#'
#' Description de EMGrank
#'
-#' @param phiInit ...
#' @param Pi Parametre de proportion
#' @param Rho Parametre initial de variance renormalisé
#' @param mini Nombre minimal d'itérations dans l'algorithme 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)
+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)
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))
+}