How can you define h to use the definition of &, so that the result is the
same as that for f and g :
]A=:((i.2 3);(,0)) ; (i. 2 3)
┌─────────┬─────┐
│┌─────┬─┐│0 1 2│
││0 1 2│0││3 4 5│
││3 4 5│ ││ │
│└─────┴─┘│ │
└─────────┴─────┘
f=: 13 :'$ each y'
f A
┌─┬───┐
│2│2 3│
└─┴───┘
g=: 13 :'$&.>y'
g A
┌─┬───┐
│2│2 3│
└─┴───┘
NB. u&.v y ↔ vi u v y
h=: 13 :'<"1 ([:$>)"0 y'
h A
┌───┬───┐
│2 0│2 3│
└───┴───┘
Linda
-----Original Message-----
From: programming-boun...@forums.jsoftware.com
[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Michal D.
Sent: Monday, September 08, 2014 11:01 AM
To: programm...@jsoftware.com
Subject: Re: [Jprogramming] Ragged Array Shapes are Trees
Thanks Pascal, that's a nice formulation for the 2-level deep case. It
breaks down of course for deeper nesting but could serve as a base.
([:|. $ ;~ $ each) ((i.2 3);(,0)) ; (i. 2 3)
+-+-------+
|2|+-+---+|
| ||2|2 3||
| |+-+---+|
+-+-------+
There's no specific problem I'm trying to solve directly in J at the
moment. It's more of a language design problem. My interest in this is a
J like language, but with shapes extended to support ragged arrays without
boxing. Failing that, we could have some optimization guarantees like 'an
array of boxes containing equal rank values are allocated contiguously'.
Cheers,
Mike
On Sat, Sep 6, 2014 at 9:28 AM, 'Pascal Jasmin' via Programming <
programm...@jsoftware.com> wrote:
> Hi Michal,
>
> maybe this is an interesting representation for what you want?
>
> ([:|. $ ;~ $ each) (i. 2 3) ; (,0) ; 0 1
> ┌─┬─────────┐
> │3│┌───┬─┬─┐│
> │ ││2 3│1│2││
> │ │└───┴─┴─┘│
> └─┴─────────┘
>
>
>
> ----- Original Message -----
> From: Michal D. <michal.dobrog...@gmail.com>
> To: programm...@jsoftware.com
> Cc:
> Sent: Saturday, September 6, 2014 12:06 PM
> Subject: [Jprogramming] Ragged Array Shapes are Trees
>
> I just came to the realization that ragged array shapes, regardless of how
> you want to represent them, are trees. I would be interested in any
> references to prior exploration of this idea.
>
> Some example data (boxes are used to display ragged arrays, but otherwise
> have no semantic meaning):
>
> ] A =. i. 2 3
> 0 1 2
> 3 4 5
> ] B =. (< @ i."0) 1+i.2
> +-+---+
> |0|0 1|
> +-+---+
> ] C =. A ; B
> +-----+-+---+
> |0 1 2|0|0 1|
> |3 4 5| | |
> +-----+-+---+
> ] D =. A ; < B
> +-----+-------+
> |0 1 2|+-+---+|
> |3 4 5||0|0 1||
> | |+-+---+|
> +-----+-------+
>
> The corresponding shape trees (monospace font required, root node is on the
> left):
>
> A: 2 - 3
>
> 1
> /
> B: 2
> \
> 2
>
> 2 - 3
> /
> C: 3 - 1
> \
> 2
>
> 2 - 3
> /
> D: 2 1
> \ /
> 2
> \
> 2
>
> In some sense the shape tree for A is compressed, the verbose alternative
> being:
>
> 3
> /
> A: 2
> \
> 3
>
> Compressing D in a similar manner leaves the full shape of the tree
> ambiguous - there is no way to distinguish the duplicate structure of leaf
> 3 from the structure of leaves 1, 2.
>
> 3
> /
> D: 2 - 2 - 1
> \
> 2
>
> We could resolving this ambiguity by listing the shapes of all the items
> explicitly. The problem here is that 'compression' could very easily lead
> to an increase in representation size, although it is nice and uniform for
> ragged arrays of uniform rank.
>
> 3
> /
> | 3
> | /
> D: 2 - 2 +
> | \
> | 1
> \
> 2
>
> Regardless of compression, I would be interested in prior work in
> representing shapes of ragged arrays as trees.
>
> Cheers,
>
> Mike
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