arma::mat exact_trans2(arma::cube joint_means_trans, Rcpp::List eigen_decomp, double time_int, arma::ivec absorb_states, int start_state, int end_state, int exact_time_index){
arma::mat rate_matrix=Rcpp::as<arma::mat>(eigen_decomp["rate"]);
arma::mat out=arma::zeros<arma::mat>(rate_matrix.n_rows,rate_matrix.n_rows);
arma::mat temp=arma::zeros<arma::mat>(rate_matrix.n_rows,rate_matrix.n_rows);
int i=start_state-1;
int j=end_state-1;
int k=0;
bool i_in_A=0;
bool j_in_A=0;
//std::cout<<absorb_states;
while(i_in_A==0 && k<absorb_states.size()){
int test=absorb_states[k]-1;
if(test==i){
i_in_A=1;
}
k++;
}
k=0;
while(j_in_A==0 && k<absorb_states.size()){
int test=absorb_states[k]-1;
if(test==j){
j_in_A=1;
}
k++;
}
int in_either=i_in_A+j_in_A;
if(in_either==0){
for(int l=0;l<absorb_states.size();l++){
int absorb_state=absorb_states[l]-1;
temp.col(absorb_state)=rate_matrix.col(absorb_state);
}
out=joint_means_trans.slice(exact_time_index)*temp;
}
if(i_in_A==0 && j_in_A==1){
arma::mat prob_mat=mat_exp_eigen_cpp(eigen_decomp,time_int);
out.col(j)=prob_mat.col(i)*rate_matrix(i,j);
}
return(out);
}
arma::mat joint_dur_dur_exact_time(int i,int j, double interval_len, arma::ivec absorb_states,Rcpp::List eigen_decomp){
arma::cx_mat Q=Rcpp::as<arma::cx_mat>(eigen_decomp["rate"]);
double t=interval_len;
arma::mat joint_dur=joint_duration_2moment(i, j,eigen_decomp,t);
arma::cx_mat temp=arma::zeros<arma::cx_mat>(Q.n_rows,Q.n_rows);
bool i_in_A=0;
bool j_in_A=0;
int k=0;
//std::cout<<absorb_states;
while(i_in_A==0 && k<absorb_states.size()){
int test=absorb_states[k];
if(test==i){
i_in_A=1;
}
k++;
}
k=0;
while(j_in_A==0 && k<absorb_states.size()){
int test=absorb_states[k];
if(test==j){
j_in_A=1;
}
k++;
}
int in_either=i_in_A+j_in_A;
if(i_in_A+j_in_A==0){
for(int l=0;l<absorb_states.size();l++){
int absorb_state=absorb_states[l];
temp.col(absorb_state)=Q.col(absorb_state);
}
temp=joint_dur*temp;
}else{
temp=arma::zeros<arma::cx_mat>(Q.n_rows,Q.n_rows);
}
arma::mat out=arma::real(temp);
return(out);
}