/* Copyright 2002-2017 CS Systèmes d'Information
* 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.orbits;
import org.hipparchus.RealFieldElement;
import org.hipparchus.geometry.euclidean.threed.FieldVector3D;
import org.hipparchus.linear.FieldDecompositionSolver;
import org.hipparchus.linear.FieldLUDecomposition;
import org.hipparchus.linear.FieldMatrix;
import org.hipparchus.linear.MatrixUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.errors.OrekitIllegalArgumentException;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitInternalError;
import org.orekit.errors.OrekitMessages;
import org.orekit.frames.Frame;
import org.orekit.frames.Transform;
import org.orekit.time.FieldAbsoluteDate;
import org.orekit.time.FieldTimeInterpolable;
import org.orekit.utils.FieldPVCoordinatesProvider;
import org.orekit.utils.TimeStampedFieldPVCoordinates;
import org.orekit.utils.TimeStampedPVCoordinates;
/**
* This class handles orbital parameters.
* <p>
* For user convenience, both the Cartesian and the equinoctial elements
* are provided by this class, regardless of the canonical representation
* implemented in the derived class (which may be classical keplerian
* elements for example).
* </p>
* <p>
* The parameters are defined in a frame specified by the user. It is important
* to make sure this frame is consistent: it probably is inertial and centered
* on the central body. This information is used for example by some
* force models.
* </p>
* <p>
* The object <code>OrbitalParameters</code> is guaranteed to be immutable.
* </p>
* @author Luc Maisonobe
* @author Guylaine Prat
* @author Fabien Maussion
* @author Véronique Pommier-Maurussane
*/
public abstract class FieldOrbit<T extends RealFieldElement<T>> implements FieldPVCoordinatesProvider<T>, FieldTimeInterpolable<FieldOrbit<T>, T> {
/** Frame in which are defined the orbital parameters. */
private final Frame frame;
/** Date of the orbital parameters. */
private final FieldAbsoluteDate<T> date;
/** Value of mu used to compute position and velocity (m³/s²). */
private final double mu;
/** Computed PVCoordinates. */
private transient TimeStampedFieldPVCoordinates<T> FieldPVCoordinates;
/** Jacobian of the orbital parameters with mean angle with respect to the Cartesian coordinates. */
private transient T[][] jacobianMeanWrtCartesian;
/** Jacobian of the Cartesian coordinates with respect to the orbital parameters with mean angle. */
private transient T[][] jacobianWrtParametersMean;
/** Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian coordinates. */
private transient T[][] jacobianEccentricWrtCartesian;
/** Jacobian of the Cartesian coordinates with respect to the orbital parameters with eccentric angle. */
private transient T[][] jacobianWrtParametersEccentric;
/** Jacobian of the orbital parameters with true angle with respect to the Cartesian coordinates. */
private transient T[][] jacobianTrueWrtCartesian;
/** Jacobian of the Cartesian coordinates with respect to the orbital parameters with true angle. */
private transient T[][] jacobianWrtParametersTrue;
/** Default constructor.
* Build a new instance with arbitrary default elements.
* @param frame the frame in which the parameters are defined
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param date date of the orbital parameters
* @param mu central attraction coefficient (m^3/s^2)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
protected FieldOrbit(final Frame frame, final FieldAbsoluteDate<T> date, final double mu)
throws IllegalArgumentException {
ensurePseudoInertialFrame(frame);
this.date = date;
this.mu = mu;
this.FieldPVCoordinates = null;
this.frame = frame;
jacobianMeanWrtCartesian = null;
jacobianWrtParametersMean = null;
jacobianEccentricWrtCartesian = null;
jacobianWrtParametersEccentric = null;
jacobianTrueWrtCartesian = null;
jacobianWrtParametersTrue = null;
}
/** Set the orbit from Cartesian parameters.
*
* <p> The acceleration provided in {@code FieldPVCoordinates} is accessible using
* {@link #getPVCoordinates()} and {@link #getPVCoordinates(Frame)}. All other methods
* use {@code mu} and the position to compute the acceleration, including
* {@link #shiftedBy(RealFieldElement)} and {@link #getPVCoordinates(FieldAbsoluteDate, Frame)}.
*
* @param FieldPVCoordinates the position and velocity in the inertial frame
* @param frame the frame in which the {@link TimeStampedPVCoordinates} are defined
* (<em>must</em> be a {@link Frame#isPseudoInertial pseudo-inertial frame})
* @param mu central attraction coefficient (m^3/s^2)
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
protected FieldOrbit(final TimeStampedFieldPVCoordinates<T> FieldPVCoordinates, final Frame frame, final double mu)
throws IllegalArgumentException {
ensurePseudoInertialFrame(frame);
this.date = FieldPVCoordinates.getDate();
this.mu = mu;
if (FieldPVCoordinates.getAcceleration().getNormSq().getReal() == 0.0) {
// the acceleration was not provided,
// compute it from Newtonian attraction
final T r2 = FieldPVCoordinates.getPosition().getNormSq();
final T r3 = r2.multiply(r2.sqrt());
this.FieldPVCoordinates = new TimeStampedFieldPVCoordinates<T>(FieldPVCoordinates.getDate(),
FieldPVCoordinates.getPosition(),
FieldPVCoordinates.getVelocity(),
new FieldVector3D<T> (r3.pow(-1).multiply(-mu), FieldPVCoordinates.getPosition()));
} else {
this.FieldPVCoordinates = FieldPVCoordinates;
}
this.frame = frame;
}
/** Get the orbit type.
* @return orbit type
*/
public abstract OrbitType getType();
/** Ensure the defining frame is a pseudo-inertial frame.
* @param frame frame to check
* @exception IllegalArgumentException if frame is not a {@link
* Frame#isPseudoInertial pseudo-inertial frame}
*/
private static void ensurePseudoInertialFrame(final Frame frame)
throws IllegalArgumentException {
if (!frame.isPseudoInertial()) {
throw new OrekitIllegalArgumentException(OrekitMessages.NON_PSEUDO_INERTIAL_FRAME,
frame.getName());
}
}
/** Get the frame in which the orbital parameters are defined.
* @return frame in which the orbital parameters are defined
*/
public Frame getFrame() {
return frame;
}
/**Transforms the FieldOrbit instance into an Orbit instance.
* @return Orbit instance with same properties
*/
public abstract Orbit toOrbit();
/** Get the semi-major axis.
* <p>Note that the semi-major axis is considered negative for hyperbolic orbits.</p>
* @return semi-major axis (m)
*/
public abstract T getA();
/** Get the first component of the equinoctial eccentricity vector.
* @return first component of the equinoctial eccentricity vector
*/
public abstract T getEquinoctialEx();
/** Get the second component of the equinoctial eccentricity vector.
* @return second component of the equinoctial eccentricity vector
*/
public abstract T getEquinoctialEy();
/** Get the first component of the inclination vector.
* @return first component of the inclination vector
*/
public abstract T getHx();
/** Get the second component of the inclination vector.
* @return second component of the inclination vector
*/
public abstract T getHy();
/** Get the eccentric longitude argument.
* @return E + ω + Ω eccentric longitude argument (rad)
*/
public abstract T getLE();
/** Get the true longitude argument.
* @return v + ω + Ω true longitude argument (rad)
*/
public abstract T getLv();
/** Get the mean longitude argument.
* @return M + ω + Ω mean longitude argument (rad)
*/
public abstract T getLM();
// Additional orbital elements
/** Get the eccentricity.
* @return eccentricity
*/
public abstract T getE();
/** Get the inclination.
* @return inclination (rad)
*/
public abstract T getI();
/** Get the central acceleration constant.
* @return central acceleration constant
*/
public double getMu() {
return mu;
}
/** Get the keplerian period.
* <p>The keplerian period is computed directly from semi major axis
* and central acceleration constant.</p>
* @return keplerian period in seconds, or positive infinity for hyperbolic orbits
*/
public T getKeplerianPeriod() {
final T a = getA();
return (a.getReal() < 0) ? getA().getField().getZero().add(Double.POSITIVE_INFINITY) : a.multiply(2 * FastMath.PI).multiply(a.divide(mu).sqrt());
}
/** Get the keplerian mean motion.
* <p>The keplerian mean motion is computed directly from semi major axis
* and central acceleration constant.</p>
* @return keplerian mean motion in radians per second
*/
public T getKeplerianMeanMotion() {
final T absA = getA().abs();
return absA.pow(-1).multiply(mu).sqrt().divide(absA);
}
/** Get the date of orbital parameters.
* @return date of the orbital parameters
*/
public FieldAbsoluteDate<T> getDate() {
return date;
}
/** Get the {@link TimeStampedPVCoordinates} in a specified frame.
* @param outputFrame frame in which the position/velocity coordinates shall be computed
* @return FieldPVCoordinates in the specified output frame
* @exception OrekitException if transformation between frames cannot be computed
* @see #getPVCoordinates()
*/
public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final Frame outputFrame)
throws OrekitException {
if (FieldPVCoordinates == null) {
FieldPVCoordinates = initFieldPVCoordinates();
}
// If output frame requested is the same as definition frame,
// PV coordinates are returned directly
if (outputFrame == frame) {
return FieldPVCoordinates;
}
// Else, PV coordinates are transformed to output frame
final Transform t = frame.getTransformTo(outputFrame, date.toAbsoluteDate()); //TODO CHECK THIS
return t.transformPVCoordinates(FieldPVCoordinates);
}
/** {@inheritDoc} */
public TimeStampedFieldPVCoordinates<T> getPVCoordinates(final FieldAbsoluteDate<T> otherDate, final Frame otherFrame)
throws OrekitException {
return shiftedBy(otherDate.durationFrom(getDate())).getPVCoordinates(otherFrame);
}
/** Get the {@link TimeStampedPVCoordinates} in definition frame.
* @return FieldPVCoordinates in the definition frame
* @see #getPVCoordinates(Frame)
*/
public TimeStampedFieldPVCoordinates<T> getPVCoordinates() {
if (FieldPVCoordinates == null) {
FieldPVCoordinates = initFieldPVCoordinates();
}
return FieldPVCoordinates;
}
/** Compute the position/velocity coordinates from the canonical parameters.
* @return computed position/velocity coordinates
*/
protected abstract TimeStampedFieldPVCoordinates<T> initFieldPVCoordinates();
/** Get a time-shifted orbit.
* <p>
* The orbit can be slightly shifted to close dates. This shift is based on
* a simple keplerian model. It is <em>not</em> intended as a replacement
* for proper orbit and attitude propagation but should be sufficient for
* small time shifts or coarse accuracy.
* </p>
* @param dt time shift in seconds
* @return a new orbit, shifted with respect to the instance (which is immutable)
*/
public abstract FieldOrbit<T> shiftedBy(T dt);
/** Compute the Jacobian of the orbital parameters with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j. This means each row corresponds to one orbital parameter
* whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
* </p>
* @param type type of the position angle to use
* @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
* is larger than 6x6, only the 6x6 upper left corner will be modified
*/
public void getJacobianWrtCartesian(final PositionAngle type, final T[][] jacobian) {
final T[][] cachedJacobian;
synchronized (this) {
switch (type) {
case MEAN :
if (jacobianMeanWrtCartesian == null) {
// first call, we need to compute the jacobian and cache it
jacobianMeanWrtCartesian = computeJacobianMeanWrtCartesian();
}
cachedJacobian = jacobianMeanWrtCartesian;
break;
case ECCENTRIC :
if (jacobianEccentricWrtCartesian == null) {
// first call, we need to compute the jacobian and cache it
jacobianEccentricWrtCartesian = computeJacobianEccentricWrtCartesian();
}
cachedJacobian = jacobianEccentricWrtCartesian;
break;
case TRUE :
if (jacobianTrueWrtCartesian == null) {
// first call, we need to compute the jacobian and cache it
jacobianTrueWrtCartesian = computeJacobianTrueWrtCartesian();
}
cachedJacobian = jacobianTrueWrtCartesian;
break;
default :
throw new OrekitInternalError(null);
}
}
// fill the user provided array
for (int i = 0; i < cachedJacobian.length; ++i) {
System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
}
}
/** Compute the Jacobian of the Cartesian parameters with respect to the orbital parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of Cartesian coordinate i of the orbit with
* respect to orbital parameter j. This means each row corresponds to one Cartesian coordinate
* x, y, z, xdot, ydot, zdot whereas columns 0 to 5 correspond to the orbital parameters.
* </p>
* @param type type of the position angle to use
* @param jacobian placeholder 6x6 (or larger) matrix to be filled with the Jacobian, if matrix
* is larger than 6x6, only the 6x6 upper left corner will be modified
*/
public void getJacobianWrtParameters(final PositionAngle type, final T[][] jacobian) {
final T[][] cachedJacobian;
synchronized (this) {
switch (type) {
case MEAN :
if (jacobianWrtParametersMean == null) {
// first call, we need to compute the jacobian and cache it
jacobianWrtParametersMean = createInverseJacobian(type);
}
cachedJacobian = jacobianWrtParametersMean;
break;
case ECCENTRIC :
if (jacobianWrtParametersEccentric == null) {
// first call, we need to compute the jacobian and cache it
jacobianWrtParametersEccentric = createInverseJacobian(type);
}
cachedJacobian = jacobianWrtParametersEccentric;
break;
case TRUE :
if (jacobianWrtParametersTrue == null) {
// first call, we need to compute the jacobian and cache it
jacobianWrtParametersTrue = createInverseJacobian(type);
}
cachedJacobian = jacobianWrtParametersTrue;
break;
default :
throw new OrekitInternalError(null);
}
}
// fill the user-provided array
for (int i = 0; i < cachedJacobian.length; ++i) {
System.arraycopy(cachedJacobian[i], 0, jacobian[i], 0, cachedJacobian[i].length);
}
}
/** Create an inverse Jacobian.
* @param type type of the position angle to use
* @return inverse Jacobian
*/
private T[][] createInverseJacobian(final PositionAngle type) {
// get the direct Jacobian
final T[][] directJacobian = MathArrays.buildArray(getA().getField(), 6, 6);
getJacobianWrtCartesian(type, directJacobian);
// invert the direct Jacobian
final FieldMatrix<T> matrix = MatrixUtils.createFieldMatrix(directJacobian);
final FieldDecompositionSolver<T> solver = new FieldLUDecomposition<T>(matrix).getSolver();
return solver.getInverse().getData();
}
/** Compute the Jacobian of the orbital parameters with mean angle with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
* whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
* </p>
* @return 6x6 Jacobian matrix
* @see #computeJacobianEccentricWrtCartesian()
* @see #computeJacobianTrueWrtCartesian()
*/
protected abstract T[][] computeJacobianMeanWrtCartesian();
/** Compute the Jacobian of the orbital parameters with eccentric angle with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
* whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
* </p>
* @return 6x6 Jacobian matrix
* @see #computeJacobianMeanWrtCartesian()
* @see #computeJacobianTrueWrtCartesian()
*/
protected abstract T[][] computeJacobianEccentricWrtCartesian();
/** Compute the Jacobian of the orbital parameters with true angle with respect to the Cartesian parameters.
* <p>
* Element {@code jacobian[i][j]} is the derivative of parameter i of the orbit with
* respect to Cartesian coordinate j. This means each row correspond to one orbital parameter
* whereas columns 0 to 5 correspond to the Cartesian coordinates x, y, z, xDot, yDot and zDot.
* </p>
* @return 6x6 Jacobian matrix
* @see #computeJacobianMeanWrtCartesian()
* @see #computeJacobianEccentricWrtCartesian()
*/
protected abstract T[][] computeJacobianTrueWrtCartesian();
/** Add the contribution of the Keplerian motion to parameters derivatives
* <p>
* This method is used by integration-based propagators to evaluate the part of Keplerian
* motion to evolution of the orbital state.
* </p>
* @param type type of the position angle in the state
* @param gm attraction coefficient to use
* @param pDot array containing orbital state derivatives to update (the Keplerian
* part must be <em>added</em> to the array components, as the array may already
* contain some non-zero elements corresponding to non-Keplerian parts)
*/
public abstract void addKeplerContribution(PositionAngle type, double gm, T[] pDot);
/** Fill a Jacobian half row with a single vector.
* @param a coefficient of the vector
* @param v vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a, final FieldVector3D<T> v, final T[] row, final int j) {
row[j] = a.multiply(v.getX());
row[j + 1] = a.multiply(v.getY());
row[j + 2] = a.multiply(v.getZ());
}
/** Fill a Jacobian half row with a linear combination of vectors.
* @param a1 coefficient of the first vector
* @param v1 first vector
* @param a2 coefficient of the second vector
* @param v2 second vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
final T[] row, final int j) {
row[j] = a1.linearCombination(a1, v1.getX(), a2, v2.getX());
row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY());
row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ());
// row[j] = a1.multiply(v1.getX()).add(a2.multiply(v2.getX()));
// row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY()));
// row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ()));
}
/** Fill a Jacobian half row with a linear combination of vectors.
* @param a1 coefficient of the first vector
* @param v1 first vector
* @param a2 coefficient of the second vector
* @param v2 second vector
* @param a3 coefficient of the third vector
* @param v3 third vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a1, final FieldVector3D<T> v1,
final T a2, final FieldVector3D<T> v2,
final T a3, final FieldVector3D<T> v3,
final T[] row, final int j) {
row[j] = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX());
row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY());
row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ());
// row[j] = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX()));
// row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY()));
// row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ()));
}
/** Fill a Jacobian half row with a linear combination of vectors.
* @param a1 coefficient of the first vector
* @param v1 first vector
* @param a2 coefficient of the second vector
* @param v2 second vector
* @param a3 coefficient of the third vector
* @param v3 third vector
* @param a4 coefficient of the fourth vector
* @param v4 fourth vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
final T[] row, final int j) {
row[j] = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX());
row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY());
row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ());
// row[j] = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX()));
// row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY()));
// row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ()));
}
/** Fill a Jacobian half row with a linear combination of vectors.
* @param a1 coefficient of the first vector
* @param v1 first vector
* @param a2 coefficient of the second vector
* @param v2 second vector
* @param a3 coefficient of the third vector
* @param v3 third vector
* @param a4 coefficient of the fourth vector
* @param v4 fourth vector
* @param a5 coefficient of the fifth vector
* @param v5 fifth vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
final T a5, final FieldVector3D<T> v5,
final T[] row, final int j) {
row[j] = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a5.multiply(v5.getX()));
row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a5.multiply(v5.getY()));
row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a5.multiply(v5.getZ()));
// row[j] = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX()));
// row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY()));
// row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ()));
}
/** Fill a Jacobian half row with a linear combination of vectors.
* @param a1 coefficient of the first vector
* @param v1 first vector
* @param a2 coefficient of the second vector
* @param v2 second vector
* @param a3 coefficient of the third vector
* @param v3 third vector
* @param a4 coefficient of the fourth vector
* @param v4 fourth vector
* @param a5 coefficient of the fifth vector
* @param v5 fifth vector
* @param a6 coefficient of the sixth vector
* @param v6 sixth vector
* @param row Jacobian matrix row
* @param j index of the first element to set (row[j], row[j+1] and row[j+2] will all be set)
*/
protected void fillHalfRow(final T a1, final FieldVector3D<T> v1, final T a2, final FieldVector3D<T> v2,
final T a3, final FieldVector3D<T> v3, final T a4, final FieldVector3D<T> v4,
final T a5, final FieldVector3D<T> v5, final T a6, final FieldVector3D<T> v6,
final T[] row, final int j) {
row[j] = a1.linearCombination(a1, v1.getX(), a2, v2.getX(), a3, v3.getX(), a4, v4.getX()).add(a1.linearCombination(a5, v5.getX(), a6, v6.getX()));
row[j + 1] = a1.linearCombination(a1, v1.getY(), a2, v2.getY(), a3, v3.getY(), a4, v4.getY()).add(a1.linearCombination(a5, v5.getY(), a6, v6.getY()));
row[j + 2] = a1.linearCombination(a1, v1.getZ(), a2, v2.getZ(), a3, v3.getZ(), a4, v4.getZ()).add(a1.linearCombination(a5, v5.getZ(), a6, v6.getZ()));
// row[j] = a1.multiply(v1.getX()).add(a2.multiply(v2.getX())).add(a3.multiply(v3.getX())).add(a4.multiply(v4.getX())).add(a5.multiply(v5.getX())).add(a6.multiply(v6.getX()));
// row[j + 1] = a1.multiply(v1.getY()).add(a2.multiply(v2.getY())).add(a3.multiply(v3.getY())).add(a4.multiply(v4.getY())).add(a5.multiply(v5.getY())).add(a6.multiply(v6.getY()));
// row[j + 2] = a1.multiply(v1.getZ()).add(a2.multiply(v2.getZ())).add(a3.multiply(v3.getZ())).add(a4.multiply(v4.getZ())).add(a5.multiply(v5.getZ())).add(a6.multiply(v6.getZ()));
}
}