1 EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
14 S = array(0, dim=c(p,m,k))
17 Gram2 = array(0, dim=c(p,p,k))
18 ps2 = array(0, dim=c(p,m,k))
20 pen = matrix(0, maxi, k)
21 X2 = array(0, dim=c(n,p,k))
22 Y2 = array(0, dim=c(n,m,k))
29 ps1 = array(0, dim=c(n,m,k))
30 nY21 = array(0, dim=c(n,m,k))
34 while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
40 #calcul associé à Y et X
44 Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
46 X2[i,,r] = sqrt(gam[i,r]) * X[i,]
48 ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
52 Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
62 b[r] = sum(abs(phi[,,r]))
64 a = sum(gam %*% log(pi))
66 #tant que les props sont negatives
68 pi2AllPositive = FALSE
69 while (!pi2AllPositive)
71 pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
72 pi2AllPositive = all(pi2 >= 0)
76 #if (ite==2) browser()
77 #t[m] la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
78 while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
79 -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
81 pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
85 pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
94 ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
95 nY21[i,mm,r] = Y2[i,mm,r]^2
97 ps[mm,r] = sum(ps1[,mm,r])
98 nY2[mm,r] = sum(nY21[,mm,r])
100 #TODO: debug rho computation
101 rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
110 S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
111 (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
112 (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
113 if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma))
115 else if(S[j,mm,r] > n*lambda*(pi[r]^gamma))
116 phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r]
118 phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
129 #precompute sq norms to numerically adjust their values
132 sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
133 shift = 0.5*min(sqNorm2)
135 #compute Gam(:,:) using shift determined above
139 #FIXME: numerical problems, because 0 < det(Rho[,,r] < EPS; what to do ?!
140 # consequence: error in while() at line 77
141 Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r] + shift) #* det(rho[,,r])
142 sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
144 sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
145 sumGamI = sum(Gam[i,])
147 gam[i,] = Gam[i,] / sumGamI
152 sumPen = sum(pi^gamma * b)
153 LLF[ite] = -sumLogLLF2/n + lambda*sumPen
155 dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
157 Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
158 Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
159 Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
160 dist2 = max(Dist1,Dist2,Dist3)
165 return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S))