PartialDerivativesEquations.java

  1. /* Copyright 2010-2011 Centre National d'Études Spatiales
  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.util.IdentityHashMap;
  20. import java.util.Map;

  22. import org.hipparchus.analysis.differentiation.DerivativeStructure;
  23. import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
  24. import org.orekit.errors.OrekitException;
  25. import org.orekit.errors.OrekitMessages;
  26. import org.orekit.forces.ForceModel;
  27. import org.orekit.propagation.FieldSpacecraftState;
  28. import org.orekit.propagation.SpacecraftState;
  29. import org.orekit.propagation.integration.AdditionalEquations;
  30. import org.orekit.utils.ParameterDriver;
  31. import org.orekit.utils.ParameterDriversList;

  33. /** Set of {@link AdditionalEquations additional equations} computing the partial derivatives
  34.  * of the state (orbit) with respect to initial state and force models parameters.
  35.  * <p>
  36.  * This set of equations are automatically added to a {@link NumericalPropagator numerical propagator}
  37.  * in order to compute partial derivatives of the orbit along with the orbit itself. This is
  38.  * useful for example in orbit determination applications.
  39.  * </p>
  40.  * <p>
  41.  * The partial derivatives with respect to initial state can be either dimension 6
  42.  * (orbit only) or 7 (orbit and mass).
  43.  * </p>
  44.  * <p>
  45.  * The partial derivatives with respect to force models parameters has a dimension
  46.  * equal to the number of selected parameters. Parameters selection is implemented at
  47.  * {@link ForceModel force models} level. Users must retrieve a {@link ParameterDriver
  48.  * parameter driver} using {@link ForceModel#getParameterDriver(String)} and then
  49.  * select it by calling {@link ParameterDriver#setSelected(boolean) setSelected(true)}.
  50.  * </p>
  51.  * <p>
  52.  * If several force models provide different {@link ParameterDriver drivers} for the
  53.  * same parameter name, selecting any of these drivers has the side effect of
  54.  * selecting all the drivers for this shared parameter. In this case, the partial
  55.  * derivatives will be the sum of the partial derivatives contributed by the
  56.  * corresponding force models. This case typically arises for central attraction
  57.  * coefficient, which has an influence on {@link org.orekit.forces.gravity.NewtonianAttraction
  58.  * Newtonian attraction}, {@link org.orekit.forces.gravity.HolmesFeatherstoneAttractionModel
  59.  * gravity field}, and {@link org.orekit.forces.gravity.Relativity relativity}.
  60.  * </p>
  61.  * @author V&eacute;ronique Pommier-Maurussane
  62.  * @author Luc Maisonobe
  63.  */
  64. public class PartialDerivativesEquations implements AdditionalEquations {

  66.     /** Propagator computing state evolution. */
  67.     private final NumericalPropagator propagator;

  69.     /** Selected parameters for Jacobian computation. */
  70.     private ParameterDriversList selected;

  72.     /** Parameters map. */
  73.     private Map<ParameterDriver, Integer> map;

  75.     /** Name. */
  76.     private final String name;

  78.     /** Flag for Jacobian matrices initialization. */
  79.     private boolean initialized;

  81.     /** Simple constructor.
  82.      * <p>
  83.      * Upon construction, this set of equations is <em>automatically</em> added to
  84.      * the propagator by calling its {@link
  85.      * NumericalPropagator#addAdditionalEquations(AdditionalEquations)} method. So
  86.      * there is no need to call this method explicitly for these equations.
  87.      * </p>
  88.      * @param name name of the partial derivatives equations
  89.      * @param propagator the propagator that will handle the orbit propagation
  90.      */
  91.     public PartialDerivativesEquations(final String name, final NumericalPropagator propagator) {
  92.         this.name                   = name;
  93.         this.selected               = null;
  94.         this.map                    = null;
  95.         this.propagator             = propagator;
  96.         this.initialized            = false;
  97.         propagator.addAdditionalEquations(this);
  98.     }

  100.     /** {@inheritDoc} */
  101.     public String getName() {
  102.         return name;
  103.     }

  105.     /** Freeze the selected parameters from the force models.
  106.      */
  107.     private void freezeParametersSelection() {
  108.         if (selected == null) {

  110.             // first pass: gather all parameters, binding similar names together
  111.             selected = new ParameterDriversList();
  112.             for (final ForceModel provider : propagator.getAllForceModels()) {
  113.                 for (final ParameterDriver driver : provider.getParametersDrivers()) {
  114.                     selected.add(driver);
  115.                 }
  116.             }

  118.             // second pass: now that shared parameter names are bound together,
  119.             // their selections status have been synchronized, we can filter them
  120.             selected.filter(true);

  122.             // third pass: sort parameters lexicographically
  123.             selected.sort();

  125.             // fourth pass: set up a map between parameters drivers and matrices columns
  126.             map = new IdentityHashMap<ParameterDriver, Integer>();
  127.             int parameterIndex = 0;
  128.             for (final ParameterDriver selectedDriver : selected.getDrivers()) {
  129.                 for (final ForceModel provider : propagator.getAllForceModels()) {
  130.                     for (final ParameterDriver driver : provider.getParametersDrivers()) {
  131.                         if (driver.getName().equals(selectedDriver.getName())) {
  132.                             map.put(driver, parameterIndex);
  133.                         }
  134.                     }
  135.                 }
  136.                 ++parameterIndex;
  137.             }

  139.         }
  140.     }

  142.     /** Get the selected parameters, in Jacobian matrix column order.
  143.      * <p>
  144.      * The force models parameters for which partial derivatives are desired,
  145.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  146.      * before this method is called, so the proper list is returned.
  147.      * </p>
  148.      * @return selected parameters, in Jacobian matrix column order which
  149.      * is lexicographic order
  150.      */
  151.     public ParameterDriversList getSelectedParameters() {
  152.         freezeParametersSelection();
  153.         return selected;
  154.     }

  156.     /** Set the initial value of the Jacobian with respect to state and parameter.
  157.      * <p>
  158.      * This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
  159.      * double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
  160.      * to a zero matrix.
  161.      * </p>
  162.      * <p>
  163.      * The force models parameters for which partial derivatives are desired,
  164.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  165.      * before this method is called, so proper matrices dimensions are used.
  166.      * </p>
  167.      * @param s0 initial state
  168.      * @return state with initial Jacobians added
  169.      * @see #getSelectedParameters()
  170.      * @since 9.0
  171.      */
  172.     public SpacecraftState setInitialJacobians(final SpacecraftState s0) {
  173.         freezeParametersSelection();
  174.         final int stateDimension = 6;
  175.         final double[][] dYdY0 = new double[stateDimension][stateDimension];
  176.         final double[][] dYdP  = new double[stateDimension][selected.getNbParams()];
  177.         for (int i = 0; i < stateDimension; ++i) {
  178.             dYdY0[i][i] = 1.0;
  179.         }
  180.         return setInitialJacobians(s0, dYdY0, dYdP);
  181.     }

  183.     /** Set the initial value of the Jacobian with respect to state and parameter.
  184.      * <p>
  185.      * This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
  186.      * double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
  187.      * to a zero matrix.
  188.      * </p>
  189.      * <p>
  190.      * The force models parameters for which partial derivatives are desired,
  191.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  192.      * before this method is called, so proper matrices dimensions are used.
  193.      * </p>
  194.      * @param s0 initial state
  195.      * @param stateDimension state dimension, must be either 6 for orbit only or 7 for orbit and mass
  196.      * @return state with initial Jacobians added
  197.      * @see #getSelectedParameters()
  198.      * @deprecated as of 9.0, replaced by {@link #setInitialJacobians(SpacecraftState)}
  199.      */
  200.     @Deprecated
  201.     public SpacecraftState setInitialJacobians(final SpacecraftState s0, final int stateDimension) {
  202.         freezeParametersSelection();
  203.         final double[][] dYdY0 = new double[stateDimension][stateDimension];
  204.         final double[][] dYdP  = new double[stateDimension][selected.getNbParams()];
  205.         for (int i = 0; i < stateDimension; ++i) {
  206.             dYdY0[i][i] = 1.0;
  207.         }
  208.         return setInitialJacobians(s0, dYdY0, dYdP);
  209.     }

  211.     /** Set the initial value of the Jacobian with respect to state and parameter.
  212.      * <p>
  213.      * The returned state must be added to the propagator (it is not done
  214.      * automatically, as the user may need to add more states to it).
  215.      * </p>
  216.      * <p>
  217.      * The force models parameters for which partial derivatives are desired,
  218.      * <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
  219.      * before this method is called, and the {@code dY1dP} matrix dimension <em>must</em>
  220.      * be consistent with the selection.
  221.      * </p>
  222.      * @param s1 current state
  223.      * @param dY1dY0 Jacobian of current state at time t₁ with respect
  224.      * to state at some previous time t₀ (must be 6x6)
  225.      * @param dY1dP Jacobian of current state at time t₁ with respect
  226.      * to parameters (may be null if no parameters are selected)
  227.      * @return state with initial Jacobians added
  228.      * @see #getSelectedParameters()
  229.      */
  230.     public SpacecraftState setInitialJacobians(final SpacecraftState s1,
  231.                                                final double[][] dY1dY0, final double[][] dY1dP) {

  233.         freezeParametersSelection();

  235.         // Check dimensions
  236.         final int stateDim = dY1dY0.length;
  237.         if (stateDim != 6 || stateDim != dY1dY0[0].length) {
  238.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_6X6,
  239.                                       stateDim, dY1dY0[0].length);
  240.         }
  241.         if (dY1dP != null && stateDim != dY1dP.length) {
  242.             throw new OrekitException(OrekitMessages.STATE_AND_PARAMETERS_JACOBIANS_ROWS_MISMATCH,
  243.                                       stateDim, dY1dP.length);
  244.         }
  245.         if ((dY1dP == null && selected.getNbParams() != 0) ||
  246.             (dY1dP != null && selected.getNbParams() != dY1dP[0].length)) {
  247.             throw new OrekitException(new OrekitException(OrekitMessages.INITIAL_MATRIX_AND_PARAMETERS_NUMBER_MISMATCH,
  248.                                                           dY1dP == null ? 0 : dY1dP[0].length, selected.getNbParams()));
  249.         }

  251.         // store the matrices as a single dimension array
  252.         initialized = true;
  253.         final JacobiansMapper mapper = getMapper();
  254.         final double[] p = new double[mapper.getAdditionalStateDimension()];
  255.         mapper.setInitialJacobians(s1, dY1dY0, dY1dP, p);

  257.         // set value in propagator
  258.         return s1.addAdditionalState(name, p);

  260.     }

  262.     /** Get a mapper between two-dimensional Jacobians and one-dimensional additional state.
  263.      * @return a mapper between two-dimensional Jacobians and one-dimensional additional state,
  264.      * with the same name as the instance
  265.           * @see #setInitialJacobians(SpacecraftState, int)
  266.      * @see #setInitialJacobians(SpacecraftState, double[][], double[][])
  267.      */
  268.     public JacobiansMapper getMapper() {
  269.         if (!initialized) {
  270.             throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_INITIALIZED);
  271.         }
  272.         return new JacobiansMapper(name, selected,
  273.                                    propagator.getOrbitType(),
  274.                                    propagator.getPositionAngleType());
  275.     }

  277.     /** {@inheritDoc} */
  278.     public double[] computeDerivatives(final SpacecraftState s, final double[] pDot) {

  280.         // initialize acceleration Jacobians to zero
  281.         final int paramDim = selected.getNbParams();
  282.         final int dim = 3;
  283.         final double[][] dAccdParam = new double[dim][paramDim];
  284.         final double[][] dAccdPos   = new double[dim][dim];
  285.         final double[][] dAccdVel   = new double[dim][dim];

  287.         final DSConverter fullConverter    = new DSConverter(s, 6, propagator.getAttitudeProvider());
  288.         final DSConverter posOnlyConverter = new DSConverter(s, 3, propagator.getAttitudeProvider());

  290.         // compute acceleration Jacobians, finishing with the largest force: Newtonian attraction
  291.         for (final ForceModel forceModel : propagator.getAllForceModels()) {

  293.             final DSConverter converter = forceModel.dependsOnPositionOnly() ? posOnlyConverter : fullConverter;
  294.             final FieldSpacecraftState<DerivativeStructure> dsState = converter.getState(forceModel);
  295.             final DerivativeStructure[] parameters = converter.getParameters(dsState, forceModel);

  297.             final FieldVector3D<DerivativeStructure> acceleration = forceModel.acceleration(dsState, parameters);
  298.             final double[] derivativesX = acceleration.getX().getAllDerivatives();
  299.             final double[] derivativesY = acceleration.getY().getAllDerivatives();
  300.             final double[] derivativesZ = acceleration.getZ().getAllDerivatives();

  302.             // update Jacobians with respect to state
  303.             addToRow(derivativesX, 0, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  304.             addToRow(derivativesY, 1, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
  305.             addToRow(derivativesZ, 2, converter.getFreeStateParameters(), dAccdPos, dAccdVel);

  307.             int index = converter.getFreeStateParameters();
  308.             for (ParameterDriver driver : forceModel.getParametersDrivers()) {
  309.                 if (driver.isSelected()) {
  310.                     final int parameterIndex = map.get(driver);
  311.                     ++index;
  312.                     dAccdParam[0][parameterIndex] += derivativesX[index];
  313.                     dAccdParam[1][parameterIndex] += derivativesY[index];
  314.                     dAccdParam[2][parameterIndex] += derivativesZ[index];
  315.                 }
  316.             }

  318.         }

  320.         // the variational equations of the complete state Jacobian matrix have the following form:

  322.         // [        |        ]   [                 |                  ]   [     |     ]
  323.         // [  Adot  |  Bdot  ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [  A  |  B  ]
  324.         // [        |        ]   [                 |                  ]   [     |     ]
  325.         // ---------+---------   ------------------+------------------- * ------+------
  326.         // [        |        ]   [                 |                  ]   [     |     ]
  327.         // [  Cdot  |  Ddot  ] = [    dAcc/dPos    |     dAcc/dVel    ]   [  C  |  D  ]
  328.         // [        |        ]   [                 |                  ]   [     |     ]

  330.         // The A, B, C and D sub-matrices and their derivatives (Adot ...) are 3x3 matrices

  332.         // The expanded multiplication above can be rewritten to take into account
  333.         // the fixed values found in the sub-matrices in the left factor. This leads to:

  335.         //     [ Adot ] = [ C ]
  336.         //     [ Bdot ] = [ D ]
  337.         //     [ Cdot ] = [ dAcc/dPos ] * [ A ] + [ dAcc/dVel ] * [ C ]
  338.         //     [ Ddot ] = [ dAcc/dPos ] * [ B ] + [ dAcc/dVel ] * [ D ]

  340.         // The following loops compute these expressions taking care of the mapping of the
  341.         // (A, B, C, D) matrices into the single dimension array p and of the mapping of the
  342.         // (Adot, Bdot, Cdot, Ddot) matrices into the single dimension array pDot.

  344.         // copy C and E into Adot and Bdot
  345.         final int stateDim = 6;
  346.         final double[] p = s.getAdditionalState(getName());
  347.         System.arraycopy(p, dim * stateDim, pDot, 0, dim * stateDim);

  349.         // compute Cdot and Ddot
  350.         for (int i = 0; i < dim; ++i) {
  351.             final double[] dAdPi = dAccdPos[i];
  352.             final double[] dAdVi = dAccdVel[i];
  353.             for (int j = 0; j < stateDim; ++j) {
  354.                 pDot[(dim + i) * stateDim + j] =
  355.                     dAdPi[0] * p[j]                + dAdPi[1] * p[j +     stateDim] + dAdPi[2] * p[j + 2 * stateDim] +
  356.                     dAdVi[0] * p[j + 3 * stateDim] + dAdVi[1] * p[j + 4 * stateDim] + dAdVi[2] * p[j + 5 * stateDim];
  357.             }
  358.         }

  360.         for (int k = 0; k < paramDim; ++k) {
  361.             // the variational equations of the parameters Jacobian matrix are computed
  362.             // one column at a time, they have the following form:
  363.             // [      ]   [                 |                  ]   [   ]   [                  ]
  364.             // [ Edot ]   [  dVel/dPos = 0  |  dVel/dVel = Id  ]   [ E ]   [  dVel/dParam = 0 ]
  365.             // [      ]   [                 |                  ]   [   ]   [                  ]
  366.             // --------   ------------------+------------------- * ----- + --------------------
  367.             // [      ]   [                 |                  ]   [   ]   [                  ]
  368.             // [ Fdot ] = [    dAcc/dPos    |     dAcc/dVel    ]   [ F ]   [    dAcc/dParam   ]
  369.             // [      ]   [                 |                  ]   [   ]   [                  ]

  371.             // The E and F sub-columns and their derivatives (Edot, Fdot) are 3 elements columns.

  373.             // The expanded multiplication and addition above can be rewritten to take into
  374.             // account the fixed values found in the sub-matrices in the left factor. This leads to:

  376.             //     [ Edot ] = [ F ]
  377.             //     [ Fdot ] = [ dAcc/dPos ] * [ E ] + [ dAcc/dVel ] * [ F ] + [ dAcc/dParam ]

  379.             // The following loops compute these expressions taking care of the mapping of the
  380.             // (E, F) columns into the single dimension array p and of the mapping of the
  381.             // (Edot, Fdot) columns into the single dimension array pDot.

  383.             // copy F into Edot
  384.             final int columnTop = stateDim * stateDim + k;
  385.             pDot[columnTop]                = p[columnTop + 3 * paramDim];
  386.             pDot[columnTop +     paramDim] = p[columnTop + 4 * paramDim];
  387.             pDot[columnTop + 2 * paramDim] = p[columnTop + 5 * paramDim];

  389.             // compute Fdot
  390.             for (int i = 0; i < dim; ++i) {
  391.                 final double[] dAdPi = dAccdPos[i];
  392.                 final double[] dAdVi = dAccdVel[i];
  393.                 pDot[columnTop + (dim + i) * paramDim] =
  394.                     dAccdParam[i][k] +
  395.                     dAdPi[0] * p[columnTop]                + dAdPi[1] * p[columnTop +     paramDim] + dAdPi[2] * p[columnTop + 2 * paramDim] +
  396.                     dAdVi[0] * p[columnTop + 3 * paramDim] + dAdVi[1] * p[columnTop + 4 * paramDim] + dAdVi[2] * p[columnTop + 5 * paramDim];
  397.             }

  399.         }

  401.         // these equations have no effect on the main state itself
  402.         return null;

  404.     }

  406.     /** Fill Jacobians rows.
  407.      * @param derivatives derivatives of a component of acceleration (along either x, y or z)
  408.      * @param index component index (0 for x, 1 for y, 2 for z)
  409.      * @param freeStateParameters number of free parameters, either 3 (position),
  410.      * 6 (position-velocity) or 7 (position-velocity-mass)
  411.      * @param dAccdPos Jacobian of acceleration with respect to spacecraft position
  412.      * @param dAccdVel Jacobian of acceleration with respect to spacecraft velocity
  413.      */
  414.     private void addToRow(final double[] derivatives, final int index, final int freeStateParameters,
  415.                           final double[][] dAccdPos, final double[][] dAccdVel) {

  417.         for (int i = 0; i < 3; ++i) {
  418.             dAccdPos[index][i] += derivatives[i + 1];
  419.         }
  420.         if (freeStateParameters > 3) {
  421.             for (int i = 0; i < 3; ++i) {
  422.                 dAccdVel[index][i] += derivatives[i + 4];
  423.             }
  424.         }

  426.     }

  428. }
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