# rwishart_chol: Sampling Cholesky factor of a Wishart matrix In stla/matrixsampling: Simulations of Matrix Variate Distributions

## Description

Samples the lower triangular Cholesky factor of a Wishart random matrix.

## Usage

 `1` ```rwishart_chol(n, nu, Sigma, epsilon = 0) ```

## Arguments

 `n` sample size, a positive integer `nu` degrees of freedom, a number strictly greater than `p-1`, where `p` is the dimension (the order of `Sigma`) `Sigma` scale matrix, a positive definite real matrix `epsilon` a number involved in the algorithm only if it positive; its role is to guarantee the invertibility of the sampled matrices; see Details

## Details

The argument `epsilon` is a threshold whose role is to guarantee that the algorithm samples invertible matrices. The matrices sampled by the algorithm are theoretically invertible. However, because of numerical precision, they are not always invertible when `nu` is close to `p-1`, i.e. when `nu-p+1` is small. In this case, the simulations of chi-squared distributions involved in the algorithm can generate zero values or values close to zero, yielding the non-invertibility of the sampled matrices. These values are replaced with `epsilon` if they are smaller than `epsilon`.

## Value

A numeric three-dimensional array; simulations are stacked along the third dimension (see example).

## Examples

 ```1 2 3 4 5 6``` ```nu <- 4 p <- 3 Sigma <- diag(p) Wsims <- rwishart_chol(10000, nu, Sigma) dim(Wsims) # 3 3 10000 Wsims[,,1] ```

stla/matrixsampling documentation built on Feb. 23, 2018, 8:36 p.m.