gencov

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

$3

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~

$3

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~.

$3

``
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

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[travis-url]: https://travis-ci.org/welch/gencov
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[npm-url]: https://www.npmjs.org/package/gencov