Commit | Line | Data |
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83ed2c0a BG |
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 | } |