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    *
    *   http://www.apache.org/licenses/LICENSE-2.0
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   * Unless required by applicable law or agreed to in writing, software
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  package org.orekit.propagation.semianalytical.dsst.utilities;
  
  import org.hipparchus.Field;
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.util.FastMath;
  
  /** Compute the G<sub>ms</sub><sup>j</sup> and the H<sub>ms</sub><sup>j</sup>
   *  polynomials in the equinoctial elements h, k and the direction cosines α and β
   *  and their partial derivatives with respect to k, h, α and β.
   *  <p>
   *  The expressions used are equations 2.7.5-(1)(2) from the Danielson paper.
   *  </p>
   *  @author Romain Di Costanzo
   *  @author Bryan Cazabonne (field translation)
   */
  public class FieldGHmsjPolynomials <T extends CalculusFieldElement<T>> {
      /** C<sub>j</sub>(k, h), S<sub>j</sub>(k, h) coefficient.
       * (k, h) are the (x, y) component of the eccentricity vector in equinoctial elements
       */
      private final FieldCjSjCoefficient<T> cjsjKH;
  
      /** C<sub>j</sub>(α, β), S<sub>j</sub>(α, β) coefficient.
       * (α, β) are the direction cosines
       */
      private final FieldCjSjCoefficient<T> cjsjAB;
  
      /** Is the orbit represented as a retrograde orbit.
       *  I = -1 if yes, +1 otherwise.
       */
      private int                   I;
  
      /** Zero for initialization. */
      private final T zero;
  
      /** Create a set of G<sub>ms</sub><sup>j</sup> and H<sub>ms</sub><sup>j</sup> polynomials.
       *  @param k X component of the eccentricity vector
       *  @param h Y component of the eccentricity vector
       *  @param alpha direction cosine α
       *  @param beta direction cosine β
       *  @param retroFactor -1 if the orbit is represented as retrograde, +1 otherwise
       *  @param field field element
       **/
      public FieldGHmsjPolynomials(final T k, final T h,
                              final T alpha, final T beta,
                              final int retroFactor,
                              final Field<T> field) {
          zero = field.getZero();
          this.cjsjKH = new FieldCjSjCoefficient<>(k, h, field);
          this.cjsjAB = new FieldCjSjCoefficient<>(alpha, beta, field);
          this.I = retroFactor;
      }
  
      /** Get the G<sub>ms</sub><sup>j</sup> coefficient.
       * @param m m subscript
       * @param s s subscript
       * @param j order
       * @return the G<sub>ms</sub><sup>j</sup>
       */
      public T getGmsj(final int m, final int s, final int j) {
          final int sMj = FastMath.abs(s - j);
          T gms = zero;
          if (FastMath.abs(s) <= m) {
              final int mMis = m - I * s;
              gms = cjsjKH.getCj(sMj).multiply(cjsjAB.getCj(mMis)).
                    subtract(cjsjKH.getSj(sMj).multiply(cjsjAB.getSj(mMis)).multiply(sgn(s - j)).multiply(I));
          } else {
              final int sMim = FastMath.abs(s - I * m);
              gms = cjsjKH.getCj(sMj).multiply(cjsjAB.getCj(sMim)).
                    add(cjsjKH.getSj(sMj).multiply(cjsjAB.getSj(sMim)).multiply(sgn(s - j)).multiply(sgn(s - m)));
          }
          return gms;
      }
  
      /** Get the H<sub>ms</sub><sup>j</sup> coefficient.
       * @param m m subscript
       * @param s s subscript
       * @param j order
       * @return the H<sub>ms</sub><sup>j</sup>
       */
      public T getHmsj(final int m, final int s, final int j) {
          final int sMj = FastMath.abs(s - j);
          T hms = zero;
          if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             hms = cjsjKH.getCj(sMj).multiply(cjsjAB.getSj(mMis)).multiply(I).
                             add(cjsjKH.getSj(sMj).multiply(cjsjAB.getCj(mMis)).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             hms = cjsjKH.getCj(sMj).multiply(cjsjAB.getSj(sMim)).multiply(-sgn(s - m)).
                   add(cjsjKH.getSj(sMj).multiply(cjsjAB.getCj(sMim)).multiply(sgn(s - j)));
         }
         return hms;
     }
 
     /** Get the dG<sub>ms</sub><sup>j</sup> / d<sub>k</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dG<sub>ms</sub><sup>j</sup> / d<sub>k</sub>
      */
     public T getdGmsdk(final int m, final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dGmsdk = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dGmsdk = cjsjKH.getDcjDk(sMj).multiply(cjsjAB.getCj(mMis)).
                      subtract(cjsjKH.getDsjDk(sMj).multiply(cjsjAB.getSj(mMis)).multiply(I).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dGmsdk = cjsjKH.getDcjDk(sMj).multiply(cjsjAB.getCj(sMim)).
                      add(cjsjKH.getDsjDk(sMj).multiply(cjsjAB.getSj(sMim)).multiply(sgn(s - m)).multiply(sgn(s - j)));
         }
         return dGmsdk;
     }
 
     /** Get the dG<sub>ms</sub><sup>j</sup> / d<sub>h</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dG<sub>ms</sub><sup>j</sup> / d<sub>h</sub>
      */
     public T getdGmsdh(final int m, final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dGmsdh = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dGmsdh = cjsjKH.getDcjDh(sMj).multiply(cjsjAB.getCj(mMis)).
                      subtract(cjsjKH.getDsjDh(sMj).multiply(cjsjAB.getSj(mMis)).multiply(I).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dGmsdh = cjsjKH.getDcjDh(sMj).multiply(cjsjAB.getCj(sMim)).
                      add(cjsjKH.getDsjDh(sMj).multiply(cjsjAB.getSj(sMim)).multiply(sgn(s - m)).multiply(sgn(s - j)));
         }
         return dGmsdh;
     }
 
     /** Get the dG<sub>ms</sub><sup>j</sup> / d<sub>α</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dG<sub>ms</sub><sup>j</sup> / d<sub>α</sub>
      */
     public T getdGmsdAlpha(final int m, final int s, final int j) {
         final int sMj  = FastMath.abs(s - j);
         T dGmsdAl = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dGmsdAl = cjsjKH.getCj(sMj).multiply(cjsjAB.getDcjDk(mMis)).
                       subtract(cjsjKH.getSj(sMj).multiply(cjsjAB.getDsjDk(mMis)).multiply(I).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dGmsdAl = cjsjKH.getCj(sMj).multiply(cjsjAB.getDcjDk(sMim)).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDsjDk(sMim)).multiply(sgn(s - j)).multiply(sgn(s - m)));
         }
         return dGmsdAl;
     }
 
     /** Get the dG<sub>ms</sub><sup>j</sup> / d<sub>β</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dG<sub>ms</sub><sup>j</sup> / d<sub>β</sub>
      */
     public T getdGmsdBeta(final int m, final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dGmsdBe = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dGmsdBe = cjsjKH.getCj(sMj).multiply(cjsjAB.getDcjDh(mMis)).
                       subtract(cjsjKH.getSj(sMj).multiply(cjsjAB.getDsjDh(mMis)).multiply(I).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dGmsdBe = cjsjKH.getCj(sMj).multiply(cjsjAB.getDcjDh(sMim)).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDsjDh(sMim)).multiply(sgn(s - j)).multiply(sgn(s - m)));
         }
         return dGmsdBe;
     }
 
     /** Get the dH<sub>ms</sub><sup>j</sup> / d<sub>k</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dH<sub>ms</sub><sup>j</sup> / d<sub>k</sub>
      */
     public T getdHmsdk(final int m, final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dHmsdk = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dHmsdk = cjsjKH.getDcjDk(sMj).multiply(cjsjAB.getSj(mMis)).multiply(I).
                      add(cjsjKH.getDsjDk(sMj).multiply(cjsjAB.getCj(mMis)).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dHmsdk = cjsjKH.getDcjDk(sMj).multiply(cjsjAB.getSj(sMim)).multiply(-sgn(s - m)).
                      add(cjsjKH.getDsjDk(sMj).multiply(cjsjAB.getCj(sMim)).multiply(sgn(s - j)));
         }
         return dHmsdk;
     }
 
     /** Get the dH<sub>ms</sub><sup>j</sup> / d<sub>h</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dH<sub>ms</sub><sup>j</sup> / d<sub>h</sub>
      */
     public T getdHmsdh(final int m,  final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dHmsdh = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dHmsdh = cjsjKH.getDcjDh(sMj).multiply(cjsjAB.getSj(mMis)).multiply(I).
                      add(cjsjKH.getDsjDh(sMj).multiply(cjsjAB.getCj(mMis)).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dHmsdh = cjsjKH.getDcjDh(sMj).multiply(cjsjAB.getSj(sMim)).multiply(-sgn(s - m)).
                      add(cjsjKH.getDsjDh(sMj).multiply(cjsjAB.getCj(sMim)).multiply(sgn(s - j)));
         }
         return dHmsdh;
     }
 
     /** Get the dH<sub>ms</sub><sup>j</sup> / d<sub>α</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dH<sub>ms</sub><sup>j</sup> / d<sub>α</sub>
      */
     public T getdHmsdAlpha(final int m, final int s, final int j) {
         final int sMj  = FastMath.abs(s - j);
         T dHmsdAl = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dHmsdAl = cjsjKH.getCj(sMj).multiply(cjsjAB.getDsjDk(mMis)).multiply(I).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDcjDk(mMis)).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dHmsdAl = cjsjKH.getCj(sMj).multiply(cjsjAB.getDsjDk(sMim)).multiply(-sgn(s - m)).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDcjDk(sMim)).multiply(sgn(s - j)));
         }
         return dHmsdAl;
     }
 
     /** Get the dH<sub>ms</sub><sup>j</sup> / d<sub>β</sub> coefficient.
      * @param m m subscript
      * @param s s subscript
      * @param j order
      * @return dH<sub>ms</sub><sup>j</sup> / d<sub>β</sub>
      */
     public T getdHmsdBeta(final int m, final int s, final int j) {
         final int sMj = FastMath.abs(s - j);
         T dHmsdBe = zero;
         if (FastMath.abs(s) <= m) {
             final int mMis = m - I * s;
             dHmsdBe = cjsjKH.getCj(sMj).multiply(cjsjAB.getDsjDh(mMis)).multiply(I).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDcjDh(mMis)).multiply(sgn(s - j)));
         } else {
             final int sMim = FastMath.abs(s - I * m);
             dHmsdBe = cjsjKH.getCj(sMj).multiply(cjsjAB.getDsjDh(sMim)).multiply(-sgn(s - m)).
                       add(cjsjKH.getSj(sMj).multiply(cjsjAB.getDcjDh(sMim)).multiply(sgn(s - j)));
         }
         return dHmsdBe;
     }
 
     /** Get the sign of an integer.
      *  @param i number on which evaluation is done
      *  @return -1 or +1 depending on sign of i
      */
     private int sgn(final int i) {
         return (i < 0) ? -1 : 1;
     }
 }