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#include "RcppArmadillo.h"
#include <Rcpp.h>
// [[Rcpp::depends(RcppArmadillo)]]
using namespace Rcpp;
using namespace std;
// [[Rcpp::export]]
Rcpp::List rq_simplex_cpp(arma::mat X,
arma::uvec Ih,
arma::uvec Ihc,
arma::mat IH,
unsigned int K,
unsigned int n,
arma::vec xB,
arma::vec P,
double tau){
arma::mat invXh = inv(X.rows(Ih));
arma::vec cB = arma::conv_to<arma::vec>::from(P < 0) + P * tau;
arma::vec cC = arma::join_cols(arma::ones<arma::vec>(K) * tau, arma::ones<arma::vec>(K) * (1-tau));
//Rcout << Xny .rows(Ihc) << "\n";
arma::mat IB2 = -(P * arma::ones<arma::vec>(K).t() % X.rows(Ihc))*invXh;
arma::vec g = IB2.t() * cB;
arma::vec d = cC - arma::join_cols(g,-g);
d.elem(find(abs(d) < 1.e-15)).fill(0);
arma::uvec s = sort_index(d);
arma::vec md = sort(d);
s = s.elem(find(md < 0));
md = md.elem(find(md < 0));
arma::vec c = arma::ones<arma::vec>(s.size());
for(unsigned int i = 0; i < s.size(); i++){
if(s(i) >= K){
s(i) = s(i) - K;
c(i) = -1;
}
}
//c.elem(s>K).fill(-1);
arma::mat C(c.size(),c.size(),arma::fill::eye);
C.diag() = c;
arma::mat h = arma::join_cols(invXh.cols(s), IB2.cols(s)) * C;
arma::vec xm = xB.elem(arma::linspace<arma::uvec>(K,xB.size()-1,xB.size()-K));
xm.elem(find(xm < 0)).fill(0);
arma::mat hm = h.rows(arma::linspace<arma::uvec>(K,xB.size()-1,xB.size()-K));
arma::vec alpha(s.size());
arma::uvec q(s.size());
arma::vec cq(s.size());
arma::uvec idx2 = arma::linspace<arma::uvec>(0,s.size()-1,s.size());
for(unsigned int k = 0; k < s.size(); k++){
arma::vec sigma = xm;
arma::uvec idx = find(hm.col(k) > 1.e-12);
sigma.elem(idx) = xm.elem(idx) / hm(idx, find(idx2 == k));
sigma(find(hm.col(k) <= 1.e-12)).fill(1.e30);
alpha.elem(find(idx2 == k)).fill(sigma.min());
q.elem(find(idx2 == k)).fill(sigma.index_min());
cq.elem(find(idx2 == k)) = c.elem(find(idx2 == k));
}
arma::vec gain = md % alpha;
arma::vec Mgain = sort(gain);
arma::uvec IMgain = sort_index(gain);
arma::uvec IhMid;
double CON = 1.e30;
unsigned int j = 0;
if(gain.size() < 1){
gain.resize(1);
gain(0) = 1;
} else {
while((CON > 1.e6) & (j < s.size())){
IhMid = Ih;
IhMid(s(IMgain(j))) = Ihc(q(IMgain(j)));
IhMid = sort(IhMid);
if(sum(abs(IH.t() - IhMid.t())) == 0){
CON = 1.e30;
} else{
CON = cond(X.rows(IhMid));
}
s = s(IMgain(j));
q = q(IMgain(j));
cq = cq(IMgain(j));
alpha = alpha(IMgain(j));
IH = arma::join_rows(IH, arma::conv_to<arma::vec>::from(IhMid));
h = h.col(IMgain(j));
gain = gain(IMgain(j));
md = md(IMgain(j));
j += 1;
}
}
return List::create(Named("CON") = CON,
Named("s") = s,
Named("g") = g,
Named("q") = q,
Named("gain") = gain,
Named("md") = md,
Named("alpha") = alpha,
Named("h") = h,
Named("IH") = IH,
Named("cq") = cq);
}