#' selectVariables
#'
#' It is a function which construct, for a given lambda, the sets of relevant variables.
#'
#' @param phiInit an initial estimator for phi (size: p*m*k)
#' @param rhoInit an initial estimator for rho (size: m*m*k)
#' @param piInit	an initial estimator for pi (size : k)
#' @param gamInit an initial estimator for gamma
#' @param mini		minimum number of iterations in EM algorithm
#' @param maxi		maximum number of iterations in EM algorithm
#' @param gamma	 power in the penalty
#' @param glambda grid of regularization parameters
#' @param X			 matrix of regressors
#' @param Y			 matrix of responses
#' @param thres	 threshold to consider a coefficient to be equal to 0
#' @param tau		 threshold to say that EM algorithm has converged
#' @param ncores Number or cores for parallel execution (1 to disable)
#'
#' @return a list of outputs, for each lambda in grid: selected,Rho,Pi
#'
#' @examples TODO
#'
#' @export
#'
selectVariables = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,glambda,
                           X,Y,thresh,tau, ncores=3, fast=TRUE)
{
  if (ncores > 1)
  {
    cl = parallel::makeCluster(ncores, outfile='')
    parallel::clusterExport(cl=cl,
                            varlist=c("phiInit","rhoInit","gamInit","mini","maxi","glambda","X","Y","thresh","tau"),
                            envir=environment())
  }
  
  # Computation for a fixed lambda
  computeCoefs <- function(lambda)
  {
    params = EMGLLF(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau,fast)
    
    p = dim(phiInit)[1]
    m = dim(phiInit)[2]
    
    #selectedVariables: list where element j contains vector of selected variables in [1,m]
    selectedVariables = lapply(1:p, function(j) {
      #from boolean matrix mxk of selected variables obtain the corresponding boolean m-vector,
      #and finally return the corresponding indices
      seq_len(m)[ apply( abs(params$phi[j,,]) > thresh, 1, any ) ]
    })
    
    list("selected"=selectedVariables,"Rho"=params$rho,"Pi"=params$pi)
  }
  
  # For each lambda in the grid, we compute the coefficients
  out <-
    if (ncores > 1)
      parLapply(cl, glambda, computeCoefs)
  else
    lapply(glambda, computeCoefs)
  if (ncores > 1)
    parallel::stopCluster(cl)
  # Suppress models which are computed twice
  #En fait, ca ca fait la comparaison de tous les parametres
  #On veut juste supprimer ceux qui ont les memes variables sélectionnées
  #sha1_array <- lapply(out, digest::sha1)
  #out[ duplicated(sha1_array) ]
  selec = lapply(out, function(model) model$selected)
  ind_dup = duplicated(selec)
  ind_uniq = which(!ind_dup)
  out2 = list()
  for (l in 1:length(ind_uniq)){
    out2[[l]] = out[[ind_uniq[l]]]
  }
  out2
}