Re: Multivariate pdf of a normal distribution

[Paul Kienzle]

Thanks.  I've included mvnrnd in octave-forge.

Looking at the code it uses chol(), and if that doesn't work, it uses 
eig().

The R manual for the MASS package has this to say about mvrnorm:

	The matrix decomposition is done via eigen; although a Choleski 
decomposition might be faster, the eigendecomposition is stabler.

        http://stat.ethz.ch/R-manual/R-patched/library/MASS/html/mvrnorm.html

Using the same test I did earlier on ill-conditioned positive definite 
matrices, eig doesn't seem to be a more accurate way to compute matrix 
inverses.  Anyone care to comment on this?

- Paul

On Nov 5, 2005, at 8:43 PM, Mike Miller wrote:

> On Sat, 5 Nov 2005, Prasenjit Kapat wrote:
>
> > > I don't know for sure that inv(r') == inv(r)' for r upper triangular.
> >
> > Analytically it is, but numerically need not be, as Paul rightly 
> > showed. Now while on this multivariate normal issue, how about 
> > generating multivariate normal random variables, given the mean and 
> > the sigma matrix ? any available/easily-writable code ?
>
>
> I found this recently:
>
> http://www.gatsby.ucl.ac.uk/~iam23/code/mvnrnd.m
>
> It is under the GPL:
>
> http://www.gatsby.ucl.ac.uk/~iam23/code/
>
> Mike



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