Jacobianizer.java
/* Copyright 2010-2011 Centre National d'Études Spatiales
* Licensed to CS Systèmes d'Information (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.Collection;
import java.util.HashMap;
import java.util.Map;
import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
import org.apache.commons.math3.geometry.euclidean.threed.FieldRotation;
import org.apache.commons.math3.geometry.euclidean.threed.FieldVector3D;
import org.apache.commons.math3.geometry.euclidean.threed.Rotation;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.Precision;
import org.orekit.attitudes.Attitude;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
import org.orekit.forces.ForceModel;
import org.orekit.frames.Frame;
import org.orekit.frames.Transform;
import org.orekit.orbits.CartesianOrbit;
import org.orekit.orbits.Orbit;
import org.orekit.propagation.SpacecraftState;
import org.orekit.time.AbsoluteDate;
import org.orekit.utils.PVCoordinates;
/** Class helping implementation of partial derivatives in {@link ForceModel force models} implementations.
* <p>
* For better performances, {@link ForceModel force models} implementations should compute their
* partial derivatives analytically. However, in some cases, it may be difficult. This class
* allows to compute the derivatives by finite differences relying only on the basic acceleration.
* </p>
* @author Véronique Pommier-Maurussane
* @author Luc Maisonobe
*/
public class Jacobianizer {
/** Wrapped force model instance. */
private final ForceModel forceModel;
/** Central attraction coefficient (m³/s²). */
private final double mu;
/** Step used for finite difference computation with respect to spacecraft position. */
private double hPos;
/** Step used for finite difference computation with respect to parameters value. */
private final Map<String, Double> hParam;
/** Simple constructor.
* @param forceModel force model instance to wrap
* @param mu central attraction coefficient (m³/s²)
* @param paramsAndSteps collection of parameters and their associated steps
* @param hPos step used for finite difference computation with respect to spacecraft position (m)
*/
public Jacobianizer(final ForceModel forceModel, final double mu,
final Collection<ParameterConfiguration> paramsAndSteps, final double hPos) {
this.forceModel = forceModel;
this.mu = mu;
this.hParam = new HashMap<String, Double>();
this.hPos = hPos;
// set up parameters for jacobian computation
for (final ParameterConfiguration param : paramsAndSteps) {
final String name = param.getParameterName();
if (forceModel.isSupported(name)) {
double step = param.getHP();
if (Double.isNaN(step)) {
step = FastMath.max(1.0, FastMath.abs(forceModel.getParameter(name))) *
FastMath.sqrt(Precision.EPSILON);
}
hParam.put(name, step);
}
}
}
/** Compute acceleration.
* @param retriever acceleration retriever to use for storing acceleration
* @param date current date
* @param frame inertial reference frame for state (both orbit and attitude)
* @param position position of spacecraft in reference frame
* @param velocity velocity of spacecraft in reference frame
* @param rotation orientation (attitude) of the spacecraft with respect to reference frame
* @param mass spacecraft mass
* @exception OrekitException if the underlying force models cannot compute the acceleration
*/
private void computeShiftedAcceleration(final AccelerationRetriever retriever,
final AbsoluteDate date, final Frame frame,
final Vector3D position, final Vector3D velocity,
final Rotation rotation, final double mass)
throws OrekitException {
final Orbit shiftedORbit = new CartesianOrbit(new PVCoordinates(position, velocity), frame, date, mu);
retriever.setOrbit(shiftedORbit);
forceModel.addContribution(new SpacecraftState(shiftedORbit,
new Attitude(date, frame, rotation, Vector3D.ZERO, Vector3D.ZERO),
mass),
retriever);
}
/** Compute acceleration and derivatives with respect to state.
* @param date current date
* @param frame inertial reference frame for state (both orbit and attitude)
* @param position position of spacecraft in reference frame
* @param velocity velocity of spacecraft in reference frame
* @param rotation orientation (attitude) of the spacecraft with respect to reference frame
* @param mass spacecraft mass
* @return acceleration with derivatives
* @exception OrekitException if the underlying force models cannot compute the acceleration
*/
public FieldVector3D<DerivativeStructure> accelerationDerivatives(final AbsoluteDate date, final Frame frame,
final FieldVector3D<DerivativeStructure> position,
final FieldVector3D<DerivativeStructure> velocity,
final FieldRotation<DerivativeStructure> rotation,
final DerivativeStructure mass)
throws OrekitException {
final int parameters = mass.getFreeParameters();
final int order = mass.getOrder();
// estimate the scalar velocity step, assuming energy conservation
// and hence differentiating equation V = sqrt(mu (2/r - 1/a))
final Vector3D p0 = position.toVector3D();
final Vector3D v0 = velocity.toVector3D();
final double r2 = p0.getNormSq();
final double hVel = mu * hPos / (v0.getNorm() * r2);
// estimate mass step, applying the same relative value as position
final double hMass = mass.getValue() * hPos / FastMath.sqrt(r2);
// compute nominal acceleration
final AccelerationRetriever nominal = new AccelerationRetriever();
computeShiftedAcceleration(nominal, date, frame, p0, v0, rotation.toRotation(), mass.getValue());
final double[] a0 = nominal.getAcceleration().toArray();
// compute accelerations with shifted states
final AccelerationRetriever shifted = new AccelerationRetriever();
// shift position by hPos alon x, y and z
computeShiftedAcceleration(shifted, date, frame, shift(position, 0, hPos), v0, shift(rotation, 0, hPos), shift(mass, 0, hPos));
final double[] derPx = new Vector3D(1 / hPos, shifted.getAcceleration(), -1 / hPos, nominal.getAcceleration()).toArray();
computeShiftedAcceleration(shifted, date, frame, shift(position, 1, hPos), v0, shift(rotation, 1, hPos), shift(mass, 1, hPos));
final double[] derPy = new Vector3D(1 / hPos, shifted.getAcceleration(), -1 / hPos, nominal.getAcceleration()).toArray();
computeShiftedAcceleration(shifted, date, frame, shift(position, 2, hPos), v0, shift(rotation, 2, hPos), shift(mass, 2, hPos));
final double[] derPz = new Vector3D(1 / hPos, shifted.getAcceleration(), -1 / hPos, nominal.getAcceleration()).toArray();
// shift velocity by hVel alon x, y and z
computeShiftedAcceleration(shifted, date, frame, p0, shift(velocity, 3, hVel), shift(rotation, 3, hVel), shift(mass, 3, hVel));
final double[] derVx = new Vector3D(1 / hVel, shifted.getAcceleration(), -1 / hVel, nominal.getAcceleration()).toArray();
computeShiftedAcceleration(shifted, date, frame, p0, shift(velocity, 4, hVel), shift(rotation, 4, hVel), shift(mass, 4, hVel));
final double[] derVy = new Vector3D(1 / hVel, shifted.getAcceleration(), -1 / hVel, nominal.getAcceleration()).toArray();
computeShiftedAcceleration(shifted, date, frame, p0, shift(velocity, 5, hVel), shift(rotation, 5, hVel), shift(mass, 5, hVel));
final double[] derVz = new Vector3D(1 / hVel, shifted.getAcceleration(), -1 / hVel, nominal.getAcceleration()).toArray();
final double[] derM;
if (parameters < 7) {
derM = null;
} else {
// shift mass by hMass
computeShiftedAcceleration(shifted, date, frame, p0, v0, shift(rotation, 6, hMass), shift(mass, 6, hMass));
derM = new Vector3D(1 / hMass, shifted.getAcceleration(), -1 / hMass, nominal.getAcceleration()).toArray();
}
final double[] derivatives = new double[1 + parameters];
final DerivativeStructure[] accDer = new DerivativeStructure[3];
for (int i = 0; i < 3; ++i) {
// first element is value of acceleration
derivatives[0] = a0[i];
// next three elements are derivatives with respect to position
derivatives[1] = derPx[i];
derivatives[2] = derPy[i];
derivatives[3] = derPz[i];
// next three elements are derivatives with respect to velocity
derivatives[4] = derVx[i];
derivatives[5] = derVy[i];
derivatives[6] = derVz[i];
if (derM != null) {
derivatives[7] = derM[i];
}
accDer[i] = new DerivativeStructure(parameters, order, derivatives);
}
return new FieldVector3D<DerivativeStructure>(accDer);
}
/** Shift a vector.
* @param nominal nominal vector
* @param index index of the variable with respect to which we shift
* @param h shift step
* @return shifted vector
*/
private Vector3D shift(final FieldVector3D<DerivativeStructure> nominal, final int index, final double h) {
final double[] delta = new double[nominal.getX().getFreeParameters()];
delta[index] = h;
return new Vector3D(nominal.getX().taylor(delta),
nominal.getY().taylor(delta),
nominal.getZ().taylor(delta));
}
/** Shift a rotation.
* @param nominal nominal rotation
* @param index index of the variable with respect to which we shift
* @param h shift step
* @return shifted rotation
*/
private Rotation shift(final FieldRotation<DerivativeStructure> nominal, final int index, final double h) {
final double[] delta = new double[nominal.getQ0().getFreeParameters()];
delta[index] = h;
return new Rotation(nominal.getQ0().taylor(delta),
nominal.getQ1().taylor(delta),
nominal.getQ2().taylor(delta),
nominal.getQ3().taylor(delta),
true);
}
/** Shift a scalar.
* @param nominal nominal scalar
* @param index index of the variable with respect to which we shift
* @param h shift step
* @return shifted scalar
*/
private double shift(final DerivativeStructure nominal, final int index, final double h) {
final double[] delta = new double[nominal.getFreeParameters()];
delta[index] = h;
return nominal.taylor(delta);
}
/** Compute acceleration and derivatives with respect to parameter.
* @param s current state
* @param paramName parameter with respect to which derivation is desired
* @return acceleration with derivatives
* @exception OrekitException if the underlying force models cannot compute the acceleration
* or the parameter is not supported
*/
public FieldVector3D<DerivativeStructure> accelerationDerivatives(final SpacecraftState s,
final String paramName)
throws OrekitException {
if (!hParam.containsKey(paramName)) {
// build the list of supported parameters
final StringBuilder builder = new StringBuilder();
for (final String available : hParam.keySet()) {
if (builder.length() > 0) {
builder.append(", ");
}
builder.append(available);
}
throw new OrekitException(OrekitMessages.UNSUPPORTED_PARAMETER_NAME,
paramName, builder.toString());
}
final double hP = hParam.get(paramName);
final AccelerationRetriever nominal = new AccelerationRetriever();
nominal.setOrbit(s.getOrbit());
forceModel.addContribution(s, nominal);
final double nx = nominal.getAcceleration().getX();
final double ny = nominal.getAcceleration().getY();
final double nz = nominal.getAcceleration().getZ();
final double paramValue = forceModel.getParameter(paramName);
forceModel.setParameter(paramName, paramValue + hP);
final AccelerationRetriever shifted = new AccelerationRetriever();
shifted.setOrbit(s.getOrbit());
forceModel.addContribution(s, shifted);
final double sx = shifted.getAcceleration().getX();
final double sy = shifted.getAcceleration().getY();
final double sz = shifted.getAcceleration().getZ();
forceModel.setParameter(paramName, paramValue);
return new FieldVector3D<DerivativeStructure>(new DerivativeStructure(1, 1, nx, (sx - nx) / hP),
new DerivativeStructure(1, 1, ny, (sy - ny) / hP),
new DerivativeStructure(1, 1, nz, (sz - nz) / hP));
}
/** Internal class for retrieving accelerations. */
private static class AccelerationRetriever implements TimeDerivativesEquations {
/** Stored acceleration. */
private Vector3D acceleration;
/** Current orbit. */
private Orbit orbit;
/** Simple constructor.
*/
protected AccelerationRetriever() {
acceleration = Vector3D.ZERO;
this.orbit = null;
}
/** Get acceleration.
* @return acceleration
*/
public Vector3D getAcceleration() {
return acceleration;
}
/** Set the current orbit.
* @param orbit current orbit
*/
public void setOrbit(final Orbit orbit) {
acceleration = Vector3D.ZERO;
this.orbit = orbit;
}
/** {@inheritDoc} */
public void addKeplerContribution(final double mu) {
final Vector3D position = orbit.getPVCoordinates().getPosition();
final double r2 = position.getNormSq();
acceleration = acceleration.subtract(mu / (r2 * FastMath.sqrt(r2)), position);
}
/** {@inheritDoc} */
public void addXYZAcceleration(final double x, final double y, final double z) {
acceleration = acceleration.add(new Vector3D(x, y, z));
}
/** {@inheritDoc} */
public void addAcceleration(final Vector3D gamma, final Frame frame)
throws OrekitException {
final Transform t = frame.getTransformTo(orbit.getFrame(), orbit.getDate());
final Vector3D gammInRefFrame = t.transformVector(gamma);
addXYZAcceleration(gammInRefFrame.getX(), gammInRefFrame.getY(), gammInRefFrame.getZ());
}
/** {@inheritDoc} */
public void addMassDerivative(final double q) {
// TODO: we don't compute (yet) the mass part of the Jacobian, we just ignore this
}
}
}