PartialDerivativesEquations.java
/* Copyright 2010-2011 Centre National d'Études Spatiales
* Licensed to CS GROUP (CS) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* CS licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.orekit.propagation.numerical;
import java.util.IdentityHashMap;
import java.util.Map;
import org.hipparchus.analysis.differentiation.Gradient;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.forces.ForceModel;
import org.orekit.propagation.FieldSpacecraftState;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.integration.AdditionalEquations;
import org.orekit.utils.ParameterDriver;
import org.orekit.utils.ParameterDriversList;
/** Set of {@link AdditionalEquations additional equations} computing the partial derivatives
* of the state (orbit) with respect to initial state and force models parameters.
* <p>
* This set of equations are automatically added to a {@link NumericalPropagator numerical propagator}
* in order to compute partial derivatives of the orbit along with the orbit itself. This is
* useful for example in orbit determination applications.
* </p>
* <p>
* The partial derivatives with respect to initial state can be either dimension 6
* (orbit only) or 7 (orbit and mass).
* </p>
* <p>
* The partial derivatives with respect to force models parameters has a dimension
* equal to the number of selected parameters. Parameters selection is implemented at
* {@link ForceModel force models} level. Users must retrieve a {@link ParameterDriver
* parameter driver} using {@link ForceModel#getParameterDriver(String)} and then
* select it by calling {@link ParameterDriver#setSelected(boolean) setSelected(true)}.
* </p>
* <p>
* If several force models provide different {@link ParameterDriver drivers} for the
* same parameter name, selecting any of these drivers has the side effect of
* selecting all the drivers for this shared parameter. In this case, the partial
* derivatives will be the sum of the partial derivatives contributed by the
* corresponding force models. This case typically arises for central attraction
* coefficient, which has an influence on {@link org.orekit.forces.gravity.NewtonianAttraction
* Newtonian attraction}, {@link org.orekit.forces.gravity.HolmesFeatherstoneAttractionModel
* gravity field}, and {@link org.orekit.forces.gravity.Relativity relativity}.
* </p>
* @author Véronique Pommier-Maurussane
* @author Luc Maisonobe
*/
public class PartialDerivativesEquations implements AdditionalEquations {
/** Propagator computing state evolution. */
private final NumericalPropagator propagator;
/** Selected parameters for Jacobian computation. */
private ParameterDriversList selected;
/** Parameters map. */
private Map<ParameterDriver, Integer> map;
/** Name. */
private final String name;
/** Flag for Jacobian matrices initialization. */
private boolean initialized;
/** Simple constructor.
* <p>
* Upon construction, this set of equations is <em>automatically</em> added to
* the propagator by calling its {@link
* NumericalPropagator#addAdditionalEquations(AdditionalEquations)} method. So
* there is no need to call this method explicitly for these equations.
* </p>
* @param name name of the partial derivatives equations
* @param propagator the propagator that will handle the orbit propagation
*/
public PartialDerivativesEquations(final String name, final NumericalPropagator propagator) {
this.name = name;
this.selected = null;
this.map = null;
this.propagator = propagator;
this.initialized = false;
propagator.addAdditionalEquations(this);
}
/** {@inheritDoc} */
public String getName() {
return name;
}
/** Freeze the selected parameters from the force models.
*/
private void freezeParametersSelection() {
if (selected == null) {
// first pass: gather all parameters, binding similar names together
selected = new ParameterDriversList();
for (final ForceModel provider : propagator.getAllForceModels()) {
for (final ParameterDriver driver : provider.getParametersDrivers()) {
selected.add(driver);
}
}
// second pass: now that shared parameter names are bound together,
// their selections status have been synchronized, we can filter them
selected.filter(true);
// third pass: sort parameters lexicographically
selected.sort();
// fourth pass: set up a map between parameters drivers and matrices columns
map = new IdentityHashMap<ParameterDriver, Integer>();
int parameterIndex = 0;
for (final ParameterDriver selectedDriver : selected.getDrivers()) {
for (final ForceModel provider : propagator.getAllForceModels()) {
for (final ParameterDriver driver : provider.getParametersDrivers()) {
if (driver.getName().equals(selectedDriver.getName())) {
map.put(driver, parameterIndex);
}
}
}
++parameterIndex;
}
}
}
/** Get the selected parameters, in Jacobian matrix column order.
* <p>
* The force models parameters for which partial derivatives are desired,
* <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
* before this method is called, so the proper list is returned.
* </p>
* @return selected parameters, in Jacobian matrix column order which
* is lexicographic order
*/
public ParameterDriversList getSelectedParameters() {
freezeParametersSelection();
return selected;
}
/** Set the initial value of the Jacobian with respect to state and parameter.
* <p>
* This method is equivalent to call {@link #setInitialJacobians(SpacecraftState,
* double[][], double[][])} with dYdY0 set to the identity matrix and dYdP set
* to a zero matrix.
* </p>
* <p>
* The force models parameters for which partial derivatives are desired,
* <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
* before this method is called, so proper matrices dimensions are used.
* </p>
* @param s0 initial state
* @return state with initial Jacobians added
* @see #getSelectedParameters()
* @since 9.0
*/
public SpacecraftState setInitialJacobians(final SpacecraftState s0) {
freezeParametersSelection();
final int stateDimension = 6;
final double[][] dYdY0 = new double[stateDimension][stateDimension];
final double[][] dYdP = new double[stateDimension][selected.getNbParams()];
for (int i = 0; i < stateDimension; ++i) {
dYdY0[i][i] = 1.0;
}
return setInitialJacobians(s0, dYdY0, dYdP);
}
/** Set the initial value of the Jacobian with respect to state and parameter.
* <p>
* The returned state must be added to the propagator (it is not done
* automatically, as the user may need to add more states to it).
* </p>
* <p>
* The force models parameters for which partial derivatives are desired,
* <em>must</em> have been {@link ParameterDriver#setSelected(boolean) selected}
* before this method is called, and the {@code dY1dP} matrix dimension <em>must</em>
* be consistent with the selection.
* </p>
* @param s1 current state
* @param dY1dY0 Jacobian of current state at time t₁ with respect
* to state at some previous time t₀ (must be 6x6)
* @param dY1dP Jacobian of current state at time t₁ with respect
* to parameters (may be null if no parameters are selected)
* @return state with initial Jacobians added
* @see #getSelectedParameters()
*/
public SpacecraftState setInitialJacobians(final SpacecraftState s1,
final double[][] dY1dY0, final double[][] dY1dP) {
freezeParametersSelection();
// Check dimensions
final int stateDim = dY1dY0.length;
if (stateDim != 6 || stateDim != dY1dY0[0].length) {
throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_6X6,
stateDim, dY1dY0[0].length);
}
if (dY1dP != null && stateDim != dY1dP.length) {
throw new OrekitException(OrekitMessages.STATE_AND_PARAMETERS_JACOBIANS_ROWS_MISMATCH,
stateDim, dY1dP.length);
}
if ((dY1dP == null && selected.getNbParams() != 0) ||
(dY1dP != null && selected.getNbParams() != dY1dP[0].length)) {
throw new OrekitException(new OrekitException(OrekitMessages.INITIAL_MATRIX_AND_PARAMETERS_NUMBER_MISMATCH,
dY1dP == null ? 0 : dY1dP[0].length, selected.getNbParams()));
}
// store the matrices as a single dimension array
initialized = true;
final JacobiansMapper mapper = getMapper();
final double[] p = new double[mapper.getAdditionalStateDimension()];
mapper.setInitialJacobians(s1, dY1dY0, dY1dP, p);
// set value in propagator
return s1.addAdditionalState(name, p);
}
/** Get a mapper between two-dimensional Jacobians and one-dimensional additional state.
* @return a mapper between two-dimensional Jacobians and one-dimensional additional state,
* with the same name as the instance
* @see #setInitialJacobians(SpacecraftState)
* @see #setInitialJacobians(SpacecraftState, double[][], double[][])
*/
public JacobiansMapper getMapper() {
if (!initialized) {
throw new OrekitException(OrekitMessages.STATE_JACOBIAN_NOT_INITIALIZED);
}
return new JacobiansMapper(name, selected,
propagator.getOrbitType(),
propagator.getPositionAngleType());
}
/** {@inheritDoc} */
public double[] computeDerivatives(final SpacecraftState s, final double[] pDot) {
// initialize acceleration Jacobians to zero
final int paramDim = selected.getNbParams();
final int dim = 3;
final double[][] dAccdParam = new double[dim][paramDim];
final double[][] dAccdPos = new double[dim][dim];
final double[][] dAccdVel = new double[dim][dim];
final NumericalGradientConverter fullConverter = new NumericalGradientConverter(s, 6, propagator.getAttitudeProvider());
final NumericalGradientConverter posOnlyConverter = new NumericalGradientConverter(s, 3, propagator.getAttitudeProvider());
// compute acceleration Jacobians, finishing with the largest force: Newtonian attraction
for (final ForceModel forceModel : propagator.getAllForceModels()) {
final NumericalGradientConverter converter = forceModel.dependsOnPositionOnly() ? posOnlyConverter : fullConverter;
final FieldSpacecraftState<Gradient> dsState = converter.getState(forceModel);
final Gradient[] parameters = converter.getParameters(dsState, forceModel);
final FieldVector3D<Gradient> acceleration = forceModel.acceleration(dsState, parameters);
final double[] derivativesX = acceleration.getX().getGradient();
final double[] derivativesY = acceleration.getY().getGradient();
final double[] derivativesZ = acceleration.getZ().getGradient();
// update Jacobians with respect to state
addToRow(derivativesX, 0, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
addToRow(derivativesY, 1, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
addToRow(derivativesZ, 2, converter.getFreeStateParameters(), dAccdPos, dAccdVel);
int index = converter.getFreeStateParameters();
for (ParameterDriver driver : forceModel.getParametersDrivers()) {
if (driver.isSelected()) {
final int parameterIndex = map.get(driver);
dAccdParam[0][parameterIndex] += derivativesX[index];
dAccdParam[1][parameterIndex] += derivativesY[index];
dAccdParam[2][parameterIndex] += derivativesZ[index];
++index;
}
}
}
// the variational equations of the complete state Jacobian matrix have the following form:
// [ | ] [ | ] [ | ]
// [ Adot | Bdot ] [ dVel/dPos = 0 | dVel/dVel = Id ] [ A | B ]
// [ | ] [ | ] [ | ]
// ---------+--------- ------------------+------------------- * ------+------
// [ | ] [ | ] [ | ]
// [ Cdot | Ddot ] = [ dAcc/dPos | dAcc/dVel ] [ C | D ]
// [ | ] [ | ] [ | ]
// The A, B, C and D sub-matrices and their derivatives (Adot ...) are 3x3 matrices
// The expanded multiplication above can be rewritten to take into account
// the fixed values found in the sub-matrices in the left factor. This leads to:
// [ Adot ] = [ C ]
// [ Bdot ] = [ D ]
// [ Cdot ] = [ dAcc/dPos ] * [ A ] + [ dAcc/dVel ] * [ C ]
// [ Ddot ] = [ dAcc/dPos ] * [ B ] + [ dAcc/dVel ] * [ D ]
// The following loops compute these expressions taking care of the mapping of the
// (A, B, C, D) matrices into the single dimension array p and of the mapping of the
// (Adot, Bdot, Cdot, Ddot) matrices into the single dimension array pDot.
// copy C and E into Adot and Bdot
final int stateDim = 6;
final double[] p = s.getAdditionalState(getName());
System.arraycopy(p, dim * stateDim, pDot, 0, dim * stateDim);
// compute Cdot and Ddot
for (int i = 0; i < dim; ++i) {
final double[] dAdPi = dAccdPos[i];
final double[] dAdVi = dAccdVel[i];
for (int j = 0; j < stateDim; ++j) {
pDot[(dim + i) * stateDim + j] =
dAdPi[0] * p[j] + dAdPi[1] * p[j + stateDim] + dAdPi[2] * p[j + 2 * stateDim] +
dAdVi[0] * p[j + 3 * stateDim] + dAdVi[1] * p[j + 4 * stateDim] + dAdVi[2] * p[j + 5 * stateDim];
}
}
for (int k = 0; k < paramDim; ++k) {
// the variational equations of the parameters Jacobian matrix are computed
// one column at a time, they have the following form:
// [ ] [ | ] [ ] [ ]
// [ Edot ] [ dVel/dPos = 0 | dVel/dVel = Id ] [ E ] [ dVel/dParam = 0 ]
// [ ] [ | ] [ ] [ ]
// -------- ------------------+------------------- * ----- + --------------------
// [ ] [ | ] [ ] [ ]
// [ Fdot ] = [ dAcc/dPos | dAcc/dVel ] [ F ] [ dAcc/dParam ]
// [ ] [ | ] [ ] [ ]
// The E and F sub-columns and their derivatives (Edot, Fdot) are 3 elements columns.
// The expanded multiplication and addition above can be rewritten to take into
// account the fixed values found in the sub-matrices in the left factor. This leads to:
// [ Edot ] = [ F ]
// [ Fdot ] = [ dAcc/dPos ] * [ E ] + [ dAcc/dVel ] * [ F ] + [ dAcc/dParam ]
// The following loops compute these expressions taking care of the mapping of the
// (E, F) columns into the single dimension array p and of the mapping of the
// (Edot, Fdot) columns into the single dimension array pDot.
// copy F into Edot
final int columnTop = stateDim * stateDim + k;
pDot[columnTop] = p[columnTop + 3 * paramDim];
pDot[columnTop + paramDim] = p[columnTop + 4 * paramDim];
pDot[columnTop + 2 * paramDim] = p[columnTop + 5 * paramDim];
// compute Fdot
for (int i = 0; i < dim; ++i) {
final double[] dAdPi = dAccdPos[i];
final double[] dAdVi = dAccdVel[i];
pDot[columnTop + (dim + i) * paramDim] =
dAccdParam[i][k] +
dAdPi[0] * p[columnTop] + dAdPi[1] * p[columnTop + paramDim] + dAdPi[2] * p[columnTop + 2 * paramDim] +
dAdVi[0] * p[columnTop + 3 * paramDim] + dAdVi[1] * p[columnTop + 4 * paramDim] + dAdVi[2] * p[columnTop + 5 * paramDim];
}
}
// these equations have no effect on the main state itself
return null;
}
/** Get the flag for the initialization of the state jacobian.
* @return true if the state jacobian is initialized
* @since 10.2
*/
public boolean isInitialize() {
return initialized;
}
/** Fill Jacobians rows.
* @param derivatives derivatives of a component of acceleration (along either x, y or z)
* @param index component index (0 for x, 1 for y, 2 for z)
* @param freeStateParameters number of free parameters, either 3 (position),
* 6 (position-velocity) or 7 (position-velocity-mass)
* @param dAccdPos Jacobian of acceleration with respect to spacecraft position
* @param dAccdVel Jacobian of acceleration with respect to spacecraft velocity
*/
private void addToRow(final double[] derivatives, final int index, final int freeStateParameters,
final double[][] dAccdPos, final double[][] dAccdVel) {
for (int i = 0; i < 3; ++i) {
dAccdPos[index][i] += derivatives[i];
}
if (freeStateParameters > 3) {
for (int i = 0; i < 3; ++i) {
dAccdVel[index][i] += derivatives[i + 3];
}
}
}
}