Re: min / max and empty intervals
> Date: Tue, 07 Jun 2011 08:43:03 +0200
> From: Arnold Neumaier <Arnold.Neumaier@xxxxxxxxxxxx>
> To: Dan Zuras Intervals <intervals08@xxxxxxxxxxxxxx>
> CC: John Pryce <j.d.pryce@xxxxxxxxxxxx>, stds-1788@xxxxxxxxxxxxxxxxx
> Subject: Re: min / max and empty intervals
>
> Dan Zuras Intervals wrote:
> > What does this all mean for 1788?
> >
> > John is correct when he says we need to define a (possibly
> > infinite) class of functions that look like:
> >
> > max(x1,x2), max(x1,x2,x3), max(x1,x2,x3,x4), ...
> >
> > More completely, the class starts with:
> >
> > max(), max(x1), max(x1,x2), max(x1,x2,x3), ...
> >
> > So what is the result of the niladic max()?
>
> I'd consider this an ill-formed constant, returning canonically Empty_ill.
> Whereas if any of the arguments x_i is Empty (with decoration emp or
> ill), the returned value is Empty, with the worst decoration of all the
> empty arguments.
> This is consistent and allows for straightforward debugging.
Oh, I think that's a bit draconian, don't you?
>
> Note that in verified computations, the rational for floating-point
> calculations no longer applies.
>
> If a matrix contains a NaN, it may have been produced by a poor float
> operation. But the corresponding interval operation will be Entire or
> Empty depending on the context, and the decoration tells sometimes more
> about this context. If we'd ignore this in a max operation by dropping
> the Empty arguments, we'd introduce uncontrolled semantics violating the
> FTDIA.
Actually, John touched on the reasonable application for
NaNs in a matrix. That of as yet unknown data.
It turns out there are spreadsheet applications out there
that want to reevaluate the entire thing each time a single
element is entered. Thus, NaNs stood in place for entries
that had not yet been entered. And, rather than display
all NaNs as a result right up until the last element is
entered, they would rather display as much of the partial
result as possible. Reasonable considering that the last
bit of data might never be entered once the partial
solution gets 'good enough'.
So, I don't know if this applies to the interval world.
In an interactive application, are you interested in
providing assured partial results or waiting until the
input is completed even if its not all needed?
Is empty a rational entry for the unknown interval or
will we need something else for that?
You guys know this stuff.
I'm just trying to figure it out.
Dan