pkg/R/EMGLLF_R.R

   1 EMGLLF_R = 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   X2 = array(0, dim=c(n,p,k))
  21   Y2 = array(0, dim=c(n,m,k))
  22   dist = 0
  23   dist2 = 0
  24   ite = 1
  25   pi2 = rep(0, k)
  26   ps = matrix(0, m,k)
  27   nY2 = matrix(0, m,k)
  28   ps1 = array(0, dim=c(n,m,k))
  29   Gam = matrix(0, n,k)
  30   EPS = 1E-15
  31
  32   while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
  33     {
  34     Phi = phi
  35     Rho = rho
  36     Pi = pi
  37
  38     #calcul associé à Y et X
  39     for(r in 1:k)
  40         {
  41       for (mm in 1:m)
  42         Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
  43       for (i in 1:n)
  44         X2[i,,r] = sqrt(gam[i,r]) * X[i,]
  45       for (mm in 1:m)
  46         ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
  47       for (j in 1:p)
  48             {
  49         for (s in 1:p)
  50           Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
  51       }
  52     }
  53
  54     ##########
  55     #Etape M #
  56     ##########
  57
  58     #pour pi
  59     for (r in 1:k)
  60       b[r] = sum(abs(phi[,,r]))
  61     gam2 = colSums(gam)
  62     a = sum(gam %*% log(pi))
  63
  64     #tant que les props sont negatives
  65     kk = 0
  66     pi2AllPositive = FALSE
  67     while (!pi2AllPositive)
  68         {
  69       pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
  70       pi2AllPositive = all(pi2 >= 0)
  71       kk = kk+1
  72     }
  73
  74     #t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
  75     while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
  76             -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
  77         {
  78       pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
  79       kk = kk + 1
  80     }
  81     t = 0.1^kk
  82     pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
  83
  84     #Pour phi et rho
  85     for (r in 1:k)
  86         {
  87       for (mm in 1:m)
  88             {
  89         for (i in 1:n)
  90                 {
  91           ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
  92         }
  93         ps[mm,r] = sum(ps1[,mm,r])
  94         nY2[mm,r] = sum(Y2[,mm,r]^2)
  95         rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
  96             }
  97     }
  98
  99     for (r in 1:k)
 100         {
 101       for (j in 1:p)
 102             {
 103         for (mm in 1:m)
 104                 {
 105           S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
 106                     if (abs(S[j,mm,r]) <= n*lambda*(pi[r]^gamma))
 107             phi[j,mm,r]=0
 108           else if(S[j,mm,r] > n*lambda*(pi[r]^gamma))
 109             phi[j,mm,r] = (n*lambda*(pi[r]^gamma)-S[j,mm,r]) / Gram2[j,j,r]
 110           else
 111             phi[j,mm,r] = -(n*lambda*(pi[r]^gamma)+S[j,mm,r]) / Gram2[j,j,r]
 112         }
 113       }
 114     }
 115
 116     ##########
 117     #Etape E #
 118     ##########
 119
 120         sumLogLLF2 = 0
 121     for (i in 1:n)
 122         {
 123       #precompute sq norms to numerically adjust their values
 124       sqNorm2 = rep(0,k)
 125       for (r in 1:k)
 126         sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )
 127
 128       #compute Gam[,]
 129       sumLLF1 = 0.0;
 130       for (r in 1:k)
 131             {
 132                 Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r]) * det(rho[,,r])
 133         sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
 134       }
 135       sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
 136       sumGamI = sum(Gam[i,])
 137       if(sumGamI > EPS)
 138         gam[i,] = Gam[i,] / sumGamI
 139       else
 140         gam[i,] = rep(0,k)
 141     }
 142
 143     sumPen = sum(pi^gamma * b)
 144     LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 145     dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
 146     Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
 147     Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
 148     Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
 149     dist2 = max(Dist1,Dist2,Dist3)
 150
 151     ite = ite+1
 152   }
 153
 154   affec = apply(gam, 1, which.max)
 155   return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec ))
 156 }