# gencov

Generate random covariance matrices, and draw MVN samples using them.

### Covariance matrix:

The `genS`

and `genArray`

functions produce random covariance matrices
(as ndarray or javascript array) with a specified variance structure.
The eigenvalues (principal component variances) V for the covariance
matrix may be specified, or may be randomly generated from within a
specified range. A random orthogonal matrix Q is generated and its
columns used as eigenvectors. The covariance matrix is then generated
as S = Q V Q~

### Sampling:

Given a covariance ndarray S, you can generate samples from the
associated multivariate normal distribution using the `mvnrnd`

function (which creates a function that draws samples from N(mean, S))

Samples x ~ N(0, S) are drawn by first drawing z ~ N(0, I) then transforming x = L z, where S = L L~.

### Example usage:

```
var gencov = require('gencov');
// generate a 3-d correlation matrix with variances between 1 and 10,
// and return it as an ndarray:
var S = gencov.genS(3);
// generate a 5-d correlation matrix with principal components,
// return as a regular array
var S = gencov.genArray([3, 2, 1, 0.5, 0.1]);
// draw 10 3d samples from a N([a,b,c], S) distribution with random S,
// return as an array of 3-vectors.
var X = Array.apply(null, 10).map(mvnrnd([a,b,c], genS(3)))
```

## dependencies

`ndarray`

: https://www.npmjs.com/package/ndarray
`ndarray-blas-level1`

: https://www.npmjs.com/package/ndarray-blas-level1
`ndarray-blas-level2`

: https://www.npmjs.com/package/ndarray-blas-level2
`ndarray-blas-dger`

: https://www.npmjs.com/package/ndarray-blas-dger
`ndarray-unpack`

: https://www.npmjs.com/package/ndarray-unpack
`ndarray-gram-schmidt-qr`

: https://www.npmjs.com/package/ndarray-gram-schmidt-qr
`ndarray-cholesky-factorization`

: https://www.npmjs.com/package/ndarray-cholesky-factorization