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   Gam = matrix(0, n,k)
  31   EPS = 1E-15
  32
  33   while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau))))
  34     {
  35     Phi = phi
  36     Rho = rho
  37     Pi = pi
  38
  39     #calcul associé à Y et X
  40     for(r in 1:k)
  41         {
  42       for (mm in 1:m)
  43         Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
  44       for (i in 1:n)
  45         X2[i,,r] = sqrt(gam[i,r]) * X[i,]
  46       for (mm in 1:m)
  47         ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
  48       for (j in 1:p)
  49             {
  50         for (s in 1:p)
  51           Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
  52       }
  53     }
  54
  55     ##########
  56     #Etape M #
  57     ##########
  58
  59     #pour pi
  60     for (r in 1:k){
  61       b[r] = sum(abs(phi[,,r]))}
  62     gam2 = colSums(gam)
  63     a = sum(gam %*% log(pi))
  64
  65     #tant que les props sont negatives
  66     kk = 0
  67     pi2AllPositive = FALSE
  68     while (!pi2AllPositive)
  69         {
  70       pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
  71       pi2AllPositive = all(pi2 >= 0)
  72       kk = kk+1
  73     }
  74
  75     #t[m] la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
  76     while( kk < 1000 && -a/n + lambda * sum(pi^gamma * b) <
  77             -sum(gam2 * log(pi2))/n + lambda * sum(pi2^gamma * b) )
  78         {
  79       pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
  80       kk = kk + 1
  81     }
  82     t = 0.1^kk
  83     pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
  84
  85     #Pour phi et rho
  86     for (r in 1:k)
  87         {
  88       for (mm in 1:m)
  89             {
  90         for (i in 1:n)
  91                 {
  92           ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
  93         }
  94         ps[mm,r] = sum(ps1[,mm,r])
  95         nY2[mm,r] = sum(Y2[,mm,r]^2)
  96         rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*gam2[r])) / (2*nY2[mm,r])
  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, setdiff(1:p,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     sumLogLLF2 = 0
 120     for (i in 1:n)
 121         {
 122       #precompute sq norms to numerically adjust their values
 123       sqNorm2 = rep(0,k)
 124       for (r in 1:k){
 125         sqNorm2[r] = sum( (Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])^2 )}
 126
 127       #compute Gam(:,:) using shift determined above
 128       sumLLF1 = 0.0;
 129       for (r in 1:k)
 130             {
 131                 Gam[i,r] = pi[r] * exp(-0.5*sqNorm2[r])* det(rho[,,r])
 132         sumLLF1 = sumLLF1 + Gam[i,r] / (2*base::pi)^(m/2)
 133       }
 134       sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
 135       sumGamI = sum(Gam[i,])
 136       if(sumGamI > EPS)
 137         gam[i,] = Gam[i,] / sumGamI
 138       else
 139         gam[i,] = rep(0,k)
 140     }
 141
 142     sumPen = sum(pi^gamma * b)
 143     LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 144
 145     dist = ifelse( ite == 1, LLF[ite], (LLF[ite]-LLF[ite-1]) / (1+abs(LLF[ite])) )
 146
 147     Dist1 = max( (abs(phi-Phi)) / (1+abs(phi)) )
 148     Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
 149     Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)) )
 150     dist2 = max(Dist1,Dist2,Dist3)
 151
 152     ite = ite+1
 153   }
 154
 155   affec = apply(gam, 1,which.max)
 156   return(list("phi"=phi, "rho"=rho, "pi"=pi, "LLF"=LLF, "S"=S, "affec" = affec ))
 157 }