"How is the generalized Kronecker product defined?": Good question.
I don't know how it is officially done, but extended the 2D-2D case in the
examples such that the axes between x and y are paired, any trailing axes
not matched by the other being padded with appended 1's.
As Raul said, if you have A of shape ijk and b of shape mno you'd end up
with a result of shape i j k * m n o.
In case of different shapes, the shortest is padded
e.g. : i j k , m n -> i j k * m n 1. My current definition just doesn't
work for scalars, which should now be passed as a 1 element rank 1, e.g. A
kp ,5.
That said, I've searched it, but found no single mention of a Kronecker
product generalised to arbitrary dimensions, so I don't even know whether
it could be useful, but it looked cute.
Possible (silly) use I could think of is:
kp=: cs ($,) dp |: *"0 _
NB. cs calculates the eventual size of result
cs=: ([: */&:> >.&# {.!.1&.> ;)&$
NB. dp axis shuffle needed to interleave corresponding axes of x and y
dp=: (+ {. [: ,@|:@i. 2 , >.)&(#@$)
AA=: 10 10 10 ?@$ 2
A=: =i. 10
B=: 6 8 15 19 21 22 23 e.~i. 5 5
load'viewmat'
viewmat A kp B
viewmat ({."1 A kp 5 5$1) * +/&.|: A kp B
Have fun!
On Fri, Oct 1, 2021, 11:08 Raul Miller <[email protected]> wrote:
> I can reproduce this issue.
>
> Furthermore, while trying to understand it, I found a workaround.
>
> A ([:*/&:>>.&#{.!.1&.>;)&$B
> |domain error
>
> A ([:*/&:>>.&#{.!.1&.>;)&{{y}}&$B
> 6 6
>
> The success of this workaround suggests an issue with special code.
>
> Thanks,
>
> --
> Raul
>
> On Fri, Oct 1, 2021 at 3:23 AM Jan-Pieter Jacobs
> <[email protected]> wrote:
> >
> > Hi,
> > Yesterday I was playing with the Kronecker product, trying to extend it
> to
> > arbitrary dimensions (not that I really needed, but it seemed fun). It
> > works on this J:
> > JVERSION
> > Engine: j902/j32/android
> > Release-a: commercial/2020-12-24T11:35:03
> > Library: 9.02.08
> > Platform: Android 32 (armeabi-v7a)
> > Installer: unknown
> > InstallPath: /mnt/sdcard/Android/data/com.jsoftware.j.android/files
> > Contact: www.jsoftware.com
> >
> > But not on beta-r, nor beta-s on windows 64, avx2.
> >
> > The definition is as follows (based on
> > https://wiki.jsoftware.com/wiki/Essays/Kronecker_Product):
> >
> > kp=: cs ($,) dp |: *"0 _
> > NB. cs calculates the eventual size of pairwise joining axes
> > cs=: ([: */&:> >.&# {.!.1&.> ;)&$
> > NB. dp calculates the axis shuffle needed to interleave corresponding
> axes
> > of x and y
> > dp=: (+ {. [: ,@|:@i. 2 , >.)&(#@$)
> >
> > A=: =i. 3 NB. identity, shape 3 3
> > B=: >:i. 2 2 NB. shape 2 2
> > AA=: 0 13 26 e.~i. 3 3 NB. shape 3 3 3
> >
> > 'A kp B' and 'AA kp B' fail because 'A cs B' and 'AA cs B' throw a domain
> > error in J903-beta-r/s I don't understand, but do work in J902. Dissect
> > mentions an inconsistency, but eventually shows the right result.
> >
> > however, removing &$ from cs and feeding in shapes directly does work.
> >
> > 3 3 3 ([: */&:> >.&# {.!.1&.> ;) 2 2
> > 6 6 3
> >
> > Am I missing something or is this an interpreter bug?
> >
> > Any comments on the Kronecker product as such, does it make sense? The
> 2x2
> > case is at least consistent with the definitions in the essay.
> > If it is sound, I'd add it to the Essay.
> >
> > Best regards,
> > Jan-Pieter.
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
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