From p.dalgaard@biostat.ku.dk  Mon Sep 27 14:58:46 1999
From: p.dalgaard@biostat.ku.dk (Peter Dalgaard BSA)
Date: 27 Sep 1999 15:58:46 +0200
Subject: chol() dimnames
In-Reply-To: Douglas Bates's message of "27 Sep 1999 07:44:15 -0500"
References: <199909271125.MAA07858@toucan.stats.ox.ac.uk> <x2905s8st3.fsf@blueberry.kubism.ku.dk> <6rbtao34o0.fsf@franz.stat.wisc.edu>
Message-ID: <x2670w8nhl.fsf@blueberry.kubism.ku.dk>

Douglas Bates <bates@stat.wisc.edu> writes:

> I believe there is a pivoting option available for the Linpack dchdc
> routine but not for the dpodc routine.  (My copy of the manual is at
> the office so I can't check this.)  That pivoting is similar to the
> pivoting in dqrdc - you specify which columns (and the corresponding
> rows in the case of dchdc) are available to be re-ordered and it
> re-orders everything in the optimal ordering.  This doesn't work well
> for model matrices or quantities derived from model matrices where you
> want to keep the columns associated with the same terms adjacent if
> possible.

Exactly, dchdc was the one I had been thinking of too. I don't really
see the problem in the reordering, though. Just put things back in
order afterwards? However, the column locking feature doesn't seem too
useful to me.

> 
> Notice that in your example the diagonal elements of the decomposition
> are strictly decreasing after pivoting.  That is what I mean by the
> optimal ordering. 

Yup. Although there are some obvious scaling issues that makes the
optimality a bit dubious (such as when you change the units on a
regressor from uM to M).

There's a variation of Cholesky where you essentially just put a zero
in the diagonal in case of singularity and proceed with the remainder
of the matrix, but noone seems to implement that.

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)             FAX: (+45) 35327907
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chol() dimnames
Peter Dalgaard BSA