UpperBounds.java
/* Copyright 2002-2024 CS GROUP
* 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.semianalytical.dsst.utilities;
import org.hipparchus.CalculusFieldElement;
import org.hipparchus.util.FastMath;
/** Utility class to compute upper bounds for truncation algorithms.
*
* @author Pascal Parraud
*/
public class UpperBounds {
/** Private constructor as the class is a utility class. */
private UpperBounds() {
}
/** Get the upper bound value D<sub>n</sub><sup>l</sup>(Χ).
*
* @param xx value of Χ²
* @param xpl value of Χ * (Χ² / 2)<sup>l</sup>
* @param n index n (power of a/R)
* @param l index l (power of eccentricity)
* @return the upper bound D<sub>n</sub><sup>l</sup>(Χ)
*/
public static double getDnl(final double xx, final double xpl, final int n, final int l) {
final int lp2 = l + 2;
if (n > lp2) {
final int ll = l * l;
double dM = xpl;
double dL = dM;
double dB = (l + 1) * xx * xpl;
for (int j = l + 3; j <= n; j++) {
final int jm1 = j - 1;
dL = dM;
dM = dB;
dB = jm1 * xx * ((2 * j - 3) * dM - (j - 2) * dL) / (jm1 * jm1 - ll);
}
return dB;
} else if (n == lp2) {
return (l + 1) * xx * xpl;
} else {
return xpl;
}
}
/** Get the upper bound value D<sub>n</sub><sup>l</sup>(Χ).
*
* @param xx value of Χ²
* @param xpl value of Χ * (Χ² / 2)<sup>l</sup>
* @param n index n (power of a/R)
* @param l index l (power of eccentricity)
* @param <T> the type of the field elements
* @return the upper bound D<sub>n</sub><sup>l</sup>(Χ)
*/
public static <T extends CalculusFieldElement<T>> T getDnl(final T xx, final T xpl, final int n, final int l) {
final int lp2 = l + 2;
if (n > lp2) {
final int ll = l * l;
T dM = xpl;
T dL = dM;
T dB = xx.multiply(xpl).multiply(l + 1);
for (int j = l + 3; j <= n; j++) {
final int jm1 = j - 1;
dL = dM;
dM = dB;
dB = xx.multiply(jm1).multiply(dM.multiply(2 * j - 3).subtract(dL.multiply(j - 2))).divide(jm1 * jm1 - ll);
}
return dB;
} else if (n == lp2) {
return xx.multiply(xpl).multiply(l + 1);
} else {
return xpl;
}
}
/** Get the upper bound value R<sup>ε</sup><sub>n,m,l</sub>(γ).
*
* @param gamma value of γ
* @param n index n
* @param l index l
* @param m index m
* @param eps ε value (+1/-1)
* @param irf retrograde factor I (+1/-1)
* @return the upper bound R<sup>ε</sup><sub>n,m,l</sub>(γ)
*/
public static double getRnml(final double gamma,
final int n, final int l, final int m,
final int eps, final int irf) {
// Initialization
final int mei = m * eps * irf;
final double sinisq = 1. - gamma * gamma;
// Set a lower bound for inclination
final double sininc = FastMath.max(0.03, FastMath.sqrt(sinisq));
final double onepig = 1. + gamma * irf;
final double sinincPowLmMEI = FastMath.pow(sininc, l - mei);
final double onepigPowLmMEI = FastMath.pow(onepig, mei);
// Bound for index 0
double rBound = sinincPowLmMEI * onepigPowLmMEI;
// If index > 0
if (n > l) {
final int lp1 = l + 1;
double dpnml = lp1 * eps;
double pnml = dpnml * gamma - m;
// If index > 1
if (n > l + 1) {
final int ll = l * l;
final int ml = m * l;
final int mm = m * m;
double pn1ml = 1.;
double dpn1ml = 0.;
double pn2ml = 1.;
double dpn2ml = 0.;
for (int in = l + 2; in <= n; in++) {
final int nm1 = in - 1;
final int tnm1 = in + nm1;
final int nnlnl = nm1 * (in * in - ll);
final int nnmnm = in * (nm1 * nm1 - mm);
final int c2nne = tnm1 * in * nm1 * eps;
final int c2nml = tnm1 * ml;
final double coef = c2nne * gamma - c2nml;
pn2ml = pn1ml;
dpn2ml = dpn1ml;
pn1ml = pnml;
dpn1ml = dpnml;
pnml = (coef * pn1ml - nnmnm * pn2ml) / nnlnl;
dpnml = (coef * dpn1ml - nnmnm * dpn2ml + c2nne * pn1ml) / nnlnl;
}
}
// Bound for index > 0
rBound *= FastMath.sqrt(pnml * pnml + dpnml * dpnml * sinisq / ((n - l) * (n + lp1)));
}
return rBound;
}
/** Get the upper bound value R<sup>ε</sup><sub>n,m,l</sub>(γ).
*
* @param gamma value of γ
* @param n index n
* @param l index l
* @param m index m
* @param eps ε value (+1/-1)
* @param irf retrograde factor I (+1/-1)
* @param <T> the type of the field elements
* @return the upper bound R<sup>ε</sup><sub>n,m,l</sub>(γ)
*/
public static <T extends CalculusFieldElement<T>> T getRnml(final T gamma,
final int n, final int l, final int m,
final int eps, final int irf) {
final T zero = gamma.getField().getZero();
// Initialization
final int mei = m * eps * irf;
final T sinisq = gamma.square().negate().add(1.);
// Set a lower bound for inclination
final T sininc = FastMath.max(zero.newInstance(0.03), FastMath.sqrt(sinisq));
final T onepig = gamma.multiply(irf).add(1.);
final T sinincPowLmMEI = FastMath.pow(sininc, l - mei);
final T onepigPowLmMEI = FastMath.pow(onepig, mei);
// Bound for index 0
T rBound = sinincPowLmMEI.multiply(onepigPowLmMEI);
// If index > 0
if (n > l) {
final int lp1 = l + 1;
T dpnml = zero.newInstance(lp1 * eps);
T pnml = gamma.multiply(dpnml).subtract(m);
// If index > 1
if (n > l + 1) {
final int ll = l * l;
final int ml = m * l;
final int mm = m * m;
T pn1ml = zero.newInstance(1.);
T dpn1ml = zero;
T pn2ml = zero.newInstance(1.);
T dpn2ml = zero;
for (int in = l + 2; in <= n; in++) {
final int nm1 = in - 1;
final int tnm1 = in + nm1;
final int nnlnl = nm1 * (in * in - ll);
final int nnmnm = in * (nm1 * nm1 - mm);
final int c2nne = tnm1 * in * nm1 * eps;
final int c2nml = tnm1 * ml;
final T coef = gamma.multiply(c2nne).subtract(c2nml);
pn2ml = pn1ml;
dpn2ml = dpn1ml;
pn1ml = pnml;
dpn1ml = dpnml;
pnml = (coef.multiply(pn1ml).subtract(pn2ml.multiply(nnmnm))).divide(nnlnl);
dpnml = (coef.multiply(dpn1ml).subtract(dpn2ml.multiply(nnmnm)).add(pn1ml.multiply(c2nne))).divide(nnlnl);
}
}
// Bound for index > 0
rBound = rBound.multiply(FastMath.sqrt(pnml.multiply(pnml).add(dpnml.multiply(dpnml).multiply(sinisq).divide((n - l) * (n + lp1)))));
}
return rBound;
}
}