Commit | Line | Data |
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567a7c38 BA |
1 | EMGLLF_R = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau) |
2 | { | |
cbfc356e | 3 | # Matrix dimensions |
567a7c38 BA |
4 | n = dim(X)[1] |
5 | p = dim(phiInit)[1] | |
6 | m = dim(phiInit)[2] | |
7 | k = dim(phiInit)[3] | |
cbfc356e BA |
8 | |
9 | # Outputs | |
567a7c38 BA |
10 | phi = phiInit |
11 | rho = rhoInit | |
12 | pi = piInit | |
cbfc356e | 13 | llh = -Inf |
567a7c38 | 14 | S = array(0, dim=c(p,m,k)) |
cbfc356e BA |
15 | |
16 | # Algorithm variables | |
567a7c38 BA |
17 | gam = gamInit |
18 | Gram2 = array(0, dim=c(p,p,k)) | |
19 | ps2 = array(0, dim=c(p,m,k)) | |
20 | b = rep(0, k) | |
21 | X2 = array(0, dim=c(n,p,k)) | |
22 | Y2 = array(0, dim=c(n,m,k)) | |
cbfc356e BA |
23 | EPS = 1e-15 |
24 | ||
25 | for (ite in 1:maxi) | |
567a7c38 | 26 | { |
cbfc356e | 27 | # Remember last pi,rho,phi values for exit condition in the end of loop |
567a7c38 BA |
28 | Phi = phi |
29 | Rho = rho | |
30 | Pi = pi | |
31 | ||
cbfc356e BA |
32 | # Calcul associé à Y et X |
33 | for (r in 1:k) | |
567a7c38 BA |
34 | { |
35 | for (mm in 1:m) | |
36 | Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm] | |
37 | for (i in 1:n) | |
38 | X2[i,,r] = sqrt(gam[i,r]) * X[i,] | |
39 | for (mm in 1:m) | |
40 | ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r]) | |
41 | for (j in 1:p) | |
42 | { | |
43 | for (s in 1:p) | |
44 | Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r]) | |
45 | } | |
46 | } | |
47 | ||
48 | ########## | |
49 | #Etape M # | |
50 | ########## | |
cbfc356e BA |
51 | |
52 | # Pour pi | |
53 | b = sapply( 1:k, function(r) sum(abs(phi[,,r])) ) | |
567a7c38 BA |
54 | gam2 = colSums(gam) |
55 | a = sum(gam %*% log(pi)) | |
56 | ||
cbfc356e | 57 | # Tant que les props sont negatives |
567a7c38 BA |
58 | kk = 0 |
59 | pi2AllPositive = FALSE | |
60 | while (!pi2AllPositive) | |
61 | { | |
62 | pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi) | |
63 | pi2AllPositive = all(pi2 >= 0) | |
64 | kk = kk+1 | |
65 | } | |
66 | ||
cbfc356e | 67 | # t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante |
567a7c38 BA |
68 | while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) < |
69 | -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) ) | |
70 | { | |
71 | pi2 = pi + 0.1^kk * (1/n*gam2 - pi) | |
72 | kk = kk + 1 | |
73 | } | |
74 | t = 0.1^kk | |
75 | pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi)) | |
76 | ||
77 | #Pour phi et rho | |
78 | for (r in 1:k) | |
79 | { | |
80 | for (mm in 1:m) | |
81 | { | |
cbfc356e | 82 | ps = 0 |
567a7c38 | 83 | for (i in 1:n) |
cbfc356e BA |
84 | ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r]) |
85 | nY2 = sum(Y2[,mm,r]^2) | |
86 | rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2) | |
567a7c38 BA |
87 | } |
88 | } | |
89 | ||
90 | for (r in 1:k) | |
91 | { | |
92 | for (j in 1:p) | |
93 | { | |
94 | for (mm in 1:m) | |
95 | { | |
96 | S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r]) | |
97 | if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma)) | |
98 | phi[j,mm,r]=0 | |
99 | else if(S[j,mm,r] > n*lambda*(pi[r]^gamma)) | |
100 | phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r] | |
101 | else | |
102 | phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r] | |
103 | } | |
104 | } | |
105 | } | |
106 | ||
107 | ########## | |
108 | #Etape E # | |
109 | ########## | |
110 | ||
cbfc356e | 111 | sumLogLLH2 = 0 |
567a7c38 BA |
112 | for (i in 1:n) |
113 | { | |
cbfc356e BA |
114 | # Update gam[,] |
115 | sumLLH1 = 0 | |
116 | sumGamI = 0 | |
567a7c38 BA |
117 | for (r in 1:k) |
118 | { | |
cbfc356e BA |
119 | gam[i,r] = pi[r] * exp(-0.5*sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )) |
120 | * det(rho[,,r]) | |
121 | sumLLH1 = sumLLH1 + gam[i,r] / (2*base::pi)^(m/2) | |
122 | sumGamI = sumGamI + gam[i,r] | |
567a7c38 | 123 | } |
cbfc356e BA |
124 | sumLogLLH2 = sumLogLLH2 + log(sumLLH1) |
125 | if(sumGamI > EPS) #else: gam[i,] is already ~=0 | |
126 | gam[i,] = gam[i,] / sumGamI | |
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127 | } |
128 | ||
129 | sumPen = sum(pi^gamma * b) | |
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130 | last_llh = llh |
131 | llh = -sumLogLLH2/n + lambda*sumPen | |
132 | dist = ifelse( ite == 1, llh, (llh-last_llh) / (1+abs(llh)) ) | |
567a7c38 BA |
133 | Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) ) |
134 | Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) ) | |
135 | Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) ) | |
136 | dist2 = max(Dist1,Dist2,Dist3) | |
137 | ||
cbfc356e BA |
138 | if (ite>=mini && (dist>= tau || dist2 >= sqrt(tau))) |
139 | break | |
567a7c38 | 140 | } |
b9b0b72a | 141 | |
567a7c38 | 142 | affec = apply(gam, 1, which.max) |
cbfc356e | 143 | list( "phi"=phi, "rho"=rho, "pi"=pi, "llh"=llh, "S"=S, "affec"=affec ) |
567a7c38 | 144 | } |