--- a
+++ b/Fun_Auxiliary.R
@@ -0,0 +1,174 @@
+# -------------------------------------------------------------------------
+get.penalityMatrix=function(adj,X1, y1){
+  feature.num = dim(adj)[2] 
+  M.c = diag(0,feature.num)
+  M.lasso = diag(0,feature.num)
+  M.elastic = diag(1,feature.num)  
+  M.network = Non.NormalizedLaplacianMatrix(adj)
+  M.AdaptNet = AdaptNet.Non.NormalizedLap(adj,X1, y1)
+  return(list(M.c=M.c,M.lasso=M.lasso,M.elastic=M.elastic,M.network=M.network,M.AdaptNet=M.AdaptNet))
+}
+# -------------------------------------------------------------------------
+# Normalized Laplacian Matrix from adjacency matrix
+laplacianMatrix = function(adj){
+  diag(adj) <- 0
+  deg <- apply(abs(adj),1,sum)
+  p <- ncol(adj)
+  L <- matrix(0,p,p)
+  nonzero <- which(deg!=0)
+  for (i in nonzero){
+    for (j in nonzero){
+      L[i,j] <- -adj[i,j]/sqrt(deg[i]*deg[j])
+    }
+  }
+  diag(L) <- 1
+  return(L)
+}
+
+# Non-Normalized Laplacian Matrix from adjacency matrix
+Non.NormalizedLaplacianMatrix = function(adj){
+  diag(adj) <- 0
+  deg <- apply(adj,1,sum)
+  D = diag(deg)
+  L = D - adj
+  return(L)
+}
+# ------------------------------------------------------
+AdaptNet.penality.matrix = function(adj, X, y){
+  
+  library(glmnet)
+  glmnet.fit = glmnet(X, y, lambda=0, family='binomial')
+  Beta = coef(glmnet.fit)
+  
+  p <- ncol(adj)
+  coeff.sign = sign(Beta)[2:(p+1)]
+  
+  diag(adj) <- 0
+  deg <- apply(abs(adj),1,sum)
+  L <- matrix(0,p,p)
+  nonzero <- which(deg!=0)
+  for (i in nonzero){
+    for (j in nonzero){
+      temp.sign = coeff.sign[i]*coeff.sign[j]
+      L[i,j] <- -temp.sign*adj[i,j]/sqrt(deg[i]*deg[j])
+    }
+  }
+  diag(L) <- 1
+  return(L_star=L)
+}
+AdaptNet.Non.NormalizedLap = function(adj,X, y){
+  library(glmnet)
+  glmnet.fit = glmnet(X, y, lambda=0, family='binomial')
+  Beta = coef(glmnet.fit)
+  
+  p <- ncol(adj)
+  coeff.sign = sign(Beta)[2:(p+1)]
+  diag(adj) <- 0
+  deg <- apply(abs(adj),1,sum)
+  L <- matrix(0,p,p)
+  nonzero <- which(deg!=0)
+  for (i in nonzero){
+    for (j in nonzero){
+      temp.sign = coeff.sign[i]*coeff.sign[j]
+      L[i,j] <- -temp.sign*adj[i,j]
+    }
+  }
+  diag(L) <- deg
+  return(L_star=L)
+}
+# -------------------------------------------------------------------------
+sen.spe = function(pred, truth){
+  #----------------------------------------
+  # 1: True sample
+  # 0: False sample
+  # truth = abs(sign(sim.data$w))
+  # pred = abs(sign(out1$w[-length(tmp)]))
+  #----------------------------------------
+  sen = length(which(pred[which(truth==1)]==1))/length(which(truth==1))
+  spe = length(which(pred[which(truth==0)]==0))/length(which(truth==0))
+  result = c(sen,spe);names(result) = c("sensitivity","specificity")
+  return(result)
+}
+
+# Prior network regularization
+Prior.network = function(adj){
+  # adj is a p x p matrix
+  # L   is a (p+1) x (p+1) matrix
+  L = laplacianMatrix(adj)
+  L = rbind(L,rep(0,p))
+  L = cbind(L,rep(0,p+1))
+  return(L)
+}
+# -------------------------------------------------------------------------
+get_sim_prior_Net = function(n,t,p11,p12){
+  A = matrix(0,nrow=n,ncol=n) 
+  for(i in 1:n){
+    for(j in 1:n){
+      if(i>j){
+        set.seed(10*i+8*j)
+        if(i<t&j<t){
+          if(runif(1)<p11) A[i,j] = 1}
+        else{
+          if(runif(1)<p12) A[i,j] = 1}  
+      }
+    }
+  }
+  A = A +t(A)
+  diag(A)=0
+  return(A)
+}
+# -------------------------------------------------------------------------
+GET.SIM.DATA = function(smaple.num, feature.num, random.seed, snrlam=0.05){
+  # smaple.num = 700; feature.num = 100; random.seed = 10; snrlam=0.05
+  ii = random.seed
+  set.seed(30)
+  w  <-c(rnorm(40),rep(0,(feature.num-40)));b = 0
+  mu <- rep(0,40)
+  Sigma <- matrix(.6, nrow=40, ncol=40) + diag(40)*.4
+  
+  set.seed(ii*2)
+  X1 <- mvrnorm(n=smaple.num, mu=mu, Sigma=Sigma)
+  
+  set.seed(ii*3)
+  X2 <- matrix(rnorm(smaple.num*(feature.num-40), mean = 0, sd = 1), nrow = smaple.num, ncol = feature.num-40)
+  X = cbind(X1,X2)
+
+  Xw <- -X%*%w 
+  pp <- 1/(1+exp(Xw))
+  y  <- rep(1,smaple.num)
+  y[pp<0.5] <- 0
+
+  p = dim(X)[1];q = dim(X)[2]
+  set.seed(ii*3)
+  XX = X + snrlam*matrix(rnorm(p*q),ncol=q)
+  
+  return(list(X=XX,y=y,w=w))
+}
+# -------------------------------------------------------------------------
+GET.SIM.DATA2 = function(smaple.num, feature.num, random.seed, snrlam=0.05){
+  # smaple.num = 700; feature.num = 100; random.seed = 10; snrlam=0.05
+  ii = 10
+  set.seed(30)
+  w  <-c(rnorm(40),rep(0,(feature.num-40)));b = 0
+  mu <- rep(0,40)
+  Sigma <- matrix(.6, nrow=40, ncol=40) + diag(40)*.4
+  
+  set.seed(ii*2)
+  X1 <- mvrnorm(n=smaple.num, mu=mu, Sigma=Sigma)
+  
+  set.seed(ii*3)
+  X2 <- matrix(rnorm(smaple.num*(feature.num-40), mean = 0, sd = 1), nrow = smaple.num, ncol = feature.num-40)
+  X = cbind(X1,X2)
+
+  Xw <- -X%*%w 
+  pp <- 1/(1+exp(Xw))
+  y  <- rep(1,smaple.num)
+  y[pp<0.5] <- 0
+  
+  p = dim(X)[1];q = dim(X)[2]
+  
+  set.seed(random.seed)
+  XX = X + snrlam*matrix(rnorm(p*q),ncol=q)
+  
+  return(list(X=XX,y=y,w=w))
+}
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