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

#  
# This script computes an approximate factorization of a low-rank matrix X into two matrices U and V
# using different implementations of the Alternating-Least-Squares (ALS) algorithm.
# Matrices U and V are computed by minimizing a loss function (with regularization).
#
# INPUT   PARAMETERS:
# ---------------------------------------------------------------------------------------------
# NAME    TYPE     DEFAULT  MEANING
# ---------------------------------------------------------------------------------------------
# X       String   ---      Location to read the input matrix X to be factorized
# rank    Int      10       Rank of the factorization
# reg     String   "L2"	    Regularization: 
#                           "L2" = L2 regularization;
#                              f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
#                                       + 0.5 * lambda * (sum (U ^ 2) + sum (V ^ 2))
#                           "wL2" = weighted L2 regularization
#                              f (U, V) = 0.5 * sum (W * (U %*% V - X) ^ 2)
#                                       + 0.5 * lambda * (sum (U ^ 2 * row_nonzeros) 
#                                       + sum (V ^ 2 * col_nonzeros))
# lambda  Double   0.000001 Regularization parameter, no regularization if 0.0
# maxi    Int      50       Maximum number of iterations
# check   Boolean  TRUE     Check for convergence after every iteration, i.e., updating U and V once
# thr     Double   0.0001   Assuming check is set to TRUE, the algorithm stops and convergence is declared 
#                           if the decrease in loss in any two consecutive iterations falls below this threshold; 
#                           if check is FALSE thr is ignored
# ---------------------------------------------------------------------------------------------
# OUTPUT:
# 1- An m x r matrix U, where r is the factorization rank 
# 2- An r x n matrix V

m_als = function(Matrix[Double] X, Integer rank = 10, String reg = "L2", Double lambda = 0.000001,
  Integer maxi = 50, Boolean check = TRUE, Double thr = 0.0001, Boolean verbose = TRUE)
  return (Matrix[Double] U, Matrix[Double] V)
{
  N = 10000; # for large problems, use scalable alsCG
  if( reg != "L2" | nrow(X) > N | ncol(X) > N )
    [U, V] = alsCG(X=X, rank=rank, reg=reg, lambda=lambda,
                   maxi=maxi, check=check, thr=thr, verbose=verbose);
  else
    [U, V] = alsDS(X=X, rank=rank, lambda=lambda, maxi=maxi,
                   check=check, thr=thr, verbose=verbose);
}
