# rndWishart¶

## Purpose¶

Computes Wishart distributed random numbers given a covariance matrix.

## Format¶

r = rndWishart(numMats, cov, df)
{ r, newstate } = rndWishart(numMats, cov, df, state)
Parameters: numMats (scalar) – number of Wishart random matrices to create. cov (matrix) – NxM covariance matrix df (scalar) – degrees of freedom. state (scalar or opaque vector) – Optional argument. scalar case state = starting seed value only. If -1, GAUSS computes the starting seed based on the system clock. opaque vector case state = the state vector returned from a previous call to one of the rnd random number functions. r (numMats * rows(cov) x N matrix) – Wishart random matrices. newstate (Opaque vector) – the updated state.

## Examples¶

// covariance matrix
cov = {  1   0.5,
0.5     1 };

// degrees of freedom
df = 7;

X = rndWishart(1, cov, df);

X = 7.6019339 4.7744799
4.7744799 7.7341260


## Remarks¶

The properties of the pseudo-random numbers in X are:

\begin{align}\begin{aligned}\begin{split}E(X) = df * cov\\\end{split}\\Var(X_{ij}) = df * (cov_{ij}^2 + cov_{ii}*cov_{jj})\end{aligned}\end{align}