AbstractGaussianContribution.java
/* Copyright 2002-2015 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
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*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
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package org.orekit.propagation.semianalytical.dsst.forces;
import org.apache.commons.math3.analysis.UnivariateVectorFunction;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.util.FastMath;
import org.orekit.attitudes.Attitude;
import org.orekit.attitudes.AttitudeProvider;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitExceptionWrapper;
import org.orekit.forces.ForceModel;
import org.orekit.frames.Frame;
import org.orekit.orbits.EquinoctialOrbit;
import org.orekit.orbits.Orbit;
import org.orekit.orbits.OrbitType;
import org.orekit.orbits.PositionAngle;
import org.orekit.propagation.SpacecraftState;
import org.orekit.propagation.numerical.TimeDerivativesEquations;
import org.orekit.propagation.semianalytical.dsst.utilities.AuxiliaryElements;
import org.orekit.propagation.semianalytical.dsst.utilities.CjSjCoefficient;
import org.orekit.propagation.semianalytical.dsst.utilities.ShortPeriodicsInterpolatedCoefficient;
import org.orekit.time.AbsoluteDate;
/** Common handling of {@link DSSTForceModel} methods for Gaussian contributions to DSST propagation.
* <p>
* This abstract class allows to provide easily a subset of {@link DSSTForceModel} methods
* for specific Gaussian contributions.
* </p><p>
* This class implements the notion of numerical averaging of the DSST theory.
* Numerical averaging is mainly used for non-conservative disturbing forces such as
* atmospheric drag and solar radiation pressure.
* </p><p>
* Gaussian contributions can be expressed as: da<sub>i</sub>/dt = δa<sub>i</sub>/δv . q<br>
* where:
* <ul>
* <li>a<sub>i</sub> are the six equinoctial elements</li>
* <li>v is the velocity vector</li>
* <li>q is the perturbing acceleration due to the considered force</li>
* </ul>
* The averaging process and other considerations lead to integrate this contribution
* over the true longitude L possibly taking into account some limits.
* </p><p>
* To create a numerically averaged contribution, one needs only to provide a
* {@link ForceModel} and to implement in the derived class the method:
* {@link #getLLimits(SpacecraftState)}.
* </p>
* @author Pascal Parraud
*/
public abstract class AbstractGaussianContribution implements DSSTForceModel {
/** Available orders for Gauss quadrature. */
private static final int[] GAUSS_ORDER = {12, 16, 20, 24, 32, 40, 48};
/** Max rank in Gauss quadrature orders array. */
private static final int MAX_ORDER_RANK = GAUSS_ORDER.length - 1;
/** Number of points for interpolation. */
private static final int INTERPOLATION_POINTS = 3;
/** Maximum value for j index. */
private static final int JMAX = 12;
// CHECKSTYLE: stop VisibilityModifierCheck
/** Retrograde factor. */
protected int I;
/** a. */
protected double a;
/** e<sub>x</sub>. */
protected double k;
/** e<sub>y</sub>. */
protected double h;
/** h<sub>x</sub>. */
protected double q;
/** h<sub>y</sub>. */
protected double p;
/** Eccentricity. */
protected double ecc;
/** Kepler mean motion: n = sqrt(μ / a³). */
protected double n;
/** Mean longitude. */
protected double lm;
/** Equinoctial frame f vector. */
protected Vector3D f;
/** Equinoctial frame g vector. */
protected Vector3D g;
/** Equinoctial frame w vector. */
protected Vector3D w;
/** A = sqrt(μ * a). */
protected double A;
/** B = sqrt(1 - h² - k²). */
protected double B;
/** C = 1 + p² + q². */
protected double C;
/** 2 / (n² * a) . */
protected double ton2a;
/** 1 / A .*/
protected double ooA;
/** 1 / (A * B) .*/
protected double ooAB;
/** C / (2 * A * B) .*/
protected double co2AB;
/** 1 / (1 + B) .*/
protected double ooBpo;
/** 1 / μ .*/
protected double ooMu;
/** μ .*/
protected double mu;
// CHECKSTYLE: resume VisibilityModifierCheck
/** Contribution to be numerically averaged. */
private final ForceModel contribution;
/** Gauss integrator. */
private final double threshold;
/** Gauss integrator. */
private GaussQuadrature integrator;
/** Flag for Gauss order computation. */
private boolean isDirty;
/** Attitude provider. */
private AttitudeProvider attitudeProvider;
/** The C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup> coefficients used to compute
* the short-periodic gaussian contribution. */
private GaussianShortPeriodicCoefficients gaussianSPCoefs;
/** The frame used to describe the orbits. */
private Frame frame;
/** Build a new instance.
*
* @param threshold tolerance for the choice of the Gauss quadrature order
* @param contribution the {@link ForceModel} to be numerically averaged
*/
protected AbstractGaussianContribution(final double threshold,
final ForceModel contribution) {
this.contribution = contribution;
this.threshold = threshold;
this.integrator = new GaussQuadrature(GAUSS_ORDER[MAX_ORDER_RANK]);
this.isDirty = true;
}
/** {@inheritDoc} */
@Override
public void initialize(final AuxiliaryElements aux, final boolean meanOnly)
throws OrekitException {
// save the frame
this.frame = aux.getFrame();
if (!meanOnly) {
// initialize the short periodic coefficient generator, if needed.
this.gaussianSPCoefs = new GaussianShortPeriodicCoefficients(JMAX, INTERPOLATION_POINTS);
}
}
/** {@inheritDoc} */
@Override
public void initializeStep(final AuxiliaryElements aux)
throws OrekitException {
// Equinoctial elements
a = aux.getSma();
k = aux.getK();
h = aux.getH();
q = aux.getQ();
p = aux.getP();
// Retrograde factor
I = aux.getRetrogradeFactor();
// Eccentricity
ecc = aux.getEcc();
// Equinoctial coefficients
A = aux.getA();
B = aux.getB();
C = aux.getC();
// Equinoctial frame vectors
f = aux.getVectorF();
g = aux.getVectorG();
w = aux.getVectorW();
// Kepler mean motion
n = aux.getMeanMotion();
// Mean longitude
lm = aux.getLM();
// 1 / A
ooA = 1. / A;
// 1 / AB
ooAB = ooA / B;
// C / 2AB
co2AB = C * ooAB / 2.;
// 1 / (1 + B)
ooBpo = 1. / (1. + B);
// 2 / (n² * a)
ton2a = 2. / (n * n * a);
// mu
mu = aux.getMu();
// 1 / mu
ooMu = 1. / mu;
}
/** {@inheritDoc} */
@Override
public double[] getMeanElementRate(final SpacecraftState state) throws OrekitException {
double[] meanElementRate = new double[6];
// Computes the limits for the integral
final double[] ll = getLLimits(state);
// Computes integrated mean element rates if Llow < Lhigh
if (ll[0] < ll[1]) {
meanElementRate = getMeanElementRate(state, integrator, ll[0], ll[1]);
if (isDirty) {
boolean next = true;
for (int i = 0; i < MAX_ORDER_RANK && next; i++) {
final double[] meanRates = getMeanElementRate(state, new GaussQuadrature(GAUSS_ORDER[i]), ll[0], ll[1]);
if (getRatesDiff(meanElementRate, meanRates) < threshold) {
integrator = new GaussQuadrature(GAUSS_ORDER[i]);
next = false;
}
}
isDirty = false;
}
}
return meanElementRate;
}
/** Compute the acceleration due to the non conservative perturbing force.
*
* @param state current state information: date, kinematics, attitude
* @return the perturbing acceleration
* @exception OrekitException if some specific error occurs
*/
protected Vector3D getAcceleration(final SpacecraftState state)
throws OrekitException {
final AccelerationRetriever retriever = new AccelerationRetriever(state);
contribution.addContribution(state, retriever);
return retriever.getAcceleration();
}
/** Compute the limits in L, the true longitude, for integration.
*
* @param state current state information: date, kinematics, attitude
* @return the integration limits in L
* @exception OrekitException if some specific error occurs
*/
protected abstract double[] getLLimits(final SpacecraftState state) throws OrekitException;
/** Computes the mean equinoctial elements rates da<sub>i</sub> / dt.
*
* @param state current state
* @param gauss Gauss quadrature
* @param low lower bound of the integral interval
* @param high upper bound of the integral interval
* @return the mean element rates
* @throws OrekitException if some specific error occurs
*/
private double[] getMeanElementRate(final SpacecraftState state,
final GaussQuadrature gauss,
final double low,
final double high) throws OrekitException {
final double[] meanElementRate = gauss.integrate(new IntegrableFunction(state, true, 0), low, high);
// Constant multiplier for integral
final double coef = 1. / (2. * FastMath.PI * B);
// Corrects mean element rates
for (int i = 0; i < 6; i++) {
meanElementRate[i] *= coef;
}
return meanElementRate;
}
/** Estimates the weighted magnitude of the difference between 2 sets of equinoctial elements rates.
*
* @param meanRef reference rates
* @param meanCur current rates
* @return estimated magnitude of weighted differences
*/
private double getRatesDiff(final double[] meanRef, final double[] meanCur) {
double maxDiff = FastMath.abs(meanRef[0] - meanCur[0]) / a;
// Corrects mean element rates
for (int i = 1; i < meanRef.length; i++) {
final double diff = FastMath.abs(meanRef[i] - meanCur[i]);
if (maxDiff < diff) maxDiff = diff;
}
return maxDiff;
}
/** {@inheritDoc} */
@Override
public void registerAttitudeProvider(final AttitudeProvider provider) {
this.attitudeProvider = provider;
}
/** {@inheritDoc} */
@Override
public double[] getShortPeriodicVariations(final AbsoluteDate date,
final double[] meanElements) throws OrekitException {
// Build an Orbit object from the mean elements
final Orbit meanOrbit = OrbitType.EQUINOCTIAL.mapArrayToOrbit(
meanElements, PositionAngle.MEAN, date, this.mu, this.frame);
// Get the True longitude L
final double L = meanOrbit.getLv();
// Compute the center (l - λ)
final double center = L - meanElements[5];
// Compute (l - λ)²
final double center2 = center * center;
// Initialize short periodic variations
final double[] shortPeriodicVariation = new double[6];
for (int i = 0; i < 6; i++) {
shortPeriodicVariation[i] = gaussianSPCoefs.getCij(i, 0, date) +
center * gaussianSPCoefs.getDij(i, 1, date);
if (i == 5) {
shortPeriodicVariation[i] += center2 * gaussianSPCoefs.getDij(i, 2, date);
}
}
for (int j = 1; j <= JMAX; j++) {
for (int i = 0; i < 6; i++) {
// Get Cij and Sij
final double cij = gaussianSPCoefs.getCij(i, j, date);
final double sij = gaussianSPCoefs.getSij(i, j, date);
// add corresponding term to the short periodic variation
shortPeriodicVariation[i] += cij * FastMath.cos(j * L);
shortPeriodicVariation[i] += sij * FastMath.sin(j * L);
}
}
return shortPeriodicVariation;
}
/** {@inheritDoc} */
@Override
public void computeShortPeriodicsCoefficients(final SpacecraftState state)
throws OrekitException {
//Compute the coefficients
gaussianSPCoefs.computeCoefficients(state);
}
/** {@inheritDoc} */
@Override
public void resetShortPeriodicsCoefficients() {
if (gaussianSPCoefs != null) {
// reset the coefficients
gaussianSPCoefs.resetCoefficients();
}
}
/** Internal class for retrieving acceleration from a {@link ForceModel}. */
private static class AccelerationRetriever implements TimeDerivativesEquations {
/** acceleration vector. */
private Vector3D acceleration;
/** state. */
private final SpacecraftState state;
/** Simple constructor.
* @param state input state
*/
public AccelerationRetriever(final SpacecraftState state) {
this.acceleration = Vector3D.ZERO;
this.state = state;
}
/** {@inheritDoc} */
@Override
public void addKeplerContribution(final double mu) {
}
/** {@inheritDoc} */
@Override
public void addXYZAcceleration(final double x, final double y,
final double z) {
//TODO How to be sure we are in the good frame ???
acceleration = new Vector3D(x, y, z);
}
/** {@inheritDoc} */
@Override
public void addAcceleration(final Vector3D gamma, final Frame frame)
throws OrekitException {
acceleration = frame.getTransformTo(state.getFrame(),
state.getDate()).transformVector(gamma);
}
/** {@inheritDoc} */
@Override
public void addMassDerivative(final double q) {
}
/** Get the acceleration vector.
* @return acceleration vector
*/
public Vector3D getAcceleration() {
return acceleration;
}
}
/** Internal class for numerical quadrature. */
private class IntegrableFunction implements UnivariateVectorFunction {
/** Current state. */
private final SpacecraftState state;
/** Signal that this class is used to compute the values required by the mean element variations
* or by the short periodic element variations. */
private final boolean meanMode;
/** The j index.
* <p>
* Used only for short periodic variation. Ignored for mean elements variation.
* </p> */
private final int j;
/** Build a new instance.
* @param state current state information: date, kinematics, attitude
* @param meanMode if true return the value associated to the mean elements variation,
* if false return the values associated to the short periodic elements variation
* @param j the j index. used only for short periodic variation. Ignored for mean elements variation.
*/
public IntegrableFunction(final SpacecraftState state, final boolean meanMode, final int j) {
this.state = state;
this.meanMode = meanMode;
this.j = j;
}
/** {@inheritDoc} */
@Override
public double[] value(final double x) {
//Compute the time difference from the true longitude difference
final double shiftedLm = trueToMean(x);
final double dLm = shiftedLm - lm;
final double dt = dLm / n;
final double cosL = FastMath.cos(x);
final double sinL = FastMath.sin(x);
final double roa = B * B / (1. + h * sinL + k * cosL);
final double roa2 = roa * roa;
final double r = a * roa;
final double X = r * cosL;
final double Y = r * sinL;
final double naob = n * a / B;
final double Xdot = -naob * (h + sinL);
final double Ydot = naob * (k + cosL);
final Vector3D vel = new Vector3D(Xdot, f, Ydot, g);
// Compute acceleration
Vector3D acc = Vector3D.ZERO;
try {
// shift the orbit to dt
final Orbit shiftedOrbit = state.getOrbit().shiftedBy(dt);
// Recompose an orbit with time held fixed to be compliant with DSST theory
final Orbit recomposedOrbit =
new EquinoctialOrbit(shiftedOrbit.getA(),
shiftedOrbit.getEquinoctialEx(),
shiftedOrbit.getEquinoctialEy(),
shiftedOrbit.getHx(),
shiftedOrbit.getHy(),
shiftedOrbit.getLv(),
PositionAngle.TRUE,
shiftedOrbit.getFrame(),
state.getDate(),
shiftedOrbit.getMu());
// Get the corresponding attitude
final Attitude recomposedAttitude =
attitudeProvider.getAttitude(recomposedOrbit,
recomposedOrbit.getDate(),
recomposedOrbit.getFrame());
// create shifted SpacecraftState with attitude at specified time
final SpacecraftState shiftedState =
new SpacecraftState(recomposedOrbit, recomposedAttitude, state.getMass());
acc = getAcceleration(shiftedState);
} catch (OrekitException oe) {
throw new OrekitExceptionWrapper(oe);
}
//Compute the derivatives of the elements by the speed
final double[] deriv = new double[6];
// da/dv
deriv[0] = getAoV(vel).dotProduct(acc);
// dex/dv
deriv[1] = getKoV(X, Y, Xdot, Ydot).dotProduct(acc);
// dey/dv
deriv[2] = getHoV(X, Y, Xdot, Ydot).dotProduct(acc);
// dhx/dv
deriv[3] = getQoV(X).dotProduct(acc);
// dhy/dv
deriv[4] = getPoV(Y).dotProduct(acc);
// dλ/dv
deriv[5] = getLoV(X, Y, Xdot, Ydot).dotProduct(acc);
// Compute mean elements rates
double[] val = null;
if (meanMode) {
val = new double[6];
for (int i = 0; i < 6; i++) {
// da<sub>i</sub>/dt
val[i] = roa2 * deriv[i];
}
} else {
val = new double [12];
//Compute cos(j*L) and sin(j*L);
final double cosjL = j == 1 ? cosL : FastMath.cos(j * x);
final double sinjL = j == 1 ? sinL : FastMath.sin(j * x);
for (int i = 0; i < 6; i++) {
// da<sub>i</sub>/dv * cos(jL)
val[i] = cosjL * deriv[i];
// da<sub>i</sub>/dv * sin(jL)
val[i + 6] = sinjL * deriv[i];
}
}
return val;
}
/** Converts true longitude to eccentric longitude.
* @param lv True longitude
* @return Eccentric longitude
*/
private double trueToEccentric (final double lv) {
final double cosLv = FastMath.cos(lv);
final double sinLv = FastMath.sin(lv);
final double num = h * cosLv - k * sinLv;
final double den = B + 1 + k * cosLv + h * sinLv;
return lv + 2 * FastMath.atan(num / den);
}
/** Converts eccentric longitude to mean longitude.
* @param le Eccentric longitude
* @return Mean longitude
*/
private double eccentricToMean (final double le) {
return le - k * FastMath.sin(le) + h * FastMath.cos(le);
}
/** Converts true longitude to mean longitude.
* @param lv True longitude
* @return Eccentric longitude
*/
private double trueToMean (final double lv) {
return eccentricToMean(trueToEccentric(lv));
}
/** Compute δa/δv.
* @param vel satellite velocity
* @return δa/δv
*/
private Vector3D getAoV(final Vector3D vel) {
return new Vector3D(ton2a, vel);
}
/** Compute δh/δv.
* @param X satellite position component along f, equinoctial reference frame 1st vector
* @param Y satellite position component along g, equinoctial reference frame 2nd vector
* @param Xdot satellite velocity component along f, equinoctial reference frame 1st vector
* @param Ydot satellite velocity component along g, equinoctial reference frame 2nd vector
* @return δh/δv
*/
private Vector3D getHoV(final double X, final double Y, final double Xdot, final double Ydot) {
final double kf = (2. * Xdot * Y - X * Ydot) * ooMu;
final double kg = X * Xdot * ooMu;
final double kw = k * (I * q * Y - p * X) * ooAB;
return new Vector3D(kf, f, -kg, g, kw, w);
}
/** Compute δk/δv.
* @param X satellite position component along f, equinoctial reference frame 1st vector
* @param Y satellite position component along g, equinoctial reference frame 2nd vector
* @param Xdot satellite velocity component along f, equinoctial reference frame 1st vector
* @param Ydot satellite velocity component along g, equinoctial reference frame 2nd vector
* @return δk/δv
*/
private Vector3D getKoV(final double X, final double Y, final double Xdot, final double Ydot) {
final double kf = Y * Ydot * ooMu;
final double kg = (2. * X * Ydot - Xdot * Y) * ooMu;
final double kw = h * (I * q * Y - p * X) * ooAB;
return new Vector3D(-kf, f, kg, g, -kw, w);
}
/** Compute δp/δv.
* @param Y satellite position component along g, equinoctial reference frame 2nd vector
* @return δp/δv
*/
private Vector3D getPoV(final double Y) {
return new Vector3D(co2AB * Y, w);
}
/** Compute δq/δv.
* @param X satellite position component along f, equinoctial reference frame 1st vector
* @return δq/δv
*/
private Vector3D getQoV(final double X) {
return new Vector3D(I * co2AB * X, w);
}
/** Compute δλ/δv.
* @param X satellite position component along f, equinoctial reference frame 1st vector
* @param Y satellite position component along g, equinoctial reference frame 2nd vector
* @param Xdot satellite velocity component along f, equinoctial reference frame 1st vector
* @param Ydot satellite velocity component along g, equinoctial reference frame 2nd vector
* @return δλ/δv
*/
private Vector3D getLoV(final double X, final double Y, final double Xdot, final double Ydot) {
final Vector3D pos = new Vector3D(X, f, Y, g);
final Vector3D v2 = new Vector3D(k, getHoV(X, Y, Xdot, Ydot), -h, getKoV(X, Y, Xdot, Ydot));
return new Vector3D(-2. * ooA, pos, ooBpo, v2, (I * q * Y - p * X) * ooA, w);
}
}
/** Class used to {@link #integrate(UnivariateVectorFunction, double, double) integrate}
* a {@link org.apache.commons.math3.analysis.UnivariateVectorFunction function}
* of the orbital elements using the Gaussian quadrature rule to get the acceleration.
*/
private static class GaussQuadrature {
// CHECKSTYLE: stop NoWhitespaceAfter
// Points and weights for the available quadrature orders
/** Points for quadrature of order 12. */
private static final double[] P_12 = {
-0.98156063424671910000,
-0.90411725637047490000,
-0.76990267419430470000,
-0.58731795428661740000,
-0.36783149899818024000,
-0.12523340851146890000,
0.12523340851146890000,
0.36783149899818024000,
0.58731795428661740000,
0.76990267419430470000,
0.90411725637047490000,
0.98156063424671910000
};
/** Weights for quadrature of order 12. */
private static final double[] W_12 = {
0.04717533638651220000,
0.10693932599531830000,
0.16007832854334633000,
0.20316742672306584000,
0.23349253653835478000,
0.24914704581340286000,
0.24914704581340286000,
0.23349253653835478000,
0.20316742672306584000,
0.16007832854334633000,
0.10693932599531830000,
0.04717533638651220000
};
/** Points for quadrature of order 16. */
private static final double[] P_16 = {
-0.98940093499164990000,
-0.94457502307323260000,
-0.86563120238783160000,
-0.75540440835500310000,
-0.61787624440264380000,
-0.45801677765722737000,
-0.28160355077925890000,
-0.09501250983763745000,
0.09501250983763745000,
0.28160355077925890000,
0.45801677765722737000,
0.61787624440264380000,
0.75540440835500310000,
0.86563120238783160000,
0.94457502307323260000,
0.98940093499164990000
};
/** Weights for quadrature of order 16. */
private static final double[] W_16 = {
0.02715245941175405800,
0.06225352393864777000,
0.09515851168249283000,
0.12462897125553388000,
0.14959598881657685000,
0.16915651939500256000,
0.18260341504492360000,
0.18945061045506847000,
0.18945061045506847000,
0.18260341504492360000,
0.16915651939500256000,
0.14959598881657685000,
0.12462897125553388000,
0.09515851168249283000,
0.06225352393864777000,
0.02715245941175405800
};
/** Points for quadrature of order 20. */
private static final double[] P_20 = {
-0.99312859918509490000,
-0.96397192727791390000,
-0.91223442825132600000,
-0.83911697182221890000,
-0.74633190646015080000,
-0.63605368072651510000,
-0.51086700195082700000,
-0.37370608871541955000,
-0.22778585114164507000,
-0.07652652113349734000,
0.07652652113349734000,
0.22778585114164507000,
0.37370608871541955000,
0.51086700195082700000,
0.63605368072651510000,
0.74633190646015080000,
0.83911697182221890000,
0.91223442825132600000,
0.96397192727791390000,
0.99312859918509490000
};
/** Weights for quadrature of order 20. */
private static final double[] W_20 = {
0.01761400713915226400,
0.04060142980038684000,
0.06267204833410904000,
0.08327674157670477000,
0.10193011981724048000,
0.11819453196151844000,
0.13168863844917678000,
0.14209610931838212000,
0.14917298647260380000,
0.15275338713072600000,
0.15275338713072600000,
0.14917298647260380000,
0.14209610931838212000,
0.13168863844917678000,
0.11819453196151844000,
0.10193011981724048000,
0.08327674157670477000,
0.06267204833410904000,
0.04060142980038684000,
0.01761400713915226400
};
/** Points for quadrature of order 24. */
private static final double[] P_24 = {
-0.99518721999702130000,
-0.97472855597130950000,
-0.93827455200273270000,
-0.88641552700440100000,
-0.82000198597390300000,
-0.74012419157855440000,
-0.64809365193697550000,
-0.54542147138883950000,
-0.43379350762604520000,
-0.31504267969616340000,
-0.19111886747361634000,
-0.06405689286260563000,
0.06405689286260563000,
0.19111886747361634000,
0.31504267969616340000,
0.43379350762604520000,
0.54542147138883950000,
0.64809365193697550000,
0.74012419157855440000,
0.82000198597390300000,
0.88641552700440100000,
0.93827455200273270000,
0.97472855597130950000,
0.99518721999702130000
};
/** Weights for quadrature of order 24. */
private static final double[] W_24 = {
0.01234122979998733500,
0.02853138862893380600,
0.04427743881741981000,
0.05929858491543691500,
0.07334648141108027000,
0.08619016153195320000,
0.09761865210411391000,
0.10744427011596558000,
0.11550566805372553000,
0.12167047292780335000,
0.12583745634682825000,
0.12793819534675221000,
0.12793819534675221000,
0.12583745634682825000,
0.12167047292780335000,
0.11550566805372553000,
0.10744427011596558000,
0.09761865210411391000,
0.08619016153195320000,
0.07334648141108027000,
0.05929858491543691500,
0.04427743881741981000,
0.02853138862893380600,
0.01234122979998733500
};
/** Points for quadrature of order 32. */
private static final double[] P_32 = {
-0.99726386184948160000,
-0.98561151154526840000,
-0.96476225558750640000,
-0.93490607593773970000,
-0.89632115576605220000,
-0.84936761373256990000,
-0.79448379596794250000,
-0.73218211874028970000,
-0.66304426693021520000,
-0.58771575724076230000,
-0.50689990893222950000,
-0.42135127613063540000,
-0.33186860228212767000,
-0.23928736225213710000,
-0.14447196158279646000,
-0.04830766568773831000,
0.04830766568773831000,
0.14447196158279646000,
0.23928736225213710000,
0.33186860228212767000,
0.42135127613063540000,
0.50689990893222950000,
0.58771575724076230000,
0.66304426693021520000,
0.73218211874028970000,
0.79448379596794250000,
0.84936761373256990000,
0.89632115576605220000,
0.93490607593773970000,
0.96476225558750640000,
0.98561151154526840000,
0.99726386184948160000
};
/** Weights for quadrature of order 32. */
private static final double[] W_32 = {
0.00701861000947013600,
0.01627439473090571200,
0.02539206530926214200,
0.03427386291302141000,
0.04283589802222658600,
0.05099805926237621600,
0.05868409347853559000,
0.06582222277636193000,
0.07234579410884862000,
0.07819389578707042000,
0.08331192422694673000,
0.08765209300440380000,
0.09117387869576390000,
0.09384439908080441000,
0.09563872007927487000,
0.09654008851472784000,
0.09654008851472784000,
0.09563872007927487000,
0.09384439908080441000,
0.09117387869576390000,
0.08765209300440380000,
0.08331192422694673000,
0.07819389578707042000,
0.07234579410884862000,
0.06582222277636193000,
0.05868409347853559000,
0.05099805926237621600,
0.04283589802222658600,
0.03427386291302141000,
0.02539206530926214200,
0.01627439473090571200,
0.00701861000947013600
};
/** Points for quadrature of order 40. */
private static final double[] P_40 = {
-0.99823770971055930000,
-0.99072623869945710000,
-0.97725994998377420000,
-0.95791681921379170000,
-0.93281280827867660000,
-0.90209880696887420000,
-0.86595950321225960000,
-0.82461223083331170000,
-0.77830565142651940000,
-0.72731825518992710000,
-0.67195668461417960000,
-0.61255388966798030000,
-0.54946712509512820000,
-0.48307580168617870000,
-0.41377920437160500000,
-0.34199409082575850000,
-0.26815218500725370000,
-0.19269758070137110000,
-0.11608407067525522000,
-0.03877241750605081600,
0.03877241750605081600,
0.11608407067525522000,
0.19269758070137110000,
0.26815218500725370000,
0.34199409082575850000,
0.41377920437160500000,
0.48307580168617870000,
0.54946712509512820000,
0.61255388966798030000,
0.67195668461417960000,
0.72731825518992710000,
0.77830565142651940000,
0.82461223083331170000,
0.86595950321225960000,
0.90209880696887420000,
0.93281280827867660000,
0.95791681921379170000,
0.97725994998377420000,
0.99072623869945710000,
0.99823770971055930000
};
/** Weights for quadrature of order 40. */
private static final double[] W_40 = {
0.00452127709853309800,
0.01049828453115270400,
0.01642105838190797300,
0.02224584919416689000,
0.02793700698002338000,
0.03346019528254786500,
0.03878216797447199000,
0.04387090818567333000,
0.04869580763507221000,
0.05322784698393679000,
0.05743976909939157000,
0.06130624249292891000,
0.06480401345660108000,
0.06791204581523394000,
0.07061164739128681000,
0.07288658239580408000,
0.07472316905796833000,
0.07611036190062619000,
0.07703981816424793000,
0.07750594797842482000,
0.07750594797842482000,
0.07703981816424793000,
0.07611036190062619000,
0.07472316905796833000,
0.07288658239580408000,
0.07061164739128681000,
0.06791204581523394000,
0.06480401345660108000,
0.06130624249292891000,
0.05743976909939157000,
0.05322784698393679000,
0.04869580763507221000,
0.04387090818567333000,
0.03878216797447199000,
0.03346019528254786500,
0.02793700698002338000,
0.02224584919416689000,
0.01642105838190797300,
0.01049828453115270400,
0.00452127709853309800
};
/** Points for quadrature of order 48. */
private static final double[] P_48 = {
-0.99877100725242610000,
-0.99353017226635080000,
-0.98412458372282700000,
-0.97059159254624720000,
-0.95298770316043080000,
-0.93138669070655440000,
-0.90587913671556960000,
-0.87657202027424800000,
-0.84358826162439350000,
-0.80706620402944250000,
-0.76715903251574020000,
-0.72403413092381470000,
-0.67787237963266400000,
-0.62886739677651370000,
-0.57722472608397270000,
-0.52316097472223300000,
-0.46690290475095840000,
-0.40868648199071680000,
-0.34875588629216070000,
-0.28736248735545555000,
-0.22476379039468908000,
-0.16122235606889174000,
-0.09700469920946270000,
-0.03238017096286937000,
0.03238017096286937000,
0.09700469920946270000,
0.16122235606889174000,
0.22476379039468908000,
0.28736248735545555000,
0.34875588629216070000,
0.40868648199071680000,
0.46690290475095840000,
0.52316097472223300000,
0.57722472608397270000,
0.62886739677651370000,
0.67787237963266400000,
0.72403413092381470000,
0.76715903251574020000,
0.80706620402944250000,
0.84358826162439350000,
0.87657202027424800000,
0.90587913671556960000,
0.93138669070655440000,
0.95298770316043080000,
0.97059159254624720000,
0.98412458372282700000,
0.99353017226635080000,
0.99877100725242610000
};
/** Weights for quadrature of order 48. */
private static final double[] W_48 = {
0.00315334605230596250,
0.00732755390127620800,
0.01147723457923446900,
0.01557931572294386600,
0.01961616045735556700,
0.02357076083932435600,
0.02742650970835688000,
0.03116722783279807000,
0.03477722256477045000,
0.03824135106583080600,
0.04154508294346483000,
0.04467456085669424000,
0.04761665849249054000,
0.05035903555385448000,
0.05289018948519365000,
0.05519950369998416500,
0.05727729210040315000,
0.05911483969839566000,
0.06070443916589384000,
0.06203942315989268000,
0.06311419228625403000,
0.06392423858464817000,
0.06446616443595010000,
0.06473769681268386000,
0.06473769681268386000,
0.06446616443595010000,
0.06392423858464817000,
0.06311419228625403000,
0.06203942315989268000,
0.06070443916589384000,
0.05911483969839566000,
0.05727729210040315000,
0.05519950369998416500,
0.05289018948519365000,
0.05035903555385448000,
0.04761665849249054000,
0.04467456085669424000,
0.04154508294346483000,
0.03824135106583080600,
0.03477722256477045000,
0.03116722783279807000,
0.02742650970835688000,
0.02357076083932435600,
0.01961616045735556700,
0.01557931572294386600,
0.01147723457923446900,
0.00732755390127620800,
0.00315334605230596250
};
// CHECKSTYLE: resume NoWhitespaceAfter
/** Node points. */
private final double[] nodePoints;
/** Node weights. */
private final double[] nodeWeights;
/** Creates a Gauss integrator of the given order.
*
* @param numberOfPoints Order of the integration rule.
*/
public GaussQuadrature(final int numberOfPoints) {
switch(numberOfPoints) {
case 12 :
this.nodePoints = P_12.clone();
this.nodeWeights = W_12.clone();
break;
case 16 :
this.nodePoints = P_16.clone();
this.nodeWeights = W_16.clone();
break;
case 20 :
this.nodePoints = P_20.clone();
this.nodeWeights = W_20.clone();
break;
case 24 :
this.nodePoints = P_24.clone();
this.nodeWeights = W_24.clone();
break;
case 32 :
this.nodePoints = P_32.clone();
this.nodeWeights = W_32.clone();
break;
case 40 :
this.nodePoints = P_40.clone();
this.nodeWeights = W_40.clone();
break;
case 48 :
default :
this.nodePoints = P_48.clone();
this.nodeWeights = W_48.clone();
break;
}
}
/** Integrates a given function on the given interval.
*
* @param f Function to integrate.
* @param lowerBound Lower bound of the integration interval.
* @param upperBound Upper bound of the integration interval.
* @return the integral of the weighted function.
*/
public double[] integrate(final UnivariateVectorFunction f,
final double lowerBound, final double upperBound) {
final double[] adaptedPoints = nodePoints.clone();
final double[] adaptedWeights = nodeWeights.clone();
transform(adaptedPoints, adaptedWeights, lowerBound, upperBound);
return basicIntegrate(f, adaptedPoints, adaptedWeights);
}
/** Performs a change of variable so that the integration
* can be performed on an arbitrary interval {@code [a, b]}.
* <p>
* It is assumed that the natural interval is {@code [-1, 1]}.
* </p>
*
* @param points Points to adapt to the new interval.
* @param weights Weights to adapt to the new interval.
* @param a Lower bound of the integration interval.
* @param b Lower bound of the integration interval.
*/
private void transform(final double[] points, final double[] weights,
final double a, final double b) {
// Scaling
final double scale = (b - a) / 2;
final double shift = a + scale;
for (int i = 0; i < points.length; i++) {
points[i] = points[i] * scale + shift;
weights[i] *= scale;
}
}
/** Returns an estimate of the integral of {@code f(x) * w(x)},
* where {@code w} is a weight function that depends on the actual
* flavor of the Gauss integration scheme.
*
* @param f Function to integrate.
* @param points Nodes.
* @param weights Nodes weights.
* @return the integral of the weighted function.
*/
private double[] basicIntegrate(final UnivariateVectorFunction f,
final double[] points,
final double[] weights) {
double x = points[0];
double w = weights[0];
double[] v = f.value(x);
final double[] y = new double[v.length];
for (int j = 0; j < v.length; j++) {
y[j] = w * v[j];
}
final double[] t = y.clone();
final double[] c = new double[v.length];
final double[] s = t.clone();
for (int i = 1; i < points.length; i++) {
x = points[i];
w = weights[i];
v = f.value(x);
for (int j = 0; j < v.length; j++) {
y[j] = w * v[j] - c[j];
t[j] = s[j] + y[j];
c[j] = (t[j] - s[j]) - y[j];
s[j] = t[j];
}
}
return s;
}
}
/** Compute the C<sub>i</sub><sup>j</sup> and the S<sub>i</sub><sup>j</sup> coefficients.
* <p>
* Those coefficients are given in Danielson paper by expression 4.4-(6)
* </p>
* @author Petre Bazavan
* @author Lucian Barbulescu
*/
private class FourierCjSjCoefficients {
/** Maximum possible value for j. */
private final int jMax;
/** The C<sub>i</sub><sup>j</sup> coefficients.
* <p>
* the index i corresponds to the following elements: <br/>
* - 0 for a <br>
* - 1 for k <br>
* - 2 for h <br>
* - 3 for q <br>
* - 4 for p <br>
* - 5 for λ <br>
* </p>
*/
private final double[][] cCoef;
/** The C<sub>i</sub><sup>j</sup> coefficients.
* <p>
* the index i corresponds to the following elements: <br/>
* - 0 for a <br>
* - 1 for k <br>
* - 2 for h <br>
* - 3 for q <br>
* - 4 for p <br>
* - 5 for λ <br>
* </p>
*/
private final double[][] sCoef;
/** Standard constructor.
* @param state the current state
* @param jMax maximum value for j
* @throws OrekitException in case of an error
*/
public FourierCjSjCoefficients(final SpacecraftState state, final int jMax) throws OrekitException {
//Initialise the fields
this.jMax = jMax;
//Allocate the arrays
cCoef = new double[jMax + 1][6];
sCoef = new double[jMax + 1][6];
//Compute the coefficients
computeCoefficients(state);
}
/**
* Compute the Fourrier coefficients.
* <p>
* Only the C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup> coefficients need to be computed
* as D<sub>i</sub><sup>m</sup> is always 0.
* </p>
* @param state the current state
* @throws OrekitException in case of an error
*/
private void computeCoefficients(final SpacecraftState state) throws OrekitException {
// Computes the limits for the integral
final double[] ll = getLLimits(state);
// Computes integrated mean element rates if Llow < Lhigh
if (ll[0] < ll[1]) {
//Compute 1 / PI
final double ooPI = 1 / FastMath.PI;
// loop through all values of j
for (int j = 0; j <= jMax; j++) {
final double[] curentCoefficients = integrator.integrate(new IntegrableFunction(state, false, j), ll[0], ll[1]);
//divide by PI and set the values for the coefficients
for (int i = 0; i < 6; i++) {
cCoef[j][i] = ooPI * curentCoefficients[i];
sCoef[j][i] = ooPI * curentCoefficients[i + 6];
}
}
}
}
/** Get the coefficient C<sub>i</sub><sup>j</sup>.
* @param i i index - corresponds to the required variation
* @param j j index
* @return the coefficient C<sub>i</sub><sup>j</sup>
*/
public double getCij(final int i, final int j) {
return cCoef[j][i];
}
/** Get the coefficient S<sub>i</sub><sup>j</sup>.
* @param i i index - corresponds to the required variation
* @param j j index
* @return the coefficient S<sub>i</sub><sup>j</sup>
*/
public double getSij(final int i, final int j) {
return sCoef[j][i];
}
}
/** This class handles the short periodic coefficients described in Danielson 2.5.3-26.
*
* <p>
* The value of M is 0. Also, since the values of the Fourier coefficient D<sub>i</sub><sup>m</sup> is 0
* then the values of the coefficients D<sub>i</sub><sup>m</sup> for m > 2 are also 0.
* </p>
* @author Petre Bazavan
* @author Lucian Barbulescu
*
*/
private class GaussianShortPeriodicCoefficients {
/** Maximum value for j index. */
private final int jMax;
/**The coefficients D<sub>i</sub><sup>j</sup>.
* <p>
* Only for j = 1 and j = 2 the coefficients are not 0. <br>
* i corresponds to the equinoctial element, as follows:
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final ShortPeriodicsInterpolatedCoefficient[][] dij;
/** The coefficients C<sub>i</sub><sup>j</sup>.
* <p>
* The index order is cij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final ShortPeriodicsInterpolatedCoefficient[][] cij;
/** The coefficients S<sub>i</sub><sup>j</sup>.
* <p>
* The index order is sij[j][i] <br/>
* i corresponds to the equinoctial element, as follows: <br/>
* - i=0 for a <br/>
* - i=1 for k <br/>
* - i=2 for h <br/>
* - i=3 for q <br/>
* - i=4 for p <br/>
* - i=5 for λ <br/>
* </p>
*/
private final ShortPeriodicsInterpolatedCoefficient[][] sij;
/** The current computed values for the ρ<sub>j</sub> and σ<sub>j</sub> coefficients.
* <p>
* Index 0 corresponds to ρ, index 1 corresponds to σ
* Used to compute the U<sub>i</sub><sup>j</sup> and V<sub>i</sub><sup>j</sup> coefficients.
* </p>
*/
private final double[][] currentRhoSigmaj;
/** Constructor.
* @param jMax maximum value for j index
* @param interpolationPoints number of points used in the interpolation process
*/
public GaussianShortPeriodicCoefficients(final int jMax, final int interpolationPoints) {
//Initialise fields
this.jMax = jMax;
this.dij = new ShortPeriodicsInterpolatedCoefficient[3][6];
this.cij = new ShortPeriodicsInterpolatedCoefficient[jMax + 1][6];
this.sij = new ShortPeriodicsInterpolatedCoefficient[jMax + 1][6];
this.currentRhoSigmaj = new double[2][3 * jMax + 1];
// Initialise the C<sub>i</sub><sup>j</sup>, S<sub>i</sub><sup>j</sup> and D<sub>i</sub><sup>j</sup> coefficients
for (int j = 0; j <= jMax; j++) {
for (int i = 0; i < 6; i++) {
this.cij[j][i] = new ShortPeriodicsInterpolatedCoefficient(interpolationPoints);
if (j > 0) {
this.sij[j][i] = new ShortPeriodicsInterpolatedCoefficient(interpolationPoints);
}
// Initialise only the non-zero D<sub>i</sub><sup>j</sup> coefficients
if (j == 1 || (j == 2 && i == 5)) {
this.dij[j][i] = new ShortPeriodicsInterpolatedCoefficient(interpolationPoints);
}
}
}
}
/** Compute the short periodic coefficients.
*
* @param state current state information: date, kinematics, attitude
* @throws OrekitException if an error occurs
*/
public void computeCoefficients(final SpacecraftState state)
throws OrekitException {
// get the current date
final AbsoluteDate date = state.getDate();
// Compute ρ<sub>j</sub> and σ<sub>j</sub>
computeRhoSigmaCoefficients(date);
// Compute the Fourier coefficients
final FourierCjSjCoefficients fourierCjSj = new FourierCjSjCoefficients(state, jMax);
// Compute the required U and V coefficients
final UijVijCoefficients uijvij = new UijVijCoefficients(currentRhoSigmaj, fourierCjSj, jMax);
// compute the k₂⁰ coefficient
final double k20 = computeK20(jMax);
// 1. / n
final double oon = 1. / n;
// 3. / (2 * a * n)
final double to2an = 1.5 * oon / a;
// 3. / (4 * a * n)
final double to4an = to2an / 2;
// Compute the coefficients for each element
for (int i = 0; i < 6; i++) {
// compute D<sub>i</sub>¹ and D<sub>i</sub>² (all others are 0)
double di1 = -oon * fourierCjSj.getCij(i, 0);
if (i == 5) {
di1 += to2an * uijvij.getU1(0, 0);
}
double di2 = 0.;
if (i == 5) {
di2 += -to4an * fourierCjSj.getCij(0, 0);
}
//the C<sub>i</sub>⁰ is computed based on all others
double currentCi0 = -di2 * k20;
for (int j = 1; j <= jMax; j++) {
// compute the current C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup>
double currentCij = oon * uijvij.getU1(j, i);
if (i == 5) {
currentCij += -to2an * uijvij.getU2(j);
}
double currentSij = oon * uijvij.getV1(j, i);
if (i == 5) {
currentSij += -to2an * uijvij.getV2(j);
}
// add the computed coefficients to C<sub>i</sub>⁰
currentCi0 += -(currentCij * currentRhoSigmaj[0][j] + currentSij * currentRhoSigmaj[1][j]);
// add the values to the interpolators
cij[j][i].addGridPoint(date, currentCij);
sij[j][i].addGridPoint(date, currentSij);
}
// add the computed values to the interpolators
cij[0][i].addGridPoint(date, currentCi0);
dij[1][i].addGridPoint(date, di1);
if (i == 5) {
dij[2][i].addGridPoint(date, di2);
}
}
}
/** Reset the coefficients.
* <p>
* For each coefficient, clear history of computed points
* </p>
*/
public void resetCoefficients() {
for (int j = 0; j <= jMax; j++) {
for (int i = 0; i < 6; i++) {
this.cij[j][i].clearHistory();
if (j > 0) {
this.sij[j][i].clearHistory();
}
if (j == 1 || (j == 2 && i == 5)) {
this.dij[j][i].clearHistory();
}
}
}
}
/**
* Compute the auxiliary quantities ρ<sub>j</sub> and σ<sub>j</sub>.
* <p>
* The expressions used are equations 2.5.3-(4) from the Danielson paper. <br/>
* ρ<sub>j</sub> = (1+jB)(-b)<sup>j</sup>C<sub>j</sub>(k, h) <br/>
* σ<sub>j</sub> = (1+jB)(-b)<sup>j</sup>S<sub>j</sub>(k, h) <br/>
* </p>
* @param date current date
*/
private void computeRhoSigmaCoefficients(final AbsoluteDate date) {
final CjSjCoefficient cjsjKH = new CjSjCoefficient(k, h);
final double b = 1. / (1 + B);
// (-b)<sup>j</sup>
double mbtj = 1;
for (int j = 1; j <= 3 * jMax; j++) {
//Compute current rho and sigma;
mbtj *= -b;
final double coef = (1 + j * B) * mbtj;
currentRhoSigmaj[0][j] = coef * cjsjKH.getCj(j);
currentRhoSigmaj[1][j] = coef * cjsjKH.getSj(j);
}
}
/** Compute the coefficient k₂⁰ by using the equation
* 2.5.3-(9a) from Danielson.
* <p>
* After inserting 2.5.3-(8) into 2.5.3-(9a) the result becomes:<br>
* k₂⁰ = Σ<sub>k=1</sub><sup>kMax</sup>[(2 / k²) * (σ<sub>k</sub>² + ρ<sub>k</sub>²)]
* </p>
* @param kMax max value fot k index
* @return the coefficient k₂⁰
*/
private double computeK20(final int kMax) {
double k20 = 0.;
for (int kIndex = 1; kIndex <= kMax; kIndex++) {
// After inserting 2.5.3-(8) into 2.5.3-(9a) the result becomes:
//k₂⁰ = Σ<sub>k=1</sub><sup>kMax</sup>[(2 / k²) * (σ<sub>k</sub>² + ρ<sub>k</sub>²)]
double currentTerm = currentRhoSigmaj[1][kIndex] * currentRhoSigmaj[1][kIndex] +
currentRhoSigmaj[0][kIndex] * currentRhoSigmaj[0][kIndex];
//multiply by 2 / k²
currentTerm *= 2. / (kIndex * kIndex);
// add the term to the result
k20 += currentTerm;
}
return k20;
}
/** Get C<sub>i</sub><sup>j</sup>.
*
* @param i i index
* @param j j index
* @param date the date
* @return C<sub>i</sub><sup>j</sup>
*/
public double getCij(final int i, final int j, final AbsoluteDate date) {
return cij[j][i].value(date);
}
/** Get S<sub>i</sub><sup>j</sup>.
*
* @param i i index
* @param j j index
* @param date the date
* @return S<sub>i</sub><sup>j</sup>
*/
public double getSij(final int i, final int j, final AbsoluteDate date) {
return sij[j][i].value(date);
}
/** Get D<sub>i</sub><sup>j</sup>.
* @param i i index
* @param j j index
* @param date target date
* @return D<sub>i</sub><sup>j</sup>
*/
public double getDij(final int i, final int j, final AbsoluteDate date) {
return dij[j][i].value(date);
}
}
/** The U<sub>i</sub><sup>j</sup> and V<sub>i</sub><sup>j</sup> coefficients described by
* equations 2.5.3-(21) and 2.5.3-(22) from Danielson.
* <p>
* The index i takes only the values 1 and 2<br>
* For U only the index 0 for j is used.
* </p>
*
* @author Petre Bazavan
* @author Lucian Barbulescu
*/
private static class UijVijCoefficients {
/** The U₁<sup>j</sup> coefficients.
* <p>
* The first index identifies the Fourier coefficients used<br>
* Those coefficients are computed for all Fourier C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup><br>
* The only exception is when j = 0 when only the coefficient for fourier index = 1 (i == 0) is needed.<br>
* Also, for fourier index = 1 (i == 0), the coefficients up to 2 * jMax are computed, because are required
* to compute the coefficients U₂<sup>j</sup>
* </p>
*/
private final double[][] u1ij;
/** The V₁<sup>j</sup> coefficients.
* <p>
* The first index identifies the Fourier coefficients used<br>
* Those coefficients are computed for all Fourier C<sub>i</sub><sup>j</sup> and S<sub>i</sub><sup>j</sup><br>
* for fourier index = 1 (i == 0), the coefficients up to 2 * jMax are computed, because are required
* to compute the coefficients V₂<sup>j</sup>
* </p>
*/
private final double[][] v1ij;
/** The U₂<sup>j</sup> coefficients.
* <p>
* Only the coefficients that use the Fourier index = 1 (i == 0) are computed as they are the only ones required.
* </p>
*/
private final double[] u2ij;
/** The V₂<sup>j</sup> coefficients.
* <p>
* Only the coefficients that use the Fourier index = 1 (i == 0) are computed as they are the only ones required.
* </p>
*/
private final double[] v2ij;
/** The current computed values for the ρ<sub>j</sub> and σ<sub>j</sub> coefficients. */
private final double[][] currentRhoSigmaj;
/** The C<sub>i</sub><sup>j</sup> and the S<sub>i</sub><sup>j</sup> Fourier coefficients. */
private final FourierCjSjCoefficients fourierCjSj;
/** The maximum value for j index. */
private final int jMax;
/** Constructor.
* @param currentRhoSigmaj the current computed values for the ρ<sub>j</sub> and σ<sub>j</sub> coefficients
* @param fourierCjSj the fourier coefficients C<sub>i</sub><sup>j</sup> and the S<sub>i</sub><sup>j</sup>
* @param jMax maximum value for j index
*/
public UijVijCoefficients(final double[][] currentRhoSigmaj, final FourierCjSjCoefficients fourierCjSj, final int jMax) {
this.currentRhoSigmaj = currentRhoSigmaj;
this.fourierCjSj = fourierCjSj;
this.jMax = jMax;
// initialize the internal arrays.
this.u1ij = new double[6][2 * jMax + 1];
this.v1ij = new double[6][2 * jMax + 1];
this.u2ij = new double[jMax + 1];
this.v2ij = new double[jMax + 1];
//compute the coefficients
computeU1V1Coefficients();
computeU2V2Coefficients();
}
/** Build the U₁<sup>j</sup> and V₁<sup>j</sup> coefficients. */
private void computeU1V1Coefficients() {
// generate the U₁<sup>j</sup> and V₁<sup>j</sup> coefficients
// for j >= 1
// also the U₁⁰ for Fourier index = 1 (i == 0) coefficient will be computed
u1ij[0][0] = 0;
for (int j = 1; j <= jMax; j++) {
// compute 1 / j
final double ooj = 1. / j;
for (int i = 0; i < 6; i++) {
//j is aready between 1 and J
u1ij[i][j] = fourierCjSj.getSij(i, j);
v1ij[i][j] = fourierCjSj.getCij(i, j);
// 1 - δ<sub>1j</sub> is 1 for all j > 1
if (j > 1) {
// k starts with 1 because j-J is less than or equal to 0
for (int kIndex = 1; kIndex <= j - 1; kIndex++) {
// C<sub>i</sub><sup>j-k</sup> * σ<sub>k</sub> +
// S<sub>i</sub><sup>j-k</sup> * ρ<sub>k</sub>
u1ij[i][j] += fourierCjSj.getCij(i, j - kIndex) * currentRhoSigmaj[1][kIndex] +
fourierCjSj.getSij(i, j - kIndex) * currentRhoSigmaj[0][kIndex];
// C<sub>i</sub><sup>j-k</sup> * ρ<sub>k</sub> -
// S<sub>i</sub><sup>j-k</sup> * σ<sub>k</sub>
v1ij[i][j] += fourierCjSj.getCij(i, j - kIndex) * currentRhoSigmaj[0][kIndex] -
fourierCjSj.getSij(i, j - kIndex) * currentRhoSigmaj[1][kIndex];
}
}
// since j must be between 1 and J-1 and is already between 1 and J
// the following sum is skiped only for j = jMax
if (j != jMax) {
for (int kIndex = 1; kIndex <= jMax - j; kIndex++) {
// -C<sub>i</sub><sup>j+k</sup> * σ<sub>k</sub> +
// S<sub>i</sub><sup>j+k</sup> * ρ<sub>k</sub>
u1ij[i][j] += -fourierCjSj.getCij(i, j + kIndex) * currentRhoSigmaj[1][kIndex] +
fourierCjSj.getSij(i, j + kIndex) * currentRhoSigmaj[0][kIndex];
// C<sub>i</sub><sup>j+k</sup> * ρ<sub>k</sub> +
// S<sub>i</sub><sup>j+k</sup> * σ<sub>k</sub>
v1ij[i][j] += fourierCjSj.getCij(i, j + kIndex) * currentRhoSigmaj[0][kIndex] +
fourierCjSj.getSij(i, j + kIndex) * currentRhoSigmaj[1][kIndex];
}
}
for (int kIndex = 1; kIndex <= jMax; kIndex++) {
// C<sub>i</sub><sup>k</sup> * σ<sub>j+k</sub> -
// S<sub>i</sub><sup>k</sup> * ρ<sub>j+k</sub>
u1ij[i][j] += -fourierCjSj.getCij(i, kIndex) * currentRhoSigmaj[1][j + kIndex] -
fourierCjSj.getSij(i, kIndex) * currentRhoSigmaj[0][j + kIndex];
// C<sub>i</sub><sup>k</sup> * ρ<sub>j+k</sub> +
// S<sub>i</sub><sup>k</sup> * σ<sub>j+k</sub>
v1ij[i][j] += fourierCjSj.getCij(i, kIndex) * currentRhoSigmaj[0][j + kIndex] +
fourierCjSj.getSij(i, kIndex) * currentRhoSigmaj[1][j + kIndex];
}
// divide by 1 / j
u1ij[i][j] *= -ooj;
v1ij[i][j] *= ooj;
// if index = 1 (i == 0) add the computed terms to U₁⁰
if (i == 0) {
//- (U₁<sup>j</sup> * ρ<sub>j</sub> + V₁<sup>j</sup> * σ<sub>j</sub>
u1ij[0][0] += -u1ij[0][j] * currentRhoSigmaj[0][j] - v1ij[0][j] * currentRhoSigmaj[1][j];
}
}
}
// Terms with j > jMax are required only when computing the coefficients
// U₂<sup>j</sup> and V₂<sup>j</sup>
// and those coefficients are only required for Fourier index = 1 (i == 0).
for (int j = jMax + 1; j <= 2 * jMax; j++) {
// compute 1 / j
final double ooj = 1. / j;
//the value of i is 0
u1ij[0][j] = 0.;
v1ij[0][j] = 0.;
//k starts from j-J as it is always greater than or equal to 1
for (int kIndex = j - jMax; kIndex <= j - 1; kIndex++) {
// C<sub>i</sub><sup>j-k</sup> * σ<sub>k</sub> +
// S<sub>i</sub><sup>j-k</sup> * ρ<sub>k</sub>
u1ij[0][j] += fourierCjSj.getCij(0, j - kIndex) * currentRhoSigmaj[1][kIndex] +
fourierCjSj.getSij(0, j - kIndex) * currentRhoSigmaj[0][kIndex];
// C<sub>i</sub><sup>j-k</sup> * ρ<sub>k</sub> -
// S<sub>i</sub><sup>j-k</sup> * σ<sub>k</sub>
v1ij[0][j] += fourierCjSj.getCij(0, j - kIndex) * currentRhoSigmaj[0][kIndex] -
fourierCjSj.getSij(0, j - kIndex) * currentRhoSigmaj[1][kIndex];
}
for (int kIndex = 1; kIndex <= jMax; kIndex++) {
// C<sub>i</sub><sup>k</sup> * σ<sub>j+k</sub> -
// S<sub>i</sub><sup>k</sup> * ρ<sub>j+k</sub>
u1ij[0][j] += -fourierCjSj.getCij(0, kIndex) * currentRhoSigmaj[1][j + kIndex] -
fourierCjSj.getSij(0, kIndex) * currentRhoSigmaj[0][j + kIndex];
// C<sub>i</sub><sup>k</sup> * ρ<sub>j+k</sub> +
// S<sub>i</sub><sup>k</sup> * σ<sub>j+k</sub>
v1ij[0][j] += fourierCjSj.getCij(0, kIndex) * currentRhoSigmaj[0][j + kIndex] +
fourierCjSj.getSij(0, kIndex) * currentRhoSigmaj[1][j + kIndex];
}
// divide by 1 / j
u1ij[0][j] *= -ooj;
v1ij[0][j] *= ooj;
}
}
/** Build the U₁<sup>j</sup> and V₁<sup>j</sup> coefficients.
* <p>
* Only the coefficients for Fourier index = 1 (i == 0) are required.
* </p>
*/
private void computeU2V2Coefficients() {
for (int j = 1; j <= jMax; j++) {
// compute 1 / j
final double ooj = 1. / j;
// only the values for i == 0 are computed
u2ij[j] = v1ij[0][j];
v2ij[j] = u1ij[0][j];
// 1 - δ<sub>1j</sub> is 1 for all j > 1
if (j > 1) {
for (int l = 1; l <= j - 1; l++) {
// U₁<sup>j-l</sup> * σ<sub>l</sub> +
// V₁<sup>j-l</sup> * ρ<sub>l</sub>
u2ij[j] += u1ij[0][j - l] * currentRhoSigmaj[1][l] +
v1ij[0][j - l] * currentRhoSigmaj[0][l];
// U₁<sup>j-l</sup> * ρ<sub>l</sub> -
// V₁<sup>j-l</sup> * σ<sub>l</sub>
v2ij[j] += u1ij[0][j - l] * currentRhoSigmaj[0][l] -
v1ij[0][j - l] * currentRhoSigmaj[1][l];
}
}
for (int l = 1; l <= jMax; l++) {
// -U₁<sup>j+l</sup> * σ<sub>l</sub> +
// U₁<sup>l</sup> * σ<sub>j+l</sub> +
// V₁<sup>j+l</sup> * ρ<sub>l</sub> -
// V₁<sup>l</sup> * ρ<sub>j+l</sub>
u2ij[j] += -u1ij[0][j + l] * currentRhoSigmaj[1][l] +
u1ij[0][l] * currentRhoSigmaj[1][j + l] +
v1ij[0][j + l] * currentRhoSigmaj[0][l] -
v1ij[0][l] * currentRhoSigmaj[0][j + l];
// U₁<sup>j+l</sup> * ρ<sub>l</sub> +
// U₁<sup>l</sup> * ρ<sub>j+l</sub> +
// V₁<sup>j+l</sup> * σ<sub>l</sub> +
// V₁<sup>l</sup> * σ<sub>j+l</sub>
u2ij[j] += u1ij[0][j + l] * currentRhoSigmaj[0][l] +
u1ij[0][l] * currentRhoSigmaj[0][j + l] +
v1ij[0][j + l] * currentRhoSigmaj[1][l] +
v1ij[0][l] * currentRhoSigmaj[1][j + l];
}
// divide by 1 / j
u2ij[j] *= -ooj;
v2ij[j] *= ooj;
}
}
/** Get the coefficient U₁<sup>j</sup> for Fourier index i.
*
* @param j j index
* @param i Fourier index (starts at 0)
* @return the coefficient U₁<sup>j</sup> for the given Fourier index i
*/
public double getU1(final int j, final int i) {
return u1ij[i][j];
}
/** Get the coefficient V₁<sup>j</sup> for Fourier index i.
*
* @param j j index
* @param i Fourier index (starts at 0)
* @return the coefficient V₁<sup>j</sup> for the given Fourier index i
*/
public double getV1(final int j, final int i) {
return v1ij[i][j];
}
/** Get the coefficient U₂<sup>j</sup> for Fourier index = 1 (i == 0).
*
* @param j j index
* @return the coefficient U₂<sup>j</sup> for Fourier index = 1 (i == 0)
*/
public double getU2(final int j) {
return u2ij[j];
}
/** Get the coefficient V₂<sup>j</sup> for Fourier index = 1 (i == 0).
*
* @param j j index
* @return the coefficient V₂<sup>j</sup> for Fourier index = 1 (i == 0)
*/
public double getV2(final int j) {
return v2ij[j];
}
}
}