have been computed.
          * @param state current spacecraft state
          * @param factor factor matrix
          * @param meanElementsPartials partials derivatives of mean elements rates with respect to the parameter driver
          * that was registered (zero if no parameters were not selected or parameter is unknown)
          */
         void partialsComputed(SpacecraftState state, RealMatrix factor, double[] meanElementsPartials);
 
     }
 
 }