#initialize model parameterss
m<-100 #number of replications in simulation
dim<-12 #dimension of random variable X
truedim<-1#dimension of B=b
qs<-dim-truedim# dimension of orthogonal complement of B
b1=c(1,1,1,1,1,1,0,0,0,0,0,0)/sqrt(6)
b<-b1#B
P<-b%*%t(b)
sigma=0.5#error standard deviation
N<-100#sample size
K<-30#number of arbitrary starting values for curvilinear optimization
MAXIT<-30#maximal number of iterations in curvilinear search algorithm 
##initailaize true covariancematrix of X
Sig<-mat.or.vec(dim,dim)
for (i in 1:dim){
  for (j in 1:dim){
    Sig[i,j]<-sigma^abs(i-j)
  }
}
Sroot<-chol(Sig)

M3_JASA<-mat.or.vec(m,8)
colnames(M3_JASA)<-c('CVE1','CVE2','CVE3','meanMAVE','csMAVE','phd','sir','save')
for (i in 1:m){
  #generate dat according to M3
  dat<-creat_sample_nor_nonstand(b,N,cos,t(Sroot),sigma) # distribution
  #est sample covariance matrix
  Sig_est<-est_varmat(dat[,-1])
  #est trace of sample covariance matrix
  tr<-var_tr(Sig_est)
  #CVE
  #calculates Vhat_k for CVE1,CVE2, CVE3 for k=qs
  CVE1<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(0.8),tr=tr),maxit = MAXIT,sclack_para = 0)
  CVE2<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(2/3),tr=tr),maxit = MAXIT,sclack_para = 0)
  CVE3<-stiefl_opt(dat,k=qs,k0=K,h=choose_h_2(dim,k=dim-truedim,N=N,nObs=(N)^(0.5),tr=tr),maxit = MAXIT,sclack_para = 0)
  #calculate orthogonal complement of Vhat_k
  #i.e. CVE1$est_base[,1:truedim] is estimator for B with dimension (dim times (dim-qs))
  CVE1$est_base<-fill_base(CVE1$est_base)
  CVE2$est_base<-fill_base(CVE2$est_base)
  CVE3$est_base<-fill_base(CVE3$est_base)
  # calculate distance between true B and estimated B
  M3_JASA[i,1]<-subspace_dist(CVE1$est_base[,1:truedim],b)
  M3_JASA[i,2]<-subspace_dist(CVE2$est_base[,1:truedim],b)
  M3_JASA[i,3]<-subspace_dist(CVE3$est_base[,1:truedim],b)
  #meanMAVE
  mod_t2<-mave(Y~.,data=as.data.frame(dat),method = 'meanMAVE')
  M3_JASA[i,4]<-subspace_dist(mod_t2$dir[[truedim]],b)
  #csMAVE
  mod_t<-mave(Y~.,data=as.data.frame(dat),method = 'csMAVE')
  M3_JASA[i,5]<-subspace_dist(mod_t$dir[[truedim]],b)
  #phd
  test4<-summary(dr(Y~.,data=as.data.frame(dat),method='phdy',numdir=truedim+1))
  M3_JASA[i,6]<-subspace_dist(orth(test4$evectors[,1:truedim]),b)
  #sir
  test5<-summary(dr(Y~.,data=as.data.frame(dat),method='sir',numdir=truedim+1))
  M3_JASA[i,7]<-subspace_dist(orth(test5$evectors[,1:truedim]),b)
  #save
  test3<-summary(dr(Y~.,data=as.data.frame(dat),method='save',numdir=truedim+1))
  M3_JASA[i,8]<-subspace_dist(orth(test3$evectors[,1:truedim]),b)

  print(paste(i,paste('/',m)))
}
boxplot(M3_JASA[,]/sqrt(2*truedim),names=colnames(M3_JASA),ylab='err',main='M3')
summary(M3_JASA[,])