[Rd] NaN and linear algebra
Martin Maechler
maechler at stat.math.ethz.ch
Wed Mar 23 09:04:32 CET 2005
>>>>> "Bill" == Bill Northcott <w.northcott at unsw.edu.au>
>>>>> on Wed, 23 Mar 2005 10:19:22 +1100 writes:
Bill> 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.
Bill> It may not violate the letter of IEEE-754 because matrix calculations
Bill> are not covered, but it certainly violates the spirit that arithmetic
Bill> 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.
Bill> You may prefer the error, but it is not in the sprit of robust
Bill> arithmetic. ie
>> d<-matrix(NaN,3,3)
>> f<-solve(d)
Bill> Error in solve.default(d) : Lapack routine dgesv: system is exactly
Bill> singular
>> f
Bill> 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?
Bill> Clearly det(d) returning 0 is wrong. As a result based on a
Bill> computation including a NaN, it should return NaN. The spirit of
Bill> IEEE-754 is that the programmer should choose the appropriate point at
Bill> which to check for NaNs. I would interpret this to mean the R
Bill> programmer not the R library developer. Surely that is why R provides
Bill> the is.nan function.
>> d
Bill> [,1] [,2] [,3]
Bill> [1,] NaN NaN NaN
Bill> [2,] NaN NaN NaN
Bill> [3,] NaN NaN NaN
>> is.nan(solve(d))
Bill> Error in solve.default(d) : Lapack routine dgesv: system is exactly
Bill> singular
Bill> This is against the spirit of IEEE-754 because it halts the program.
>> is.nan(det(d))
Bill> [1] FALSE
Bill> 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?
Bill> However, this problem is in the Apple library not R.
Bill> Bill Northcott
Indeed!
I pretty much entirely agree with your points, Bill, and would
tend to declare that this Apple library is ``broken''
for building a correctly running R.
Let me ask one question I've been wondering about now for a
while:
Did you run "make check" after building R,
and "make check" ran to completion without an error?
If yes (which I doubt quite a bit), there *is* a bug in R's
quality control / quality assurance tools -- and I would want to
add a check for the misbehavior you've mentioned.
Martin Maechler, ETH Zurich
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