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lambda_funtion<-function(G,E,y,weight,nlambda1=20,nlambda2=20){
X=E
Z=G
Y=y
X=X[weight>0,]
Z=Z[weight>0,]
Y=Y[weight>0]
weight1=weight[weight>0]
n<-dim(X)[1]
q<-dim(X)[2]
p<-dim(Z)[2]
pp=p*(q+1)
y=Y
W=matrix(0,n,p*(q+1))
W[,seq(from=1,to=p*(q+1),by=(q+1))]=Z
for (i in 1:n){
temp3=matrix(X[i,],q,1)%*%Z[i,]
W[i,setdiff(seq(from=1,to=p*(q+1),by=1),seq(from=1,to=p*(q+1),by=q+1))]=matrix(temp3,p*q,1)
}
m_W=t(weight1)%*%W/sum(weight1)
W = (W-matrix(1,n,1)%*%m_W)*(sqrt(weight1)%*%matrix(1,1,pp))
group_inf=seq(from=1,to=p*(q+1),by=(q+1))
R=list()
for (j in 1:p){
if (j<p){
id=group_inf[j]:(group_inf[j+1]-1)
}
else {
id=group_inf[j]:pp
}
a=W[,id]
b=(t(a)%*%a*(1/n))
R[[j]] = chol(b);
W[,id]=t(solve(t(R[[j]]),t(a)))
}
alpha0=solve(t(X)%*%X,t(X)%*%y);
r=y-X%*%alpha0;
C_s=matrix(0,p,1);
for (j in 1:p){
if (j<p){
id=group_inf[j]:(group_inf[j+1]-1);}
else {
id=group_inf[j]:pp;
}
S=t(W[,id])%*%r/n
C_s[j]=norm(S,"2")/(sqrt(q+1))
}
lambda1_max=max(abs(C_s))/sqrt(1+q);
e=(log(lambda1_max)-log(lambda1_max*0.01))/(nlambda1-1);
lambda1_set=exp(seq(from=log(lambda1_max),to=log(lambda1_max*0.01),by=-e));
lambda2_max=lambda1_max/(1+q);
e=(log(lambda2_max)-log(lambda2_max*0.01))/(nlambda2-1);
lambda2_set=exp(seq(from=log(lambda2_max),to=log(lambda2_max*0.01),by=-e));
return=list(lambda1_set=lambda1_set,lambda2_set=lambda2_set)
}
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