CoefficientsFactory.java

  1. /* Copyright 2002-2025 CS GROUP
  2.  * Licensed to CS GROUP (CS) under one or more
  3.  * contributor license agreements.  See the NOTICE file distributed with
  4.  * this work for additional information regarding copyright ownership.
  5.  * CS licenses this file to You under the Apache License, Version 2.0
  6.  * (the "License"); you may not use this file except in compliance with
  7.  * the License.  You may obtain a copy of the License at
  8.  *
  9.  *   http://www.apache.org/licenses/LICENSE-2.0
  10.  *
  11.  * Unless required by applicable law or agreed to in writing, software
  12.  * distributed under the License is distributed on an "AS IS" BASIS,
  13.  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  14.  * See the License for the specific language governing permissions and
  15.  * limitations under the License.
  16.  */
  17. package org.orekit.propagation.semianalytical.dsst.utilities;

  19. import org.hipparchus.CalculusFieldElement;
  20. import org.hipparchus.Field;
  21. import org.hipparchus.util.CombinatoricsUtils;
  22. import org.hipparchus.util.FastMath;
  23. import org.hipparchus.util.MathArrays;
  24. import org.orekit.errors.OrekitException;
  25. import org.orekit.errors.OrekitMessages;

  27. import java.util.SortedMap;
  28. import java.util.concurrent.ConcurrentSkipListMap;

  30. /**
  31.  * This class is designed to provide coefficient from the DSST theory.
  32.  *
  33.  * @author Romain Di Costanzo
  34.  */
  35. public class CoefficientsFactory {

  37.     /** Internal storage of the polynomial values. Reused for further computation. */
  38.     private static SortedMap<NSKey, Double> VNS = new ConcurrentSkipListMap<>();

  40.     /** Last computed order for V<sub>ns</sub> coefficients. */
  41.     private static int         LAST_VNS_ORDER = 2;

  43.     /** Static initialization for the V<sub>ns</sub> coefficient. */
  44.     static {
  45.         // Initialization
  46.         VNS.put(new NSKey(0, 0), 1.);
  47.         VNS.put(new NSKey(1, 0), 0.);
  48.         VNS.put(new NSKey(1, 1), 0.5);
  49.     }

  51.     /** Private constructor as the class is a utility class.
  52.      */
  53.     private CoefficientsFactory() {
  54.     }

  56.     /** Compute the Q<sub>n,s</sub> coefficients evaluated at γ from the recurrence formula 2.8.3-(2).
  57.      *  <p>
  58.      *  Q<sub>n,s</sub> coefficients are computed for n = 0 to nMax
  59.      *  and s = 0 to sMax + 1 in order to also get the derivative dQ<sub>n,s</sub>/dγ = Q(n, s + 1)
  60.      *  </p>
  61.      *  @param gamma γ angle
  62.      *  @param nMax n max value
  63.      *  @param sMax s max value
  64.      *  @return Q<sub>n,s</sub> coefficients array
  65.      */
  66.     public static double[][] computeQns(final double gamma, final int nMax, final int sMax) {

  68.         // Initialization
  69.         final int sDim = FastMath.min(sMax + 1, nMax) + 1;
  70.         final int rows = nMax + 1;
  71.         final double[][] Qns = new double[rows][];
  72.         for (int i = 0; i <= nMax; i++) {
  73.             final int snDim = FastMath.min(i + 1, sDim);
  74.             Qns[i] = new double[snDim];
  75.         }

  77.         // first element
  78.         Qns[0][0] = 1;

  80.         for (int n = 1; n <= nMax; n++) {
  81.             final int snDim = FastMath.min(n + 1, sDim);
  82.             for (int s = 0; s < snDim; s++) {
  83.                 if (n == s) {
  84.                     Qns[n][s] = (2. * s - 1.) * Qns[s - 1][s - 1];
  85.                 } else if (n == (s + 1)) {
  86.                     Qns[n][s] = (2. * s + 1.) * gamma * Qns[s][s];
  87.                 } else {
  88.                     Qns[n][s] = (2. * n - 1.) * gamma * Qns[n - 1][s] - (n + s - 1.) * Qns[n - 2][s];
  89.                     Qns[n][s] /= n - s;
  90.                 }
  91.             }
  92.         }

  94.         return Qns;
  95.     }

  97.     /** Compute the Q<sub>n,s</sub> coefficients evaluated at γ from the recurrence formula 2.8.3-(2).
  98.      *  <p>
  99.      *  Q<sub>n,s</sub> coefficients are computed for n = 0 to nMax
  100.      *  and s = 0 to sMax + 1 in order to also get the derivative dQ<sub>n,s</sub>/dγ = Q(n, s + 1)
  101.      *  </p>
  102.      *  @param gamma γ angle
  103.      *  @param nMax n max value
  104.      *  @param sMax s max value
  105.      *  @param <T> the type of the field elements
  106.      *  @return Q<sub>n,s</sub> coefficients array
  107.      */
  108.     public static <T extends CalculusFieldElement<T>> T[][] computeQns(final T gamma, final int nMax, final int sMax) {

  110.         // Initialization
  111.         final int sDim = FastMath.min(sMax + 1, nMax) + 1;
  112.         final int rows = nMax + 1;
  113.         final T[][] Qns = MathArrays.buildArray(gamma.getField(), rows, FastMath.min(nMax + 1, sDim) - 1);
  114.         for (int i = 0; i <= nMax; i++) {
  115.             final int snDim = FastMath.min(i + 1, sDim);
  116.             Qns[i] = MathArrays.buildArray(gamma.getField(), snDim);
  117.         }

  119.         // first element
  120.         Qns[0][0] = gamma.subtract(gamma).add(1.);

  122.         for (int n = 1; n <= nMax; n++) {
  123.             final int snDim = FastMath.min(n + 1, sDim);
  124.             for (int s = 0; s < snDim; s++) {
  125.                 if (n == s) {
  126.                     Qns[n][s] = Qns[s - 1][s - 1].multiply(2. * s - 1.);
  127.                 } else if (n == (s + 1)) {
  128.                     Qns[n][s] = Qns[s][s].multiply(gamma).multiply(2. * s + 1.);
  129.                 } else {
  130.                     Qns[n][s] = Qns[n - 1][s].multiply(gamma).multiply(2. * n - 1.).subtract(Qns[n - 2][s].multiply(n + s - 1.));
  131.                     Qns[n][s] = Qns[n][s].divide(n - s);
  132.                 }
  133.             }
  134.         }

  136.         return Qns;
  137.     }

  139.     /** Compute recursively G<sub>s</sub> and H<sub>s</sub> polynomials from equation 3.1-(5).
  140.      *  @param k x-component of the eccentricity vector
  141.      *  @param h y-component of the eccentricity vector
  142.      *  @param alpha 1st direction cosine
  143.      *  @param beta 2nd direction cosine
  144.      *  @param order development order
  145.      *  @return Array of G<sub>s</sub> and H<sub>s</sub> polynomials for s from 0 to order.<br>
  146.      *          The 1st column contains the G<sub>s</sub> values.
  147.      *          The 2nd column contains the H<sub>s</sub> values.
  148.      */
  149.     public static double[][] computeGsHs(final double k, final double h,
  150.                                          final double alpha, final double beta,
  151.                                          final int order) {
  152.         // Constant terms
  153.         final double hamkb = h * alpha - k * beta;
  154.         final double kaphb = k * alpha + h * beta;
  155.         // Initialization
  156.         final double[][] GsHs = new double[2][order + 1];
  157.         GsHs[0][0] = 1.;
  158.         GsHs[1][0] = 0.;

  160.         for (int s = 1; s <= order; s++) {
  161.             // Gs coefficient
  162.             GsHs[0][s] = kaphb * GsHs[0][s - 1] - hamkb * GsHs[1][s - 1];
  163.             // Hs coefficient
  164.             GsHs[1][s] = hamkb * GsHs[0][s - 1] + kaphb * GsHs[1][s - 1];
  165.         }

  167.         return GsHs;
  168.     }

  170.     /** Compute recursively G<sub>s</sub> and H<sub>s</sub> polynomials from equation 3.1-(5).
  171.      *  @param k x-component of the eccentricity vector
  172.      *  @param h y-component of the eccentricity vector
  173.      *  @param alpha 1st direction cosine
  174.      *  @param beta 2nd direction cosine
  175.      *  @param order development order
  176.      *  @param field field of elements
  177.      *  @param <T> the type of the field elements
  178.      *  @return Array of G<sub>s</sub> and H<sub>s</sub> polynomials for s from 0 to order.<br>
  179.      *          The 1st column contains the G<sub>s</sub> values.
  180.      *          The 2nd column contains the H<sub>s</sub> values.
  181.      */
  182.     public static <T extends CalculusFieldElement<T>> T[][] computeGsHs(final T k, final T h,
  183.                                          final T alpha, final T beta,
  184.                                          final int order, final Field<T> field) {
  185.         // Zero for initialization
  186.         final T zero = field.getZero();

  188.         // Constant terms
  189.         final T hamkb = h.multiply(alpha).subtract(k.multiply(beta));
  190.         final T kaphb = k.multiply(alpha).add(h.multiply(beta));
  191.         // Initialization
  192.         final T[][] GsHs = MathArrays.buildArray(field, 2, order + 1);
  193.         GsHs[0][0] = zero.newInstance(1.);
  194.         GsHs[1][0] = zero;

  196.         for (int s = 1; s <= order; s++) {
  197.             // Gs coefficient
  198.             GsHs[0][s] = kaphb.multiply(GsHs[0][s - 1]).subtract(hamkb.multiply(GsHs[1][s - 1]));
  199.             // Hs coefficient
  200.             GsHs[1][s] = hamkb.multiply(GsHs[0][s - 1]).add(kaphb.multiply(GsHs[1][s - 1]));
  201.         }

  203.         return GsHs;
  204.     }

  206.     /** Compute the V<sub>n,s</sub> coefficients from 2.8.2-(1)(2).
  207.      * @param order Order of the computation. Computation will be done from 0 to order -1
  208.      * @return Map of the V<sub>n, s</sub> coefficients
  209.      * @since 11.3.3
  210.      */
  211.     public static SortedMap<NSKey, Double> computeVns(final int order) {

  213.         if (order > LAST_VNS_ORDER) {
  214.             // Compute coefficient
  215.             // Need previous computation as recurrence relation is done at s + 1 and n + 2
  216.             final int min = FastMath.max(LAST_VNS_ORDER - 2, 0);
  217.             for (int n = min; n < order; n++) {
  218.                 for (int s = 0; s < n + 1; s++) {
  219.                     if ((n - s) % 2 != 0) {
  220.                         VNS.put(new NSKey(n, s), 0.);
  221.                     } else {
  222.                         // s = n
  223.                         if (n == s && (s + 1) < order) {
  224.                             VNS.put(new NSKey(s + 1, s + 1), VNS.get(new NSKey(s, s)) / (2 * s + 2.));
  225.                         }
  226.                         // otherwise
  227.                         if ((n + 2) < order) {
  228.                             VNS.put(new NSKey(n + 2, s), VNS.get(new NSKey(n, s)) * (-n + s - 1.) / (n + s + 2.));
  229.                         }
  230.                     }
  231.                 }
  232.             }
  233.             LAST_VNS_ORDER = order;
  234.         }
  235.         return new ConcurrentSkipListMap<>(VNS);
  236.     }

  238.     /** Get the V<sub>n,s</sub><sup>m</sup> coefficient from V<sub>n,s</sub>.
  239.      *  <br>See § 2.8.2 in Danielson paper.
  240.      * @param m m
  241.      * @param n n
  242.      * @param s s
  243.      * @return The V<sub>n, s</sub> <sup>m</sup> coefficient
  244.      */
  245.     public static double getVmns(final int m, final int n, final int s) {
  246.         if (m > n) {
  247.             throw new OrekitException(OrekitMessages.DSST_VMNS_COEFFICIENT_ERROR_MS, m, n);
  248.         }
  249.         final double fns = CombinatoricsUtils.factorialDouble(n + FastMath.abs(s));
  250.         final double fnm = CombinatoricsUtils.factorialDouble(n  - m);

  252.         double result = 0;
  253.         // If (n - s) is odd, the Vmsn coefficient is null
  254.         if ((n - s) % 2 == 0) {
  255.             // Update the Vns coefficient
  256.             if ((n + 1) > LAST_VNS_ORDER) {
  257.                 computeVns(n + 1);
  258.             }
  259.             if (s >= 0) {
  260.                 result = fns  * VNS.get(new NSKey(n, s)) / fnm;
  261.             } else {
  262.                 // If s < 0 : Vmn-s = (-1)^(-s) Vmns
  263.                 final int mops = (s % 2 == 0) ? 1 : -1;
  264.                 result = mops * fns * VNS.get(new NSKey(n, -s)) / fnm;
  265.             }
  266.         }
  267.         return result;
  268.     }

  270.     /** Key formed by two integer values. */
  271.     public static class NSKey implements Comparable<NSKey> {

  273.         /** n value. */
  274.         private final int n;

  276.         /** s value. */
  277.         private final int s;

  279.         /** Simple constructor.
  280.          * @param n n
  281.          * @param s s
  282.          */
  283.         public NSKey(final int n, final int s) {
  284.             this.n = n;
  285.             this.s = s;
  286.         }

  288.         /** Get n.
  289.          * @return n
  290.          */
  291.         public int getN() {
  292.             return n;
  293.         }

  295.         /** Get s.
  296.          * @return s
  297.          */
  298.         public int getS() {
  299.             return s;
  300.         }

  302.         /** {@inheritDoc} */
  303.         public int compareTo(final NSKey key) {
  304.             int result = 1;
  305.             if (n == key.n) {
  306.                 if (s < key.s) {
  307.                     result = -1;
  308.                 } else if (s == key.s) {
  309.                     result = 0;
  310.                 }
  311.             } else if (n < key.n) {
  312.                 result = -1;
  313.             }
  314.             return result;
  315.         }

  317.         /** {@inheritDoc} */
  318.         public boolean equals(final Object key) {

  320.             if (key == this) {
  321.                 // first fast check
  322.                 return true;
  323.             }

  325.             if (key instanceof NSKey) {
  326.                 return n == ((NSKey) key).n && s == ((NSKey) key).s;
  327.             }

  329.             return false;

  331.         }

  333.         /** {@inheritDoc} */
  334.         public int hashCode() {
  335.             return 0x998493a6 ^ (n << 8) ^ s;
  336.         }

  338.     }

  340. }
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