chol() dimnames

[Peter Dalgaard BSA]

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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