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#THIS SCRIPT APPLIES THE ESTIMATED PARAMETERS OF MULTINOMIAL LOGISTIC REGRESSION TO A NEW (TEST) DATASET
#
# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME  TYPE   DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# X     Double  ---     Data Matrix X
# B     Double  ---     Regression parameters betas
# Y     Double  ---     Response vector Y
# ---------------------------------------------------------------------------------------------
# OUTPUT: Matrix M of predicted means/probabilities, some statistics in CSV format (see below)
# OUTPUT:
# ---------------------------------------------------------------------------------------------
# NAME               TYPE   DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# M                  Double  ---     Matrix M of predicted means/probabilities
# predicted_Y        Double  ---     Predicted response vector
# accuracy           Double  ---     scalar value of accuracy
# ---------------------------------------------------------------------------------------------


m_multiLogRegPredict = function(Matrix[Double] X, Matrix[Double] B, Matrix[Double] Y, Boolean verbose = FALSE)
return(Matrix[Double] M, Matrix[Double] predicted_Y, Double accuracy)
{  
  if(min(Y) <= 0)
    stop("class labels should be greater than zero")
    
  num_records = nrow(X);
  num_features = ncol(X);
  beta = B[1:ncol(X), ];
  intercept = B[nrow(B), ];

  if (nrow(B) == ncol(X))
    intercept = 0.0 * intercept; 
  else
    num_features = num_features + 1;

  ones_rec = matrix(1, rows = num_records, cols = 1);
  linear_terms = X %*% beta + ones_rec %*% intercept;

  M = probabilities(linear_terms); # compute the probablitites on unknown data
  predicted_Y = rowIndexMax(M); # extract the class labels

  if(nrow(Y) != 0)
    accuracy = sum((predicted_Y - Y) == 0) / num_records * 100;
  
  if(verbose)
    print("Accuracy (%): " + accuracy);
}

probabilities = function (Matrix[double] linear_terms)
  return (Matrix[double] means) {
   # PROBABLITIES FOR MULTINOMIAL LOGIT DISTRIBUTION
  num_points = nrow (linear_terms);
  elt = exp (linear_terms);
  ones_pts = matrix (1, rows = num_points, cols = 1);
  elt = cbind (elt, ones_pts);
  ones_ctg = matrix (1, rows = ncol (elt), cols = 1);
  means = elt / (rowSums (elt) %*% t(ones_ctg));
}