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    * contributor license agreements.  See the NOTICE file distributed with
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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.estimation.leastsquares;
  
  import org.hipparchus.linear.Array2DRowRealMatrix;
  import org.hipparchus.linear.ArrayRealVector;
  import org.hipparchus.linear.MatrixUtils;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.linear.RealVector;
  import org.hipparchus.optim.nonlinear.vector.leastsquares.MultivariateJacobianFunction;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.Incrementor;
  import org.hipparchus.util.Pair;
  import org.orekit.estimation.measurements.EstimatedMeasurement;
  import org.orekit.estimation.measurements.EstimatedMeasurementBase;
  import org.orekit.estimation.measurements.ObservedMeasurement;
  import org.orekit.orbits.Orbit;
  import org.orekit.propagation.MatricesHarvester;
  import org.orekit.propagation.Propagator;
  import org.orekit.propagation.PropagatorsParallelizer;
  import org.orekit.propagation.SpacecraftState;
  import org.orekit.propagation.conversion.PropagatorBuilder;
  import org.orekit.propagation.sampling.MultiSatStepHandler;
  import org.orekit.time.AbsoluteDate;
  import org.orekit.time.ChronologicalComparator;
  import org.orekit.utils.ParameterDriver;
  import org.orekit.utils.ParameterDriversList;
  import org.orekit.utils.ParameterDriversList.DelegatingDriver;
  import org.orekit.utils.TimeSpanMap;
  import org.orekit.utils.TimeSpanMap.Span;
  
  import java.util.ArrayList;
  import java.util.Arrays;
  import java.util.Collections;
  import java.util.HashMap;
  import java.util.IdentityHashMap;
  import java.util.List;
  import java.util.Map;
  
  /** Bridge between {@link ObservedMeasurement measurements} and {@link
   * org.hipparchus.optim.nonlinear.vector.leastsquares.LeastSquaresProblem
   * least squares problems}.
   * @author Luc Maisonobe
   * @author Bryan Cazabonne
   * @author Thomas Paulet
   * @author Melina Vanel
   * @since 11.0
   */
  public abstract class AbstractBatchLSModel implements MultivariateJacobianFunction {
  
      /** Builders for propagators. */
      private final PropagatorBuilder[] builders;
  
      /** Array of each builder's selected orbit drivers. Orbit drivers
       * should have only 1 span on their value TimeSpanMap.
       * @since 11.1
       */
      private final ParameterDriversList[] estimatedOrbitalParameters;
  
      /** Array of each builder's selected propagation drivers. */
      private final ParameterDriversList[] estimatedPropagationParameters;
  
      /** Estimated measurements parameters. */
      private final ParameterDriversList estimatedMeasurementsParameters;
  
      /** Measurements. */
      private final List<ObservedMeasurement<?>> measurements;
  
      /** Start columns for each estimated orbit. */
      private final int[] orbitsStartColumns;
  
      /** End columns for each estimated orbit. */
      private final int[] orbitsEndColumns;
  
      /** Indirection array in measurements jacobians.
       * @since 11.2
       */
      private final int[] orbitsJacobianColumns;
  
      /** Map for propagation parameters columns. */
      private final Map<String, Integer> propagationParameterColumns;
  
      /** Map for measurements parameters columns. */
      private final Map<String, Integer> measurementParameterColumns;
  
     /** Last evaluations. */
     private final Map<ObservedMeasurement<?>, EstimatedMeasurement<?>> evaluations;
 
     /** Observer to be notified at orbit changes. */
     private final ModelObserver observer;
 
     /** Counter for the evaluations. */
     private Incrementor evaluationsCounter;
 
     /** Counter for the iterations. */
     private Incrementor iterationsCounter;
 
     /** Date of the first enabled measurement. */
     private AbsoluteDate firstDate;
 
     /** Date of the last enabled measurement. */
     private AbsoluteDate lastDate;
 
     /** Boolean indicating if the propagation will go forward or backward. */
     private final boolean forwardPropagation;
 
     /** Model function value. */
     private final RealVector value;
 
     /** Harvesters for extracting State Transition Matrices and Jacobians from integrated states.
      * @since 11.1
      */
     private final MatricesHarvester[] harvesters;
 
     /** Initial states of the propagators built at the current iteration.
      * <p>
      * These are the states the builder parameters refer to, hence the states at which the
      * {@link MatricesHarvester#getStateJacobianVsBuilderParameters(SpacecraftState) dY₀/dB₀} Jacobians must be
      * evaluated.
      * </p>
      * @since 14.0
      */
     private final SpacecraftState[] initialStates;
 
     /** Model function Jacobian. */
     private final RealMatrix jacobian;
 
     /**
      * Constructor.
      * @param propagatorBuilders builders to use for propagation
      * @param measurements measurements
      * @param estimatedMeasurementsParameters estimated measurements parameters
      * @param observer observer to be notified at model calls
      */
     protected AbstractBatchLSModel(final PropagatorBuilder[] propagatorBuilders,
                                    final List<ObservedMeasurement<?>> measurements,
                                    final ParameterDriversList estimatedMeasurementsParameters,
                                    final ModelObserver observer) {
 
         this.builders                        = propagatorBuilders.clone();
         this.measurements                    = measurements;
         this.estimatedMeasurementsParameters = estimatedMeasurementsParameters;
         this.measurementParameterColumns     = new HashMap<>(estimatedMeasurementsParameters.getNbValuesToEstimate());
         this.estimatedOrbitalParameters      = new ParameterDriversList[builders.length];
         this.estimatedPropagationParameters  = new ParameterDriversList[builders.length];
         this.evaluations                     = new IdentityHashMap<>(measurements.size());
         this.observer                        = observer;
         this.harvesters                      = new MatricesHarvester[builders.length];
         this.initialStates                   = new SpacecraftState[builders.length];
 
         // allocate vector and matrix
         int rows = 0;
         for (final ObservedMeasurement<?> measurement : measurements) {
             rows += measurement.getDimension();
         }
 
         this.orbitsStartColumns    = new int[builders.length];
         this.orbitsEndColumns      = new int[builders.length];
         this.orbitsJacobianColumns = new int[builders.length * 6];
         Arrays.fill(orbitsJacobianColumns, -1);
         int columns = 0;
         for (int i = 0; i < builders.length; ++i) {
             this.orbitsStartColumns[i] = columns;
             final List<ParameterDriversList.DelegatingDriver> orbitalParametersDrivers =
                             builders[i].getOrbitalParameterFactory().getOrbitalParametersDrivers().getDrivers();
             for (int j = 0; j < orbitalParametersDrivers.size(); ++j) {
                 if (orbitalParametersDrivers.get(j).isSelected()) {
                     orbitsJacobianColumns[columns] = j;
                     ++columns;
                 }
             }
             this.orbitsEndColumns[i] = columns;
         }
 
         // Gather all the propagation drivers names in a list
         final List<String> estimatedPropagationParametersNames = new ArrayList<>();
         for (int i = 0; i < builders.length; ++i) {
             // The index i in array estimatedPropagationParameters (attribute of the class) is populated
             // when the first call to getSelectedPropagationDriversForBuilder(i) is made
             for (final DelegatingDriver delegating : getSelectedPropagationDriversForBuilder(i).getDrivers()) {
 
                 final TimeSpanMap<String> delegatingNameSpanMap = delegating.getNamesSpanMap();
                 // for each span (for each estimated value) corresponding name is added
                 Span<String> currentNameSpan = delegatingNameSpanMap.getFirstSpan();
                 // Add the driver name if it has not been added yet and the number of estimated values for this param
                 if (!estimatedPropagationParametersNames.contains(currentNameSpan.getData())) {
                     estimatedPropagationParametersNames.add(currentNameSpan.getData());
                 }
                 for (int spanNumber = 1; spanNumber < delegatingNameSpanMap.getSpansNumber(); ++spanNumber) {
                     currentNameSpan = delegatingNameSpanMap.getSpan(currentNameSpan.getEnd());
                     // Add the driver name if it has not been added yet and the number of estimated values for this param
                     if (!estimatedPropagationParametersNames.contains(currentNameSpan.getData())) {
                         estimatedPropagationParametersNames.add(currentNameSpan.getData());
                     }
                 }
             }
         }
 
         // Populate the map of propagation drivers' columns and update the total number of columns
         propagationParameterColumns = new HashMap<>(estimatedPropagationParametersNames.size());
         for (final String driverName : estimatedPropagationParametersNames) {
             propagationParameterColumns.put(driverName, columns);
             ++columns;
         }
         // Populate the map of measurement drivers' columns and update the total number of columns
         for (final ParameterDriver parameter : estimatedMeasurementsParameters.getDrivers()) {
             for (Span<String> span = parameter.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 measurementParameterColumns.put(span.getData(), columns);
                 columns++;
             }
         }
 
         // Initialize point and value
         value    = new ArrayRealVector(rows);
         jacobian = MatrixUtils.createRealMatrix(rows, columns);
 
         // Decide whether the propagation will be done forward or backward.
         // Minimize the duration between first measurement treated and orbit determination date
         // Propagator builder number 0 holds the reference date for orbit determination
         final AbsoluteDate refDate = builders[0].getOrbitalParameterFactory().getDate();
 
         // Sort the measurement list chronologically
         measurements.sort(new ChronologicalComparator());
         firstDate = measurements.getFirst().getDate();
         lastDate  = measurements.getLast().getDate();
 
         // Decide the direction of propagation
         forwardPropagation = FastMath.abs(refDate.durationFrom(firstDate)) <= FastMath.abs(refDate.durationFrom(lastDate));
     }
 
     /** Set the counter for evaluations.
      * @param evaluationsCounter counter for evaluations
      */
     public void setEvaluationsCounter(final Incrementor evaluationsCounter) {
         this.evaluationsCounter = evaluationsCounter;
     }
 
     /** Set the counter for iterations.
      * @param iterationsCounter counter for iterations
      */
     public void setIterationsCounter(final Incrementor iterationsCounter) {
         this.iterationsCounter = iterationsCounter;
     }
 
     /** Return the forward propagation flag.
      * @return the forward propagation flag
      */
     public boolean isForwardPropagation() {
         return forwardPropagation;
     }
 
     /** Configure the propagator to compute derivatives.
      * @param propagator {@link Propagator} to configure
      * @return harvester harvester to retrive the State Transition Matrix and Jacobian Matrix
      */
     protected abstract MatricesHarvester configureHarvester(Propagator propagator);
 
     /** Configure the current estimated orbits.
      * <p>
      * For DSST orbit determination, short period derivatives are also calculated.
      * </p>
      * @param harvester harvester for matrices
      * @param propagator the orbit propagator
      * @return the current estimated orbits
      */
     protected abstract Orbit configureOrbits(MatricesHarvester harvester, Propagator propagator);
 
     /** {@inheritDoc} */
     @Override
     public Pair<RealVector, RealMatrix> value(final RealVector point) {
 
         // Set up the propagators parallelizer
         final Propagator[] propagators = createPropagators(point);
         final Orbit[] orbits = new Orbit[propagators.length];
         for (int i = 0; i < propagators.length; ++i) {
             harvesters[i] = configureHarvester(propagators[i]);
             orbits[i]     = configureOrbits(harvesters[i], propagators[i]);
             // base state is used here on purpose: retrieving the full initial state would
             // trigger the additional data providers, hence the harvester derivatives cache
             initialStates[i] = propagators[i].getBaseInitialState();
         }
         final PropagatorsParallelizer parallelizer =
                         new PropagatorsParallelizer(Arrays.asList(propagators), configureMeasurements(point));
 
         // Reset value and Jacobian
         evaluations.clear();
         value.set(0.0);
         for (int i = 0; i < jacobian.getRowDimension(); ++i) {
             for (int j = 0; j < jacobian.getColumnDimension(); ++j) {
                 jacobian.setEntry(i, j, 0.0);
             }
         }
 
         // Run the propagation, gathering residuals on the fly
         if (isForwardPropagation()) {
             // Propagate forward from firstDate
             parallelizer.propagate(firstDate.shiftedBy(-1.0), lastDate.shiftedBy(+1.0));
         } else {
             // Propagate backward from lastDate
             parallelizer.propagate(lastDate.shiftedBy(+1.0), firstDate.shiftedBy(-1.0));
         }
 
         observer.modelCalled(orbits, evaluations);
 
         return new Pair<>(value, jacobian);
 
     }
 
     /** Get the selected orbital drivers for a propagatorBuilder.
      * @param iBuilder index of the builder in the builders' array
      * @return the list of selected orbital drivers for propagatorBuilder of index iBuilder
      * @since 11.1
      */
     public ParameterDriversList getSelectedOrbitalParametersDriversForBuilder(final int iBuilder) {
 
         // Lazy evaluation, create the list only if it hasn't been created yet
         if (estimatedOrbitalParameters[iBuilder] == null) {
 
             // Gather the drivers
             final ParameterDriversList drivers = builders[iBuilder].
                                                  getOrbitalParameterFactory().
                                                  getOrbitalParametersDrivers();
             final ParameterDriversList selectedOrbitalDrivers = new ParameterDriversList();
             for (final DelegatingDriver delegating : drivers.getDrivers()) {
                 if (delegating.isSelected()) {
                     for (final ParameterDriver driver : delegating.getRawDrivers()) {
                         selectedOrbitalDrivers.add(driver);
                     }
                 }
             }
 
             // Add the list of selected orbital parameters drivers to the array
             estimatedOrbitalParameters[iBuilder] = selectedOrbitalDrivers;
         }
         return estimatedOrbitalParameters[iBuilder];
     }
 
     /** Get the selected propagation drivers for a propagatorBuilder.
      * @param iBuilder index of the builder in the builders' array
      * @return the list of selected propagation drivers for propagatorBuilder of index iBuilder
      */
     public ParameterDriversList getSelectedPropagationDriversForBuilder(final int iBuilder) {
 
         // Lazy evaluation, create the list only if it hasn't been created yet
         if (estimatedPropagationParameters[iBuilder] == null) {
 
             // Gather the drivers
             final ParameterDriversList selectedPropagationDrivers = new ParameterDriversList();
             for (final DelegatingDriver delegating : builders[iBuilder].getPropagationParametersDrivers().getDrivers()) {
                 if (delegating.isSelected()) {
                     for (final ParameterDriver driver : delegating.getRawDrivers()) {
                         selectedPropagationDrivers.add(driver);
                     }
                 }
             }
 
             // List of propagation drivers are sorted in the BatchLSEstimator class.
             // Hence we need to sort this list so the parameters' indexes match
             selectedPropagationDrivers.sort();
 
             // Add the list of selected propagation drivers to the array
             estimatedPropagationParameters[iBuilder] = selectedPropagationDrivers;
         }
         return estimatedPropagationParameters[iBuilder];
     }
 
     /** Create the propagators and parameters corresponding to an evaluation point.
      * @param point evaluation point
      * @return an array of new propagators
      */
     public Propagator[] createPropagators(final RealVector point) {
 
         final Propagator[] propagators = new Propagator[builders.length];
 
 
         // Set up the propagators
         for (int i = 0; i < builders.length; ++i) {
 
             int element = 0;
             // Get the number of values to estimate for selected orbital drivers in the builder
             final int nbOrb    = orbitsEndColumns[i] - orbitsStartColumns[i];
 
             // Get the list of selected propagation drivers in the builder and its size
             final ParameterDriversList selectedPropagationDrivers = getSelectedPropagationDriversForBuilder(i);
             final int nbParams = selectedPropagationDrivers.getNbParams();
             final int nbValuesToEstimate = selectedPropagationDrivers.getNbValuesToEstimate();
 
             // Init the array of normalized parameters for the builder
             final double[] propagatorArray = new double[nbOrb + nbValuesToEstimate];
 
             // Add the orbital drivers normalized values
             for (int j = 0; j < nbOrb; ++j) {
                 propagatorArray[element++] = point.getEntry(orbitsStartColumns[i] + j);
             }
 
             // Add the propagation drivers normalized values
             for (int j = 0; j < nbParams; ++j) {
                 final DelegatingDriver driver = selectedPropagationDrivers.getDrivers().get(j);
                 final TimeSpanMap<String> delegatingNameSpanMap = driver.getNamesSpanMap();
                 // get point entry for each span (for each estimated value), point is sorted
                 // with following parameters values and for each parameter driver
                 // span value are sorted in chronological order
                 Span<String> currentNameSpan = delegatingNameSpanMap.getFirstSpan();
                 propagatorArray[element++] = point.getEntry(propagationParameterColumns.get(currentNameSpan.getData()));
 
                 for (int spanNumber = 1; spanNumber < delegatingNameSpanMap.getSpansNumber(); ++spanNumber) {
                     currentNameSpan = delegatingNameSpanMap.getSpan(currentNameSpan.getEnd());
                     propagatorArray[element++] = point.getEntry(propagationParameterColumns.get(currentNameSpan.getData()));
 
                 }
             }
 
             // Build the propagator
             propagators[i] = builders[i].buildPropagator(propagatorArray);
         }
 
         return propagators;
 
     }
 
     /** Fetch a measurement that was evaluated during propagation.
      * @param index index of the measurement first component
      * @param evaluation measurement evaluation
      */
     public void fetchEvaluatedMeasurement(final int index, final EstimatedMeasurement<?> evaluation) {
 
         // States and observed measurement
         final SpacecraftState[]      evaluationStates    = evaluation.getStates();
         final ObservedMeasurement<?> observedMeasurement = evaluation.getObservedMeasurement();
 
         // compute weighted residuals
         evaluations.put(observedMeasurement, evaluation);
         if (evaluation.getStatus() == EstimatedMeasurementBase.Status.REJECTED) {
             return;
         }
 
         final double[] evaluated = evaluation.getEstimatedValue();
         final double[] observed  = observedMeasurement.getObservedValue();
         final double[] sigma     = observedMeasurement.getTheoreticalStandardDeviation();
         final double[] weight    = evaluation.getObservedMeasurement().getBaseWeight();
         for (int i = 0; i < evaluated.length; ++i) {
             value.setEntry(index + i, weight[i] * (evaluated[i] - observed[i]) / sigma[i]);
         }
 
         for (int k = 0; k < evaluationStates.length; ++k) {
 
             final int p = observedMeasurement.getSatellites().get(k).getPropagatorIndex();
 
             // partial derivatives of the current Cartesian coordinates with respect to current orbital state
             final double[][] aCY = new double[6][6];
             final Orbit currentOrbit = evaluationStates[k].getOrbit();
             currentOrbit.getJacobianWrtParameters(builders[p].getOrbitalParameterFactory().getPositionAngleType(),
                                                   aCY);
             final RealMatrix dCdY = new Array2DRowRealMatrix(aCY, false);
 
             // Jacobian of the measurement with respect to current orbital state
             final RealMatrix dMdC = new Array2DRowRealMatrix(evaluation.getStateDerivatives(k), false);
             final RealMatrix dMdY = dMdC.multiply(dCdY);
 
             // Jacobian of the measurement with respect to initial orbital state
             final ParameterDriversList selectedOrbitalDrivers = getSelectedOrbitalParametersDriversForBuilder(p);
             final int nbOrbParams = selectedOrbitalDrivers.getNbParams();
             if (nbOrbParams > 0) {
                 RealMatrix dYdY0 = harvesters[p].getStateTransitionMatrix(evaluationStates[k]);
                 if (dYdY0.getRowDimension() == 7) {
                     // mass was included in STM propagation, removed it now
                     dYdY0 = dYdY0.getSubMatrix(0, 5, 0, 5);
                 }
                 final RealMatrix dMdY0  = dMdY.multiply(dYdY0);
                 final RealMatrix dY0dB0 = harvesters[p].getStateJacobianVsBuilderParameters(initialStates[p]);
                 final RealMatrix dMdB0  = dY0dB0 == null ? dMdY0 : dMdY0.multiply(dY0dB0);
                 for (int i = 0; i < dMdB0.getRowDimension(); ++i) {
                     for (int j = orbitsStartColumns[p]; j < orbitsEndColumns[p]; ++j) {
                         final ParameterDriver driver =
                                         selectedOrbitalDrivers.getDrivers().get(j - orbitsStartColumns[p]);
                         final double partial = dMdB0.getEntry(i, orbitsJacobianColumns[j]);
                         jacobian.setEntry(index + i, j,
                                           weight[i] * partial / sigma[i] * driver.getScale());
                     }
                 }
             }
 
             // Jacobian of the measurement with respect to propagation parameters
             final ParameterDriversList selectedPropagationDrivers = getSelectedPropagationDriversForBuilder(p);
             final int nbParams = selectedPropagationDrivers.getNbParams();
             if (nbParams > 0) {
                 RealMatrix dYdPp = harvesters[p].getParametersJacobian(evaluationStates[k]);
                 if (dYdPp.getRowDimension() == 7) {
                     // mass was included in STM propagation, removed it now
                     dYdPp = dYdPp.getSubMatrix(0, 5, 0, dYdPp.getColumnDimension() - 1);
                 }
                 final RealMatrix dMdPp = dMdY.multiply(dYdPp);
 
                 for (int i = 0; i < dMdPp.getRowDimension(); ++i) {
                     int col = 0;
 
                     // Add the propagation drivers normalized values
                     for (int j = 0; j < nbParams; ++j) {
                         final ParameterDriver delegating = selectedPropagationDrivers.getDrivers().get(j);
                         final TimeSpanMap<String> delegatingNameSpanMap = delegating.getNamesSpanMap();
                         // get point entry for each span (for each estimated value), point is sorted
                         for (Span<String> currentNameSpan = delegatingNameSpanMap.getFirstSpan(); currentNameSpan != null; currentNameSpan = currentNameSpan.next()) {
                             jacobian.addToEntry(index + i, propagationParameterColumns.get(currentNameSpan.getData()),
                                     weight[i] * dMdPp.getEntry(i, col++) / sigma[i] * delegating.getScale());
                         }
                     }
                 }
             }
         }
         // Jacobian of the measurement with respect to measurements parameters
         for (final ParameterDriver driver : observedMeasurement.getParametersDrivers()) {
             if (driver.isSelected()) {
                 for (Span<String> span = driver.getNamesSpanMap().getFirstSpan(); span != null; span = span.next()) {
                     final double[] aMPm = evaluation.getParameterDerivatives(driver, span.getStart());
                     for (int i = 0; i < aMPm.length; ++i) {
                         jacobian.setEntry(index + i, measurementParameterColumns.get(span.getData()),
                                           weight[i] * aMPm[i] / sigma[i] * driver.getScale());
                     }
                 }
             }
         }
 
     }
 
     /** Configure the multi-satellites handler to handle measurements.
      * @param point evaluation point
      * @return multi-satellites handler to handle measurements
      */
     private MultiSatStepHandler configureMeasurements(final RealVector point) {
 
         // Set up the measurement parameters
         int index = orbitsEndColumns[builders.length - 1] + propagationParameterColumns.size();
         for (final ParameterDriver parameter : estimatedMeasurementsParameters.getDrivers()) {
 
             for (Span<Double> span = parameter.getValueSpanMap().getFirstSpan(); span != null; span = span.next()) {
                 parameter.setNormalizedValue(point.getEntry(index++), span.getStart());
             }
         }
 
         // Set up measurements handler
         final List<PreCompensation> precompensated = new ArrayList<>();
         for (final ObservedMeasurement<?> measurement : measurements) {
             if (measurement.isEnabled()) {
                 precompensated.add(new PreCompensation(measurement, evaluations.get(measurement)));
             }
         }
         precompensated.sort(new ChronologicalComparator());
 
         // Assign first and last date
         firstDate = precompensated.getFirst().getDate();
         lastDate  = precompensated.getLast().getDate();
 
         // Reverse the list in case of backward propagation
         if (!forwardPropagation) {
             Collections.reverse(precompensated);
         }
 
         return new MeasurementHandler(this, precompensated);
 
     }
 
     /** Get the iterations count.
      * @return iterations count
      */
     public int getIterationsCount() {
         return iterationsCounter.getCount();
     }
 
     /** Get the evaluations count.
      * @return evaluations count
      */
     public int getEvaluationsCount() {
         return evaluationsCounter.getCount();
     }
 
 }