Re: Definition of intervals as subsets of R - the bad news
Siegfried M. Rump schrieb:
Aah, it took me a while to understand. You mean
[1,2] - inf = empty
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.
Probably nobody would ever notice it, just as nobody noticed
that your current implementation gives [-Inf,Inf]+Inf = [NaN,Inf],
which is incorrect under _any_ interpretation.
But should someone notice it (most likely during debugging),
they would remember, or look up the documentation, learn, and
fix the part of the program that produced the inf in the first
place - since that is where things went wrong.
Careful programmers writing high quality verification software
would in any case use the arithmetic according to the standard.
On the other hand, if you treat inf as an uncertain real number
above realmax, you cannot avoid at all the problem you complained
about, since then any inf must be converted into a proper interval,
and interval matrix times real matrix would become even more
expensive!
Arnold Neumaier