-EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau){
+EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
+{
#matrix dimensions
n = dim(X)[1]
p = dim(phiInit)[1]
#init outputs
phi = phiInit
rho = rhoInit
- Pi = piInit
+ 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))
dist = 0
dist2 = 0
ite = 1
- Pi2 = rep(0, k)
+ 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)))){
+ while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
+ {
Phi = phi
Rho = rho
- PI = Pi
+ 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] ##bon calcul ? idem pour X2 ??...
- }
- for(i in 1:n){
- X2[i,,r] = X[i,] *sqrt(gam[i,r])
- }
- for(mm in 1:m){
+ 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){
+ for (j in 1:p)
+ {
+ for (s in 1:p)
Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
- }
}
}
##########
#pour pi
- for(r in 1:k){
- b[r] = sum(sum(abs(phi[,,r])))
- }
+ for (r in 1:k)
+ b[r] = sum(abs(phi[,,r]))
gam2 = colSums(gam)
- a = sum(gam%*%(log(Pi)))
+ a = sum(gam %*% log(pi))
#tant que les props sont negatives
kk = 0
pi2AllPositive = FALSE
- while(pi2AllPositive == FALSE){
- Pi2 = Pi + 0.1^kk * ((1/n)*gam2 - Pi)
- pi2AllPositive = TRUE
- for(r in 1:k){
- if(Pi2[r] < 0){
- pi2AllPositive = false;
- break
- }
- }
+ while (!pi2AllPositive)
+ {
+ pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+ pi2AllPositive = all(pi2 >= 0)
kk = kk+1
}
- #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)%*%t(b)))<(-1/n*gam2%*%t(log(Pi2))+lambda*(Pi2^gamma)%*%t(b)) && kk<1000){
- Pi2 = Pi+0.1^kk*(1/n*gam2-Pi)
- kk = kk+1
+ #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))
+ 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] * (X2[i,,r]%*%(phi[,mm,r]))
- nY21[i,mm,r] = (Y2[i,mm,r])^2
+ 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])
+ nY21[i,mm,r] = Y2[i,mm,r]^2
}
ps[mm,r] = sum(ps1[,mm,r])
nY2[mm,r] = sum(nY21[,mm,r])
- rho[mm,mm,r] = ((ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r])))/(2*nY2[mm,r]))
+ 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){
- p1 = p-1
- for(j in 1:p1){
- for(mm in 1:m){
- j1 = j-1
- j2 = j+1
- v1 = c(1:j1)
- v2 = c(j2:p)
- S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + phi[v1,mm,r]%*%(Gram2[j,v1,r]) + phi[v2,mm,r]%*%(Gram2[j,v2,r]) #erreur indice
- if(abs(S[j,mm,r]) <= n*lambda*(Pi[r]^gamma)){
+ 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] +
+ (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]
- }
- }
+ 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 dot products to numerically adjust their values
- dotProducts = rep(0,k)
- for(r in 1:k){
- dotProducts[r] = tcrossprod(Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])
- }
- shift = 0.5*min(dotProducts)
-
+ 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 )
+ shift = 0.5*min(sqNorm2)
+
#compute Gam(:,:) using shift determined above
sumLLF1 = 0.0;
- for(r in 1:k){
- Gam[i,r] = Pi[r]*det(rho[,,r])*exp(-0.5*dotProducts[r] + shift)
- sumLLF1 = sumLLF1 + Gam[i,r]/(2*pi)^(m/2)
+ 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] + shift) * 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 = 0
- for(r in 1:k){
- sumPen = sumPen + Pi[r]^gamma^b[r]
+ gam[i,] = rep(0,k)
}
- LLF[ite] = -(1/n)*sumLogLLF2 + lambda*sumPen
-
- if(ite == 1)
- dist = LLF[ite]
- else
- dist = (LLF[ite]-LLF[ite-1])/(1+abs(LLF[ite]))
-
- Dist1=max(max(max((abs(phi-Phi))/(1+abs(phi)))))
- Dist2=max(max(max((abs(rho-Rho))/(1+abs(rho)))))
- Dist3=max(max((abs(Pi-PI))/(1+abs(PI))))
- dist2=max(c(Dist1,Dist2,Dist3))
-
- ite=ite+1
+
+ 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
}
-
- Pi = t(Pi)
- return(list("phi"=phi, "rho"=rho, "pi"=Pi, "LLF"=LLF, "S"=S))
+
+ return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S))
}
projects / valse.git / blobdiff