R help - Oct 2003 - detecting singular matrices

My colleague runs R 1.7.1 under Windows XP. He remarks:
>> A
>     [,1] [,2] [,3]
> [1,]    1    2    3
> [2,]    4    5    6
> [3,]    7    8    9
>>
>> b
> [1] 1 2 3
>> solve(A,b)
> [1] -0.3333333  0.6666667  0.0000000
>> solve(A)
>            [,1]         [,2]        [,3]
> [1,] -4.5036e+15  9.00720e+15 -4.5036e+15
> [2,]  9.0072e+15 -1.80144e+16  9.0072e+15
> [3,] -4.5036e+15  9.00720e+15 -4.5036e+15
>> eigen(A)
> $values
> [1]  1.611684e+01 -1.116844e+00 -1.303678e-15
> 
> with a condition number of  1.236260e+16 I think I'd like it to tell me
it's singular like it used to :) and I know it is singular
Under 1.6.0 also on XP I get

 > solve(A,1:3)
Error in solve.default(A, 1:3) : singular matrix `a' in solve
 > solve(A)
Error in solve.default(A) : singular matrix `a' in solve
 > eigen(A)
$values
[1]  1.611684e+01 -1.116844e+00 -1.120190e-16

$vectors
            [,1]        [,2]       [,3]
[1,] -0.2719964 -0.76169140  0.3734378
[2,] -0.6159646 -0.08408654 -0.7468756
[3,] -0.9599328  0.59351831  0.3734378


Which seems to be preferable output.

Murray

-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    +64 7 849 6486 home    Mobile 021 1395 862

On Fri, 10 Oct 2003, Murray Jorgensen wrote:
> >
> > with a condition number of 1.236260e+16 I think I'd like it to
tell me
> > it's singular like it used to :) and I know it is singular
This was found during code freeze (and I suggested to Martin that he file
a bug report on it then, so that we could say "Known Issue" when
someone
reported it).

Unlike the old LINPACK code the LAPACK code reports singularity only when
it encounters an exactly zero pivot. This doesn't happen very often.
There is another, more complicated LAPACK routine that reports an
estimated condition number and reports when the matrix is singular to
within working precision, and we should probably use that one instead.
We need to investigate things like relative speed as well.

	-thomas