| 1 | EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau){ |
| 2 | #matrix dimensions |
| 3 | n = dim(X)[1] |
| 4 | p = dim[phiInit][1] |
| 5 | m = dim[phiInit][2] |
| 6 | k = dim[phiInit][3] |
| 7 | |
| 8 | #init outputs |
| 9 | phi = phiInit |
| 10 | rho = rhoInit |
| 11 | Pi = piInit |
| 12 | LLF = rep(0, maxi) |
| 13 | S = array(0, dim=c(p,m,k)) |
| 14 | |
| 15 | |
| 16 | gam = gamInit |
| 17 | Gram2 = array(0, dim=c(p,p,k)) |
| 18 | ps2 = array(0, dim=c(p,m,k)) |
| 19 | b = rep(0, k) |
| 20 | pen = matrix(0, maxi, k) |
| 21 | X2 = array(0, dim=c(n,p,k)) |
| 22 | Y2 = array(0, dim=c(p,m,k)) |
| 23 | dist = 0 |
| 24 | dist2 = 0 |
| 25 | ite = 1 |
| 26 | Pi2 = rep(0, k) |
| 27 | ps = matrix(0, m,k) |
| 28 | nY2 = matrix(0, m,k) |
| 29 | ps1 = array(0, dim=c(n,m,k)) |
| 30 | nY21 = array(0, dim=c(n,m,k)) |
| 31 | Gam = matrix(0, n,k) |
| 32 | EPS = 1E-15 |
| 33 | |
| 34 | while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau)))){ |
| 35 | Phi = phi |
| 36 | Rho = rho |
| 37 | PI = Pi |
| 38 | #calcul associé à Y et X |
| 39 | for(r in 1:k){ |
| 40 | for(mm in 1:m){ |
| 41 | Y2[,mm,r] = sqrt(gam[,r]) .* Y[,mm] |
| 42 | } |
| 43 | for(i in 1:n){ |
| 44 | X2[i,,r] = X[i,] .* sqrt(gam[i,r]) |
| 45 | } |
| 46 | for(mm in 1:m){ |
| 47 | ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r]) |
| 48 | } |
| 49 | for(j in 1:p){ |
| 50 | for(s in 1:p){ |
| 51 | Gram2[j,s,r] = tcrossprod(X2[,j,r], X2[,s,r]) |
| 52 | } |
| 53 | } |
| 54 | } |
| 55 | |
| 56 | ########## |
| 57 | #Etape M # |
| 58 | ########## |
| 59 | |
| 60 | #pour pi |
| 61 | for(r in 1:k){ |
| 62 | b[r] = sum(sum(abs(phi[,,r]))) |
| 63 | } |
| 64 | gam2 = sum(gam[1,]) #BIG DOUTE |
| 65 | a = sum(gam*t(log(Pi))) |
| 66 | |
| 67 | #tant que les props sont negatives |
| 68 | kk = 0 |
| 69 | pi2AllPositive = FALSE |
| 70 | while(pi2AllPositive == FALSE){ |
| 71 | pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi) |
| 72 | pi2AllPositive = TRUE |
| 73 | for(r in 1:k){ |
| 74 | if(pi2[r] < 0){ |
| 75 | pi2AllPositive = false; |
| 76 | break |
| 77 | } |
| 78 | } |
| 79 | kk = kk+1 |
| 80 | } |
| 81 | |
| 82 | #t[m]la plus grande valeur dans la grille O.1^k tel que ce soit |
| 83 | #décroissante ou constante |
| 84 | while((-1/n*a+lambda*((pi.^gamma)*b))<(-1/n*gam2*t(log(pi2))+lambda.*(pi2.^gamma)*b) && kk<1000){ |
| 85 | pi2 = pi+0.1^kk*(1/n*gam2-pi) |
| 86 | kk = kk+1 |
| 87 | } |
| 88 | t = 0.1^(kk) |
| 89 | pi = (pi+t*(pi2-pi)) / sum(pi+t*(pi2-pi)) |
| 90 | |
| 91 | #Pour phi et rho |
| 92 | for(r in 1:k){ |
| 93 | for(mm in 1:m){ |
| 94 | for(i in 1:n){ |
| 95 | ps1[i,mm,r] = Y2[i,mm,r] * dot(X2(i,:,r), phi(:,mm,r)) |
| 96 | nY21[i,mm,r] = (Y2[i,mm,r])^2 |
| 97 | } |
| 98 | ps[mm,r] = sum(ps1(:,mm,r)); |
| 99 | nY2[mm,r] = sum(nY21(:,mm,r)); |
| 100 | rho[mm,mm,r] = ((ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r])))/(2*nY2[mm,r])) |
| 101 | } |
| 102 | } |
| 103 | for(r in 1:k){ |
| 104 | for(j in 1:p){ |
| 105 | for(mm in 1:m){ |
| 106 | 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]) |
| 107 | if(abs(S(j,mm,r)) <= n*lambda*(pi(r)^gamma)) |
| 108 | phi[j,mm,r]=0 |
| 109 | else{ |
| 110 | if(S[j,mm,r]> n*lambda*(Pi[r]^gamma)) |
| 111 | phi[j,mm,r] = (n*lambda*(Pi[r]^gamma)-S[j,mm,r])/Gram2[j,j,r] |
| 112 | else |
| 113 | phi[j,mm,r] = -(n*lambda*(Pi[r]^gamma)+S[j,mm,r])/Gram2[j,j,r] |
| 114 | } |
| 115 | } |
| 116 | } |
| 117 | } |
| 118 | |
| 119 | ########## |
| 120 | #Etape E # |
| 121 | ########## |
| 122 | sumLogLLF2 = 0 |
| 123 | for(i in 1:n){ |
| 124 | #precompute dot products to numerically adjust their values |
| 125 | dotProducts = rep(0,k) |
| 126 | for(r in 1:k){ |
| 127 | dotProducts[r] = tcrossprod(Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r]) |
| 128 | } |
| 129 | shift = 0.5*min(dotProducts) |
| 130 | |
| 131 | #compute Gam(:,:) using shift determined above |
| 132 | sumLLF1 = 0.0; |
| 133 | for(r in 1:k){ |
| 134 | Gam[i,r] = Pi[r]*det(rho[,,r])*exp(-0.5*dotProducts[r] + shift) |
| 135 | sumLLF1 = sumLLF1 + Gam[i,r]/(2*pi)^(m/2) |
| 136 | } |
| 137 | sumLogLLF2 = sumLogLLF2 + log(sumLLF1) |
| 138 | sumGamI = sum(Gam[i,]) |
| 139 | if(sumGamI > EPS) |
| 140 | gam[i,] = Gam[i,] / sumGamI |
| 141 | else |
| 142 | gam[i,] = rep(0,k) |
| 143 | } |
| 144 | |
| 145 | |
| 146 | sumPen = 0 |
| 147 | for(r in 1:k){ |
| 148 | sumPen = sumPen + Pi[r].^gamma^b[r] |
| 149 | } |
| 150 | LLF[ite] = -(1/n)*sumLogLLF2 + lambda*sumPen |
| 151 | |
| 152 | if(ite == 1) |
| 153 | dist = LLF[ite] |
| 154 | else |
| 155 | dist = (LLF[ite]-LLF[ite-1])/(1+abs(LLF[ite])) |
| 156 | |
| 157 | Dist1=max(max(max((abs(phi-Phi))./(1+abs(phi))))) |
| 158 | Dist2=max(max(max((abs(rho-Rho))./(1+abs(rho))))) |
| 159 | Dist3=max(max((abs(Pi-PI))./(1+abs(PI)))) |
| 160 | dist2=max([Dist1,Dist2,Dist3]) |
| 161 | |
| 162 | ite=ite+1 |
| 163 | } |
| 164 | |
| 165 | Pi = transpose(Pi) |
| 166 | return(list(phi=phi, rho=rho, Pi=Pi, LLF=LLF, S=S)) |
| 167 | } |