\name{rgwish}
\alias{rgwish}

\title{Sampling from G-Wishart distribution}

\description{
Generates random matrices, distributed according to the G-Wishart distribution with parameters b and D, \eqn{W_G(b, D)}.
}

\usage{rgwish( n = 1, adj.g = NULL, b = 3, D = NULL )}

\arguments{
  \item{n}{The number of samples required. }
  \item{adj.g}{
    The adjacency matrix corresponding to the graph structure. It should be an upper triangular matrix in which \eqn{a_{ij}=1} 
    if there is a link between notes \eqn{i}{i} and \eqn{j}{j}, otherwise \eqn{a_{ij}=0}.
    }
  \item{b}{The degree of freedom for G-Wishart distribution, \eqn{W_G(b, D)}. }
  \item{D}{The positive definite \eqn{(p \times p)} "scale" matrix for G-Wishart distribution, \eqn{W_G(b, D)}. 
           The default is an identity matrix.}
}

\details{
Sampling from G-Wishart distribution, \eqn{K \sim W_G(b, D)}, with density:

  \deqn{Pr(K) \propto |K| ^ {(b - 2) / 2} \exp \left\{- \frac{1}{2} \mbox{trace}(K \times D)\right\},}

which \eqn{b > 2} is the degree of freedom and D is a symmetric positive definite matrix.
}

\value{
A numeric array, say A, of dimension \eqn{(p \times p \times n)}, where each \eqn{A[,,i]}{A[,,i]} is a positive 
definite matrix, a realization of the G-Wishart distribution, \eqn{W_G(b, D)}.
}

\references{
Lenkoski, A. (2013). A direct sampler for G-Wishart variates, \emph{Stat}, 2:119-128

Mohammadi, A. and E. Wit (2015). Bayesian Structure Learning in Sparse Gaussian Graphical Models, \emph{Bayesian Analysis}, 10(1):109-138

Mohammadi, A. and E. Wit (2015). \pkg{BDgraph}: An \code{R} Package for Bayesian Structure Learning in Graphical Models, \emph{arXiv:1501.05108} 

Mohammadi, A. et al (2017). Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models, \emph{Journal of the Royal Statistical Society: Series C} 

Mohammadi, A., Massam H., and G. Letac (2017). The Ratio of Normalizing Constants for Bayesian Graphical Gaussian Model Selection, \emph{arXiv:1706.04416} 
}

\author{ Abdolreza Mohammadi and Ernst Wit }

\examples{
\dontrun{
graph.sim <- bdgraph.sim( p = 5, graph = "cycle" )
adj.g     <- graph.sim $ G
adj.g    # adjacency of graph with 5 nodes and 4 links
   
sample <- rgwish( n = 3, adj.g = adj.g, b = 3, D = diag(5) )
round( sample, 2 )  
}
}