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README.Rmd
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---
output: github_document
---
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[](https://github.com/gzt/CholWishart/actions)
[](https://www.gnu.org/licenses/gpl-3.0.en.html)
[](https://lifecycle.r-lib.org/articles/stages.html)
[](https://cran.r-project.org/package=CholWishart)
---
[](https://cran.r-project.org/)
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---
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<!-- README.md is generated from README.Rmd. Please edit that file -->
# CholWishart
The most common use for this package is likely fast sampling from the
inverse Wishart or use of the multivariate gamma or digamma functions. This is
a package for fast computation of various functions related to the Wishart distribution,
such as sampling from the Cholesky factorization of the Wishart,
sampling from the inverse Wishart,
sampling from the Cholesky factorization of the inverse Wishart,
sampling from the pseudo Wishart,
computing densities for the Wishart and inverse Wishart,
and computing a few auxiliary functions such as the multivariate gamma
and digamma functions. Many of these functions are written in C to maximize
efficiency.
The output of the sampling functions is in the same format as the output
of `stats::rWishart()`.
The main idea: sampling for multivariate or matrix variate statistics often
makes use of distributions related to the Wishart. There are implementations
in a few packages but they are often in R and much slower than the
basic `stats::rWishart()` or there is a lot of associated overhead in the
package. Here, then, is a small package with some of those distributions
and related functions. As the name suggests, the initial purpose was
sampling from the Cholesky factorization of a Wishart distribution.
# Usage
The package offers the following distributions:
* The inverse Wishart:
```
rInvWishart(n = 1,df = 5,Sigma = diag(4)))
```
* The Cholesky decomposition of the inverse Wishart:
```
rInvCholWishart(n = 1,df = 5,Sigma = diag(4)))
```
* The Cholesky decomposition of the Wishart
```
rCholWishart(n = 1,df = 5,Sigma = diag(4)))
```
* The pseudo Wishart and its pseudo-inverse, the generalized inverse Wishart (`df` less than
the dimension of `Sigma` minus 1):
```
rPseudoWishart(n = 1,df = 3,Sigma = diag(5)))
rGenInvWishart(n = 1,df = 3,Sigma = diag(5)))
```
* The package also offers density functions for the Wishart and inverse Wishart distributions:
```
dInvWishart(x = diag(4), df = 5, Sigma = diag(4), log = TRUE)
dWishart(x = diag(4), df = 5, Sigma = diag(4), log = TRUE)
```
In addition to this, the package offers the multivariate gamma function and multivariate digamma function, the multivariate counterparts of the gamma and digamma (derivative of the log of the gamma) functions.
```
mvgamma(x = 5, p = 3)
mvdigamma(x = 5, p = 3)
```
I suspect the most useful functions for most people will be the `mvgamma` and `rInvWishart` functions.
# Installation
Now available on CRAN, install it at:
```
install.packages('CholWishart')
```
Install the latest development version at:
```
# install.packages('devtools')
devtools::install_github("gzt/CholWishart")
```
# Calling from other packages
The header `inst/install/CholWishart.h` is available so that the exported functions
can be called in C from other packages.
# Contributing
Please note that the 'CholWishart' project is released with a [Contributor Code of Conduct](https://gzt.github.io/CholWishart/CODE_OF_CONDUCT.html). By contributing to this project, you agree to abide by its terms.