[Rd] NaN and linear algebra
Bill Northcott
w.northcott at unsw.edu.au
Wed Mar 23 00:19:22 CET 2005
On 23/03/2005, at 12:55 AM, Simon Urbanek wrote:
>> As I see it, the MacOS X behaviour is not IEEE-754 compliant.
>>
>> I had a quick look at the IEEE web site and it seems quite clear that
>> NaNs should not cause errors, but propagate through calculations to
>> be tested at some appropriate (not too frequent) point.
>
> This is not quite correct and in fact irrelevant to the problem you
> describe. NaNs may or may not signal, depending on how they are used.
> Certain operations on NaN must signal by the IEEE-754 standard. The
> error you get is not a trap, and it's not a result of a signal check,
> either. The whole problem is that depending on which algorithm is
> used, the NaNs will be used different ways and thus may or may not use
> signaling operations.
It may not violate the letter of IEEE-754 because matrix calculations
are not covered, but it certainly violates the spirit that arithmetic
should be robust and programs should not halt on these sorts of errors.
>
> I don't consider the `solve' error a bug - in fact I would rather get
> an error telling me that something is wrong (although I agree that the
> error is misleading - the error given in Linux is a bit more helpful)
> than getting a wrong result.
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
> If I would mark something in your example as a bug that would be
> det(m)=0, because it should return NaN (remember, NaN==NaN is FALSE;
> furthermore if det was calculated inefficiently using Laplace
> expansion, the result would be NaN according to IEEE rules). det=0 is
> consistent with the error given, though. Should we check this in R
> before calling Lapack - if the vector contains NaNs, det/determinant
> should return NaN right away?
Clearly det(d) returning 0 is wrong. As a result based on a
computation including a NaN, it should return NaN. The spirit of
IEEE-754 is that the programmer should choose the appropriate point at
which to check for NaNs. I would interpret this to mean the R
programmer not the R library developer. Surely that is why R provides
the is.nan function.
> d
[,1] [,2] [,3]
[1,] NaN NaN NaN
[2,] NaN NaN NaN
[3,] NaN NaN NaN
> is.nan(solve(d))
Error in solve.default(d) : Lapack routine dgesv: system is exactly
singular
This is against the spirit of IEEE-754 because it halts the program.
> is.nan(det(d))
[1] FALSE
That is plain wrong.
>
> 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.
Bill Northcott
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