Re: Some questions on the interval package

[Oliver Heimlich]

Hi Joel,

On 14.06.2017 12:05, Joel Dahne wrote:
> Hi!
> 
> I have begun the work on adding support for constructing and printing
> N-dimensional interval arrays.

I have reviewed and merged your first bulk of work.  Review comments:

Revision 892 (@infsup/disp.m): You can probably eliminate the for loop
(1:ndims (x) - 2) with: sprintf (repmat (",%d", 1, ndims (x) - 2), …

Revision 893 (@infsup/display.m): You should start the new for loop
(3:ndims(x)) from 2, or use repmat like above to simplify the code.

Revision 895 (hull.m):
 - Why is the dimension mismatch case no longer an error?
 - Before the new check for “or (targetsize == sizes, sizes == 1)” you
should add “warning ("off", "Octave:broadcast", "local");” Otherwise
Octave 3.8 will complain.

Revision 902 (nai.m): The new test should explicitly check against the
expected result “true (2, 2, 2)”.

Revision 904 (size.m): You should change the texinfo macro @defmethod
into @deftypemethod and put the output arguments into curly braces.
Also you should format the new help text with @command{size} macros
(instead of plain quation marks).


> Most of the functions are just wrappers
> around Octaves standard functions and thus do not need much
> changes.

Nevertheless you have to check them, so no need to play down the work
that you do ;-)  It's good to see how well you handle the cases where
change is required.


> However for some functions I'm not sure how to handle the
> changes for. I list the ones I have questions about. More information about
> the rest of the work will come in a blog-post tomorrow or on Friday. I
> have pushed most of the changes to my remote repository, so if you want
> to try the new functionality you can clone that.

Done and already merged your changes.  Nice work so far!


> disp.m: When printing an array with more than 2 dimensions I have
> followed the normal Octave style. It looks like
>  ans(:,:,1) =
> 
>    [0]   [0]
>    [0]   [0]

Two small observations:

 1. The matrix label “ans(:,:,…)” should not be indented.
 2. Before the matrix label you need an additional blank line (not
before the first one). Remark: disp.m currently only supports “format
loose”, where there are blank lines between matrix labels and matrices.
Feel free to add support for “format compact”, but I don't know how to
properly detect the current display mode.


> Should we use an equality sign here only when the representation is
> exact and a subset sign otherwise? It might happen that some submatrices
> are exact and others not. Should we use a subset sign on all submatrices
> if at least one is not exact? Currently I use equality signs everywhere.

I'd prefer to either support the subset sign at this point, or
completely get rid of the subset sign (for consistency).  If you want to
support the subset sign, you probably have to change the isexact output
argument of “intervaltotext” into an N-D array (instead of a scalar).
That means you also have to dig into mpfr_to_string_d.


> linspace.m and mince.m: In the standard implementation these can only
> take scalars or vectors as input. They could however be generalized to
> also allow for N-dimensional arrays as input, but this has not been
> done. Should we implement this for intervals? The same questions goes
> for mince.m which is just an interval generalization if linspace.m.

Yes, that'd be useful to support N-D arrays as input.  Following the
behavior of the standard linspace in Octave, I'd say that we should
simply convert the input into column vectors.  IIRC, this is already
done inside mpfr_linspace_d.  The output will always be 2-D then.


I will answer your other remaining questions later in a second mail.

Best
Oliver