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Mplasso.R
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library(class)
S_func <- function(x, a) { # Soft Thresholding Operator
return( pmax(abs(x) - a,0) * sign(x))
}
#library(RGCCA)# soft threshold
#_func=soft.threshold
Log<-function(y,pr){
if(isTRUE(y==0)==T){a<-0
} else{
a<- y*log((y/pr))
}
return(a)
}
errfun.binomial=function(y,yhat,w=rep(1,length(y))){
prob_min = 1e-05
prob_max = 1 - prob_min
predmat = pmin(pmax(yhat, prob_min), prob_max)
-w*(y*log(predmat)+(1-y)*log(1-predmat))
}
######
library(pracma)
reg<-function(r,Z){
K=ncol(Z)
my_one<-matrix(1,nrow(Z))
my_w=data.frame(Z,my_one)
my_w<-as.matrix(my_w)
my_inv<-pinv(t(my_w)%*%my_w)
my_res<-my_inv%*%(t(my_w)%*%r)
# new<- lm(r~1,na.action=na.exclude)
beta0<-matrix(my_res[(K+1)])
# new1<- lm(r~Z,singular.ok = TRUE)
theta0<- matrix(my_res[c(1:(K))])
return(list(beta0,theta0))
}
error.bars <-function(x, upper, lower, width = 0.02, ...) {
xlim <- range(x)
barw <- diff(xlim) * width
segments(x, upper, x, lower, ...)
segments(x - barw, upper, x + barw, upper, ...)
segments(x - barw, lower, x + barw, lower, ...)
#range(upper, lower)
}
twonorm<-function(x){
sqrt(sum(x*x))
}
objective<-function(r,beta,theta,alpha,lambda){
p=length(beta)
norm_1= lapply(seq_len(p),
function(g)( lambda*(1-alpha)*(norm(matrix(c(beta[g],theta[g,])),type = "F") +norm(matrix(c(theta[g,])),type = "F") ) + lambda*alpha* sum(abs(theta[g,])) ))
objective_1 <- sum(r^2) / (2 * N) +
sum(unlist(norm_1))
return(objective_1)
}
gradient_j<-function(beta,theta,U,U2,U3,y,X,W,r,alpha,lambda,K,j,N){
theta_j<- matrix(as.numeric(theta[j,]),nrow = 1)
dJ_dtheta_j<-matrix(0,nrow = 1,ncol = K)
R<-c()
if (isTRUE(any(c((beta[j]), theta_j)!=0))==T) {
u<-as.numeric(beta[j])/norm(matrix(c(beta[j], theta_j)),type= "F")
U<-c(U,u)
} else{
if(length(U)>=1){
for (z in 1:length(U)) {
if (norm(matrix(U[z]),type = "F")<=1) {
R<-c(R,U[z])
next(z)
} else{
next(z)
}
}
}else{R=c(R,0)}
u<-sample (c(R), size=1)
U<-c(U,u)
}
dJ_dbeta_j=-(t(matrix(X[,j] )) %*% matrix((matrix(r)) ) )/N+(1-alpha)*lambda*u
#DJ_BETA[j]<-dJ_dbeta_j
#for (n in 1:K) {
R<-c()
if (isTRUE(any(c((beta[j]), theta_j)!=0))==T) {
u2<-as.numeric(theta_j)/norm(matrix(c(as.numeric(beta[j]), theta_j)),type= "F")
U2<-c(U2,u2)
} else{
if(length(U2)>=1){
for (z in 1:length(U2)) {
if (norm(matrix(U2[z]),type = "F")<=1) {
R<-c(R,U2[z])
next(z)
} else{
next(z)
}
}
}else{R=c(R,0)}
u2<-sample (c(R), size=1)
U2<-c(U2,u2)
}
d<-c()
if (isTRUE(any(c(theta_j)!=0))==T) {
u3<-as.numeric(theta_j)/norm(matrix(c(theta_j)),type= "F")
U3<-c(U3,u3)
} else{
if(length(U3)>=1){
for (z in 1:length(U3)) {
if (norm(matrix(U3[z]),type = "F")<=1) {
d<-c(d,U3[z])
next(z)
} else{
next(z)
}
}
}else{d=c(d,0)}
u3<-sample (c(d), size=1)
U3<-c(U3,u3)
}
v<-sign(as.numeric(theta_j))
dJ_dtheta_j= -((t(data.frame(W[j]) )%*% matrix(matrix((r) ) ) ))/N+(1-alpha)*lambda*(u2+u3)+alpha*lambda*v
#}
#DJ_THETA[j,]<-dJ_dtheta_j
L1<- dJ_dbeta_j
L2<- dJ_dtheta_j
return(list(L1,L2,U,U2,U3))
}
compute_pliable<-function(X, Z, theta){
p=ncol(X)
N=nrow(X)
K=ncol(Z)
xz_theta <- lapply(seq_len(p),
function(j) (matrix(X[, j], nrow = N, ncol = K) * Z) %*% t(theta)[, j])
xz_term<- (Reduce(f = '+', x = xz_theta))
return(xz_term)
}
concat_beta_theta<-function(beta, theta){
p=length(beta); K =ncol(theta)
my_matrix = matrix(0,p, (K+1))
my_matrix[, c(1:K)] = theta
my_matrix[, (K+1)] = beta
return (my_matrix)
}
model<-function(beta0, theta0, beta, theta, X, Z){
p=ncol(X)
N=nrow(X)
K=ncol(Z)
#The pliable lasso model described in the paper
#y ~ f(X)
#formulated as
#y ~ b_0 + Z theta_0 + X b + \sum( w_j theta_ji )
intercepts = as.numeric(beta0)+Z%*%(matrix(theta0))
shared_model = X%*%matrix(beta)
pliable = compute_pliable(X, Z, theta)
return( intercepts + shared_model + pliable)
}
model_min_j<-function(beta0, theta0, beta, theta, X, Z, j, W ){
#y ~ f(x) with X_j removed from the model
beta[j] = 0.0
theta[j, ] = 0.0
return (model(beta0, theta0, beta, theta, X, Z))
}
model_j<-function(beta_j, theta_j, x_j, W, j, Z){
#r_j ~ beta_j * X_j + W_j @ theta_j
#Only a the residual fit on a single predictor is made
# Caching is disabled
#zz=matrix(compute_w_j(x_j, Z,matrix(theta_j,1)))
w_j = as.matrix(data.frame(W[j]))
zz<- w_j%*%theta_j
return (beta_j * x_j + zz)
}
penalties_min_j<-function(beta_0, theta_0, beta, theta, X, Z, y, W, j,E,n_i,b){
# Compute the MSE, penalty 1 and penalty 2 when the jth predictor is not in the model.
N=nrow(X)
p=ncol(X)
#y_hat_min_j = model_min_j(beta_0, theta_0, beta, theta, X, Z, j, W)
n_i_b<-model_min_j(beta_0, theta_0, beta, theta, X, Z, j, W)
#E1=E
# E1[,b]<-0
pr_b<- (matrix(as.numeric(exp(n_i_b)/( (rowSums(E)))),N))
B<-pr_b*(1-pr_b)
B[B==0]=as.numeric(10e-9)
y1=1*(y==b)
M<-(y1-pr_b)
A<-n_i_b+M/B
rv<-B*(A-n_i_b)
mse = (1/(2*N))/ sum((rv)^2)
coef_matrix = concat_beta_theta(beta, theta)
# Ignore the jth modifier from the model
coef_matrix[j, ] = 0.0
theta[j, ] = 0.0
# Compute penalties
penalty_1=0; penalty_2 = 0.0
for (j in 1: p){
penalty_1= penalty_1 + twonorm(matrix(coef_matrix[j, ]))
penalty_2=penalty_2 + twonorm(matrix(theta[j, ]))
}
penalty_3 = sum(abs(theta))
return (list(mse, penalty_1, penalty_2, penalty_3))
}
objective_j<-function(beta0,theta0,beta,theta,X,Z,y,W,alpha,lambda,p,K,N,j,r_min_j,b,n_i,E,B){
beta_j<-beta[j]
theta_j<-theta[j,]
theta_transpose<-t(theta_j)
K=length(theta_j)
# print(j)
precomputed_penalties_minus_j = penalties_min_j(beta0, theta0, beta, theta, X, Z, y, W, j,E,n_i,b)
#
#
mse<-as.numeric(unlist(precomputed_penalties_minus_j[1]))
penalty_1<-as.numeric(unlist(precomputed_penalties_minus_j[2]))
penalty_2<-as.numeric(unlist(precomputed_penalties_minus_j[3]))
penalty_3<-as.numeric(unlist(precomputed_penalties_minus_j[4]))
#r_min_j = ((model_min_j(beta0, theta0, beta, theta, X, Z, j, W )))
# print(theta_j)
# zz<- as.matrix(data.frame(W[j]))%*%theta_j
#print(zz)
r_hat = model_j(beta[j], theta[j,], X[, j], W, j, Z)
mse_1 = (1 / (2*N)) * ( sum( (r_min_j - B*r_hat )^2 )) +mse
# Penalty 1
coef_vector = matrix(0,(K+1))
coef_vector[c(1:K)] = as.numeric(theta_j)
coef_vector[(K+1)] = beta_j
penalty_1 =penalty_1+ twonorm(matrix(coef_vector) )
# Penalty 2
penalty_2 =penalty_2+ twonorm(matrix(theta_j))
# Penalty 3
penalty_3 =penalty_3+ sum(abs(theta_j))
objective_l = mse_1 + (1-alpha) * lambda * (penalty_1 + penalty_2) + alpha * lambda * penalty_3
# norm_1_l= lambda*(1-alpha)*(norm(matrix(c(beta_j,theta_j)),type = "F") +norm(matrix(c(theta_j)),type = "F") ) + lambda*alpha* sum(abs(theta_j))
#objective_l=apply(apply(prob_d, 2, FUN="!=", y), 2, sum)/length(y)
return( objective_l)
}
#
# res_min_j<-function(beta_0, theta_0, beta, theta, X, Z, y, W,b,n_i,E,pr,j){
# # Compute the MSE, penalty 1 and penalty 2 when the jth predictor is not in the model.
# N=nrow(X)
# p=ncol(X)
#
#
# y_hat_min_j = model_min_j(beta_0, theta_0, beta, theta, X, Z, j, W)
# n_i_b<-model_min_j(beta_0, theta_0, beta, theta, X, Z, j, W)
# E1=E
# E1[,b]<-0
#
# pr[b]<-list(matrix(as.numeric(1/( exp(-n_i_b)*rowSums(E1)+1),N)))
# pr_b<-matrix(unlist(pr[b]),N)
#
#
#
#
#
#
# B<-pr_b*(1-pr_b)
#
#
# B[B==0]=as.numeric(10e-9)
#
#
# y1=1*(y==b)
#
# M<-(y1-pr_b)
#
# A<-n_i_b+M/B
# rv<-B*(A-n_i_b)
#
#
#
# return (rv)
#
# }
#
###############################################################
###############################################################
###############################################################
###############################################################
###############################################################
###############################################################
###############################################################
####################TRAIN TRUE WORK#################################
for_v=10;sv=0;fq=50;st=50;mv=20;ms=50;tol=1e-3
plasso_fit1 <- function(y, X, Z, nlambda, alpha,new_t,my_mbeta,number, intercept,step,maxgrid,tol,run,lambda_min,my_lambda=NULL,tt=NULL,for_v,sv,fq,st,mv,ms,cv_run,max_iter=100){
# xbar=colMeans(X)
#zbar=colMeans(Z)
#X=scale(X,xbar,F)
# Z=scale(Z,zbar,F)
# print(Z)
orig.X=X
#y=as.vector(y)
N <- length(y)
p <- ncol(X)
K <- ncol(Z)
#X=matrix(as.numeric(X),N,p)
# Z=matrix(as.numeric(Z),N,K)
#if (p<N) {rat<-1e-5
# } else {rat<-1e-2}
rat=lambda_min
tolerance=tol
W <- lapply(seq_len(p),
function(j) (matrix(X[, j], nrow = N, ncol = K) * Z))
#for (n in 1:max(y)) {
# BETA0[n]<-data.frame(matrix(0)); BETA[n]<-data.frame(matrix(0)); THETA0[n]<-data.frame(matrix(0)); THETA[n]<-data.frame(matrix(0)); Y_hat[n]<-data.frame(matrix(0)); Lambda[n]<-data.frame(lambda); non_zero[n]<-data.frame(matrix(0, nrow= nlambda))
# }
# BETA0<-matrix(0,nrow = (nlambda)); BETA<-matrix(0,nrow = (nlambda)); THETA0<-matrix(0,nrow = (nlambda)); THETA<-matrix(0,nrow =( nlambda));
Y_hat<-matrix(0, nrow = (nlambda)); Lambda<-matrix(0, nrow = (nlambda)); non_zero<-matrix(0, nrow= (nlambda),ncol = max(y));non_zero_theta<-matrix(0, nrow= (nlambda),ncol = max(y));DEV<-matrix(0, nrow = (nlambda),ncol = 1);DEV1<-matrix(0, nrow = (nlambda),ncol = 1)
#
BETA0<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = (nlambda))))
BETA<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow=p,ncol=nlambda)))
THETA0<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow=K,ncol=nlambda)))
THETA<-lapply(seq_len(max(y)),
function(j)(array(0,c(p,K,nlambda))))
#y_Hat <- X%*%matrix(beta) + XZ_termnggb
#beta01<-beta; theta01<-theta
# BETA0[1]<-list(beta0); BETA[1]<-list(matrix(0,p,max(y))); THETA0[1]<-list(theta0); THETA[1]<-list(theta)
# while (lambda>=Lambda_min ){
#
BETA01<-lapply(seq_len(max(y)),
function(j)(0))
old_BETA01<-lapply(seq_len(max(y)),
function(j)(0))
BETA1<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = 1,ncol = p)))
old_BETA1<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = 1,ncol = p)))
#
THETA01<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = 1,ncol = K)))
old_THETA01<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = 1,ncol = K)))
THETA1<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = p,ncol = K)))
old_THETA1<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = p,ncol = K)))
Y_hat1<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
XZ_term<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
n_i<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
pr<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
n_il<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
n_ir<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
prl<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
prr<-lapply(seq_len(max(y)),
function(j)(matrix(0,nrow = N)))
for (x in 1:max(y)) {
#beta0<-unlist(BETA01[x])
# beta <- matrix(unlist(BETA1[x]),p)
# my_X<-scale(X,-xbar,FALSE) ; my_Z<-scale(Z,-zbar,FALSE)
my_X<-X ; my_Z<-Z
#my_X=matrix(as.numeric(my_X),N,p)
#my_Z=matrix(as.numeric(my_Z),N,K)
beta0<-BETA0[[x]][1]
beta <- BETA[[x]][,1]
# print(beta)
theta <-as.matrix(THETA[[x]][,,1]) ; theta_transpose <- t(theta)
theta0 <-THETA0[[x]][,1]
# n_i<-beta0*as.numeric(beta0)*matrix(1,nrow = N,ncol = 1)+Z%*%(theta0)+X%*%matrix(beta) + XZ_term
n_i[x]<-list(model(beta0, theta0, beta, theta, X, Z))
}
E<-matrix(0,N,max(y))
for (x in 1:max(y)) {
E[,x]<-exp(unlist(n_i[x]))
}
my_pr<-matrix(0,N,(max(y)-1))
for (x in 1:(max(y))) {
n_i_b<-matrix(unlist(n_i[x]),N)
#E_1<-E
#E_1[,x]<-0
pr[x]<-list(matrix(as.numeric(exp(n_i_b)/( (rowSums(E)))),N))
#my_pr[,x]<-(matrix(as.numeric(exp(n_i_b)/( (rowSums(E)))),N))
}
# pr[max(y)]<- list(matrix(1- rowSums(my_pr),N))
if(is.null(my_lambda)){
O_1<-matrix(0,max(y),1)
#active_set1<-matrix(0,p,max(y))
# strong_set<-matrix(0,p,max(y))
#strong_set1<-matrix(0,p,max(y))
for(b in 1:max(y)) {
n_i_b<-matrix(unlist(n_i[b]),N)
#beta0<-matrix(unlist(BETA01[b]))
pr_b<-matrix(unlist(pr[b]),N)
B<-pr_b*(1-pr_b)
B[B==0]=as.numeric(10e-9)
# O<-B
y1=1*(y==b)
M<-(y1-pr_b)
A<-n_i_b+M/B
# rv<-B*(A-n_i_b)
r<-B*(A-n_i_b)
#
# r=y1
## Define_Parameters
#beta01<-beta0
O_1[b]=max(abs(t(X)%*%r)/length(r))/(1-alpha)
#print(O)
}
print(O_1)
# lambda_to_use<-matrix(0,nlambda,max(y))
#for (i in 1:max(y)) {
# lambda_max_to_select<-matrix(0,max(y))
#for (j in 1:max(y)) {
lambda_max_to_select<- max(O_1)
#}
lambda<-max(lambda_max_to_select)
print(lambda)
big_lambda<-lambda
#lambda_i<-matrix(0,maxgrid,max(y))
Lambda_min<- rat*big_lambda
print(Lambda_min)
# lambda_i<-matrix(0,maxgrid)
#for (g in 2:(maxgrid-1)) {
#lambda_i[g]<- big_lambda*(Lambda_min/big_lambda)^(g/maxgrid)
#}
lambda_i<- exp(seq(log(big_lambda),log(big_lambda*rat),length=maxgrid))
lambda_i[1]<-big_lambda;lambda_i[maxgrid]<-Lambda_min
# lambda_i<-exp(seq(log(big_lambda),log(big_lambda*rat), (log(big_lambda*rat) - log(big_lambda))/(maxgrid-1)))
print(lambda_i)
#lambda_i[1]<-big_lambda ;lambda_i[maxgrid]<-Lambda_min
#lambda_i[1]<-lambda_max_to_select;lambda_i[maxgrid]<-Lambda_min
# lambda_to_use[,i]<-lambda_i
# }
}else{
lambda_i<-my_lambda
}
big_t<-matrix(0,nlambda,max(y))
Mbeta<-matrix(0,nlambda)
#lambda<-lambda_i[1]
#t=new_t
mbeta=my_mbeta
#v_beta<-0
#v_theta<-matrix(0,1,K)
#old_beta_hat<-matrix(0,p,1)
#old_theta_hat<-matrix(0,p,K)
#nes_lambda<-matrix(0,nlambda+1)
#for (i in 1:nlambda) {
# nes_lambda[1]<-0
# nes_lambda[i+1]<-(1+sqrt(1+4*(nes_lambda[i])^2))/2
#}
dev_percent<-matrix(0,nlambda)
sec_active1<-matrix(0,p,max(y))
sec_active2<-matrix(0,p,max(y))
ACTIVE<-matrix(0,nlambda,max(y))
ACTIVE1<-matrix(0,nlambda,max(y))
my_v<-sv
my_V<-for_v
active_set1<-matrix(0,p,max(y))
active_set2<-matrix(0,p,max(y))
strong_set<-matrix(0,p,max(y))
strong_set1<-matrix(0,p,max(y))
my_q=1
my_ok<-0
q=1
U<-matrix(0); U2<-matrix(0); U3<-matrix(0)
while (isTRUE(my_ok==0)==T | isTRUE(q<=nlambda)==T ) {
#for (i in 1:nlambda ) {
my_v<-my_v
my_V<-my_V
# print(c(my_v,my_V))
if(q<=1){
i=q
lambda<-lambda_i[i]
for (b in 1:max(y)) {
# lambda_i<- lambda_to_use[,b]
# for (it in 1:max_it) {
beta0=BETA0[[b]][q]
beta = BETA[[b]][,q]
# print(beta)
v_beta=beta
theta =(THETA[[b]][,,q]) ; theta_transpose <- t(theta)
v_theta=theta;theta_transpose1 = t(v_theta)
theta0 = THETA0[[b]][,q]
theta01=theta0
beta01=beta0
beta1 = beta
theta1 = theta ; theta_transpose1 = t(theta1)
theta01 = theta
norm1<-matrix(0,p,1);norm3<-matrix(0,p,1)
for( iii in 1: max_iter){
# iter_prev_score = objective(
# beta0, theta0, beta, theta,
# X, Z, y,
# alpha, lam, W
# )
# n_i<-beta0*as.numeric(beta0)*matrix(1,nrow = N,ncol = 1)+Z%*%(theta0)+X%*%matrix(beta) + XZ_term
n_i[b]<-list(model(beta0, theta0, beta, theta, X, Z))
n_i_b<-matrix(unlist(n_i[b]),N)
# E1=E
#E1[,b]<-0
E[,b]<-exp(unlist(n_i[b]))
pr[b]<-list( (matrix(as.numeric(exp(n_i_b)/( (rowSums(E)))),N)))
pr_b<-matrix(unlist(pr[b]),N)
B<-pr_b*(1-pr_b)
B[B==0]=as.numeric(10e-9)
y1=1*(y==b)
M<-(y1-pr_b)
A<-n_i_b+M/B
rv<-B*(A-n_i_b)
#objective<-function(r,beta,theta,alpha,lambda)
iter_prev_score= objective(rv,beta,theta,alpha,lambda)
#iter_prev_score = objective(rv,beta,theta,alpha,lambda )
#r<-(A-n_i_b)
v=reg(rv,Z)
if (b==max(y)) {
my_beta0<-matrix(0,(max(y)-1))
for (l in 1:(max(y)-1)) {
my_beta0[l]<-BETA0[[l]][i]
}
beta0<-1-sum(my_beta0)
theta0<-matrix(unlist(v[2]))
} else{
beta0<-matrix(unlist(v[1]))
theta0<-matrix(unlist(v[2]))
}
# theta03<- matrix(0,N,K)
# xz_theta <- lapply(seq_len(p),
# function(j) (matrix(X[, j], nrow = N, ncol = K) * Z) %*% theta_transpose[, j])
# XZ_term <- Reduce(f = '+', x = xz_theta)
# for (k in 1:K) {
# theta03[,k]<- (Z[,k]*(B)*Z[,k])
# }
# theta03<- colSums(theta03)
# theta03<- (matrix(theta03))^-1
# theta02<-t(Z)%*%((B)*(A-(as.numeric(beta0)+X%*%matrix(beta) + XZ_term)))
# theta0<- theta03*theta02
#ACTIVE[i,b]<-sum(strong_set)
#######################line search###########
for (j in 1:p) {
if(is.null(tt)){
t=NULL
} else{t=tt[q]}
# Strong screening rule (https://statweb.stanford.edu/~tibs/ftp/strong.pdf)
if(i<=1){checkk=2*lambda-lambda_i[1] }else{checkk=( 2*lambda-lambda_i[i-1] )}
# print(c(i,as.numeric(abs( (t(matrix(X[,j]*c(y) ))%*% matrix((r1) ) ) )/(N*alpha) ), checkk ))
if(as.numeric(abs( (t(matrix( (X[,j]) ) )%*% matrix(((rv)) ) ) )/(N*alpha) )< checkk ){
next(j)
} else {
#w_j = ( data.frame(W[j]) )
res_j<- rv+B*model_j(beta[j], theta[j,], X[,j], W, j, Z)
cond1<- as.numeric(abs((t(matrix(X[,j]))%*% matrix( res_j ))/N))
cond2<-as.numeric(norm(matrix(S_func((t(data.frame(W[j]))%*%( res_j ) )/N, alpha*(lambda))), type="F"))
# cond1<- as.numeric(abs((t(matrix(X[,j]))%*% matrix(y1-pr_b))/N))
# cond2<-as.numeric(norm(matrix(S_func((t(data.frame(W[j]))%*%(y1-pr_b))/N, alpha*(lambda))), type="F"))
# cond1<- as.numeric(abs((t(matrix(X[,v]))%*% matrix(r_j))/N))
# cond2<-as.numeric(norm(matrix(S_func((t(data.frame(W[v]))%*%(r_j))/N, alpha*(lambda))), type="F"))
#lambda_i[0]<-0
#if(isTRUE(active_set1[v,b]==1)==T){
# strong_set[v]<-1
# next(v)
# } else
if (cond1<= (1-alpha)*(lambda)){
strong_set[j,b]<-0
} else{
strong_set[j,b]<-1
}
# print(c(cond1,(1-alpha)*(lambda)))
if (cond2<= 2*(1-alpha)*(lambda)){
strong_set1[j,b]<- 0
} else{
strong_set1[j,b]<-1
}
# print(c(cond1,(1-alpha)*(lambda),cond2,2*(1-alpha)*(lambda)))
if(strong_set[j,b]==0 & strong_set1[j,b]==0){
#beta[j]<-0;theta[j,]<-0
next(j)
}else {
# beta1_j<- (N/(t(B)%*%(matrix(X[,j]))^2))* S_func((t(B*matrix(X[,j]))%*%matrix(r_j))/N,(1-alpha)*lambda)
# cond3<- norm(matrix(S_func((t(data.frame(W[j]))%*%((r_j)-(B)*matrix(X[,j])*as.numeric(beta1_j))/N),alpha*(lambda))),type="F")
beta1_j<- (N/sum(B*(matrix(X[,j])*matrix(X[,j]))))* S_func((t(matrix(X[,j]))%*%matrix(res_j ))/N,(1-alpha)*lambda)
# #
# #
#print(beta1_j)
# #
# #
# }
cond3<- norm(matrix(S_func(t(data.frame(W[j]))%*%( ( res_j )-(B)*matrix(X[,j])*as.numeric(beta1_j))/N,alpha*lambda)),type="F")
if (isTRUE(cond3<= 2*(1-alpha)*lambda)==T) {
beta[j]<-as.numeric(beta1_j)
# theta[j,]<-as.numeric(0)
active_set1[j,b]<-1
# v_beta[j]<-unlist(value1[[1]]); v_theta[j,]<- unlist(value1[[2]]); beta[j]<-unlist(value1[[3]]);theta[j,]<-unlist(value1[[4]])
next(j)
} else {
# L=mbeta; mu=intercept
#h=t; my_b= (1-nes_lambda[i])/nes_lambda[i+1]
# quadratic=function(L1,L2, beta_j ,theta_j, alpha,lambda,t,mbeta,v_beta,v_theta,my_n,beta0,theta0,j,W,X,Z,y1,y,N)
value1<- quadratic(beta,theta, alpha,lambda,beta0,theta0,j,b,W,X,Z,y,N,n_i,xbar,zbar,t=t,r_min_j = res_j)
#value1<- quadratic(L1, L2, beta_j=as.numeric(beta[j]),theta_j=as.numeric(theta[j,]), alpha,lambda,t,mbeta,v_beta[j],v_theta[j,],my_n=(i-1))
beta[j]<-unlist(value1[[1]]);theta[j,]<-unlist(value1[[2]]);t=unlist(value1[[3]])
# v_beta[j]<-unlist(value1[[1]]); v_theta[j,]<- unlist(value1[[2]]); beta[j]<-unlist(value1[[3]]);theta[j,]<-unlist(value1[[4]])
active_set1[j,b]<-1
active_set2[j,b]<-1
next(j)} #theta
}
}
}#J
# n_i<-beta0*as.numeric(beta0)*matrix(1,nrow = N,ncol = 1)+Z%*%(theta0)+X%*%matrix(beta) + XZ_term
n_i[b]<-list(model(beta0, theta0, beta, theta, X, Z))
n_i_b<-matrix(unlist(n_i[b]),N)