--- /dev/null
+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]
+
+ #init outputs
+ phi = phiInit
+ rho = rhoInit
+ pi = piInit
+ LLF = rep(0, maxi)
+ S = array(0, dim=c(p,m,k))
+
+ gam = gamInit
+ Gram2 = array(0, dim=c(p,p,k))
+ ps2 = array(0, dim=c(p,m,k))
+ b = rep(0, k)
+ pen = matrix(0, maxi, k)
+ X2 = array(0, dim=c(n,p,k))
+ Y2 = array(0, dim=c(n,m,k))
+ dist = 0
+ dist2 = 0
+ ite = 1
+ pi2 = rep(0, k)
+ ps = matrix(0, m,k)
+ nY2 = matrix(0, m,k)
+ ps1 = array(0, dim=c(n,m,k))
+ Gam = matrix(0, n,k)
+ EPS = 1E-15
+
+ while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
+ {
+ Phi = phi
+ Rho = rho
+ Pi = pi
+
+ #calcul associé à Y et X
+ for(r in 1:k)
+ {
+ for (mm in 1:m)
+ Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
+ for (i in 1:n)
+ X2[i,,r] = sqrt(gam[i,r]) * X[i,]
+ for (mm in 1:m)
+ ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
+ for (j in 1:p)
+ {
+ for (s in 1:p)
+ Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
+ }
+ }
+
+ ##########
+ #Etape M #
+ ##########
+
+ #pour pi
+ for (r in 1:k){
+ b[r] = sum(abs(phi[,,r]))}
+ gam2 = colSums(gam)
+ a = sum(gam %*% log(pi))
+
+ #tant que les props sont negatives
+ kk = 0
+ pi2AllPositive = FALSE
+ while (!pi2AllPositive)
+ {
+ pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+ pi2AllPositive = all(pi2 >= 0)
+ kk = kk+1
+ }
+
+#if (ite==2) browser()
+ #t[m] la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
+ while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
+ -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
+ {
+ 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))
+
+ #Pour phi et rho
+ for (r in 1:k)
+ {
+ for (mm in 1:m)
+ {
+ for (i in 1:n)
+ {
+ ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
+ }
+ ps[mm,r] = sum(ps1[,mm,r])
+ nY2[mm,r] = sum(Y2[,mm,r]^2)
+ rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
+ }
+ }
+ 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] + sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p, j),r])
+# (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
+# (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
+ 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))
+ 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]
+ }
+ }
+ }
+
+ ##########
+ #Etape E #
+ ##########
+ sumLogLLF2 = 0
+ for (i in 1:n)
+ {
+ #precompute sq norms to numerically adjust their values
+ sqNorm2 = rep(0,k)
+ for (r in 1:k){
+ sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )}
+
+ #compute Gam(:,:) using shift determined above
+ sumLLF1 = 0.0;
+ for (r in 1:k)
+ {
+ #FIXME: numerical problems, because 0 < det(Rho[,,r] < EPS; what to do ?!
+ # consequence: error in while() at line 77
+ Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r])* det(rho[,,r])
+ sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
+ }
+ sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
+ sumGamI = sum(Gam[i,])
+ if(sumGamI > EPS)
+ gam[i,] = Gam[i,] / sumGamI
+ else
+ gam[i,] = rep(0,k)
+ }
+
+ sumPen = sum(pi^gamma * b)
+ LLF[ite] = -sumLogLLF2/n + lambda*sumPen
+
+ dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
+
+ Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
+ Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
+ Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
+ dist2 = max(Dist1,Dist2,Dist3)
+
+ ite = ite+1
+ }
+
+ affec = apply(gam, 1,which.max)
+ return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec ))
+}
projects / valse.git / blobdiff