Re: Definition of intervals as subsets of R - the bad news
On 19 Feb 2009, at 13:50, Arnold Neumaier wrote:
I don't see why this makes expensive alterations necessary.
Convert any real +-inf to NaN before doing the standard operation,
and you get the correct result.
Setting x(isinf(x))=NaN before executing an operation with a
real argument x is cheap, vectorizes, and should do the trick.
That's what I was about to propose. On the assumption (my preference)
that any real x is regarded as [x,x] if finite, and emptyset if
infinite, this seems to work for aa+b, aa-b, aa*b, aa/b, as well with
the arguments swapped. What am I missing?
John
A minor point is that x(isinf(x)) causes an error for large arrays
for which indices cannot be linearized. Since INTLAB is also intended
for huge matrices I have to work around this. It is done, but it is nasty
(see the INTLAB code).
Aah, it took me a while to understand. You mean
[1,2] - inf = empty
anyway, and also
[1e300,1e300] - 1e400 = empty
in double precision. It comes back to the "conversion of inf"-problem.
The behavior above is so far out of my mind that it took me a while to
understand your point.
You can write in the documentation/definition of interval arithmetic
what you want, users would not understand this. It is academic.
I think it is a BAD MISTAKE to enforce such a definition.
The behavior is perfectly documented, but it is perfectly what most users
would NOT expect. It may be correct, but it is not right.
And after a short while people forget it - if they ever knew it - and
results become incorrect: The worst what can happen in the interval arena.
As you see, I already forgot it.
I am positive my INTLAB users would grill me if I implement this.
Cheers, Siegfried
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