void lmMean(const mat& x,const mat& z, const rowvec& vec_beta, mat& mean){
int P= mean.n_cols;
mat xt=x, zt=z;
xt.each_row() %=vec_beta.subvec(0,P-1);
zt.each_row() %=vec_beta.subvec(P,2*P-1);
mean= xt + zt;
mean.each_row() += vec_beta.subvec(P*2,P*3-1);
}
void updateSigma() {
mat diff2K = zeros<mat>(p, K);
vec sum_total_weights = zeros<vec>(K);
#pragma omp parallel for
for (int k = 0; k < K; ++k) {
mat diff = y.each_row() - mu.row(k);
vec zeta_local = zeta.col(k);
diff2K.col(k) = (zeta_local.t() * (diff % diff)).t();
double total_weights = accu(zeta_local);
sum_total_weights(k) = total_weights;
}
Sigma = sum(diff2K, 1) / accu(sum_total_weights);
}
// [[Rcpp::depends(RcppArmadillo)]]
// [[Rcpp::export]]
List inseq(mat M, bool adjust=true)
{
int i, m, trun;
mat mu=mean(M);
//center the rows
M.each_row() -= mu;
int n=M.n_rows, p=M.n_cols;
//Dtm is the vector of det(Sig)'s
NumericVector Dtm;
//gam_0 and gam_1 are for gam_2m and gam_2m+1, resp.
mat gam0(p,p), gam1(p,p), Gam(p,p), Sig(p,p), Sig1(p,p), Gamadj(p,p), eigvec(p,p);
//for adjustment, set initial increment in Gam=0
Gamadj.zeros();
//store the eigenvalues and eigenvectors of each Gam
vec eigval(p),eigvalneg(p);
double dtm;
int sn= n/2;
for (m=0; m<n/2; m++)
{
gam0.zeros(); gam1.zeros();
//calculate gam_2m (gam0) and gam_2m+1 (gam1)
for(i=0; i<(n-2*m);i++) gam0+=trans(M.row(i))*M.row(i+2*m);
gam0=gam0/n;
for(i=0; i<(n-2*m-1);i++) gam1+=trans(M.row(i))*M.row(i+2*m+1);
gam1=gam1/n;
//Gam_m=gam_2m+gam_2m+1, then symmetrize
Gam=gam0+gam1; Gam=(Gam+Gam.t())/2;
if (m==0) Sig=-gam0+2*Gam;
else Sig=Sig+2*Gam;
if (eig_sym(Sig)(0)>0)
{
sn=m;
break;
}
}
if (sn>n/2-1)
{
stop("Not enough samples.");
}
Dtm=det(Sig);
for (m=sn+1; m<n/2; m++)
{
gam0.zeros(); gam1.zeros();
//calculate gam_2m (gam0) and gam_2m+1 (gam1)
for(i=0; i<(n-2*m);i++) gam0+=trans(M.row(i))*M.row(i+2*m);
gam0=gam0/n;
for(i=0; i<(n-2*m-1);i++) gam1+=trans(M.row(i))*M.row(i+2*m+1);
gam1=gam1/n;
//Gam_m=gam_2m+gam_2m+1, then symmetrize
Gam=gam0+gam1; Gam=(Gam+Gam.t())/2;
//Sig_m=Sig_m-1+2Gam_m
Sig1=Sig+2*Gam;
dtm=det(Sig1);
//if dtm1>dtm, continue
if (dtm<=Dtm(m-sn-1)) break;
//update Sig
Sig=Sig1;
//record dtm
Dtm.push_back(dtm);
//to adjust the original Sig, subtract the negative part of Gam
if (adjust)
{
//calculate eigenvalues and eigenvectors of Gam
eig_sym(eigval,eigvec,Gam);
eigvalneg=eigval;
eigvalneg.elem(find(eigvalneg>0)).zeros();
Gamadj-=eigvec*diagmat(eigvalneg)*eigvec.t();
}
}
trun = Dtm.size()-1+sn;
List res; res["Sig"]=Sig; res["Dtm"]=Dtm; res["trunc"]= trun; res["sn"]=sn;
if (adjust) res["Sigadj"]=Sig+2*Gamadj;
return res;
}