CoefficientsFactory.java

  1. /* Copyright 2002-2018 CS Systèmes d'Information
  2.  * Licensed to CS Systèmes d'Information (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 java.util.TreeMap;

  21. import org.hipparchus.util.CombinatoricsUtils;
  22. import org.hipparchus.util.FastMath;
  23. import org.orekit.errors.OrekitException;
  24. import org.orekit.errors.OrekitMessages;

  26. /**
  27.  * This class is designed to provide coefficient from the DSST theory.
  28.  *
  29.  * @author Romain Di Costanzo
  30.  */
  31. public class CoefficientsFactory {

  33.     /** Internal storage of the polynomial values. Reused for further computation. */
  34.     private static TreeMap<NSKey, Double> VNS = new TreeMap<NSKey, Double>();

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

  39.     /** Static initialization for the V<sub>ns</sub> coefficient. */
  40.     static {
  41.         // Initialization
  42.         VNS.put(new NSKey(0, 0), 1.);
  43.         VNS.put(new NSKey(1, 0), 0.);
  44.         VNS.put(new NSKey(1, 1), 0.5);
  45.     }

  47.     /** Private constructor as the class is a utility class.
  48.      */
  49.     private CoefficientsFactory() {
  50.     }

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

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

  73.         // first element
  74.         Qns[0][0] = 1;

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

  90.         return Qns;
  91.     }

  93.     /** Compute recursively G<sub>s</sub> and H<sub>s</sub> polynomials from equation 3.1-(5).
  94.      *  @param k x-component of the eccentricity vector
  95.      *  @param h y-component of the eccentricity vector
  96.      *  @param alpha 1st direction cosine
  97.      *  @param beta 2nd direction cosine
  98.      *  @param order development order
  99.      *  @return Array of G<sub>s</sub> and H<sub>s</sub> polynomials for s from 0 to order.<br>
  100.      *          The 1st column contains the G<sub>s</sub> values.
  101.      *          The 2nd column contains the H<sub>s</sub> values.
  102.      */
  103.     public static double[][] computeGsHs(final double k, final double h,
  104.                                          final double alpha, final double beta,
  105.                                          final int order) {
  106.         // Constant terms
  107.         final double hamkb = h * alpha - k * beta;
  108.         final double kaphb = k * alpha + h * beta;
  109.         // Initialization
  110.         final double[][] GsHs = new double[2][order + 1];
  111.         GsHs[0][0] = 1.;
  112.         GsHs[1][0] = 0.;

  114.         for (int s = 1; s <= order; s++) {
  115.             // Gs coefficient
  116.             GsHs[0][s] = kaphb * GsHs[0][s - 1] - hamkb * GsHs[1][s - 1];
  117.             // Hs coefficient
  118.             GsHs[1][s] = hamkb * GsHs[0][s - 1] + kaphb * GsHs[1][s - 1];
  119.         }

  121.         return GsHs;
  122.     }

  124.     /** Compute the V<sub>n,s</sub> coefficients from 2.8.2-(1)(2).
  125.      * @param order Order of the computation. Computation will be done from 0 to order -1
  126.      * @return Map of the V<sub>n, s</sub> coefficients
  127.      */
  128.     public static TreeMap<NSKey, Double> computeVns(final int order) {

  130.         if (order > LAST_VNS_ORDER) {
  131.             // Compute coefficient
  132.             // Need previous computation as recurrence relation is done at s + 1 and n + 2
  133.             final int min = (LAST_VNS_ORDER - 2 < 0) ? 0 : (LAST_VNS_ORDER - 2);
  134.             for (int n = min; n < order; n++) {
  135.                 for (int s = 0; s < n + 1; s++) {
  136.                     if ((n - s) % 2 != 0) {
  137.                         VNS.put(new NSKey(n, s), 0.);
  138.                     } else {
  139.                         // s = n
  140.                         if (n == s && (s + 1) < order) {
  141.                             VNS.put(new NSKey(s + 1, s + 1), VNS.get(new NSKey(s, s)) / (2 * s + 2.));
  142.                         }
  143.                         // otherwise
  144.                         if ((n + 2) < order) {
  145.                             VNS.put(new NSKey(n + 2, s), VNS.get(new NSKey(n, s)) * (-n + s - 1.) / (n + s + 2.));
  146.                         }
  147.                     }
  148.                 }
  149.             }
  150.             LAST_VNS_ORDER = order;
  151.         }
  152.         return VNS;
  153.     }

  155.     /** Get the V<sub>n,s</sub><sup>m</sup> coefficient from V<sub>n,s</sub>.
  156.      *  <br>See § 2.8.2 in Danielson paper.
  157.      * @param m m
  158.      * @param n n
  159.      * @param s s
  160.      * @return The V<sub>n, s</sub> <sup>m</sup> coefficient
  161.      * @throws OrekitException if m &gt; n
  162.      */
  163.     public static double getVmns(final int m, final int n, final int s)
  164.         throws OrekitException {
  165.         if (m > n) {
  166.             throw new OrekitException(OrekitMessages.DSST_VMNS_COEFFICIENT_ERROR_MS, m, n);
  167.         }
  168.         final double fns = CombinatoricsUtils.factorialDouble(n + FastMath.abs(s));
  169.         final double fnm = CombinatoricsUtils.factorialDouble(n  - m);

  171.         double result = 0;
  172.         // If (n - s) is odd, the Vmsn coefficient is null
  173.         if ((n - s) % 2 == 0) {
  174.             // Update the Vns coefficient
  175.             if ((n + 1) > LAST_VNS_ORDER) {
  176.                 computeVns(n + 1);
  177.             }
  178.             if (s >= 0) {
  179.                 result = fns  * VNS.get(new NSKey(n, s)) / fnm;
  180.             } else {
  181.                 // If s < 0 : Vmn-s = (-1)^(-s) Vmns
  182.                 final int mops = (s % 2 == 0) ? 1 : -1;
  183.                 result = mops * fns * VNS.get(new NSKey(n, -s)) / fnm;
  184.             }
  185.         }
  186.         return result;
  187.     }

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

  192.         /** n value. */
  193.         private final int n;

  195.         /** s value. */
  196.         private final int s;

  198.         /** Simple constructor.
  199.          * @param n n
  200.          * @param s s
  201.          */
  202.         public NSKey(final int n, final int s) {
  203.             this.n = n;
  204.             this.s = s;
  205.         }

  207.         /** Get n.
  208.          * @return n
  209.          */
  210.         public int getN() {
  211.             return n;
  212.         }

  214.         /** Get s.
  215.          * @return s
  216.          */
  217.         public int getS() {
  218.             return s;
  219.         }

  221.         /** {@inheritDoc} */
  222.         public int compareTo(final NSKey key) {
  223.             int result = 1;
  224.             if (n == key.n) {
  225.                 if (s < key.s) {
  226.                     result = -1;
  227.                 } else if (s == key.s) {
  228.                     result = 0;
  229.                 }
  230.             } else if (n < key.n) {
  231.                 result = -1;
  232.             }
  233.             return result;
  234.         }

  236.         /** {@inheritDoc} */
  237.         public boolean equals(final Object key) {

  239.             if (key == this) {
  240.                 // first fast check
  241.                 return true;
  242.             }

  244.             if ((key != null) && (key instanceof NSKey)) {
  245.                 return (n == ((NSKey) key).n) && (s == ((NSKey) key).s);
  246.             }

  248.             return false;

  250.         }

  252.         /** {@inheritDoc} */
  253.         public int hashCode() {
  254.             return 0x998493a6 ^ (n << 8) ^ s;
  255.         }

  257.     }

  259. }
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