CoefficientsFactory.java
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* this work for additional information regarding copyright ownership.
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*
* http://www.apache.org/licenses/LICENSE-2.0
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package org.orekit.propagation.semianalytical.dsst.utilities;
import java.util.TreeMap;
import org.hipparchus.Field;
import org.hipparchus.RealFieldElement;
import org.hipparchus.util.CombinatoricsUtils;
import org.hipparchus.util.FastMath;
import org.hipparchus.util.MathArrays;
import org.orekit.errors.OrekitException;
import org.orekit.errors.OrekitMessages;
/**
* This class is designed to provide coefficient from the DSST theory.
*
* @author Romain Di Costanzo
*/
public class CoefficientsFactory {
/** Internal storage of the polynomial values. Reused for further computation. */
private static TreeMap<NSKey, Double> VNS = new TreeMap<NSKey, Double>();
/** Last computed order for V<sub>ns</sub> coefficients. */
private static int LAST_VNS_ORDER = 2;
/** Static initialization for the V<sub>ns</sub> coefficient. */
static {
// Initialization
VNS.put(new NSKey(0, 0), 1.);
VNS.put(new NSKey(1, 0), 0.);
VNS.put(new NSKey(1, 1), 0.5);
}
/** Private constructor as the class is a utility class.
*/
private CoefficientsFactory() {
}
/** Compute the Q<sub>n,s</sub> coefficients evaluated at γ from the recurrence formula 2.8.3-(2).
* <p>
* Q<sub>n,s</sub> coefficients are computed for n = 0 to nMax
* and s = 0 to sMax + 1 in order to also get the derivative dQ<sub>n,s</sub>/dγ = Q(n, s + 1)
* </p>
* @param gamma γ angle
* @param nMax n max value
* @param sMax s max value
* @return Q<sub>n,s</sub> coefficients array
*/
public static double[][] computeQns(final double gamma, final int nMax, final int sMax) {
// Initialization
final int sDim = FastMath.min(sMax + 1, nMax) + 1;
final int rows = nMax + 1;
final double[][] Qns = new double[rows][];
for (int i = 0; i <= nMax; i++) {
final int snDim = FastMath.min(i + 1, sDim);
Qns[i] = new double[snDim];
}
// first element
Qns[0][0] = 1;
for (int n = 1; n <= nMax; n++) {
final int snDim = FastMath.min(n + 1, sDim);
for (int s = 0; s < snDim; s++) {
if (n == s) {
Qns[n][s] = (2. * s - 1.) * Qns[s - 1][s - 1];
} else if (n == (s + 1)) {
Qns[n][s] = (2. * s + 1.) * gamma * Qns[s][s];
} else {
Qns[n][s] = (2. * n - 1.) * gamma * Qns[n - 1][s] - (n + s - 1.) * Qns[n - 2][s];
Qns[n][s] /= n - s;
}
}
}
return Qns;
}
/** Compute the Q<sub>n,s</sub> coefficients evaluated at γ from the recurrence formula 2.8.3-(2).
* <p>
* Q<sub>n,s</sub> coefficients are computed for n = 0 to nMax
* and s = 0 to sMax + 1 in order to also get the derivative dQ<sub>n,s</sub>/dγ = Q(n, s + 1)
* </p>
* @param gamma γ angle
* @param nMax n max value
* @param sMax s max value
* @param <T> the type of the field elements
* @return Q<sub>n,s</sub> coefficients array
*/
public static <T extends RealFieldElement<T>> T[][] computeQns(final T gamma, final int nMax, final int sMax) {
// Initialization
final int sDim = FastMath.min(sMax + 1, nMax) + 1;
final int rows = nMax + 1;
final T[][] Qns = MathArrays.buildArray(gamma.getField(), rows, FastMath.min(nMax + 1, sDim) - 1);
for (int i = 0; i <= nMax; i++) {
final int snDim = FastMath.min(i + 1, sDim);
Qns[i] = MathArrays.buildArray(gamma.getField(), snDim);
}
// first element
Qns[0][0] = gamma.subtract(gamma).add(1.);
for (int n = 1; n <= nMax; n++) {
final int snDim = FastMath.min(n + 1, sDim);
for (int s = 0; s < snDim; s++) {
if (n == s) {
Qns[n][s] = Qns[s - 1][s - 1].multiply(2. * s - 1.);
} else if (n == (s + 1)) {
Qns[n][s] = Qns[s][s].multiply(gamma).multiply(2. * s + 1.);
} else {
Qns[n][s] = Qns[n - 1][s].multiply(gamma).multiply(2. * n - 1.).subtract(Qns[n - 2][s].multiply(n + s - 1.));
Qns[n][s] = Qns[n][s].divide(n - s);
}
}
}
return Qns;
}
/** Compute recursively G<sub>s</sub> and H<sub>s</sub> polynomials from equation 3.1-(5).
* @param k x-component of the eccentricity vector
* @param h y-component of the eccentricity vector
* @param alpha 1st direction cosine
* @param beta 2nd direction cosine
* @param order development order
* @return Array of G<sub>s</sub> and H<sub>s</sub> polynomials for s from 0 to order.<br>
* The 1st column contains the G<sub>s</sub> values.
* The 2nd column contains the H<sub>s</sub> values.
*/
public static double[][] computeGsHs(final double k, final double h,
final double alpha, final double beta,
final int order) {
// Constant terms
final double hamkb = h * alpha - k * beta;
final double kaphb = k * alpha + h * beta;
// Initialization
final double[][] GsHs = new double[2][order + 1];
GsHs[0][0] = 1.;
GsHs[1][0] = 0.;
for (int s = 1; s <= order; s++) {
// Gs coefficient
GsHs[0][s] = kaphb * GsHs[0][s - 1] - hamkb * GsHs[1][s - 1];
// Hs coefficient
GsHs[1][s] = hamkb * GsHs[0][s - 1] + kaphb * GsHs[1][s - 1];
}
return GsHs;
}
/** Compute recursively G<sub>s</sub> and H<sub>s</sub> polynomials from equation 3.1-(5).
* @param k x-component of the eccentricity vector
* @param h y-component of the eccentricity vector
* @param alpha 1st direction cosine
* @param beta 2nd direction cosine
* @param order development order
* @param field field of elements
* @param <T> the type of the field elements
* @return Array of G<sub>s</sub> and H<sub>s</sub> polynomials for s from 0 to order.<br>
* The 1st column contains the G<sub>s</sub> values.
* The 2nd column contains the H<sub>s</sub> values.
*/
public static <T extends RealFieldElement<T>> T[][] computeGsHs(final T k, final T h,
final T alpha, final T beta,
final int order, final Field<T> field) {
// Zero for initialization
final T zero = field.getZero();
// Constant terms
final T hamkb = h.multiply(alpha).subtract(k.multiply(beta));
final T kaphb = k.multiply(alpha).add(h.multiply(beta));
// Initialization
final T[][] GsHs = MathArrays.buildArray(field, 2, order + 1);
GsHs[0][0] = zero.add(1.);
GsHs[1][0] = zero;
for (int s = 1; s <= order; s++) {
// Gs coefficient
GsHs[0][s] = kaphb.multiply(GsHs[0][s - 1]).subtract(hamkb.multiply(GsHs[1][s - 1]));
// Hs coefficient
GsHs[1][s] = hamkb.multiply(GsHs[0][s - 1]).add(kaphb.multiply(GsHs[1][s - 1]));
}
return GsHs;
}
/** Compute the V<sub>n,s</sub> coefficients from 2.8.2-(1)(2).
* @param order Order of the computation. Computation will be done from 0 to order -1
* @return Map of the V<sub>n, s</sub> coefficients
*/
public static TreeMap<NSKey, Double> computeVns(final int order) {
if (order > LAST_VNS_ORDER) {
// Compute coefficient
// Need previous computation as recurrence relation is done at s + 1 and n + 2
final int min = (LAST_VNS_ORDER - 2 < 0) ? 0 : (LAST_VNS_ORDER - 2);
for (int n = min; n < order; n++) {
for (int s = 0; s < n + 1; s++) {
if ((n - s) % 2 != 0) {
VNS.put(new NSKey(n, s), 0.);
} else {
// s = n
if (n == s && (s + 1) < order) {
VNS.put(new NSKey(s + 1, s + 1), VNS.get(new NSKey(s, s)) / (2 * s + 2.));
}
// otherwise
if ((n + 2) < order) {
VNS.put(new NSKey(n + 2, s), VNS.get(new NSKey(n, s)) * (-n + s - 1.) / (n + s + 2.));
}
}
}
}
LAST_VNS_ORDER = order;
}
return VNS;
}
/** Get the V<sub>n,s</sub><sup>m</sup> coefficient from V<sub>n,s</sub>.
* <br>See § 2.8.2 in Danielson paper.
* @param m m
* @param n n
* @param s s
* @return The V<sub>n, s</sub> <sup>m</sup> coefficient
*/
public static double getVmns(final int m, final int n, final int s) {
if (m > n) {
throw new OrekitException(OrekitMessages.DSST_VMNS_COEFFICIENT_ERROR_MS, m, n);
}
final double fns = CombinatoricsUtils.factorialDouble(n + FastMath.abs(s));
final double fnm = CombinatoricsUtils.factorialDouble(n - m);
double result = 0;
// If (n - s) is odd, the Vmsn coefficient is null
if ((n - s) % 2 == 0) {
// Update the Vns coefficient
if ((n + 1) > LAST_VNS_ORDER) {
computeVns(n + 1);
}
if (s >= 0) {
result = fns * VNS.get(new NSKey(n, s)) / fnm;
} else {
// If s < 0 : Vmn-s = (-1)^(-s) Vmns
final int mops = (s % 2 == 0) ? 1 : -1;
result = mops * fns * VNS.get(new NSKey(n, -s)) / fnm;
}
}
return result;
}
/** Key formed by two integer values. */
public static class NSKey implements Comparable<NSKey> {
/** n value. */
private final int n;
/** s value. */
private final int s;
/** Simple constructor.
* @param n n
* @param s s
*/
public NSKey(final int n, final int s) {
this.n = n;
this.s = s;
}
/** Get n.
* @return n
*/
public int getN() {
return n;
}
/** Get s.
* @return s
*/
public int getS() {
return s;
}
/** {@inheritDoc} */
public int compareTo(final NSKey key) {
int result = 1;
if (n == key.n) {
if (s < key.s) {
result = -1;
} else if (s == key.s) {
result = 0;
}
} else if (n < key.n) {
result = -1;
}
return result;
}
/** {@inheritDoc} */
public boolean equals(final Object key) {
if (key == this) {
// first fast check
return true;
}
if ((key != null) && (key instanceof NSKey)) {
return (n == ((NSKey) key).n) && (s == ((NSKey) key).s);
}
return false;
}
/** {@inheritDoc} */
public int hashCode() {
return 0x998493a6 ^ (n << 8) ^ s;
}
}
}