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#-------------------------------------------------------------

# Principal Component Analysis (PCA) for reconstruction of approximation of the original data.
# 
# This methods allows to reconstruct an approximation of the original matrix, and is usefull for
# calculating how much information is lost in the PCA.
#
# ---------------------------------------------------------------------------------------------
# NAME          TYPE    DEFAULT       MEANING
# ---------------------------------------------------------------------------------------------
# X             Matrix  ---           Input features that have PCA applied to them
# Centering     Matrix  empty matrix  The column means of the PCA model, subtracted to construct the PCA
# ScaleFactor   Matrix  empty matrix  The scaling of each dimension in the PCA model
# ---------------------------------------------------------------------------------------------
# Y             Matrix  ---           Output feature matrix reconstructing and approximation of the original matrix
# ---------------------------------------------------------------------------------------------

m_pcaInverse = function(Matrix[Double] Y, Matrix[Double] Clusters, 
  Matrix[Double] Centering = matrix(0, rows= 0, cols=0), 
  Matrix[Double] ScaleFactor = matrix(0, rows= 0, cols=0))
  return (Matrix[Double] X) 
{
  X = Y %*% t(Clusters)

  if(nrow(ScaleFactor) > 0 & ncol(ScaleFactor) > 0){
    X = X * ScaleFactor
  }

  if(nrow(Centering) > 0 & ncol(Centering) > 0){
    X = X + Centering
  }

}
