NumericalPropagator.java

  1. /* Copyright 2002-2016 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.numerical;

  19. import java.io.NotSerializableException;
  20. import java.io.Serializable;
  21. import java.util.ArrayList;
  22. import java.util.Arrays;
  23. import java.util.List;

  25. import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
  26. import org.apache.commons.math3.ode.AbstractIntegrator;
  27. import org.apache.commons.math3.util.FastMath;
  28. import org.orekit.attitudes.Attitude;
  29. import org.orekit.attitudes.AttitudeProvider;
  30. import org.orekit.errors.OrekitIllegalArgumentException;
  31. import org.orekit.errors.OrekitException;
  32. import org.orekit.errors.OrekitMessages;
  33. import org.orekit.errors.PropagationException;
  34. import org.orekit.forces.ForceModel;
  35. import org.orekit.forces.gravity.NewtonianAttraction;
  36. import org.orekit.frames.Frame;
  37. import org.orekit.frames.Transform;
  38. import org.orekit.orbits.Orbit;
  39. import org.orekit.orbits.OrbitType;
  40. import org.orekit.orbits.PositionAngle;
  41. import org.orekit.propagation.SpacecraftState;
  42. import org.orekit.propagation.events.EventDetector;
  43. import org.orekit.propagation.integration.AbstractIntegratedPropagator;
  44. import org.orekit.propagation.integration.StateMapper;
  45. import org.orekit.time.AbsoluteDate;
  46. import org.orekit.utils.PVCoordinates;
  47. import org.orekit.utils.TimeStampedPVCoordinates;

  49. /** This class propagates {@link org.orekit.orbits.Orbit orbits} using
  50.  * numerical integration.
  51.  * <p>Numerical propagation is much more accurate than analytical propagation
  52.  * like for example {@link org.orekit.propagation.analytical.KeplerianPropagator
  53.  * keplerian} or {@link org.orekit.propagation.analytical.EcksteinHechlerPropagator
  54.  * Eckstein-Hechler}, but requires a few more steps to set up to be used properly.
  55.  * Whereas analytical propagators are configured only thanks to their various
  56.  * constructors and can be used immediately after construction, numerical propagators
  57.  * configuration involve setting several parameters between construction time
  58.  * and propagation time.</p>
  59.  * <p>The configuration parameters that can be set are:</p>
  60.  * <ul>
  61.  *   <li>the initial spacecraft state ({@link #setInitialState(SpacecraftState)})</li>
  62.  *   <li>the central attraction coefficient ({@link #setMu(double)})</li>
  63.  *   <li>the various force models ({@link #addForceModel(ForceModel)},
  64.  *   {@link #removeForceModels()})</li>
  65.  *   <li>the {@link OrbitType type} of orbital parameters to be used for propagation
  66.  *   ({@link #setOrbitType(OrbitType)}),
  67.  *   <li>the {@link PositionAngle type} of position angle to be used in orbital parameters
  68.  *   to be used for propagation where it is relevant ({@link
  69.  *   #setPositionAngleType(PositionAngle)}),
  70.  *   <li>whether {@link org.orekit.propagation.integration.AdditionalEquations additional equations}
  71.  *   (for example {@link PartialDerivativesEquations Jacobians}) should be propagated along with orbital state
  72.  *   ({@link #addAdditionalEquations(org.orekit.propagation.integration.AdditionalEquations)}),
  73.  *   <li>the discrete events that should be triggered during propagation
  74.  *   ({@link #addEventDetector(EventDetector)},
  75.  *   {@link #clearEventsDetectors()})</li>
  76.  *   <li>the binding logic with the rest of the application ({@link #setSlaveMode()},
  77.  *   {@link #setMasterMode(double, org.orekit.propagation.sampling.OrekitFixedStepHandler)},
  78.  *   {@link #setMasterMode(org.orekit.propagation.sampling.OrekitStepHandler)},
  79.  *   {@link #setEphemerisMode()}, {@link #getGeneratedEphemeris()})</li>
  80.  * </ul>
  81.  * <p>From these configuration parameters, only the initial state is mandatory. The default
  82.  * propagation settings are in {@link OrbitType#EQUINOCTIAL equinoctial} parameters with
  83.  * {@link PositionAngle#TRUE true} longitude argument. If the central attraction coefficient
  84.  * is not explicitly specified, the one used to define the initial orbit will be used.
  85.  * However, specifying only the initial state and perhaps the central attraction coefficient
  86.  * would mean the propagator would use only keplerian forces. In this case, the simpler {@link
  87.  * org.orekit.propagation.analytical.KeplerianPropagator KeplerianPropagator} class would
  88.  * perhaps be more effective.</p>
  89.  * <p>The underlying numerical integrator set up in the constructor may also have its own
  90.  * configuration parameters. Typical configuration parameters for adaptive stepsize integrators
  91.  * are the min, max and perhaps start step size as well as the absolute and/or relative errors
  92.  * thresholds.</p>
  93.  * <p>The state that is seen by the integrator is a simple seven elements double array.
  94.  * The six first elements are either:
  95.  * <ul>
  96.  *   <li>the {@link org.orekit.orbits.EquinoctialOrbit equinoctial orbit parameters} (a, e<sub>x</sub>,
  97.  *   e<sub>y</sub>, h<sub>x</sub>, h<sub>y</sub>, λ<sub>M</sub> or λ<sub>E</sub>
  98.  *   or λ<sub>v</sub>) in meters and radians,</li>
  99.  *   <li>the {@link org.orekit.orbits.KeplerianOrbit Keplerian orbit parameters} (a, e, i, ω, Ω,
  100.  *   M or E or v) in meters and radians,</li>
  101.  *   <li>the {@link org.orekit.orbits.CircularOrbit circular orbit parameters} (a, e<sub>x</sub>, e<sub>y</sub>, i,
  102.  *   Ω, α<sub>M</sub> or α<sub>E</sub> or α<sub>v</sub>) in meters
  103.  *   and radians,</li>
  104.  *   <li>the {@link org.orekit.orbits.CartesianOrbit Cartesian orbit parameters} (x, y, z, v<sub>x</sub>,
  105.  *   v<sub>y</sub>, v<sub>z</sub>) in meters and meters per seconds.
  106.  * </ul>
  107.  * The last element is the mass in kilograms.
  108.  * </p>
  109.  * <p>The following code snippet shows a typical setting for Low Earth Orbit propagation in
  110.  * equinoctial parameters and true longitude argument:</p>
  111.  * <pre>
  112.  * final double dP       = 0.001;
  113.  * final double minStep  = 0.001;
  114.  * final double maxStep  = 500;
  115.  * final double initStep = 60;
  116.  * final double[][] tolerance = NumericalPropagator.tolerances(dP, orbit, OrbitType.EQUINOCTIAL);
  117.  * AdaptiveStepsizeIntegrator integrator = new DormandPrince853Integrator(minStep, maxStep, tolerance[0], tolerance[1]);
  118.  * integrator.setInitialStepSize(initStep);
  119.  * propagator = new NumericalPropagator(integrator);
  120.  * </pre>
  121.  * <p>The same propagator can be reused for several orbit extrapolations, by resetting
  122.  * the initial state without modifying the other configuration parameters. However, the
  123.  * same instance cannot be used simultaneously by different threads, the class is <em>not</em>
  124.  * thread-safe.</p>

  126.  * @see SpacecraftState
  127.  * @see ForceModel
  128.  * @see org.orekit.propagation.sampling.OrekitStepHandler
  129.  * @see org.orekit.propagation.sampling.OrekitFixedStepHandler
  130.  * @see org.orekit.propagation.integration.IntegratedEphemeris
  131.  * @see TimeDerivativesEquations
  132.  *
  133.  * @author Mathieu Rom&eacute;ro
  134.  * @author Luc Maisonobe
  135.  * @author Guylaine Prat
  136.  * @author Fabien Maussion
  137.  * @author V&eacute;ronique Pommier-Maurussane
  138.  */
  139. public class NumericalPropagator extends AbstractIntegratedPropagator {

  141.     /** Central body attraction. */
  142.     private NewtonianAttraction newtonianAttraction;

  144.     /** Force models used during the extrapolation of the Orbit, without jacobians. */
  145.     private final List<ForceModel> forceModels;

  147.     /** Create a new instance of NumericalPropagator, based on orbit definition mu.
  148.      * After creation, the instance is empty, i.e. the attitude provider is set to an
  149.      * unspecified default law and there are no perturbing forces at all.
  150.      * This means that if {@link #addForceModel addForceModel} is not
  151.      * called after creation, the integrated orbit will follow a keplerian
  152.      * evolution only. The defaults are {@link OrbitType#EQUINOCTIAL}
  153.      * for {@link #setOrbitType(OrbitType) propagation
  154.      * orbit type} and {@link PositionAngle#TRUE} for {@link
  155.      * #setPositionAngleType(PositionAngle) position angle type}.
  156.      * @param integrator numerical integrator to use for propagation.
  157.      */
  158.     public NumericalPropagator(final AbstractIntegrator integrator) {
  159.         super(integrator, true);
  160.         forceModels = new ArrayList<ForceModel>();
  161.         initMapper();
  162.         setAttitudeProvider(DEFAULT_LAW);
  163.         setMu(Double.NaN);
  164.         setSlaveMode();
  165.         setOrbitType(OrbitType.EQUINOCTIAL);
  166.         setPositionAngleType(PositionAngle.TRUE);
  167.     }

  169.      /** Set the central attraction coefficient μ.
  170.      * @param mu central attraction coefficient (m³/s²)
  171.      * @see #addForceModel(ForceModel)
  172.      */
  173.     public void setMu(final double mu) {
  174.         super.setMu(mu);
  175.         newtonianAttraction = new NewtonianAttraction(mu);
  176.     }

  178.     /** Add a force model to the global perturbation model.
  179.      * <p>If this method is not called at all, the integrated orbit will follow
  180.      * a keplerian evolution only.</p>
  181.      * @param model perturbing {@link ForceModel} to add
  182.      * @see #removeForceModels()
  183.      * @see #setMu(double)
  184.      */
  185.     public void addForceModel(final ForceModel model) {
  186.         forceModels.add(model);
  187.     }

  189.     /** Remove all perturbing force models from the global perturbation model.
  190.      * <p>Once all perturbing forces have been removed (and as long as no new force
  191.      * model is added), the integrated orbit will follow a keplerian evolution
  192.      * only.</p>
  193.      * @see #addForceModel(ForceModel)
  194.      */
  195.     public void removeForceModels() {
  196.         forceModels.clear();
  197.     }

  199.     /** Get perturbing force models list.
  200.      * @return list of perturbing force models
  201.      * @see #addForceModel(ForceModel)
  202.      * @see #getNewtonianAttractionForceModel()
  203.      */
  204.     public List<ForceModel> getForceModels() {
  205.         return forceModels;
  206.     }

  208.     /** Get the Newtonian attraction from the central body force model.
  209.      * @return Newtonian attraction force model
  210.      * @see #setMu(double)
  211.      * @see #getForceModels()
  212.      */
  213.     public NewtonianAttraction getNewtonianAttractionForceModel() {
  214.         return newtonianAttraction;
  215.     }

  217.     /** Set propagation orbit type.
  218.      * @param orbitType orbit type to use for propagation
  219.      */
  220.     public void setOrbitType(final OrbitType orbitType) {
  221.         super.setOrbitType(orbitType);
  222.     }

  224.     /** Get propagation parameter type.
  225.      * @return orbit type used for propagation
  226.      */
  227.     public OrbitType getOrbitType() {
  228.         return super.getOrbitType();
  229.     }

  231.     /** Set position angle type.
  232.      * <p>
  233.      * The position parameter type is meaningful only if {@link
  234.      * #getOrbitType() propagation orbit type}
  235.      * support it. As an example, it is not meaningful for propagation
  236.      * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  237.      * </p>
  238.      * @param positionAngleType angle type to use for propagation
  239.      */
  240.     public void setPositionAngleType(final PositionAngle positionAngleType) {
  241.         super.setPositionAngleType(positionAngleType);
  242.     }

  244.     /** Get propagation parameter type.
  245.      * @return angle type to use for propagation
  246.      */
  247.     public PositionAngle getPositionAngleType() {
  248.         return super.getPositionAngleType();
  249.     }

  251.     /** Set the initial state.
  252.      * @param initialState initial state
  253.      * @exception PropagationException if initial state cannot be set
  254.      */
  255.     public void setInitialState(final SpacecraftState initialState) throws PropagationException {
  256.         resetInitialState(initialState);
  257.     }

  259.     /** {@inheritDoc} */
  260.     public void resetInitialState(final SpacecraftState state) throws PropagationException {
  261.         super.resetInitialState(state);
  262.         if (newtonianAttraction == null) {
  263.             setMu(state.getMu());
  264.         }
  265.         setStartDate(null);
  266.     }

  268.     /** {@inheritDoc} */
  269.     public TimeStampedPVCoordinates getPVCoordinates(final AbsoluteDate date, final Frame frame)
  270.         throws OrekitException {
  271.         return propagate(date).getPVCoordinates(frame);
  272.     }

  274.     /** {@inheritDoc} */
  275.     protected StateMapper createMapper(final AbsoluteDate referenceDate, final double mu,
  276.                                        final OrbitType orbitType, final PositionAngle positionAngleType,
  277.                                        final AttitudeProvider attitudeProvider, final Frame frame) {
  278.         return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  279.     }

  281.     /** Internal mapper using directly osculating parameters. */
  282.     private static class OsculatingMapper extends StateMapper implements Serializable {

  284.         /** Serializable UID. */
  285.         private static final long serialVersionUID = 20130621L;

  287.         /** Simple constructor.
  288.          * <p>
  289.          * The position parameter type is meaningful only if {@link
  290.          * #getOrbitType() propagation orbit type}
  291.          * support it. As an example, it is not meaningful for propagation
  292.          * in {@link OrbitType#CARTESIAN Cartesian} parameters.
  293.          * </p>
  294.          * @param referenceDate reference date
  295.          * @param mu central attraction coefficient (m³/s²)
  296.          * @param orbitType orbit type to use for mapping
  297.          * @param positionAngleType angle type to use for propagation
  298.          * @param attitudeProvider attitude provider
  299.          * @param frame inertial frame
  300.          */
  301.         OsculatingMapper(final AbsoluteDate referenceDate, final double mu,
  302.                          final OrbitType orbitType, final PositionAngle positionAngleType,
  303.                          final AttitudeProvider attitudeProvider, final Frame frame) {
  304.             super(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  305.         }

  307.         /** {@inheritDoc} */
  308.         public SpacecraftState mapArrayToState(final AbsoluteDate date, final double[] y, final boolean meanOnly)
  309.             throws OrekitException {
  310.             // the parameter meanOnly is ignored for the Numerical Propagator

  312.             final double mass = y[6];
  313.             if (mass <= 0.0) {
  314.                 throw new PropagationException(OrekitMessages.SPACECRAFT_MASS_BECOMES_NEGATIVE, mass);
  315.             }

  317.             final Orbit orbit       = getOrbitType().mapArrayToOrbit(y, getPositionAngleType(), date, getMu(), getFrame());
  318.             final Attitude attitude = getAttitudeProvider().getAttitude(orbit, date, getFrame());

  320.             return new SpacecraftState(orbit, attitude, mass);

  322.         }

  324.         /** {@inheritDoc} */
  325.         public void mapStateToArray(final SpacecraftState state, final double[] y) {
  326.             getOrbitType().mapOrbitToArray(state.getOrbit(), getPositionAngleType(), y);
  327.             y[6] = state.getMass();
  328.         }

  330.         /** Replace the instance with a data transfer object for serialization.
  331.          * @return data transfer object that will be serialized
  332.          * @exception NotSerializableException if the state mapper cannot be serialized (typically for DSST propagator)
  333.          */
  334.         private Object writeReplace() throws NotSerializableException {
  335.             return new DataTransferObject(getReferenceDate(), getMu(), getOrbitType(),
  336.                                           getPositionAngleType(), getAttitudeProvider(), getFrame());
  337.         }

  339.         /** Internal class used only for serialization. */
  340.         private static class DataTransferObject implements Serializable {

  342.             /** Serializable UID. */
  343.             private static final long serialVersionUID = 20130621L;

  345.             /** Reference date. */
  346.             private final AbsoluteDate referenceDate;

  348.             /** Central attraction coefficient (m³/s²). */
  349.             private final double mu;

  351.             /** Orbit type to use for mapping. */
  352.             private final OrbitType orbitType;

  354.             /** Angle type to use for propagation. */
  355.             private final PositionAngle positionAngleType;

  357.             /** Attitude provider. */
  358.             private final AttitudeProvider attitudeProvider;

  360.             /** Inertial frame. */
  361.             private final Frame frame;

  363.             /** Simple constructor.
  364.              * @param referenceDate reference date
  365.              * @param mu central attraction coefficient (m³/s²)
  366.              * @param orbitType orbit type to use for mapping
  367.              * @param positionAngleType angle type to use for propagation
  368.              * @param attitudeProvider attitude provider
  369.              * @param frame inertial frame
  370.              */
  371.             DataTransferObject(final AbsoluteDate referenceDate, final double mu,
  372.                                       final OrbitType orbitType, final PositionAngle positionAngleType,
  373.                                       final AttitudeProvider attitudeProvider, final Frame frame) {
  374.                 this.referenceDate     = referenceDate;
  375.                 this.mu                = mu;
  376.                 this.orbitType         = orbitType;
  377.                 this.positionAngleType = positionAngleType;
  378.                 this.attitudeProvider  = attitudeProvider;
  379.                 this.frame             = frame;
  380.             }

  382.             /** Replace the deserialized data transfer object with a {@link OsculatingMapper}.
  383.              * @return replacement {@link OsculatingMapper}
  384.              */
  385.             private Object readResolve() {
  386.                 return new OsculatingMapper(referenceDate, mu, orbitType, positionAngleType, attitudeProvider, frame);
  387.             }
  388.         }

  390.     }

  392.     /** {@inheritDoc} */
  393.     protected MainStateEquations getMainStateEquations(final AbstractIntegrator integrator) {
  394.         return new Main(integrator);
  395.     }

  397.     /** Internal class for osculating parameters integration. */
  398.     private class Main implements MainStateEquations, TimeDerivativesEquations {

  400.         /** Derivatives array. */
  401.         private final double[] yDot;

  403.         /** Current orbit. */
  404.         private Orbit orbit;

  406.         /** Jacobian of the orbital parameters with respect to the cartesian parameters. */
  407.         private double[][] jacobian;

  409.         /** Simple constructor.
  410.          * @param integrator numerical integrator to use for propagation.
  411.          */
  412.         Main(final AbstractIntegrator integrator) {

  414.             this.yDot     = new double[7];
  415.             this.jacobian = new double[6][6];

  417.             for (final ForceModel forceModel : forceModels) {
  418.                 final EventDetector[] modelDetectors = forceModel.getEventsDetectors();
  419.                 if (modelDetectors != null) {
  420.                     for (final EventDetector detector : modelDetectors) {
  421.                         setUpEventDetector(integrator, detector);
  422.                     }
  423.                 }
  424.             }

  426.         }

  428.         /** {@inheritDoc} */
  429.         public double[] computeDerivatives(final SpacecraftState state) throws OrekitException {

  431.             orbit = state.getOrbit();
  432.             Arrays.fill(yDot, 0.0);
  433.             orbit.getJacobianWrtCartesian(getPositionAngleType(), jacobian);

  435.             // compute the contributions of all perturbing forces
  436.             for (final ForceModel forceModel : forceModels) {
  437.                 forceModel.addContribution(state, this);
  438.             }

  440.             // finalize derivatives by adding the Kepler contribution
  441.             newtonianAttraction.addContribution(state, this);

  443.             return yDot.clone();

  445.         }

  447.         /** {@inheritDoc} */
  448.         public void addKeplerContribution(final double mu) {
  449.             orbit.addKeplerContribution(getPositionAngleType(), mu, yDot);
  450.         }

  452.         /** {@inheritDoc} */
  453.         public void addXYZAcceleration(final double x, final double y, final double z) {
  454.             for (int i = 0; i < 6; ++i) {
  455.                 final double[] jRow = jacobian[i];
  456.                 yDot[i] += jRow[3] * x + jRow[4] * y + jRow[5] * z;
  457.             }
  458.         }

  460.         /** {@inheritDoc} */
  461.         public void addAcceleration(final Vector3D gamma, final Frame frame)
  462.             throws OrekitException {
  463.             final Transform t = frame.getTransformTo(orbit.getFrame(), orbit.getDate());
  464.             final Vector3D gammInRefFrame = t.transformVector(gamma);
  465.             addXYZAcceleration(gammInRefFrame.getX(), gammInRefFrame.getY(), gammInRefFrame.getZ());
  466.         }

  468.         /** {@inheritDoc} */
  469.         public void addMassDerivative(final double q) {
  470.             if (q > 0) {
  471.                 throw new OrekitIllegalArgumentException(OrekitMessages.POSITIVE_FLOW_RATE, q);
  472.             }
  473.             yDot[6] += q;
  474.         }

  476.     }

  478.     /** Estimate tolerance vectors for integrators.
  479.      * <p>
  480.      * The errors are estimated from partial derivatives properties of orbits,
  481.      * starting from a scalar position error specified by the user.
  482.      * Considering the energy conservation equation V = sqrt(mu (2/r - 1/a)),
  483.      * we get at constant energy (i.e. on a Keplerian trajectory):
  484.      * <pre>
  485.      * V² r |dV| = mu |dr|
  486.      * </pre>
  487.      * So we deduce a scalar velocity error consistent with the position error.
  488.      * From here, we apply orbits Jacobians matrices to get consistent errors
  489.      * on orbital parameters.
  490.      * </p>
  491.      * <p>
  492.      * The tolerances are only <em>orders of magnitude</em>, and integrator tolerances
  493.      * are only local estimates, not global ones. So some care must be taken when using
  494.      * these tolerances. Setting 1mm as a position error does NOT mean the tolerances
  495.      * will guarantee a 1mm error position after several orbits integration.
  496.      * </p>
  497.      * @param dP user specified position error
  498.      * @param orbit reference orbit
  499.      * @param type propagation type for the meaning of the tolerance vectors elements
  500.      * (it may be different from {@code orbit.getType()})
  501.      * @return a two rows array, row 0 being the absolute tolerance error and row 1
  502.      * being the relative tolerance error
  503.      * @exception PropagationException if Jacobian is singular
  504.      */
  505.     public static double[][] tolerances(final double dP, final Orbit orbit, final OrbitType type)
  506.         throws PropagationException {

  508.         // estimate the scalar velocity error
  509.         final PVCoordinates pv = orbit.getPVCoordinates();
  510.         final double r2 = pv.getPosition().getNormSq();
  511.         final double v  = pv.getVelocity().getNorm();
  512.         final double dV = orbit.getMu() * dP / (v * r2);

  514.         final double[] absTol = new double[7];
  515.         final double[] relTol = new double[7];

  517.         // we set the mass tolerance arbitrarily to 1.0e-6 kg, as mass evolves linearly
  518.         // with trust, this often has no influence at all on propagation
  519.         absTol[6] = 1.0e-6;

  521.         if (type == OrbitType.CARTESIAN) {
  522.             absTol[0] = dP;
  523.             absTol[1] = dP;
  524.             absTol[2] = dP;
  525.             absTol[3] = dV;
  526.             absTol[4] = dV;
  527.             absTol[5] = dV;
  528.         } else {

  530.             // convert the orbit to the desired type
  531.             final double[][] jacobian = new double[6][6];
  532.             final Orbit converted = type.convertType(orbit);
  533.             converted.getJacobianWrtCartesian(PositionAngle.TRUE, jacobian);

  535.             for (int i = 0; i < 6; ++i) {
  536.                 final double[] row = jacobian[i];
  537.                 absTol[i] = FastMath.abs(row[0]) * dP +
  538.                             FastMath.abs(row[1]) * dP +
  539.                             FastMath.abs(row[2]) * dP +
  540.                             FastMath.abs(row[3]) * dV +
  541.                             FastMath.abs(row[4]) * dV +
  542.                             FastMath.abs(row[5]) * dV;
  543.                 if (Double.isNaN(absTol[i])) {
  544.                     throw new PropagationException(OrekitMessages.SINGULAR_JACOBIAN_FOR_ORBIT_TYPE, type);
  545.                 }
  546.             }

  548.         }

  550.         Arrays.fill(relTol, dP / FastMath.sqrt(r2));

  552.         return new double[][] {
  553.             absTol, relTol
  554.         };

  556.     }

  558. }
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