#-------------------------------------------------------------
#
# Licensed to the Apache Software Foundation (ASF) under one
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# to you under the Apache License, Version 2.0 (the
# "License"); you may not use this file except in compliance
# with the License.  You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
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# specific language governing permissions and limitations
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#-------------------------------------------------------------

# INPUT PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME   TYPE   DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# INPUT  String ---      Location to read the matrix A of feature vectors
# K      Int    ---      Indicates dimension of the new vector space constructed from eigen vector
# CENTER Int    0        Indicates whether or not to center data
# SCALE  Int    0        Indicates whether or not to scale data
# PROJDATA Int  0      This argument indicates if the data should be projected or not
# ---------------------------------------------------------------------------------------------

PCA = function(Matrix[Double] A, Integer K = ncol(A), Integer center = 1, Integer scale = 1,
    Integer projectData = 1) return(Matrix[Double] newA)
{
  evec_dominant = matrix(0,cols=1,rows=1);

  N = nrow(A);
  D = ncol(A);

  # perform z-scoring (centering and scaling)
  A = scale(A, center==1, scale==1);

  # co-variance matrix
  mu = colSums(A)/N;
  C = (t(A) %*% A)/(N-1) - (N/(N-1))*t(mu) %*% mu;

  # compute eigen vectors and values
  [evalues, evectors] = eigen(C);

  decreasing_Idx = order(target=evalues,by=1,decreasing=TRUE,index.return=TRUE);
  diagmat = table(seq(1,D),decreasing_Idx);
  # sorts eigenvalues by decreasing order
  evalues = diagmat %*% evalues;
  # sorts eigenvectors column-wise in the order of decreasing eigenvalues
  evectors = evectors %*% diagmat;


  # select K dominant eigen vectors
  nvec = ncol(evectors);

  eval_dominant = evalues[1:K, 1];
  evec_dominant = evectors[,1:K];

  # the square root of eigenvalues
  eval_stdev_dominant = sqrt(eval_dominant);

  if (projectData == 1){
    # Construct new data set by treating computed dominant eigenvectors as the basis vectors
    newA = A %*% evec_dominant;
  }
}

A = rand(rows=100, cols=10, seed=42);
R = matrix(0, rows=1, cols=ncol(A));
for (i in 1:ncol(A)) {
  newA = PCA(A=A, K=i);
  while(FALSE){}
  R[,i] = sum(newA);
}
write(R, $1, format="text");