GSF : KL Mixture Reduction helpers comments/made code a bit more clear explict.

This MR does not change the actual distance calculation formalism we use. It adds comments and a struct to make it easier to follow the formalism used, plus uses double precision for the calculation involving small/large numbers.

Mentionig @amorley who initially introduced the code.

This is probably a first step to facilitate studying the different methods here https://arxiv.org/pdf/2001.00727.pdf formulas 10-13. Currently we use formula 10 but without accounting for the weights.

Actually, Track Fitting with non-Gaussian noise references the original publication for formula 10 (same author as the arxiv above) but does not include the weights explicitly. So it seems our current implementation does not use them either.

A next step would be to formulate a simple but kind of realistic test of a merging procedure and test alternatives.

Although we merge 72->12 (so we keep relative high numbers) the final result quality is not 100% independent of the method.

Tracking/TrkFitter/TrkGaussianSumFilter/TrkGaussianSumFilter/KLGaussianMixtureReduction.h

@@ -2,15 +2,13 @@
   Copyright (C) 2002-2020 CERN for the benefit of the ATLAS collaboration
 */
 
-/*********************************************************************************
-  KLGaussianMixReduction.h  -  description
-  -------------------------------------------------
-begin                : 26th November 2019
-author               : amorley, Christos
-decription           : Function that help implement a
-"Kullback-Leibler Approach to Gaussian Mixture Reduction"
- *********************************************************************************/
-
+/**
+* @file  KLGaussianMixtureReduction.h
+* @author amorley
+* @author Anastopoulos
+* @date 26th November 2019
+* @brief Function that help implement component merging .
+*/
 #ifndef KLGaussianMixReductionUtils_H
 #define KLGaussianMixReductionUtils_H
 
@@ -21,28 +19,31 @@ decription           : Function that help implement a
 
 namespace GSFUtils {
 
-/*
+/**
  * Alignment used  for SIMD
  */
-
 constexpr int32_t alignment =32;
 
 /**
  * The main pupropse of the utilities here
  * are to facilitate the calculation of the 
- * Kullback-Leible divergence between components
- * of the mixture and the merging of the componets.
+ * divergence between components of the mixture 
+ * and the merging of similar componets.
  *
- * The dissimilarity measure/distance metric 
- * 2*[ D(P1||P2)+ D(P2||P1)]
+ * For a revies of available methods look 
+ * https://arxiv.org/pdf/2001.00727.pdf
  *
- * For 1D Normal distributions with this is given
- * by
+ * Here we opt for formula 10. 
+ * For an 1D Normal distributions this becomes: 
  *
  * (variance1-variance2) (1/variance1 - 1/variance2) - 
  * (mean1-mean2)(1/variance+1/variance)(mean1-mean2)
+ *
+ * We use doubles for the intermediate calculations
+ * but we store the final distances to short in an array
+ * of floats.
+ *
 */
-
 struct Component1D{
   double mean=0.;
   double cov=0.;
@@ -82,7 +83,7 @@ struct triangularToIJ{
   int32_t J=-1;
 };
 
-/*
+/**
  * Some usefull typedefs
  */
 typedef float* ATH_RESTRICT floatPtrRestrict;
@@ -127,13 +128,17 @@ recalculateDistances(const componentPtrRestrict componentsIn,
                      const int32_t mini,
                      const int32_t n);
 
-// Calculate the distances for all pairs
+/** 
+ * Calculate the distances for all component pairs
+ */
 void
 calculateAllDistances(const componentPtrRestrict componentsIn,
                       floatPtrRestrict distancesIn,
                       const int32_t n);
 
-// Reset the distances for a row
+/*
+ * Reset the distances wrt to a mini index
+ */
 void
 resetDistances(floatPtrRestrict distancesIn,
                const int32_t mini,