+library(MASS) #generalized inverse of matrix Monroe-Penrose
+
+vec_bin = function(X,r){
+ Z = c()
+ indice = c()
+ j=1
+ for(i in 1:length(X)){
+ if(X[i] == r){
+ Z[i] = 1
+ indice[j] = i
+ j=j+1
+ }
+ else{
+ Z[i] = 0
+ }
+ }
+ return(list(Z,indice))
+}
+
+initSmallEM = function(k,X,Y,tau){
+ n = nrow(Y)
+ m = ncol(Y)
+ p = ncol(X)
+
+ betaInit1 = array(0, dim=c(p,m,k,20))
+ sigmaInit1 = array(0, dim = c(m,m,k,20))
+ phiInit1 = array(0, dim = c(p,m,k,20))
+ rhoInit1 = array(0, dim = c(m,m,k,20))
+ piInit1 = matrix(0,20,k)
+ gamInit1 = array(0, dim=c(n,k,20))
+ LLFinit1 = list()
+
+
+ for(repet in 1:20){
+ clusters = hclust(dist(y)) #default distance : euclidean
+ clusterCut = cutree(clusters,k)
+ Zinit1[,repet] = clusterCut #retourne les indices (à quel cluster indiv_i appartient) d'un clustering hierarchique (nb de cluster = k)
+
+ for(r in 1:k){
+ Z = Zinit1[,repet]
+ Z_bin = vec_bin(Z,r)
+ Z_vec = Z_bin[[1]] #vecteur 0 et 1 aux endroits où Z==r
+ Z_indice = Z_bin[[2]] #renvoit les indices où Z==r
+
+ betaInit1[,,r,repet] = ginv(t(x[Z_indice,])%*%x[Z_indice,])%*%t(x[Z_indice,])%*%y[Z_indice,]
+ sigmaInit1[,,r,repet] = diag(m)
+ phiInit1[,,r,repet] = betaInit1[,,r,repet]/sigmaInit1[,,r,repet]
+ rhoInit1[,,r,repet] = solve(sigmaInit1[,,r,repet])
+ piInit1[repet,r] = sum(Z_vec)/n
+ }
+
+ for(i in 1:n){
+ for(r in 1:k){
+ dotProduct = (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet]) %*% (y[i,]%*%rhoInit1[,,r,repet]-x[i,]%*%phiInit1[,,r,repet])
+ Gam[i,r] = piInit1[repet,r]*det(rhoInit1[,,r,repet])*exp(-0.5*dotProduct)
+ }
+ sumGamI = sum(gam[i,])
+ gamInit1[i,,repet]= Gam[i,] / sumGamI
+ }
+
+ miniInit = 10
+ maxiInit = 11
+
+ new_EMG = EMGLLF(phiInit1[,,,repet],rhoInit1[,,,repet],piInit1[repet,],gamInit1[,,repet],miniInit,maxiInit,1,0,x,y,tau)
+ ##.C("EMGLLF", phiInit = phiInit, rhoInit = rhoInit, ...)
+ LLFEessai = new_EMG[[4]]
+ LLFinit1[[repet]] = LLFEessai[[length(LLFEessai)]]
+ }
+
+ b = which.max(LLFinit1)
+
+ phiInit = phiInit1[,,,b]
+ rhoInit = rhoInit1[,,,b]
+ piInit = piInit1[b,]
+ gamInit = gamInit1[,,b]
+
+ return(list(phiInit, rhoInit, piInit, gamInit))
+}
+
+