CoefficientsFactory.java

  1. /* Copyright 2002-2022 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 java.util.TreeMap;

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

  29. /**
  30.  * This class is designed to provide coefficient from the DSST theory.
  31.  *
  32.  * @author Romain Di Costanzo
  33.  */
  34. public class CoefficientsFactory {

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

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

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

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

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

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

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

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

  93.         return Qns;
  94.     }

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

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

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

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

  135.         return Qns;
  136.     }

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

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

  166.         return GsHs;
  167.     }

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

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

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

  202.         return GsHs;
  203.     }

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

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

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

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

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

  271.         /** n value. */
  272.         private final int n;

  274.         /** s value. */
  275.         private final int s;

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

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

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

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

  315.         /** {@inheritDoc} */
  316.         public boolean equals(final Object key) {

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

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

  327.             return false;

  329.         }

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

  336.     }

  338. }
Created with JaCoCo 0.8.7.202105040129