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    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
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    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
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  package org.orekit.ssa.collision.shorttermencounter.probability.twod;
  
  import org.hipparchus.CalculusFieldElement;
  import org.hipparchus.linear.BlockFieldMatrix;
  import org.hipparchus.linear.BlockRealMatrix;
  import org.hipparchus.linear.FieldLUDecomposition;
  import org.hipparchus.linear.FieldMatrix;
  import org.hipparchus.linear.LUDecomposition;
  import org.hipparchus.linear.RealMatrix;
  import org.hipparchus.util.MathArrays;
  import org.orekit.ssa.metrics.FieldProbabilityOfCollision;
  import org.orekit.ssa.metrics.ProbabilityOfCollision;
  
  /**
   * Abstract class for Alfriend1999 normal and maximised methods as they share lots of similarities.
   *
   * @author Vincent Cucchietti
   * @since 12.0
   */
  public abstract class AbstractAlfriend1999 extends AbstractShortTermEncounter2DPOCMethod {
  
      /**
       * Default constructor.
       *
       * @param name name of the method
       */
      protected AbstractAlfriend1999(final String name) {
          super(name);
      }
  
      /** {@inheritDoc} */
      @Override
      public ProbabilityOfCollision compute(final double xm, final double ym, final double sigmaX, final double sigmaY,
                                            final double radius) {
          // Reconstruct necessary values from inputs
          final double squaredMahalanobisDistance =
                  ShortTermEncounter2DDefinition.computeSquaredMahalanobisDistance(xm, ym, sigmaX, sigmaY);
  
          // Compute covariance matrix determinant
          final double covarianceMatrixDeterminant = computeCovarianceMatrixDeterminant(sigmaX, sigmaY);
  
          // Compute probability of collision
          final double value = computeValue(radius, squaredMahalanobisDistance, covarianceMatrixDeterminant);
  
          return new ProbabilityOfCollision(value, getName(), this.isAMaximumProbabilityOfCollisionMethod());
      }
  
      /** {@inheritDoc} */
      @Override
      public <T extends CalculusFieldElement<T>> FieldProbabilityOfCollision<T> compute(final T xm, final T ym, final T sigmaX,
                                                                                        final T sigmaY,
                                                                                        final T radius) {
          // Reconstruct necessary values from inputs
          final T squaredMahalanobisDistance =
                  FieldShortTermEncounter2DDefinition.computeSquaredMahalanobisDistance(xm, ym, sigmaX, sigmaY);
  
          // Compute covariance matrix determinant
          final T covarianceMatrixDeterminant = computeCovarianceMatrixDeterminant(sigmaX, sigmaY);
  
          // Compute probability of collision
          final T value = computeValue(radius, squaredMahalanobisDistance, covarianceMatrixDeterminant);
  
          return new FieldProbabilityOfCollision<>(value, getName(), this.isAMaximumProbabilityOfCollisionMethod());
      }
  
      /**
       * Compute the covariance matrix determinant.
       *
       * @param sigmaX square root of the x-axis eigen value of the diagonalized combined covariance matrix projected onto the
       * collision plane (m)
       * @param sigmaY square root of the y-axis eigen value of the diagonalized combined covariance matrix projected onto the
       * collision plane (m)
       *
       * @return covariance matrix determinant
       */
      private double computeCovarianceMatrixDeterminant(final double sigmaX, final double sigmaY) {
          // Rebuild covariance matrix
          final RealMatrix covarianceMatrix = new BlockRealMatrix(new double[][] {
                  { sigmaX * sigmaX, 0 },
                  { 0, sigmaY * sigmaY }
          });
  
          // Compute determinant
         return new LUDecomposition(covarianceMatrix).getDeterminant();
     }
 
     /**
      * Compute the covariance matrix determinant.
      *
      * @param sigmaX square root of the x-axis eigen value of the diagonalized combined covariance matrix projected onto the
      * collision plane (m)
      * @param sigmaY square root of the y-axis eigen value of the diagonalized combined covariance matrix projected onto the
      * collision plane (m)
      * @param <T> type of the field elements
      *
      * @return covariance matrix determinant
      */
     private <T extends CalculusFieldElement<T>> T computeCovarianceMatrixDeterminant(final T sigmaX, final T sigmaY) {
         // Rebuild covariance matrix
         final T[][] covarianceMatrixData = MathArrays.buildArray(sigmaX.getField(), 2, 2);
         covarianceMatrixData[0][0] = sigmaX.multiply(sigmaX);
         covarianceMatrixData[1][1] = sigmaY.multiply(sigmaY);
 
         final FieldMatrix<T> covarianceMatrix = new BlockFieldMatrix<>(covarianceMatrixData);
 
         // Compute determinant
         return new FieldLUDecomposition<>(covarianceMatrix).getDeterminant();
     }
 
     /**
      * Compute the value of the probability of collision.
      *
      * @param radius sum of primary and secondary collision object equivalent sphere radii (m)
      * @param squaredMahalanobisDistance squared Mahalanobis distance
      * @param covarianceMatrixDeterminant covariance matrix determinant
      *
      * @return value of the probability of collision
      */
     abstract double computeValue(double radius, double squaredMahalanobisDistance, double covarianceMatrixDeterminant);
 
     /**
      * Compute the value of the probability of collision.
      *
      * @param radius sum of primary and secondary collision object equivalent sphere radii (m)
      * @param squaredMahalanobisDistance squared Mahalanobis distance
      * @param covarianceMatrixDeterminant covariance matrix determinant
      * @param <T> type of the field elements
      *
      * @return value of the probability of collision
      */
     abstract <T extends CalculusFieldElement<T>> T computeValue(T radius, T squaredMahalanobisDistance,
                                                                 T covarianceMatrixDeterminant);
 }