EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau){
#matrix dimensions
n = dim(X)[1]
- p = dim[phiInit][1]
- m = dim[phiInit][2]
- k = dim[phiInit][3]
+ p = dim(phiInit)[1]
+ m = dim(phiInit)[2]
+ k = dim(phiInit)[3]
#init outputs
phi = phiInit
kk = 0
pi2AllPositive = FALSE
while(pi2AllPositive == FALSE){
- pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+ Pi2 = Pi + 0.1^kk * ((1/n)*gam2 - Pi)
pi2AllPositive = TRUE
for(r in 1:k){
- if(pi2[r] < 0){
+ if(Pi2[r] < 0){
pi2AllPositive = false;
break
}
#t[m]la plus grande valeur dans la grille O.1^k tel que ce soit
#décroissante ou constante
- while((-1/n*a+lambda*((pi.^gamma)*b))<(-1/n*gam2*t(log(pi2))+lambda.*(pi2.^gamma)*b) && kk<1000){
- pi2 = pi+0.1^kk*(1/n*gam2-pi)
+ while((-1/n*a+lambda*((Pi.^gamma)*b))<(-1/n*gam2*t(log(Pi2))+lambda.*(Pi2.^gamma)*b) && kk<1000){
+ Pi2 = Pi+0.1^kk*(1/n*gam2-Pi)
kk = kk+1
}
t = 0.1^(kk)
- pi = (pi+t*(pi2-pi)) / sum(pi+t*(pi2-pi))
+ Pi = (Pi+t*(Pi2-Pi)) / sum(Pi+t*(Pi2-Pi))
#Pour phi et rho
for(r in 1:k){
for(j in 1:p){
for(mm in 1:m){
S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + dot(phi[1:j-1,mm,r],Gram2[j,1:j-1,r]) + dot(phi[j+1:p,mm,r],Gram2[j,j+1:p,r])
- if(abs(S(j,mm,r)) <= n*lambda*(pi(r)^gamma))
+ if(abs(S(j,mm,r)) <= n*lambda*(Pi[r]^gamma)){
phi[j,mm,r]=0
- else{
- if(S[j,mm,r]> n*lambda*(Pi[r]^gamma))
+ }else{
+ if(S[j,mm,r]> n*lambda*(Pi[r]^gamma)){
phi[j,mm,r] = (n*lambda*(Pi[r]^gamma)-S[j,mm,r])/Gram2[j,j,r]
- else
- phi[j,mm,r] = -(n*lambda*(Pi[r]^gamma)+S[j,mm,r])/Gram2[j,j,r]
+ }else{
+ phi[j,mm,r] = -(n*lambda*(Pi[r]^gamma)+S[j,mm,r])/Gram2[j,j,r]
+ }
}
}
}
--- /dev/null
+EMGLLF = 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)
+ Pi = piInit
+ LLF = 0
+
+ #local variables
+ Phi = array(0, dim=c(p,m,k))
+ deltaPhi = c(0)
+ sumDeltaPhi = 0
+ deltaPhiBufferSize = 20
+
+ #main loop
+ ite = 1
+ while(ite<=mini || (ite<=maxi && sumDeltaPhi>tau)){
+ #M step: Mise à jour de Beta (et donc phi)
+ for(r in 1:k){
+ Z_bin = vec_bin(Z,r)
+ Z_vec = Z_bin$vec #vecteur 0 et 1 aux endroits o? Z==r
+ Z_indice = Z_bin$indice
+ if(sum(Z_indice) == 0){
+ next
+ }
+ #U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
+ [U,S,V] = svd(ginv(crossprod(X[Z_indice,]))%*% (X[Z_indice,])%*%Y[Z_indice,] )
+ #Set m-rank(r) singular values to zero, and recompose
+ #best rank(r) approximation of the initial product
+ S[rank(r)+1:end,] = 0
+ phi[,,r] = U %*%S%*%t(V)%*%Rho[,,r]
+ }
+
+ #Etape E et calcul de LLF
+ sumLogLLF2 = 0
+ for(i in 1:n){
+ sumLLF1 = 0
+ maxLogGamIR = -Inf
+ for(r in 1: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(max(max((abs(phi-Phi))/(1+abs(phi))))) )
+ 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))
+}
\ No newline at end of file
{
print(paste("Checking ",varName,sep=""))
maxError = max(abs(array - refArray))
- if(maxError >= tol)
- {
+ if(maxError >= tol){
print(paste("Inaccuracy: max(abs(error)) = ",maxError," >= ",tol,sep=""))
- } else
- {
+ } else{
print("OK")
}
}
covariance = function(p,a)
{
A = matrix(a, p,p)
- for (i in 1:p)
+ for (i in 1:p){
A[i,] = A[i,]^abs(i-(1:p))
-
+ }
return (A)
}