From bates at stat.wisc.edu  Thu Dec 29 23:27:52 2011
From: bates at stat.wisc.edu (Douglas Bates)
Date: Thu, 29 Dec 2011 16:27:52 -0600
Subject: [Rd] Cholesky update/downdate
In-Reply-To: <4EFC73A8.1080901@alpestat.com>
References: <4EFC73A8.1080901@alpestat.com>
Message-ID: <CAO7JsnS3z_-1WYB-28DTicbR4E6ABrDtsR3KU01gsPZ6D3GDdg@mail.gmail.com>

On Thu, Dec 29, 2011 at 8:05 AM, Yves Deville <deville.yves at alpestat.com> wrote:
> Dear R-devel members,

> I am looking for a fast Cholesky update/downdate. The matrix A being
> symmetric positive definite (n, n) and factorized as
> A = L %*% t(L), the goal is to factor the new matrix ?A +- C %*% t(C) where
> C is (n, r). For instance, C is 1-column when adding/removing an observation
> in a linear regression. Of special interest is the case where A is sparse.

> Looking at the 'Matrix' package (help and source code), it seems that the
> CHOLMOD library shipped with 'Matrix' allows this,
> but is not (yet?) interfaced in 'Matrix', where the 'update' method for
> Cholesky decomposition objects seems limited to a new matrix A + m*I with a
> scalar (diagonal) modification.

The CHOLMOD library provides sparse matrix methods, especially the
Cholesky decomposition and modifications to that decomposition, which
is where the name comes from.  Do you expect to work with sparse
matrices?

I haven't seem too much code for update/downdate operations on the
Cholesky decomposition for dense matrices.  There were rank-1
update/downdate methods in Linpack but they didn't make it through to
Lapack.
> If this is true: are there plans to implement such up/downdates?
>
> Best,
>
> Yves
>
> Yves Deville, statistical consultant, France.
>
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[Rd] Cholesky update/downdate
Douglas Bates