cosmetics

[valse.git] / pkg / R / EMGrank.R

#' EMGrank
#'
#' Description de EMGrank
#'
#' @param Pi Parametre de proportion
#' @param Rho Parametre initial de variance renormalisé
#' @param mini Nombre minimal d'itérations dans l'algorithme EM
#' @param maxi Nombre maximal d'itérations dans l'algorithme EM
#' @param X Régresseurs
#' @param Y Réponse
#' @param tau Seuil pour accepter la convergence
#' @param rank Vecteur des rangs possibles
#'
#' @return A list ...
#'   phi : parametre de moyenne renormalisé, calculé par l'EM
#'   LLF : log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
#'
#' @export
EMGrank <- function(Pi, Rho, mini, maxi, X, Y, tau, rank, fast=TRUE)
{
	if (!fast)
	{
		# Function in R
		return (.EMGrank_R(Pi, Rho, mini, maxi, X, Y, tau, rank))
	}

	# Function in C
	n = nrow(X) #nombre d'echantillons
	p = ncol(X) #nombre de covariables
	m = ncol(Y) #taille de Y (multivarié)
	k = length(Pi) #nombre de composantes dans le mélange
	.Call("EMGrank",
		Pi, Rho, mini, maxi, X, Y, tau, rank,
		phi=double(p*m*k), LLF=double(1),
		n, p, m, k,
		PACKAGE="valse")
}

#helper to always have matrices as arg (TODO: put this elsewhere? improve?)
# --> Yes, we should use by-columns storage everywhere... [later!]
matricize <- function(X)
{
	if (!is.matrix(X))
		return (t(as.matrix(X)))
	return (X)
}

# R version - slow but easy to read
.EMGrank_R = function(Pi, Rho, mini, maxi, X, Y, tau, rank)
{
  #matrix dimensions
  n = dim(X)[1]
  p = dim(X)[2]
  m = dim(Rho)[2]
  k = dim(Rho)[3]

  #init outputs
  phi = array(0, dim=c(p,m,k))
  Z = rep(1, n)
  LLF = 0

  #local variables
  Phi = array(0, dim=c(p,m,k))
  deltaPhi = c()
  sumDeltaPhi = 0.
  deltaPhiBufferSize = 20

  #main loop
  ite = 1
  while (ite<=mini || (ite<=maxi && sumDeltaPhi>tau))
	{
    #M step: update for Beta ( and then phi)
    for(r in 1:k)
		{
      Z_indice = seq_len(n)[Z==r] #indices where Z == r
      if (length(Z_indice) == 0)
        next
      #U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
      s = svd( MASS::ginv(crossprod(matricize(X[Z_indice,]))) %*%
				crossprod(matricize(X[Z_indice,]),matricize(Y[Z_indice,])) )
      S = s$d
      #Set m-rank(r) singular values to zero, and recompose
      #best rank(r) approximation of the initial product
      if(rank[r] < length(S))
        S[(rank[r]+1):length(S)] = 0
      phi[,,r] = s$u %*% diag(S) %*% t(s$v) %*% Rho[,,r]
    }

		#Step E and computation of the loglikelihood
		sumLogLLF2 = 0
		for(i in seq_len(n))
		{
			sumLLF1 = 0
			maxLogGamIR = -Inf
			for (r in seq_len(k))
			{
				dotProduct = tcrossprod(Y[i,]%*%Rho[,,r]-X[i,]%*%phi[,,r])
				logGamIR = log(Pi[r]) + log(det(Rho[,,r])) - 0.5*dotProduct
				#Z[i] = index of max (gam[i,])
				if(logGamIR > maxLogGamIR)
				{
					Z[i] = r
					maxLogGamIR = logGamIR
				}
				sumLLF1 = sumLLF1 + exp(logGamIR) / (2*pi)^(m/2)
			}
			sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
		}

		LLF = -1/n * sumLogLLF2

		#update distance parameter to check algorithm convergence (delta(phi, Phi))
		deltaPhi = c( deltaPhi, max( (abs(phi-Phi)) / (1+abs(phi)) ) ) #TODO: explain?
		if (length(deltaPhi) > deltaPhiBufferSize)
		  deltaPhi = deltaPhi[2:length(deltaPhi)]
		sumDeltaPhi = sum(abs(deltaPhi))

		#update other local variables
		Phi = phi
		ite = ite+1
  }
  return(list("phi"=phi, "LLF"=LLF))
}