[Jprogramming] Boxing columns

[Marshall Lochbaum]

Aha! Raul's solution can be rewritten as

,"_2/^:3 >zz

(negative rank is quite a useful concept). Since ,. is (exactly) ,"_1
the two-dimensional solution is

,"_1/^:2 >z

Extending the pattern, we can reduce a blocked array using

merge =: 3 : 0
r =. #$y
,"(1-r)/^:r >y
)

This works on block arrays with large rank.
   (-: [: merge (,:~2 3 4 5) <;._3 ]) i.4 9 16 25
1

Marshall

On Thu, Nov 20, 2014 at 12:28:07PM -0500, Raul Miller wrote:
> Perhaps
>    ,"1/,"2/,"3/>zz
> 
> Thanks,
> 
> -- 
> Raul
> 
> On Thu, Nov 20, 2014 at 10:42 AM, Ben Gorte - CITG
> <B.G.H.Gorte at tudelft.nl> wrote:
> > If I'm allowed to jump in here, I'm using ;. a lot to subdivide images into 2x2 blocks (think wavelet), and I guess it's okay to do it like:
> >
> >    ]z =: (2 2,:2 2) < ;. _3 i.4 6
> > +-----+-----+-----+
> > |0 1  |2 3  | 4  5|
> > |6 7  |8 9  |10 11|
> > +-----+-----+-----+
> > |12 13|14 15|16 17|
> > |18 19|20 21|22 23|
> > +-----+-----+-----+
> >
> > I was quite happy to discover that:
> >
> >    ,./,./> z
> >  0  1  2  3  4  5
> >  6  7  8  9 10 11
> > 12 13 14 15 16 17
> > 18 19 20 21 22 23
> >
> > does the inverse (it's even pleasant to type).
> >
> > Now I'm smoothly moving to 3d with
> >
> >    ]zz =: (2 2 2,:2 2 2) < ;. _3 i.4 6 8
> >
> > but as the inverse is concerned I'm sort of stuck at:
> >
> >    CutBack =: [: ([: ,/ ([: ,./ ,./)"4) 1 2 4 5&|:
> >    (i.4 6 8) -: CutBack >zz
> > 1
> >
> > which I'm sure can be improved. Any suggestions?
> >
> > Thanks,
> > Ben
> > ________________________
> > From: programming-bounces at forums.jsoftware.com [programming-bounces at forums.jsoftware.com] on behalf of Henry Rich [HenryHRich at nc.rr.com]
> > Sent: Wednesday, November 19, 2014 23:40
> > To: programming at jsoftware.com
> > Subject: Re: [Jprogramming] Boxing columns
> >
> > Is the inverse implemented using ^:_1 ?  I couldn't find it.
> >
> > I come up with ,.&:>/ as an inverse for ('';1)&(<;.1)  .
> >
> > Henry Rich
> >
> > On 11/19/2014 5:28 PM, Roger Hui wrote:
> >> The inverse of this "block matrices cut" is also interesting.
> >>
> >>
> >> On Wed, Nov 19, 2014 at 2:27 PM, Roger Hui <rogerhui.canada at gmail.com>
> >> wrote:
> >>
> >>>     ('';1) <;.1 i.3 3
> >>> ┌─┬─┬─┐
> >>> │0│1│2│
> >>> │3│4│5│
> >>> │6│7│8│
> >>> └─┴─┴─┘
> >>>
> >>>
> >>> On Wed, Nov 19, 2014 at 2:05 PM, Henry Rich <HenryHRich at nc.rr.com> wrote:
> >>>
> >>>>     boxcols i. 3 3
> >>>> +-+-+-+
> >>>> |0|1|2|
> >>>> |3|4|5|
> >>>> |6|7|8|
> >>>> +-+-+-+
> >>>>
> >>>> Can you write boxcols?
> >>>>
> >>>> Can you write it tacitly without using a hook, fork, compose, or appose?
> >>>>
> >>>> Henry Rich
> >>>> ----------------------------------------------------------------------
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> >>>>
> >>>
> >>>
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