fix test.constructionModelesLassoMLE; TODO: det(rho[,,r]) ? numerical errors ? ....
[valse.git] / src / test / generate_test_data / helpers / EMGLLF.R
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1EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
2{
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3 #matrix dimensions
4 n = dim(X)[1]
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5 p = dim(phiInit)[1]
6 m = dim(phiInit)[2]
7 k = dim(phiInit)[3]
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8
9 #init outputs
10 phi = phiInit
11 rho = rhoInit
ef67d338 12 pi = piInit
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13 LLF = rep(0, maxi)
14 S = array(0, dim=c(p,m,k))
15
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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))
6e22eb7b 22 Y2 = array(0, dim=c(n,m,k))
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23 dist = 0
24 dist2 = 0
25 ite = 1
ef67d338 26 pi2 = rep(0, k)
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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
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34 while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
35 {
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36 Phi = phi
37 Rho = rho
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38 Pi = pi
39
83ed2c0a 40 #calcul associé à Y et X
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41 for(r in 1:k)
42 {
43 for (mm in 1:m)
44 Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
45 for (i in 1:n)
46 X2[i,,r] = sqrt(gam[i,r]) * X[i,]
47 for (mm in 1:m)
83ed2c0a 48 ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
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49 for (j in 1:p)
50 {
51 for (s in 1:p)
6e22eb7b 52 Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
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53 }
54 }
55
56 ##########
57 #Etape M #
58 ##########
59
60 #pour pi
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61 for (r in 1:k)
62 b[r] = sum(abs(phi[,,r]))
87fea89a 63 gam2 = colSums(gam)
ef67d338 64 a = sum(gam %*% log(pi))
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65
66 #tant que les props sont negatives
67 kk = 0
68 pi2AllPositive = FALSE
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69 while (!pi2AllPositive)
70 {
71 pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
72 pi2AllPositive = all(pi2 >= 0)
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73 kk = kk+1
74 }
75
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76 #t[m] la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
77 while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
78 -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
79 {
80 pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
81 kk = kk + 1
83ed2c0a 82 }
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83 t = 0.1^kk
84 pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
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85
86 #Pour phi et rho
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87 for (r in 1:k)
88 {
89 for (mm in 1:m)
90 {
91 for (i in 1:n)
92 {
93 ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
94 nY21[i,mm,r] = Y2[i,mm,r]^2
83ed2c0a 95 }
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96 ps[mm,r] = sum(ps1[,mm,r])
97 nY2[mm,r] = sum(nY21[,mm,r])
ef67d338 98 rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
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99 }
100 }
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101 for (r in 1:k)
102 {
103 for (j in 1:p)
104 {
105 for (mm in 1:m)
106 {
107 S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
108 (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
109 (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
110 if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma))
83ed2c0a 111 phi[j,mm,r]=0
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112 else if(S[j,mm,r] > n*lambda*(pi[r]^gamma))
113 phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r]
114 else
115 phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
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116 }
117 }
118 }
ef67d338 119
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120 ##########
121 #Etape E #
122 ##########
123 sumLogLLF2 = 0
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124 for (i in 1:n)
125 {
126 #precompute sq norms to numerically adjust their values
127 sqNorm2 = rep(0,k)
128 for (r in 1:k)
129 sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
130 shift = 0.5*min(sqNorm2)
131
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132 #compute Gam(:,:) using shift determined above
133 sumLLF1 = 0.0;
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134 for (r in 1:k)
135 {
136 #FIXME: numerical problems, because 0 < det(Rho[,,r] < EPS; what to do ?!
137 # consequence: error in while() at line 77
46a2e676 138 Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r] + shift) #* det(rho[,,r])
ef67d338 139 sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
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140 }
141 sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
142 sumGamI = sum(Gam[i,])
143 if(sumGamI > EPS)
144 gam[i,] = Gam[i,] / sumGamI
145 else
ef67d338 146 gam[i,] = rep(0,k)
83ed2c0a 147 }
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148
149 sumPen = sum(pi^gamma * b)
150 LLF[ite] = -sumLogLLF2/n + lambda*sumPen
151
152 dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
153
154 Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
155 Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
156 Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
157 dist2 = max(Dist1,Dist2,Dist3)
158
159 ite = ite+1
83ed2c0a 160 }
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161
162 return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S))
87fea89a 163}