From p.dalgaard@biostat.ku.dk  Mon Sep 27 13:03:52 1999
From: p.dalgaard@biostat.ku.dk (Peter Dalgaard BSA)
Date: 27 Sep 1999 14:03:52 +0200
Subject: chol() dimnames
In-Reply-To: Prof Brian Ripley's message of "Mon, 27 Sep 1999 12:25:05 +0100 (BST)"
References: <199909271125.MAA07858@toucan.stats.ox.ac.uk>
Message-ID: <x2905s8st3.fsf@blueberry.kubism.ku.dk>

Prof Brian Ripley <ripley@stats.ox.ac.uk> writes:

> I believe all one actually knows is that the colnames of R should be the
> colnames of x, if the row and column names of x match. However, the 
> prototype does preserve the names.  Should we just preserve the colnames?

That would make OK sense to me. By assumption X == t(X) so if it doesn't
have the same row and column names, something is wrong anyway and we
can do whatever we please to fix things up.

However: Somewhere in the back of my mind lies a note to the effect
that chol() should really handle the rank-deficient cases better, via
some sort of pivoting. Will this muck things up (possibly not if it
only removes singularities and plugs in rows/cols of zeroes)? I seem to
recall that the current chol() got lme() in trouble. I got as far as
locating the candidate replacement for chol.f on Netlib and then got
away from it.

Currently, we get

> z<-matrix(rnorm(15),3,5)
> x<-t(z)*z
> chol(x)
Error: singular matrix in chol

The prototype (Splus 3.4) handles this a bit better:
> chol(x)
         [,1]      [,2]        [,3]          [,4]          [,5] 
[1,] 1.703739 1.9199843 -0.94401977 -1.129732e+00 -8.387157e-01
[2,] 0.000000 0.7605888  0.08437014  8.385107e-01 -2.259906e-01
[3,] 0.000000 0.0000000  0.86549993  7.381480e-01  5.811783e-01
[4,] 0.000000 0.0000000  0.00000000 -7.771561e-16  1.110223e-16
[5,] 0.000000 0.0000000  0.00000000  0.000000e+00  0.000000e+00
attr(, "rank"):
[1] 3
Warning messages:
  Choleski decomposition not of full rank in: chol(x)

It also allows pivoting, but I don't think we want their algorithm:

> chol(x,piv=T)
         [,1]       [,2]       [,3]          [,4]          [,5] 
[1,] 2.065148 -0.7414994 -0.8465894  1.583980e+00 -8.629924e-01
[2,] 0.000000  1.4051462  0.8172503 -5.339291e-01  3.893657e-01
[3,] 0.000000  0.0000000  0.5126111  3.296278e-01  4.426312e-01
[4,] 0.000000  0.0000000  0.0000000  2.107342e-08  5.268356e-09
[5,] 0.000000  0.0000000  0.0000000  0.000000e+00  7.850462e-17
attr(, "pivot"):
[1] 2 4 3 1 5
attr(, "rank"):
[1] 5
    ^
    !
oops....


-- 
   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