TMVA::MethodFisher

 standard constructor for the "Fisher" 

 constructor to calculate the Fisher-MVA from previously generatad 
 coefficients (weight file)

 default initialisation called by all constructors

 MethodFisher options:
 format and syntax of option string: "type"
 where type is "Fisher" or "Mahalanobis"

 process user options

 destructor

 computation of Fisher coefficients by series of matrix operations

 returns the Fisher value (no fixed range)

 initialisaton method; creates global matrices and vectors
 should never be called without existing trainingTree

 compute mean values of variables in each sample, and the overall means

 the matrix of covariance 'within class' reflects the dispersion of the
 events relative to the center of gravity of their own class  

 the matrix of covariance 'between class' reflects the dispersion of the
 events of a class relative to the global center of gravity of all the class
 hence the separation between classes

 compute full covariance matrix from sum of within and between matrices

 Fisher = Sum { [coeff]*[variables] }

 let Xs be the array of the mean values of variables for signal evts
 let Xb be the array of the mean values of variables for backgd evts
 let InvWith be the inverse matrix of the 'within class' correlation matrix

 then the array of Fisher coefficients is 
 [coeff] =sqrt(fNsig*fNbgd)/fNevt*transpose{Xs-Xb}*InvWith

 computation of discrimination power indicator for each variable
 small values of "fWith" indicates little compactness of sig & of backgd
 big values of "fBetw" indicates large separation between sig & backgd

 we want signal & backgd classes as compact and separated as possible
 the discriminating power is then defined as the ration "fBetw/fWith"

 computes ranking of input variables

 display Fisher coefficients and discriminating power for each variable
 check maximum length of variable name

 save the weights

 read Fisher coefficients from weight file