Re: hyperoperators and multi-dimensional datastructures
On Thursday 19 May 2005 12:48, Uri Guttman wrote:
> > "LP" == Luke Palmer <[EMAIL PROTECTED]> writes:
>
> LP> On 5/18/05, Anthony Heading <[EMAIL PROTECTED]> wrote:
> >> Is there a way to target hyperoperators at different axes
> >> of a multi-dimensional array? This is an attractive
> >> feature of various APL-like languages, viz. e.g. in J:
> >>
> >> a =. 2 5 $ i. 7 - a simple 2-by-5 array
> >> a
> >> 0 1 2 3 4 - like this
> >> 5 6 0 1 2
> >>
> >>
> >> +/"1 a - sum reduce over axis 1
> >> 10 14
That is, break the array into rows, and reduce each row.
> LP> [+]<< @a
>
> >> +/"2 a - sum reduce over axis 2
> >> 5 7 2 4 6
Actually, that's sum reduce over planes, which gives the default
behavior when applied to a single plane, of breaking the plane
into rows, and adding the rows to each other. The result is the
same as from +/a .
The rank conjunction (") is tersely explained at
http://www.jsoftware.com/books/help/dictionary/intro20.htm
and more fully in The J Primer, J for C Programmers, and other
online publications at
http://www.jsoftware.com/publications_books.htm
> LP> Can't think of any for this one. Or maybe it's this one
> that I can LP> think of it for, and the other one which I
> can't.
>
> i can't spit out the syntax but here is the conceptual way i
> would do it. we do have multidimensional slices so we could
> grab each slice (maybe with zip?) and pass that to [+] and
> then grab the list of results back into a array/matrix with
> one less dimension than the original.
Exactly how Iverson conceived rank for reduction.
> so it would be something like this: (very wacko pseudo code):
>
> @in[ * ; 2 ; * ] ==>
> map [+] ==>
> @out
>
> that was an (bad) attempt to slice the third entry in the
> second dimension to be summed.
You might find it useful to examine this published source code
for an early version of J
http://www.math.uwaterloo.ca/apl_archives/j/early_j/src/j7/
to see how Iverson's crew implemented rank.
The numbering is confusing, because they restarted at some point,
so J5.0.4 is current.
> LP> I think we're beginning to re-invent PDL.
APL and J, too.
> Poorly.
Amen.
> but is there a p6 pdl yet? they may not need much with
> multi-dim ops, slices, hyper and reduce all built in! also
> with type int (patform ints), they can get the dense storage
> needed (but losing any dimensional flexibility).
>
> uri
--
Edward Cherlin
Generalist & activist--Linux, languages, literacy and more
"A knot! Oh, do let me help to undo it!"
--Alice in Wonderland
http://cherlin.blogspot.com
Re: hyperoperators and multi-dimensional datastructures
Uri Guttman wrote:
i can't spit out the syntax but here is the conceptual way i would do
it. we do have multidimensional slices so we could grab each slice
(maybe with zip?) and pass that to [+] and then grab the list of results
back into a array/matrix with one less dimension than the original.
Yup. I wonder though if that formulation is made simpler by
the notion of iterating a data structure at a given
depth. It might even be useful for $data{$x}{$y}{$z}[$i] or
similar, where e.g. map() could make a deep copy down to a
certain depth where it then operates elementwise.
so it would be something like this: (very wacko pseudo code):
@in[ * ; 2 ; * ] ==>
map [+] ==>
@out
One limiting thing about this is that the data being 3-dimensional
and the focus on the second dimension are explicit in the syntax:
presumably not possible to reduce a $j dimensional array over
dimension $i in the same way. Equivalently, the autoindexing described
in Synopsis 9 looks like it enables
do -> $i, $j, $k { @sum[$i, $k] = @data[$i, $j, $k] }
which is very elegant. But if I was wanting to write a library
which handles arbitrary data "cubes", it would be nice to specify
the dimensions using variables.
LP> I think we're beginning to re-invent PDL. Poorly.
but is there a p6 pdl yet? they may not need much with multi-dim ops,
slices, hyper and reduce all built in! also with type int (patform
ints), they can get the dense storage needed (but losing any dimensional
flexibility).
Yes. I don't quite understand that point. I rather see PDL as a limited
version of MATLAB, and MATLAB as a limited version of APL. The right
set of vector primitives can be combined powerfully in some very
non-obvious ways (c.f. in fact the recent post by Edward Cherlin), and
APL and successors have worked this out over 30+ years. To hold PDL as
a design benchmark instead doesn't seem quite right.
Rgds
Anthony
Re: hyperoperators and multi-dimensional datastructures
> "LP" == Luke Palmer <[EMAIL PROTECTED]> writes: LP> On 5/18/05, Anthony Heading <[EMAIL PROTECTED]> wrote: >> Is there a way to target hyperoperators at different axes of a >> multi-dimensional array? This is an attractive feature of >> various APL-like languages, viz. e.g. in J: >> >> a =. 2 5 $ i. 7 - a simple 2-by-5 array >> a >> 0 1 2 3 4 - like this >> 5 6 0 1 2 >> >> >> +/"1 a - sum reduce over axis 1 >> 10 14 LP> [+]<< @a >> +/"2 a - sum reduce over axis 2 >> 5 7 2 4 6 LP> Can't think of any for this one. Or maybe it's this one that I can LP> think of it for, and the other one which I can't. i can't spit out the syntax but here is the conceptual way i would do it. we do have multidimensional slices so we could grab each slice (maybe with zip?) and pass that to [+] and then grab the list of results back into a array/matrix with one less dimension than the original. so it would be something like this: (very wacko pseudo code): @in[ * ; 2 ; * ] ==> map [+] ==> @out that was an (bad) attempt to slice the third entry in the second dimension to be summed. LP> I think we're beginning to re-invent PDL. Poorly. but is there a p6 pdl yet? they may not need much with multi-dim ops, slices, hyper and reduce all built in! also with type int (patform ints), they can get the dense storage needed (but losing any dimensional flexibility). uri -- Uri Guttman -- [EMAIL PROTECTED] http://www.stemsystems.com --Perl Consulting, Stem Development, Systems Architecture, Design and Coding- Search or Offer Perl Jobs http://jobs.perl.org
Re: hyperoperators and multi-dimensional datastructures
On 5/18/05, Anthony Heading <[EMAIL PROTECTED]> wrote: > Is there a way to target hyperoperators at different axes of a > multi-dimensional array? This is an attractive feature of > various APL-like languages, viz. e.g. in J: > > a =. 2 5 $ i. 7 - a simple 2-by-5 array > a > 0 1 2 3 4 - like this > 5 6 0 1 2 > > > +/"1 a - sum reduce over axis 1 > 10 14 [+]<< @a > +/"2 a - sum reduce over axis 2 > 5 7 2 4 6 Can't think of any for this one. Or maybe it's this one that I can think of it for, and the other one which I can't. I think we're beginning to re-invent PDL. Poorly. Luke
hyperoperators and multi-dimensional datastructures
Is there a way to target hyperoperators at different axes of a multi-dimensional array? This is an attractive feature of various APL-like languages, viz. e.g. in J: a =. 2 5 $ i. 7 - a simple 2-by-5 array a 0 1 2 3 4 - like this 5 6 0 1 2 +/"1 a - sum reduce over axis 1 10 14 +/"2 a - sum reduce over axis 2 5 7 2 4 6 Anthony
