two_class_LDA_with_optimal_cut_point_pair_vowel<- function(XTrain,labelsTrain,XTest,labelsTest, indexClassOne,indexClassTwo ){
  #
  # R code to compare the classification of
  #     two class LDA (with the optimal cut point) specified vs. standard LDA 
  #
  # See the section entitled Linear discriminant Analysis where this is suggesteed
  # in Chapter 4 from the book ESLII
  #
  # Inputs:
  #
  # Written by:
  # -- 
  # John L. Weatherwax                2009-04-21
  # 
  # email: wax@alum.mit.edu
  # 
  # Please send comments and especially bug reports to the
  # above email address.
  # 
  #-----
  source("two_class_LDA_with_optimal_cut_point.R")

  inds        = ( labelsTrain == indexClassOne ) | ( labelsTrain == indexClassTwo ) 
  XTrain      = XTrain[ inds, ] 
  labelsTrain = labelsTrain[ inds ]
  inds        = ( labelsTest == indexClassOne ) | ( labelsTest == indexClassTwo )
  XTest       = XTest[ inds, ]
  labelsTest  = labelsTest[ inds ]
  
  # map all classification labels to the integers #1 and #2 so that LDA words correctly below:
  #
  uLabels = sort(unique(labelsTrain))
  inds1   = labelsTrain == uLabels[1]
  inds2   = !inds1
  labelsTrain[inds1] = 1
  labelsTrain[inds2] = 2
  inds1   = labelsTest == uLabels[1]
  inds2   = !inds1
  labelsTest[inds1] = 1
  labelsTest[inds2] = 2


  out = two_class_LDA_with_optimal_cut_point( XTrain, labelsTrain, doPlots=F ) 
  A   = out[[1]] # the expression such that x^T A is the discrimiant
  cp  = out[[2]] # the optimal cut point 
  eRateTrain = out[[3]] # the optmimal error rate

  # Classify the testing set using this method:
  #
  N                       = dim( XTest )[1]
  uLabels                 = unique(labelsTrain)
  predictedLabels         = mat.or.vec( N, 1 ) + uLabels[1] # everything starts predicted as class #1 
  discriminant            = as.matrix( XTest ) %*% A 
  class2                  = discriminant > cp # but these would be classified as class #2 
  predictedLabels[class2] = uLabels[2]
  eRateTest               = sum( abs(predictedLabels - labelsTest)!=0 ) / length(labelsTest)

  eRLDAOptTrain = eRateTrain
  eRLDAOptTest  = eRateTest
  
  #print(sprintf("%20s: (%3d, %3d): eRateTraining= %10.6f; eRateTest= %10.6f","LDA with OCP",indexClassOne,indexClassTwo,eRateTrain,eRateTest))


  #
  # TRAIN A LDA MODEL:
  #
  ldam = lda( XTrain, labelsTrain ) 

  # get this models predictions on the training data
  # 
  predTrain = predict( ldam, XTrain ) 
  tpLabels  = as.double( predTrain$class ) 

  numCC      = sum( (tpLabels - labelsTrain) == 0 )
  numICC     = length(tpLabels)-numCC 
  eRateTrain = numICC / length(tpLabels) 

  # get this models predictions on the testing data
  # 
  predTest = predict( ldam, XTest ) 
  tpLabels = as.double( predTest$class ) 

  numCC     = sum( (tpLabels - labelsTest) == 0 )
  numICC    = length(tpLabels)-numCC 
  eRateTest = numICC / length(tpLabels)

  eRLDATrain = eRateTrain
  eRLDATest  = eRateTest 

  #print(sprintf("%20s: (%3d, %3d): eRateTraining= %10.6f; eRateTest= %10.6f","LDA",indexClassOne,indexClassTwo,eRateTrain,eRateTest))
  
  print(sprintf("%20s: (%3d, %3d): eRateTest= %10.6f/%10.6f","LDA with OCP vs. LDA",indexClassOne,indexClassTwo,eRLDAOptTest,eRLDATest))

  if( eRLDAOptTest < eRLDATest ){ # return whether the new method is better or not 
    return( TRUE )
  }else{
    return( FALSE )
  }
}