https://github.com/gzt/cholwishart

Functions for Wishart distributions, including sampling from the inverse Wishart and sampling from the Cholesky factorization of a Wishart.
https://github.com/gzt/cholwishart

cholesky-decomposition cholesky-factorization cran digamma-functions gamma multivariate pseudo-wishart r wishart wishart-distributions

Last synced: 3 months ago
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Functions for Wishart distributions, including sampling from the inverse Wishart and sampling from the Cholesky factorization of a Wishart.

• Host: GitHub
• URL: https://github.com/gzt/cholwishart
• Owner: gzt
• Created: 2018-02-24T06:30:25.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2024-09-30T18:41:08.000Z (about 1 year ago)
• Last Synced: 2025-04-23T20:17:36.687Z (6 months ago)
• Topics: cholesky-decomposition, cholesky-factorization, cran, digamma-functions, gamma, multivariate, pseudo-wishart, r, wishart, wishart-distributions
• Language: R
• Homepage: https://gzt.github.io/CholWishart
• Size: 413 KB
• Stars: 7
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.Rmd
  • Changelog: NEWS.md
  • Contributing: .github/CONTRIBUTING.md
  • Code of conduct: .github/CODE_OF_CONDUCT.md

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README

          
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# 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.