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#include "nll_pcountOpen.h"
#include "tranprobs.h"
#include "distr.h"
using namespace Rcpp ;
SEXP nll_pcountOpen( SEXP y_, SEXP Xlam_, SEXP Xgam_, SEXP Xom_, SEXP Xp_, SEXP Xiota_, SEXP beta_lam_, SEXP beta_gam_, SEXP beta_om_, SEXP beta_p_, SEXP beta_iota_, SEXP log_alpha_, SEXP Xlam_offset_, SEXP Xgam_offset_, SEXP Xom_offset_, SEXP Xp_offset_, SEXP Xiota_offset_, SEXP ytna_, SEXP yna_, SEXP lk_, SEXP mixture_, SEXP first_, SEXP last_, SEXP M_, SEXP J_, SEXP T_, SEXP delta_, SEXP dynamics_, SEXP fix_, SEXP go_dims_, SEXP immigration_, SEXP I_, SEXP I1_, SEXP Ib_, SEXP Ip_) {
int lk = as<int>(lk_);
Rcpp::IntegerVector N = seq_len(lk)-1;
int M = as<int>(M_);
int J = as<int>(J_);
int T = as<int>(T_);
arma::imat ym = as<arma::imat>(y_);
arma::mat Xlam = as<arma::mat>(Xlam_);
arma::mat Xgam = as<arma::mat>(Xgam_);
arma::mat Xom = as<arma::mat>(Xom_);
arma::mat Xp = as<arma::mat>(Xp_);
arma::mat Xiota = as<arma::mat>(Xiota_);
arma::colvec beta_lam = as<arma::colvec>(beta_lam_);
arma::colvec beta_gam = as<arma::colvec>(beta_gam_);
arma::colvec beta_om = as<arma::colvec>(beta_om_);
arma::colvec beta_p = as<arma::colvec>(beta_p_);
arma::colvec beta_iota = as<arma::colvec>(beta_iota_);
double log_alpha = as<double>(log_alpha_);
arma::colvec Xlam_offset = as<arma::colvec>(Xlam_offset_);
arma::colvec Xgam_offset = as<arma::colvec>(Xgam_offset_);
arma::colvec Xom_offset = as<arma::colvec>(Xom_offset_);
arma::colvec Xp_offset = as<arma::colvec>(Xp_offset_);
arma::colvec Xiota_offset = as<arma::colvec>(Xiota_offset_);
std::string mixture = as<std::string>(mixture_);
std::string dynamics = as<std::string>(dynamics_);
std::string fix = as<std::string>(fix_);
std::string go_dims = as<std::string>(go_dims_);
bool immigration = as<bool>(immigration_);
arma::imat I = as<arma::imat>(I_);
arma::imat I1 = as<arma::imat>(I1_);
Rcpp::List Ib(Ib_);
Rcpp::List Ip(Ip_);
int nrI = I.n_rows;
int nrI1 = I1.n_rows;
double alpha=0.0, psi=0.0;
if(mixture=="NB")
alpha = exp(log_alpha);
else if(mixture=="ZIP")
psi = 1.0/(1.0+exp(-log_alpha));
Rcpp::IntegerVector first(first_);
Rcpp::IntegerVector last(last_);
arma::imat ytna = as<arma::imat>(ytna_); // y[i,,t] are all NA
arma::imat ynam = as<arma::imat>(yna_); // y[i,j,t] is NA
arma::imat delta = as<arma::imat>(delta_);
// linear predictors
arma::colvec lam = exp(Xlam*beta_lam + Xlam_offset);
arma::mat omv = arma::ones<arma::colvec>(M*(T-1));
if((fix != "omega") && (dynamics != "trend")) {
if((dynamics == "ricker") || (dynamics == "gompertz"))
omv = exp(Xom*beta_om + Xom_offset);
else if((dynamics == "constant") || (dynamics == "autoreg") || (dynamics == "notrend"))
omv = 1.0/(1.0+exp(-1*(Xom*beta_om + Xom_offset)));
}
omv.reshape(T-1, M);
arma::mat om = arma::trans(omv);
arma::mat gam = arma::zeros<arma::mat>(M, T-1);
if(dynamics == "notrend") {
arma::mat lamMat = arma::repmat(lam, 1, T-1);
gam = (1-om) % lamMat;
} else {
if(fix != "gamma") {
arma::mat gamv = exp(Xgam*beta_gam + Xgam_offset);
gamv.reshape(T-1, M);
gam = arma::trans(gamv);
}
}
arma::mat pv = 1.0/(1.0+exp(-1*(Xp*beta_p + Xp_offset)));
pv.reshape(J*T, M);
arma::mat pm = trans(pv);
//Immigration
arma::mat iotav = arma::zeros<arma::colvec>(M*(T-1));
if(immigration) {
iotav = exp(Xiota*beta_iota + Xiota_offset);
}
iotav.reshape(T-1, M);
arma::mat iota = arma::trans(iotav);
// format matrices as cubes (shouldn't be done in likelihood)
arma::icube y(M,J,T);
arma::cube p(M,J,T);
arma::icube yna(M,J,T);
for(int q=0; q<(M*J*T); q++) {
y(q) = ym(q);
p(q) = pm(q);
yna(q) = ynam(q);
}
// initialize
double ll=0.0;
double ll_i=0.0;
int first_i=0;
int last_i=0;
int first1=0;
arma::colvec g_star = arma::ones<arma::colvec>(lk);
arma::mat g3 = arma::zeros<arma::mat>(lk, lk);
arma::mat g3_d = arma::zeros<arma::mat>(lk, lk);
arma::colvec g1_t = arma::zeros<arma::colvec>(lk);
arma::colvec g1_t_star = arma::zeros<arma::colvec>(lk);
arma::colvec g1 = arma::zeros<arma::colvec>(lk);
arma::colvec g2 = arma::zeros<arma::colvec>(lk);
arma::colvec g1_star = arma::zeros<arma::colvec>(lk);
arma::cube g3_t = arma::zeros<arma::cube>(lk,lk,T-1);
// shouldn't be done in likelihood
for(int i=0; i<M; i++) {
if(first[i]==1) {
first1=i; // site with no missing values at t=1
break;
}
}
// compute g3 if there are no covariates of omega/gamma
if(go_dims == "scalar") {
if(dynamics=="constant" || dynamics=="notrend")
tp1(g3, nrI, nrI1, N, I, I1, Ib, Ip, gam(first1,0), om(first1,0));
else if(dynamics=="autoreg")
tp2(g3, lk, gam(first1,0), om(first1,0), iota(first1,0));
else if(dynamics=="trend")
tp3(g3, lk, gam(first1,0), iota(first1,0));
else if(dynamics=="ricker")
tp4(g3, lk, gam(first1,0), om(first1,0), iota(first1,0));
else if(dynamics=="gompertz")
tp5(g3, lk, gam(first1,0), om(first1,0), iota(first1,0));
} else if(go_dims == "rowvec") {
for(int t=0; t<(T-1); t++) {
if(ytna(first1,t)==1) { // FIXME: this is not generic!
continue;
}
if(dynamics=="constant" || dynamics=="notrend") {
tp1(g3_t.slice(t), nrI, nrI1, N, I, I1, Ib, Ip, gam(first1,t), om(first1,t));
}
else if(dynamics=="autoreg") {
tp2(g3_t.slice(t), lk, gam(first1,t), om(first1,t), iota(first1,t));
}
else if(dynamics=="trend")
tp3(g3_t.slice(t), lk, gam(first1,t), iota(first1,t));
else if(dynamics=="ricker")
tp4(g3_t.slice(t), lk, gam(first1,t), om(first1,t), iota(first1,t));
else if(dynamics=="gompertz")
tp5(g3_t.slice(t), lk, gam(first1,t), om(first1,t), iota(first1,t));
}
}
// loop over sites
for(int i=0; i<M; i++) {
first_i = first[i]-1; // remember 0=1st location in C++
last_i = last[i]-1;
g_star.ones();
if(last_i > first_i) {
// loop over time periods in reverse order, up to second occasion
for(int t=last_i; t>first_i; t--) {
if(ytna(i,t)==1) {
continue; //
}
g1_t.zeros();
// loop over possible value of N at time t
for(int k=0; k<lk; k++) {
for(int j=0; j<J; j++) {
if(yna(i,j,t)==0) {
g1_t(k) += Rf_dbinom(y(i,j,t), k, p(i,j,t), true);
}
}
g1_t(k) = exp(g1_t(k));
g1_t_star(k) = g1_t(k) * g_star(k);
}
// computes transition probs for g3
if(go_dims == "matrix") {
g3.zeros();
if(dynamics=="constant" || dynamics=="notrend") {
// tp1(g3, lk, gam(i,t-1), om(i,t-1));
tp1(g3, nrI, nrI1, N, I, I1, Ib, Ip, gam(i,t-1), om(i,t-1));
}
else if(dynamics=="autoreg") {
tp2(g3, lk, gam(i,t-1), om(i,t-1), iota(i,t-1));
}
else if(dynamics=="trend")
tp3(g3, lk, gam(i,t-1), iota(i,t-1));
else if(dynamics=="ricker")
tp4(g3, lk, gam(i,t-1), om(i,t-1), iota(i,t-1));
else if(dynamics=="gompertz")
tp5(g3, lk, gam(i,t-1), om(i,t-1), iota(i,t-1));
} else if(go_dims == "rowvec") {
g3 = g3_t.slice(t-1);
}
int delta_it = delta(i,t);
// matrix multiply transition probs over time gaps
if(delta_it>1) {
g3_d = g3;
for(int d=1; d<delta_it; d++) {
g3_d = g3_d * g3;
}
g_star = g3_d * g1_t_star;
} else
g_star = g3 * g1_t_star;
}
}
ll_i=0.0;
int delta_i0 = delta(i,0);
g1.zeros();
for(int k=0; k<lk; k++) { // loop over possible values of N
for(int j=0; j<J; j++) {
if(yna(i,j,first_i)==0) {
g1(k) += Rf_dbinom(y(i,j,first_i), k, p(i,j,first_i), true);
}
}
g1(k) = exp(g1(k));
if(delta_i0>1)
g1_star(k) = g1(k) * g_star(k);
if(mixture=="P")
g2(k) = Rf_dpois(k, lam(i), false);
else if(mixture=="NB")
g2(k) = dnbinom_mu(k, alpha, lam(i), false);
else if(mixture=="ZIP")
g2(k) = dzip(k, lam(i), psi);
if(delta_i0==1)
ll_i += g1(k) * g2(k) * g_star(k);
}
if(delta_i0>1) {
g3_d = g3;
for(int d=0; d<delta_i0; d++) {
g3_d = g3_d * g3;
}
g_star = g3_d * g1_star;
ll_i = arma::dot(g2, g_star);
}
ll += log(ll_i + DBL_MIN);
}
return wrap(-ll);
}
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