Remove and ignore Rstudio project files
[valse.git] / src / test / generate_test_data / EMGLLF.R
1 EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau)
2 {
3 #matrix dimensions
4 n = dim(X)[1]
5 p = dim(phiInit)[1]
6 m = dim(phiInit)[2]
7 k = dim(phiInit)[3]
8
9 #init outputs
10 phi = phiInit
11 rho = rhoInit
12 pi = piInit
13 LLF = rep(0, maxi)
14 S = array(0, dim=c(p,m,k))
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(n,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 {
36 Phi = phi
37 Rho = rho
38 Pi = pi
39
40 #calcul associé à Y et X
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)
48 ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
49 for (j in 1:p)
50 {
51 for (s in 1:p)
52 Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
53 }
54 }
55
56 ##########
57 #Etape M #
58 ##########
59
60 #pour pi
61 for (r in 1:k)
62 b[r] = sum(abs(phi[,,r]))
63 gam2 = colSums(gam)
64 a = sum(gam %*% log(pi))
65
66 #tant que les props sont negatives
67 kk = 0
68 pi2AllPositive = FALSE
69 while (!pi2AllPositive)
70 {
71 pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
72 pi2AllPositive = all(pi2 >= 0)
73 kk = kk+1
74 }
75
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) )
80 {
81 pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
82 kk = kk + 1
83 }
84 t = 0.1^kk
85 pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
86
87 #Pour phi et rho
88 for (r in 1:k)
89 {
90 for (mm in 1:m)
91 {
92 for (i in 1:n)
93 {
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
96 }
97 ps[mm,r] = sum(ps1[,mm,r])
98 nY2[mm,r] = sum(nY21[,mm,r])
99
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])
102 }
103 }
104 for (r in 1:k)
105 {
106 for (j in 1:p)
107 {
108 for (mm in 1:m)
109 {
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))
114 phi[j,mm,r]=0
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]
117 else
118 phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
119 }
120 }
121 }
122
123 ##########
124 #Etape E #
125 ##########
126 sumLogLLF2 = 0
127 for (i in 1:n)
128 {
129 #precompute sq norms to numerically adjust their values
130 sqNorm2 = rep(0,k)
131 for (r in 1:k)
132 sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
133 shift = 0.5*min(sqNorm2)
134
135 #compute Gam(:,:) using shift determined above
136 sumLLF1 = 0.0;
137 for (r in 1:k)
138 {
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)
143 }
144 sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
145 sumGamI = sum(Gam[i,])
146 if(sumGamI > EPS)
147 gam[i,] = Gam[i,] / sumGamI
148 else
149 gam[i,] = rep(0,k)
150 }
151
152 sumPen = sum(pi^gamma * b)
153 LLF[ite] = -sumLogLLF2/n + lambda*sumPen
154
155 dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
156
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)
161
162 ite = ite+1
163 }
164
165 return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S))
166 }