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BLassopl.cpp
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BLassopl.cpp
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#include <iostream>
#include<RcppArmadillo.h>
#include<math.h>
//Sampling Scheme from Inverse Gaussian Distribution
//[[Rcpp::export]]
Rcpp::NumericVector inversegauss(int k,Rcpp::NumericVector mu_ig_v,Rcpp::NumericVector lambda_ig_v){
//variable declaration
Rcpp::NumericVector x_ig_v(k);
Rcpp::NumericVector UniRand = Rcpp::runif(k); //sampling a vector from U(0,1)
Rcpp::NumericVector NormRand = Rcpp::rnorm(k); //sampling a vector from N(0,1)
for(int i =0; i<k ; i++){
//variable declaration
double mu_ig = mu_ig_v(i);
double lambda_ig = lambda_ig_v(i);
double y_ig;
double x_ig;
// returns 0, when we sample from inverse gauss(0.0,lambda)
if(mu_ig!=0.0) {
y_ig = pow(NormRand[i],2) ;
x_ig = mu_ig + (pow(mu_ig,2)*y_ig)/(2*lambda_ig) - (mu_ig/(2*lambda_ig))*sqrt(4*mu_ig*lambda_ig*y_ig+ pow(mu_ig,2)*pow(y_ig,2));
if (UniRand[i] >= mu_ig/(mu_ig+x_ig)) {
x_ig_v[i] = (pow(mu_ig,2))/x_ig;
} else {
x_ig_v[i] = x_ig;
}
} else {
x_ig_v[i] = 0.0;
}
}
return x_ig_v;
}
//Sampling Beta from Multivariate Normal
//[[Rcpp::depends(RcppArmadillo)]]
//[[Rcpp::export]]
Rcpp::NumericVector sampleBetainC(double sigma2, Rcpp::NumericMatrix Lambda,Rcpp::NumericMatrix XtX,Rcpp::NumericVector XtYminusYbar){
int n=XtX.nrow(), p=XtX.ncol();
arma::mat xtx(XtX.begin(),n,p,false) ;
arma::mat lambda(Lambda.begin(),p,p,false) ;
arma::vec xtyminusybar(XtYminusYbar.begin(),XtYminusYbar.size(),false);
arma::mat cov_beta = sigma2*arma::inv(xtx + lambda);
arma::vec mean_beta = (1/sigma2)*cov_beta*xtyminusybar ;
arma::mat U(p,p) ;
arma::vec s(p) ;
arma::mat V(p,p);
arma::svd(U,s,V,cov_beta);
arma::mat d(p,p);
s = arma::pow(s,.5) ;
d = arma::diagmat(s);
Rcpp::NumericVector mean = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(mean_beta));
Rcpp::NumericMatrix cov = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(cov_beta));
arma::vec beta(p);
arma::vec normrand = Rcpp::as<arma::vec>(Rcpp::rnorm(p)) ;
//arma::vec normrand(p, arma::fill::randn) ;
//beta = mean_beta + std::sqrt(sigma2)*arma::chol(cov_beta)*normrand;
beta = mean_beta +U*d*normrand;
return Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(beta));
}
//[[Rcpp::depends(RcppArmadillo)]]
//[[Rcpp::export]]
Rcpp::List BLassopl(Rcpp::NumericMatrix X,Rcpp::NumericVector Y,double a_shape,double b_rate, double sigsc_hyper, double sigsh_hyper,int niter, int nburn,int nthin)
{
// 0. Variable Declaration
// RNGScope scope;
int ncol = X.ncol() ;
int nrow = X.nrow() ;
double sigma2 ;
double sigma2_shape;
double sigma2_scale;
int N = niter/nthin;
Rcpp::NumericVector tau_inv(ncol) ;
Rcpp::NumericMatrix XtX(ncol,ncol) ;
Rcpp::NumericVector Beta(nrow);
Rcpp::NumericVector XtY(ncol) ;
Rcpp::NumericVector Mu(ncol);
Rcpp::NumericMatrix TauInverse(ncol,ncol);
Rcpp::NumericVector Lambdasquare(ncol) ;
arma::mat XX(nrow,ncol) ;
arma::colvec one(nrow,arma::fill::ones);
arma::colvec onecol(ncol,arma::fill::ones);
arma::rowvec XX_mean(ncol) ;
arma::mat XttX(ncol,ncol) ;
arma::mat dtau_inv(ncol,ncol);
arma::colvec XttY(ncol) ;
arma::colvec Beta2(ncol) ;
arma::colvec YY(nrow) ;
arma::colvec Lambda2(ncol);
arma::colvec mu(ncol) ;
arma::colvec Beta1(ncol);
arma::colvec tau_inverse(ncol);
arma::mat Betahist(N,ncol);
arma::mat Tausqhist(N,ncol);
Rcpp::NumericVector sigma2hist(N);
Rcpp::NumericVector Lambda2hist(N);
arma::colvec Betahat(ncol);
arma::colvec Tausqhat(ncol);
double sigma2hat;
double Lambda2hat;
int count;
// 1. Data Scaling
XX = Rcpp::as<arma::mat>(X) ;
XX_mean = arma::sum(XX,0)/nrow;
YY = Rcpp::as<arma::colvec>(Y) ;
YY = YY - arma::accu(YY)*one/nrow ;
XX = XX - one*XX_mean;
X = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(XX)) ;
XttX = XX.t()*XX ;
XtX = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(XttX)) ;
XttY = XX.t()*YY ;
XtY = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(XttY)) ;
// 2. Starting Values
sigma2 = R::runif(0,1)*9.9 + 0.1;
double lambda_sq = R::rgamma(a_shape,1/b_rate);
// double lambda_sq = std::pow(lambda,2);
for ( int i =0 ; i < ncol;i++)
{
tau_inv[i] = 1/R::rgamma(1,2/lambda_sq) ;
Beta[i]= 0 ;
Lambda2[i] = lambda_sq;
}
tau_inverse = Rcpp::as<arma::colvec>(tau_inv) ;
dtau_inv = arma::diagmat(tau_inverse) ;
// 3. For Posterior
// 4a Displaying in the R window when the job started
// 4. MCMC Sampling
tau_inverse = Rcpp::as<arma::colvec>(tau_inv) ;
dtau_inv = arma::diagmat(tau_inverse) ;
// 3. For Posterior
// 4a Displaying in the R window when the job started
// 4. MCMC Sampling
///*
for (int i=0 ;i < niter ; i++)
{
//*/
//int i=1;
TauInverse = Rcpp::as<Rcpp::NumericMatrix>(Rcpp::wrap(dtau_inv)) ;
Beta = sampleBetainC(sigma2,TauInverse,XtX,XtY) ;
Beta1 = Rcpp::as<arma::colvec>(Beta) ;
Beta2 = arma::square(Beta1) ;
double a = ncol + a_shape;
double b = Rcpp::as<double>(Rcpp::wrap(.5*arma::accu(arma::pow(tau_inverse,-1)))) +b_rate;
lambda_sq = R::rgamma(a_shape,1/b_rate);
Lambda2 = onecol*lambda_sq;
//*/
mu = arma::sqrt(sigma2*Lambda2%arma::pow(Beta2,-1)) ;
Mu = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(mu)) ;
Lambdasquare = Rcpp::as<Rcpp::NumericVector>(Rcpp::wrap(Lambda2));
tau_inv = inversegauss(ncol,Mu,Lambdasquare) ;
tau_inverse = Rcpp::as<arma::colvec>(tau_inv) ;
dtau_inv = arma::diagmat(tau_inverse) ;
sigma2_shape =(ncol + nrow -1)/2 +sigsh_hyper;
sigma2_scale =Rcpp::as<double>(Rcpp::wrap(.5*(YY.t() -(XX*Beta1).t())*(YY -(XX*Beta1)) + .5*(Beta1.t()*(dtau_inv*Beta1)))) +sigsc_hyper;
sigma2 = 1/(R::rgamma(sigma2_shape,1/sigma2_scale) );
if( (1+i)%nthin == 0)
{
Betahist.row(i) = Beta1.t() ;
Tausqhist.row(i) = arma::pow(tau_inverse.t(),-1) ;
sigma2hist[i] = sigma2;
Lambda2hist[i] = lambda_sq ;
if( (1+i) > nburn ) {
Betahat = Betahat + Beta1 ;
Tausqhat = Tausqhat + arma::pow(tau_inverse,-1);
sigma2hat = sigma2hat + sigma2;
count = count + 1;
Lambda2hat = Lambda2hat + lambda_sq;
}
}
// /*
}
//*/
// 5. Full Conditional Posterior
Betahat = Betahat/count;
Tausqhat = Tausqhat/count;
sigma2hat = sigma2hat/count;
Lambda2hat = Lambda2hat/count;
// 6. Inference
// 7. Return
///*
return Rcpp::List::create(Rcpp::Named("Betahat")=Betahat,Rcpp::Named("Tausqhat")=Tausqhat,Rcpp::Named("sigma2hat")=sigma2hat,Rcpp::Named("Betahist")=Betahist,Rcpp::Named("Tausqhist")=Tausqhist,Rcpp::Named("sigma2hist")=sigma2hist);
//*/
//return 0;
}