From: Benjamin Goehry <benjamin.goehry@math.u-psud.fr>
Date: Tue, 17 Jan 2017 16:47:20 +0000 (+0100)
Subject: EMGLLF in R
X-Git-Url: https://git.auder.net/doc/html/css/img/assets/pieces/%7B%7B%20targetUrl%20%7D%7D?a=commitdiff_plain;h=83ed2c0a1924fe874d0d12f82ad46c42b6ae4e97;p=valse.git

EMGLLF in R
---

diff --git a/src/test/generate_test_data/helpers/EMGLLF.R b/src/test/generate_test_data/helpers/EMGLLF.R
new file mode 100644
index 0000000..f108a38
--- /dev/null
+++ b/src/test/generate_test_data/helpers/EMGLLF.R
@@ -0,0 +1,167 @@
+EMGLLF = function(phiInit,rhoInit,piInit,gamInit,mini,maxi,gamma,lambda,X,Y,tau){
+  #matrix dimensions
+  n = dim(X)[1]
+  p = dim[phiInit][1]
+  m = dim[phiInit][2]
+  k = dim[phiInit][3]
+  
+  #init outputs
+  phi = phiInit
+  rho = rhoInit
+  Pi = piInit
+  LLF = rep(0, maxi)
+  S = array(0, dim=c(p,m,k))
+  
+  
+  gam = gamInit
+  Gram2 = array(0, dim=c(p,p,k))
+  ps2 = array(0, dim=c(p,m,k))
+  b = rep(0, k)
+  pen = matrix(0, maxi, k)
+  X2 = array(0, dim=c(n,p,k))
+  Y2 = array(0, dim=c(p,m,k))
+  dist = 0
+  dist2 = 0
+  ite = 1
+  Pi2 = rep(0, k)
+  ps = matrix(0, m,k)
+  nY2 = matrix(0, m,k)
+  ps1 = array(0, dim=c(n,m,k))
+  nY21 = array(0, dim=c(n,m,k))
+  Gam = matrix(0, n,k)
+  EPS = 1E-15
+  
+  while(ite <= mini || (ite<= maxi && (dist>= tau || dist2 >= sqrt(tau)))){
+    Phi = phi
+    Rho = rho
+    PI = Pi
+    #calcul associé à Y et X
+    for(r in 1:k){
+      for(mm in 1:m){
+        Y2[,mm,r] = sqrt(gam[,r]) .* Y[,mm]
+      }
+      for(i in 1:n){
+        X2[i,,r] = X[i,] .* sqrt(gam[i,r])
+      }
+      for(mm in 1:m){
+        ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
+      }
+      for(j in 1:p){
+        for(s in 1:p){
+          Gram2[j,s,r] = tcrossprod(X2[,j,r], X2[,s,r])
+        }
+      }
+    }
+    
+    ##########
+    #Etape M #
+    ##########
+    
+    #pour pi
+    for(r in 1:k){
+      b[r] = sum(sum(abs(phi[,,r])))
+    }
+    gam2 = sum(gam[1,])  #BIG DOUTE
+    a = sum(gam*t(log(Pi)))
+    
+    #tant que les props sont negatives
+    kk = 0
+    pi2AllPositive = FALSE
+    while(pi2AllPositive == FALSE){
+      pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+      pi2AllPositive = TRUE
+      for(r in 1:k){
+        if(pi2[r] < 0){
+          pi2AllPositive = false;
+          break
+        }
+      }
+      kk = kk+1
+    }
+    
+    #t[m]la plus grande valeur dans la grille O.1^k tel que ce soit
+    #décroissante ou constante
+    while((-1/n*a+lambda*((pi.^gamma)*b))<(-1/n*gam2*t(log(pi2))+lambda.*(pi2.^gamma)*b) && kk<1000){
+      pi2 = pi+0.1^kk*(1/n*gam2-pi)
+      kk = kk+1
+    }
+    t = 0.1^(kk)
+    pi = (pi+t*(pi2-pi)) / sum(pi+t*(pi2-pi))
+    
+    #Pour phi et rho
+    for(r in 1:k){
+      for(mm in 1:m){
+        for(i in 1:n){
+          ps1[i,mm,r] = Y2[i,mm,r] * dot(X2(i,:,r), phi(:,mm,r))
+          nY21[i,mm,r] = (Y2[i,mm,r])^2
+        }
+        ps[mm,r] = sum(ps1(:,mm,r));
+        nY2[mm,r] = sum(nY21(:,mm,r));
+        rho[mm,mm,r] = ((ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r])))/(2*nY2[mm,r]))
+      }
+    }
+    for(r in 1:k){
+      for(j in 1:p){
+        for(mm in 1:m){
+          S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + dot(phi[1:j-1,mm,r],Gram2[j,1:j-1,r])  + dot(phi[j+1:p,mm,r],Gram2[j,j+1:p,r])
+          if(abs(S(j,mm,r)) <= n*lambda*(pi(r)^gamma))
+            phi[j,mm,r]=0
+          else{
+            if(S[j,mm,r]> n*lambda*(Pi[r]^gamma))
+              phi[j,mm,r] = (n*lambda*(Pi[r]^gamma)-S[j,mm,r])/Gram2[j,j,r]
+          else
+            phi[j,mm,r] = -(n*lambda*(Pi[r]^gamma)+S[j,mm,r])/Gram2[j,j,r]
+          }
+        }
+      }
+    }
+    
+    ##########
+    #Etape E #
+    ##########
+    sumLogLLF2 = 0
+    for(i in 1:n){
+      #precompute dot products to numerically adjust their values
+      dotProducts = rep(0,k)
+      for(r in 1:k){
+        dotProducts[r] = tcrossprod(Y[i,]%*%rho[,,r]-X[i,]%*%phi[,,r])
+      }
+      shift = 0.5*min(dotProducts)
+    
+      #compute Gam(:,:) using shift determined above
+      sumLLF1 = 0.0;
+      for(r in 1:k){
+        Gam[i,r] = Pi[r]*det(rho[,,r])*exp(-0.5*dotProducts[r] + shift)
+        sumLLF1 = sumLLF1 + Gam[i,r]/(2*pi)^(m/2)
+      }
+      sumLogLLF2 = sumLogLLF2 + log(sumLLF1)
+      sumGamI = sum(Gam[i,])
+      if(sumGamI > EPS)
+        gam[i,] = Gam[i,] / sumGamI
+      else
+        gam[i,] = rep(0,k) 
+    }
+    
+    
+    sumPen = 0
+    for(r in 1:k){
+      sumPen = sumPen + Pi[r].^gamma^b[r]
+    }
+    LLF[ite] = -(1/n)*sumLogLLF2 + lambda*sumPen
+    
+    if(ite == 1)
+      dist = LLF[ite]
+    else
+      dist = (LLF[ite]-LLF[ite-1])/(1+abs(LLF[ite]))
+    
+    Dist1=max(max(max((abs(phi-Phi))./(1+abs(phi)))))
+    Dist2=max(max(max((abs(rho-Rho))./(1+abs(rho)))))
+    Dist3=max(max((abs(Pi-PI))./(1+abs(PI))))
+    dist2=max([Dist1,Dist2,Dist3])
+    
+    ite=ite+1
+  }
+    
+  Pi = transpose(Pi)
+  return(list(phi=phi, rho=rho, Pi=Pi, LLF=LLF, S=S))
+}
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