[Rd] NaN and linear algebra

[Prof Brian Ripley]

On Wed, 23 Mar 2005, Simon Urbanek wrote:

> On Mar 22, 2005, at 6:19 PM, Bill Northcott wrote:
>
>> On 23/03/2005, at 12:55 AM, Simon Urbanek wrote:
>> 
>> You may prefer the error, but it is not in the sprit of robust arithmetic. 
>> ie
>> > d<-matrix(NaN,3,3)
>> > f<-solve(d)
>> Error in solve.default(d) : Lapack routine dgesv: system is exactly 
>> singular
>> > f
>> Error: Object "f" not found
>
> For the record: this is the behavior on all platforms I tested (Mac, Linux, 
> IRIX) - the only platform with a different result is reportedly Windows. So 
> what I was saying is that this is not "IEEE-754 non-compliance of MacOS X" as 
> you put it.

Hmm: all the platforms I have tested using R's internal blas and some 
with external BLASes pass this test.  Only those with ATLAS and Goto 
BLAS' fail for me.

>> Clearly det(d) returning 0 is wrong.  As a result based on a computation 
>> including a NaN, it should return NaN.
>
> That's exactly what I was pointing out, and, yes, this is a bug in vecLib.
>
> @Martin: I guess the most simple test for this would be probably
> is.nan(det(matrix(NaN,2,2)))
>
>>> Many functions in R will actually bark at NaN inputs (e.g. qr, eigen, ...) 
>>> - maybe you're saying that we should check for NaNs in solve before 
>>> proceeding and raising an error?
>> 
>> However, this problem is in the Apple library not R.
>
> Since you're referencing the "solve" problem here, again, it's not.
>
> As I was explaining the the previous e-mail, there are at least two 
> completely separate issues - handling of NaNs in solve and determinant of NaN 
> matrices. The latter is a bug in vecLib, the first one is not an OS X 
> specific problem.

No, but it does appears to be an external BLAS-specific problem.

> Many R functions will object to taking NaN inputs such as qr.solve which 
> was the previous implementation of solve. At any rate this is error 
> handling in R and not Lapack. The "example" on the top doesn't make any 
> sense because when you type "f" you know that it doesn't exist and both 
> are R errors. If you used that in a script you have both choices: abort 
> and that point or continue with whatever fallback you choose.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595