On Mon, Aug 30, 2010 at 8:19 PM, Dan Elliott <danelliotts...@gmail.com>wrote:
> Thanks for the reply. > > David Warde-Farley <dwf <at> cs.toronto.edu> writes: > > On 2010-08-30, at 11:28 AM, Daniel Elliott wrote: > > > Large matrices (e.g. 10K x 10K) > > > > > Is there a function for performing the inverse or even the pdf of a > > > multinomial normal in these situations as well? > > > > There's a function for the inverse, but you almost never want to use it, > especially if your goal is the > > multivariate normal density. A basic explanation of why is available > here: > > http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/ > > > > In the case of the multivariate normal density the covariance is assumed > to be > positive definite, and thus a > > Cholesky decomposition is appropriate. scipy.linalg.solve() (NOT > numpy.linalg.solve()) with the > > sym_pos=True argument will do this for you. > > You don't think this will choke on a large (e.g. 10K x 10K) covariance > matrix? > > Should work, give it a shot. It's an n^3 problem, so might take a bit. > Given what you know about how it computes the log determinant and how the > Cholesky decomposition, do you suppose I would be better off using eigen- > decomposition to do this since I will also get the determinant from the sum > of > the logs of the eigenvalues? > > I don't see what the connection with the determinant is. The log determinant will be calculated using the ordinary LU decomposition as that works for more general matrices. Chuck
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